%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV480+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:34:08 AM UTC 2025
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV480+1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n005.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 09:52:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 tff(leq_type, type, (
% 0.19/0.43 leq: ( $i * $i ) > $o)).
% 0.19/0.43 tff(host_type, type, (
% 0.19/0.43 host: $i > $i)).
% 0.19/0.43 tff(tptp_fun_V0_7_type, type, (
% 0.19/0.43 tptp_fun_V0_7: $i)).
% 0.19/0.43 tff(tptp_fun_Y0_8_type, type, (
% 0.19/0.43 tptp_fun_Y0_8: $i)).
% 0.19/0.43 tff(tptp_fun_X_4_type, type, (
% 0.19/0.43 tptp_fun_X_4: $i)).
% 0.19/0.43 tff(cons_type, type, (
% 0.19/0.43 cons: ( $i * $i ) > $i)).
% 0.19/0.43 tff(tptp_fun_V_5_type, type, (
% 0.19/0.43 tptp_fun_V_5: $i)).
% 0.19/0.43 tff(m_Down_type, type, (
% 0.19/0.43 m_Down: $i > $i)).
% 0.19/0.43 tff(tptp_fun_Y_3_type, type, (
% 0.19/0.43 tptp_fun_Y_3: $i)).
% 0.19/0.43 tff(queue_type, type, (
% 0.19/0.43 queue: $i > $i)).
% 0.19/0.43 tff(s_type, type, (
% 0.19/0.43 s: $i > $i)).
% 0.19/0.43 tff(elem_type, type, (
% 0.19/0.43 elem: ( $i * $i ) > $o)).
% 0.19/0.43 tff(nbr_proc_type, type, (
% 0.19/0.43 nbr_proc: $i)).
% 0.19/0.43 tff(elec_1_type, type, (
% 0.19/0.43 elec_1: $i)).
% 0.19/0.43 tff(index_type, type, (
% 0.19/0.43 index: ( $i * $i ) > $i)).
% 0.19/0.43 tff(status_type, type, (
% 0.19/0.43 status: $i)).
% 0.19/0.43 tff(tptp_fun_V0_11_type, type, (
% 0.19/0.43 tptp_fun_V0_11: ( $i * $i ) > $i)).
% 0.19/0.43 tff(zero_type, type, (
% 0.19/0.43 zero: $i)).
% 0.19/0.43 tff(setIn_type, type, (
% 0.19/0.43 setIn: ( $i * $i ) > $o)).
% 0.19/0.43 tff(down_type, type, (
% 0.19/0.43 down: $i)).
% 0.19/0.43 tff(norm_type, type, (
% 0.19/0.43 norm: $i)).
% 0.19/0.43 tff(ldr_type, type, (
% 0.19/0.43 ldr: $i)).
% 0.19/0.43 tff(alive_type, type, (
% 0.19/0.43 alive: $i)).
% 0.19/0.43 tff(elec_2_type, type, (
% 0.19/0.43 elec_2: $i)).
% 0.19/0.43 tff(m_Ack_type, type, (
% 0.19/0.43 m_Ack: ( $i * $i ) > $i)).
% 0.19/0.43 tff(elid_type, type, (
% 0.19/0.43 elid: $i)).
% 0.19/0.43 tff(wait_type, type, (
% 0.19/0.43 wait: $i)).
% 0.19/0.43 tff(pendack_type, type, (
% 0.19/0.43 pendack: $i)).
% 0.19/0.43 tff(m_Ldr_type, type, (
% 0.19/0.43 m_Ldr: $i > $i)).
% 0.19/0.43 tff(tptp_fun_W0_10_type, type, (
% 0.19/0.43 tptp_fun_W0_10: $i)).
% 0.19/0.43 tff(tptp_fun_X0_9_type, type, (
% 0.19/0.43 tptp_fun_X0_9: $i)).
% 0.19/0.43 tff(acks_type, type, (
% 0.19/0.43 acks: $i)).
% 0.19/0.43 tff(tptp_fun_Z_6_type, type, (
% 0.19/0.43 tptp_fun_Z_6: $i)).
% 0.19/0.43 tff(1,plain,
% 0.19/0.43 (^[X: $i, Y: $i] : refl((~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y))) <=> (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(2,plain,
% 0.19/0.43 (![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y))) <=> ![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.43 tff(3,plain,
% 0.19/0.43 (^[X: $i, Y: $i] : trans(trans(monotonicity(rewrite((leq(X, Y) & leq(Y, X)) <=> (~((~leq(X, Y)) | (~leq(Y, X))))), (((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> ((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y)))), rewrite(((~((~leq(X, Y)) | (~leq(Y, X)))) <=> (X = Y)) <=> (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))), (((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y))))), rewrite((~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y))) <=> (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))), (((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(4,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> ![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.43 tff(5,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y)) <=> ![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(6,axiom,(![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_61')).
% 0.19/0.43 tff(7,plain,
% 0.19/0.43 (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.43 tff(8,plain,(
% 0.19/0.43 ![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) <=> (X = Y))),
% 0.19/0.43 inference(skolemize,[status(sab)],[7])).
% 0.19/0.43 tff(9,plain,
% 0.19/0.43 (![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.19/0.43 tff(10,plain,
% 0.19/0.43 (![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.43 tff(11,plain,
% 0.19/0.43 ((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7)))) <=> (host(V0!7) = host(Y0!8))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(12,plain,
% 0.19/0.43 (~(((~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7)))) <=> (host(V0!7) = host(Y0!8)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.19/0.43 tff(13,plain,
% 0.19/0.43 ((leq(host(X!4), host(Y!3)) & setIn(X!4, alive) & ((~setIn(host(Z!6), index(acks, host(X!4)))) & (host(X!4) = host(V0!7)) & setIn(V0!7, alive) & (~(host(X!4) = host(Y0!8))) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1)) & leq(nbr_proc, index(pendack, host(X!4))) & ((index(status, host(X!4)) = elec_2) & (host(Y!3) = 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] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~setIn(Z, alive)) | (~leq(host(Z), host(Pid0))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid30) = host(Pid0))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_1))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((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)))) | (~(index(status, host(Pid0)) = elec_1)) | (~leq(nbr_proc, s(host(Pid0)))) | (~elem(m_Down(Pid30), queue(host(Pid0)))) | (~(host(Pid30) = s(host(Pid0))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))) <=> (leq(host(X!4), host(Y!3)) & setIn(X!4, alive) & (~setIn(host(Z!6), index(acks, host(X!4)))) & (host(X!4) = host(V0!7)) & setIn(V0!7, alive) & (~(host(X!4) = host(Y0!8))) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1) & leq(nbr_proc, index(pendack, host(X!4))) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = 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] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~setIn(Z, alive)) | (~leq(host(Z), host(Pid0))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid30) = host(Pid0))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_1))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((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)))) | (~(index(status, host(Pid0)) = elec_1)) | (~leq(nbr_proc, s(host(Pid0)))) | (~elem(m_Down(Pid30), queue(host(Pid0)))) | (~(host(Pid30) = s(host(Pid0))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(14,plain,
% 0.19/0.44 ((![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] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~setIn(Z, alive)) | (~leq(host(Z), host(Pid0))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid30) = host(Pid0))) | (~(index(status, host(Z)) = elec_2)) | (~(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))) | ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~setIn(Pid0, alive)) | (~leq(nbr_proc, s(host(Pid0)))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~elem(m_Down(Pid30), queue(host(Pid0)))) | (~(host(Pid30) = s(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5))) <=> (![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] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~setIn(Z, alive)) | (~leq(host(Z), host(Pid0))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid30) = host(Pid0))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_1))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((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)))) | (~(index(status, host(Pid0)) = elec_1)) | (~leq(nbr_proc, s(host(Pid0)))) | (~elem(m_Down(Pid30), queue(host(Pid0)))) | (~(host(Pid30) = s(host(Pid0))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(15,plain,
% 0.19/0.44 (((~setIn(host(Z!6), index(acks, host(X!4)))) & ((host(X!4) = host(V0!7)) & setIn(V0!7, alive) & (~(host(X!4) = host(Y0!8))) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))) <=> ((~setIn(host(Z!6), index(acks, host(X!4)))) & (host(X!4) = host(V0!7)) & setIn(V0!7, alive) & (~(host(X!4) = host(Y0!8))) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(16,plain,
% 0.19/0.44 (((host(X!4) = host(V0!7)) & (setIn(V0!7, alive) & (host(X!4) = host(V0!7)) & (~(host(X!4) = host(Y0!8))) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))) <=> ((host(X!4) = host(V0!7)) & setIn(V0!7, alive) & (~(host(X!4) = host(Y0!8))) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(17,plain,
% 0.19/0.44 (((setIn(V0!7, alive) & (host(X!4) = host(V0!7))) & (~(host(X!4) = host(Y0!8))) & (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))) <=> (setIn(V0!7, alive) & (host(X!4) = host(V0!7)) & (~(host(X!4) = host(Y0!8))) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(18,plain,
% 0.19/0.44 ((![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1)) <=> (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(19,plain,
% 0.19/0.45 (((setIn(V0!7, alive) & (host(X!4) = host(V0!7))) & (~(host(X!4) = host(Y0!8))) & (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))) <=> ((setIn(V0!7, alive) & (host(X!4) = host(V0!7))) & (~(host(X!4) = host(Y0!8))) & (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[18])).
% 0.19/0.45 tff(20,plain,
% 0.19/0.45 (((setIn(V0!7, alive) & (host(X!4) = host(V0!7))) & (~(host(X!4) = host(Y0!8))) & (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))) <=> (setIn(V0!7, alive) & (host(X!4) = host(V0!7)) & (~(host(X!4) = host(Y0!8))) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))),
% 0.19/0.45 inference(transitivity,[status(thm)],[19, 17])).
% 0.19/0.45 tff(21,plain,
% 0.19/0.45 (((host(X!4) = host(V0!7)) & ((setIn(V0!7, alive) & (host(X!4) = host(V0!7))) & (~(host(X!4) = host(Y0!8))) & (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1)))) <=> ((host(X!4) = host(V0!7)) & (setIn(V0!7, alive) & (host(X!4) = host(V0!7)) & (~(host(X!4) = host(Y0!8))) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[20])).
% 0.19/0.45 tff(22,plain,
% 0.19/0.45 (((host(X!4) = host(V0!7)) & ((setIn(V0!7, alive) & (host(X!4) = host(V0!7))) & (~(host(X!4) = host(Y0!8))) & (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1)))) <=> ((host(X!4) = host(V0!7)) & setIn(V0!7, alive) & (~(host(X!4) = host(Y0!8))) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))),
% 0.19/0.45 inference(transitivity,[status(thm)],[21, 16])).
% 0.19/0.45 tff(23,plain,
% 0.19/0.45 (((~setIn(host(Z!6), index(acks, host(X!4)))) & ((host(X!4) = host(V0!7)) & ((setIn(V0!7, alive) & (host(X!4) = host(V0!7))) & (~(host(X!4) = host(Y0!8))) & (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))))) <=> ((~setIn(host(Z!6), index(acks, host(X!4)))) & ((host(X!4) = host(V0!7)) & setIn(V0!7, alive) & (~(host(X!4) = host(Y0!8))) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[22])).
% 0.19/0.45 tff(24,plain,
% 0.19/0.45 (((~setIn(host(Z!6), index(acks, host(X!4)))) & ((host(X!4) = host(V0!7)) & ((setIn(V0!7, alive) & (host(X!4) = host(V0!7))) & (~(host(X!4) = host(Y0!8))) & (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))))) <=> ((~setIn(host(Z!6), index(acks, host(X!4)))) & (host(X!4) = host(V0!7)) & setIn(V0!7, alive) & (~(host(X!4) = host(Y0!8))) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))),
% 0.19/0.45 inference(transitivity,[status(thm)],[23, 15])).
% 0.19/0.45 tff(25,plain,
% 0.19/0.45 ((leq(host(X!4), host(Y!3)) & setIn(X!4, alive) & ((~setIn(host(Z!6), index(acks, host(X!4)))) & ((host(X!4) = host(V0!7)) & ((setIn(V0!7, alive) & (host(X!4) = host(V0!7))) & (~(host(X!4) = host(Y0!8))) & (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))))) & leq(nbr_proc, index(pendack, host(X!4))) & ((index(status, host(X!4)) = elec_2) & (host(Y!3) = 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] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~setIn(Z, alive)) | (~leq(host(Z), host(Pid0))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid30) = host(Pid0))) | (~(index(status, host(Z)) = elec_2)) | (~(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))) | ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~setIn(Pid0, alive)) | (~leq(nbr_proc, s(host(Pid0)))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~elem(m_Down(Pid30), queue(host(Pid0)))) | (~(host(Pid30) = s(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))) <=> (leq(host(X!4), host(Y!3)) & setIn(X!4, alive) & ((~setIn(host(Z!6), index(acks, host(X!4)))) & (host(X!4) = host(V0!7)) & setIn(V0!7, alive) & (~(host(X!4) = host(Y0!8))) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1)) & leq(nbr_proc, index(pendack, host(X!4))) & ((index(status, host(X!4)) = elec_2) & (host(Y!3) = 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] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~setIn(Z, alive)) | (~leq(host(Z), host(Pid0))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid30) = host(Pid0))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_1))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((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)))) | (~(index(status, host(Pid0)) = elec_1)) | (~leq(nbr_proc, s(host(Pid0)))) | (~elem(m_Down(Pid30), queue(host(Pid0)))) | (~(host(Pid30) = s(host(Pid0))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[24, 14])).
% 0.19/0.46 tff(26,plain,
% 0.19/0.46 ((leq(host(X!4), host(Y!3)) & setIn(X!4, alive) & ((~setIn(host(Z!6), index(acks, host(X!4)))) & ((host(X!4) = host(V0!7)) & ((setIn(V0!7, alive) & (host(X!4) = host(V0!7))) & (~(host(X!4) = host(Y0!8))) & (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1))))) & leq(nbr_proc, index(pendack, host(X!4))) & ((index(status, host(X!4)) = elec_2) & (host(Y!3) = 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] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~setIn(Z, alive)) | (~leq(host(Z), host(Pid0))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid30) = host(Pid0))) | (~(index(status, host(Z)) = elec_2)) | (~(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))) | ((~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~setIn(Pid0, alive)) | (~leq(nbr_proc, s(host(Pid0)))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~elem(m_Down(Pid30), queue(host(Pid0)))) | (~(host(Pid30) = s(host(Pid0)))) | (~(index(status, host(Pid0)) = elec_1)))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))) <=> (leq(host(X!4), host(Y!3)) & setIn(X!4, alive) & (~setIn(host(Z!6), index(acks, host(X!4)))) & (host(X!4) = host(V0!7)) & setIn(V0!7, alive) & (~(host(X!4) = host(Y0!8))) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1) & leq(nbr_proc, index(pendack, host(X!4))) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = 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] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~setIn(Z, alive)) | (~leq(host(Z), host(Pid0))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid30) = host(Pid0))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_1))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((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)))) | (~(index(status, host(Pid0)) = elec_1)) | (~leq(nbr_proc, s(host(Pid0)))) | (~elem(m_Down(Pid30), queue(host(Pid0)))) | (~(host(Pid30) = s(host(Pid0))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))),
% 0.19/0.46 inference(transitivity,[status(thm)],[25, 13])).
% 0.19/0.46 tff(27,plain,
% 0.19/0.46 ((~![V: $i, X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~setIn(X, alive)) | ![Z: $i] : (setIn(host(Z), index(acks, host(X))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), queue(host(Y0))) & elem(m_Down(X0), queue(host(Y0))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(status, host(X)) = elec_2) & (host(Y) = 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] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Z, alive) & leq(host(Z), host(Pid0)) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid30) = host(Pid0)) & (index(status, host(Z)) = elec_2) & (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))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Pid0, alive) & leq(nbr_proc, s(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Down(Pid30), queue(host(Pid0))) & (host(Pid30) = s(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V)))))) <=> (~![V: $i, X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~setIn(X, alive)) | ![Z: $i] : (setIn(host(Z), index(acks, host(X))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), queue(host(Y0))) & elem(m_Down(X0), queue(host(Y0))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(status, host(X)) = elec_2) & (host(Y) = 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] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Z, alive) & leq(host(Z), host(Pid0)) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid30) = host(Pid0)) & (index(status, host(Z)) = elec_2) & (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))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Pid0, alive) & leq(nbr_proc, s(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Down(Pid30), queue(host(Pid0))) & (host(Pid30) = s(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(28,plain,
% 0.19/0.47 ((~![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] : (((~(Pid0 = Z)) & (host(Pid0) = host(Z))) => ((~setIn(Z, alive)) | (~setIn(Pid0, alive))))) & ![Z: $i] : ((((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive)) => (index(elid, host(Z)) = Z))) & ![Z: $i, Pid0: $i] : ((((setIn(Z, alive) & setIn(Pid0, alive)) & setIn(host(Pid0), index(down, host(Z)))) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(Pid0)), host(Z)))) & ![Z: $i, Pid0: $i] : (((setIn(Pid0, alive) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid0))) => (~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((setIn(Z, alive) & setIn(Pid0, alive)) & elem(m_Down(Pid20), queue(host(Z)))) & (host(Pid0) = host(Pid20))) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(Pid0)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((((setIn(Pid0, alive) & (host(Pid20) = host(Pid0))) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid0))) => (~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))))) & ![Z: $i, Pid0: $i] : ((((((setIn(Z, alive) & setIn(Pid0, alive)) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm)) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid0))) => (Pid0 = Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((~leq(host(Pid20), host(Pid0))) & 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, Pid30: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid20) = host(Z))) & setIn(Z, alive)) & setIn(Pid20, alive)) & (host(Pid30) = host(Z))) & (host(Pid0) = host(Pid20))) => (~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid20) = host(Z))) & setIn(Z, alive)) & setIn(Pid20, alive)) & (host(Pid30) = host(Z))) & (host(Pid0) = host(Pid20))) => (~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive)) & elem(m_Down(Z), queue(host(Pid0)))) & (host(Pid20) = host(Z))) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid20))) => (~((setIn(Pid20, alive) & (index(status, host(Pid20)) = norm)) & (index(ldr, host(Pid20)) = host(Pid20)))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive)) & elem(m_Down(Z), queue(host(Pid0)))) & (host(Pid20) = host(Z))) & (index(status, host(Pid0)) = wait)) & (host(index(elid, host(Pid0))) = host(Pid20))) => (~((setIn(Pid20, alive) & (index(status, host(Pid20)) = norm)) & (index(ldr, host(Pid20)) = host(Pid20)))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : (((((((![V0: $i] : (((~leq(host(Pid0), V0)) & leq(s(zero), V0)) => (setIn(V0, index(down, host(Pid0))) | (V0 = host(Pid20)))) & setIn(Z, alive)) & leq(host(Z), host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0)))) & (host(Pid30) = host(Pid0))) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_1)) => (~elem(m_Ack(Z, Pid30), queue(host(Z)))))) & ![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)))) & setIn(Pid0, alive)) & leq(nbr_proc, s(host(Pid0)))) & elem(m_Down(Pid20), queue(host(Pid0)))) & elem(m_Down(Pid30), queue(host(Pid0)))) & (host(Pid30) = s(host(Pid0)))) & (index(status, host(Pid0)) = elec_1)) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & (queue(host(X)) = cons(m_Down(Y), V))) => (setIn(X, alive) => (leq(host(X), host(Y)) => (((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)))) => ![V0: $i] : ((host(X) = host(V0)) => ![W0: $i, X0: $i, Y0: $i] : ((~(host(X) = host(Y0))) => (((((((![V1: $i] : (((~leq(host(Y0), V1)) & leq(s(zero), V1)) => (setIn(V1, index(down, host(Y0))) | (V1 = host(X0)))) & setIn(Y0, alive)) & leq(nbr_proc, s(host(Y0)))) & elem(m_Down(W0), queue(host(Y0)))) & elem(m_Down(X0), queue(host(Y0)))) & (host(W0) = s(host(Y0)))) & (index(status, host(Y0)) = elec_1)) => (~(setIn(V0, alive) & (host(X) = host(V0)))))))))))))) <=> (~![V: $i, X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~setIn(X, alive)) | ![Z: $i] : (setIn(host(Z), index(acks, host(X))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), queue(host(Y0))) & elem(m_Down(X0), queue(host(Y0))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(status, host(X)) = elec_2) & (host(Y) = 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] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Z, alive) & leq(host(Z), host(Pid0)) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid30) = host(Pid0)) & (index(status, host(Z)) = elec_2) & (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))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Pid0, alive) & leq(nbr_proc, s(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Down(Pid30), queue(host(Pid0))) & (host(Pid30) = s(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(29,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] : (((~(Pid0 = Z)) & (host(Pid0) = host(Z))) => ((~setIn(Z, alive)) | (~setIn(Pid0, alive))))) & ![Z: $i] : ((((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive)) => (index(elid, host(Z)) = Z))) & ![Z: $i, Pid0: $i] : ((((setIn(Z, alive) & setIn(Pid0, alive)) & setIn(host(Pid0), index(down, host(Z)))) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(Pid0)), host(Z)))) & ![Z: $i, Pid0: $i] : (((setIn(Pid0, alive) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid0))) => (~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((setIn(Z, alive) & setIn(Pid0, alive)) & elem(m_Down(Pid20), queue(host(Z)))) & (host(Pid0) = host(Pid20))) & (index(status, host(Pid0)) = elec_2)) => leq(index(pendack, host(Pid0)), host(Z)))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((((setIn(Pid0, alive) & (host(Pid20) = host(Pid0))) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid0))) => (~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))))) & ![Z: $i, Pid0: $i] : ((((((setIn(Z, alive) & setIn(Pid0, alive)) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm)) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid0))) => (Pid0 = Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((~leq(host(Pid20), host(Pid0))) & 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, Pid30: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid20) = host(Z))) & setIn(Z, alive)) & setIn(Pid20, alive)) & (host(Pid30) = host(Z))) & (host(Pid0) = host(Pid20))) => (~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid20) = host(Z))) & setIn(Z, alive)) & setIn(Pid20, alive)) & (host(Pid30) = host(Z))) & (host(Pid0) = host(Pid20))) => (~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive)) & elem(m_Down(Z), queue(host(Pid0)))) & (host(Pid20) = host(Z))) & (index(status, host(Pid0)) = norm)) & (index(ldr, host(Pid0)) = host(Pid20))) => (~((setIn(Pid20, alive) & (index(status, host(Pid20)) = norm)) & (index(ldr, host(Pid20)) = host(Pid20)))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (((((((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive)) & elem(m_Down(Z), queue(host(Pid0)))) & (host(Pid20) = host(Z))) & (index(status, host(Pid0)) = wait)) & (host(index(elid, host(Pid0))) = host(Pid20))) => (~((setIn(Pid20, alive) & (index(status, host(Pid20)) = norm)) & (index(ldr, host(Pid20)) = host(Pid20)))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : (((((((![V0: $i] : (((~leq(host(Pid0), V0)) & leq(s(zero), V0)) => (setIn(V0, index(down, host(Pid0))) | (V0 = host(Pid20)))) & setIn(Z, alive)) & leq(host(Z), host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0)))) & (host(Pid30) = host(Pid0))) & (index(status, host(Z)) = elec_2)) & (index(status, host(Pid0)) = elec_1)) => (~elem(m_Ack(Z, Pid30), queue(host(Z)))))) & ![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)))) & setIn(Pid0, alive)) & leq(nbr_proc, s(host(Pid0)))) & elem(m_Down(Pid20), queue(host(Pid0)))) & elem(m_Down(Pid30), queue(host(Pid0)))) & (host(Pid30) = s(host(Pid0)))) & (index(status, host(Pid0)) = elec_1)) => (~((setIn(Z, alive) & (index(ldr, host(Z)) = host(Z))) & (index(status, host(Z)) = norm))))) & (queue(host(X)) = cons(m_Down(Y), V))) => (setIn(X, alive) => (leq(host(X), host(Y)) => (((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)))) => ![V0: $i] : ((host(X) = host(V0)) => ![W0: $i, X0: $i, Y0: $i] : ((~(host(X) = host(Y0))) => (((((((![V1: $i] : (((~leq(host(Y0), V1)) & leq(s(zero), V1)) => (setIn(V1, index(down, host(Y0))) | (V1 = host(X0)))) & setIn(Y0, alive)) & leq(nbr_proc, s(host(Y0)))) & elem(m_Down(W0), queue(host(Y0)))) & elem(m_Down(X0), queue(host(Y0)))) & (host(W0) = s(host(Y0)))) & (index(status, host(Y0)) = elec_1)) => (~(setIn(V0, alive) & (host(X) = host(V0)))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj')).
% 0.19/0.47 tff(30,plain,
% 0.19/0.47 (~![V: $i, X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~setIn(X, alive)) | ![Z: $i] : (setIn(host(Z), index(acks, host(X))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), queue(host(Y0))) & elem(m_Down(X0), queue(host(Y0))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(status, host(X)) = elec_2) & (host(Y) = 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] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Z, alive) & leq(host(Z), host(Pid0)) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid30) = host(Pid0)) & (index(status, host(Z)) = elec_2) & (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))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Pid0, alive) & leq(nbr_proc, s(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Down(Pid30), queue(host(Pid0))) & (host(Pid30) = s(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.47 tff(31,plain,
% 0.19/0.47 (~![V: $i, X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~setIn(X, alive)) | ![Z: $i] : (setIn(host(Z), index(acks, host(X))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), queue(host(Y0))) & elem(m_Down(X0), queue(host(Y0))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(status, host(X)) = elec_2) & (host(Y) = 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] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Z, alive) & leq(host(Z), host(Pid0)) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid30) = host(Pid0)) & (index(status, host(Z)) = elec_2) & (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))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Pid0, alive) & leq(nbr_proc, s(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Down(Pid30), queue(host(Pid0))) & (host(Pid30) = s(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[30, 27])).
% 0.19/0.48 tff(32,plain,
% 0.19/0.48 (~![V: $i, X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~setIn(X, alive)) | ![Z: $i] : (setIn(host(Z), index(acks, host(X))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), queue(host(Y0))) & elem(m_Down(X0), queue(host(Y0))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(status, host(X)) = elec_2) & (host(Y) = 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] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Z, alive) & leq(host(Z), host(Pid0)) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid30) = host(Pid0)) & (index(status, host(Z)) = elec_2) & (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))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Pid0, alive) & leq(nbr_proc, s(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Down(Pid30), queue(host(Pid0))) & (host(Pid30) = s(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.19/0.48 tff(33,plain,
% 0.19/0.48 (~![V: $i, X: $i, Y: $i] : ((~leq(host(X), host(Y))) | (~setIn(X, alive)) | ![Z: $i] : (setIn(host(Z), index(acks, host(X))) | ![V0: $i] : ((~(host(X) = host(V0))) | ![W0: $i, X0: $i, Y0: $i] : ((~(setIn(V0, alive) & (host(X) = host(V0)))) | (host(X) = host(Y0)) | (~(![V1: $i] : ((V1 = host(X0)) | setIn(V1, index(down, host(Y0))) | (~((~leq(host(Y0), V1)) & leq(s(zero), V1)))) & setIn(Y0, alive) & leq(nbr_proc, s(host(Y0))) & elem(m_Down(W0), queue(host(Y0))) & elem(m_Down(X0), queue(host(Y0))) & (host(W0) = s(host(Y0))) & (index(status, host(Y0)) = elec_1)))))) | (~leq(nbr_proc, index(pendack, host(X)))) | (~((index(status, host(X)) = elec_2) & (host(Y) = 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] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Z, alive) & leq(host(Z), host(Pid0)) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid30) = host(Pid0)) & (index(status, host(Z)) = elec_2) & (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))) | (~(![V0: $i] : ((V0 = host(Pid20)) | setIn(V0, index(down, host(Pid0))) | (~((~leq(host(Pid0), V0)) & leq(s(zero), V0)))) & setIn(Pid0, alive) & leq(nbr_proc, s(host(Pid0))) & elem(m_Down(Pid20), queue(host(Pid0))) & elem(m_Down(Pid30), queue(host(Pid0))) & (host(Pid30) = s(host(Pid0))) & (index(status, host(Pid0)) = elec_1)))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[32, 27])).
% 0.19/0.48 tff(34,plain,
% 0.19/0.48 (leq(host(X!4), host(Y!3)) & setIn(X!4, alive) & (~setIn(host(Z!6), index(acks, host(X!4)))) & (host(X!4) = host(V0!7)) & setIn(V0!7, alive) & (~(host(X!4) = host(Y0!8))) & ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) & setIn(Y0!8, alive) & leq(nbr_proc, s(host(Y0!8))) & elem(m_Down(W0!10), queue(host(Y0!8))) & elem(m_Down(X0!9), queue(host(Y0!8))) & (host(W0!10) = s(host(Y0!8))) & (index(status, host(Y0!8)) = elec_1) & leq(nbr_proc, index(pendack, host(X!4))) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = 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] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i] : ((~(((index(status, host(Z)) = elec_1) | (index(status, host(Z)) = elec_2)) & setIn(Z, alive))) | (index(elid, host(Z)) = Z)) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(host(Pid0), index(down, host(Z))))) | (~(setIn(Pid0, alive) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & elem(m_Down(Pid20), queue(host(Z))))) | (~(setIn(Pid0, alive) & (host(Pid20) = host(Pid0)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0))))) & ![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid0)))) | (Pid0 = Z)) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((~leq(host(Pid20), host(Pid0))) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Pid0))) & (host(Pid20) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & setIn(host(Pid30), index(down, host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = norm) & (index(ldr, host(Pid0)) = host(Pid20))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Pid20, alive) & (index(status, host(Pid20)) = norm) & (index(ldr, host(Pid20)) = host(Pid20)))) | (~((~(host(Pid0) = host(Pid20))) & setIn(Pid0, alive) & elem(m_Down(Z), queue(host(Pid0))) & (host(Pid20) = host(Z)) & (index(status, host(Pid0)) = wait) & (host(index(elid, host(Pid0))) = host(Pid20))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~elem(m_Ack(Z, Pid30), queue(host(Z)))) | (~((tptp_fun_V0_11(Pid0, Pid20) = host(Pid20)) | setIn(tptp_fun_V0_11(Pid0, Pid20), index(down, host(Pid0))) | (~((~leq(host(Pid0), tptp_fun_V0_11(Pid0, Pid20))) & leq(s(zero), tptp_fun_V0_11(Pid0, Pid20)))))) | (~setIn(Z, alive)) | (~leq(host(Z), host(Pid0))) | (~elem(m_Down(Pid20), queue(host(Pid0)))) | (~(host(Pid30) = host(Pid0))) | (~(index(status, host(Z)) = elec_2)) | (~(index(status, host(Pid0)) = elec_1))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(setIn(Z, alive) & (index(ldr, host(Z)) = host(Z)) & (index(status, host(Z)) = norm))) | (~((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)))) | (~(index(status, host(Pid0)) = elec_1)) | (~leq(nbr_proc, s(host(Pid0)))) | (~elem(m_Down(Pid30), queue(host(Pid0)))) | (~(host(Pid30) = s(host(Pid0))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.19/0.48 tff(35,plain,
% 0.19/0.48 (host(X!4) = host(V0!7)),
% 0.19/0.48 inference(and_elim,[status(thm)],[34])).
% 0.19/0.48 tff(36,plain,
% 0.19/0.48 (host(V0!7) = host(X!4)),
% 0.19/0.48 inference(symmetry,[status(thm)],[35])).
% 0.19/0.48 tff(37,plain,
% 0.19/0.48 ((host(V0!7) = host(Y0!8)) <=> (host(X!4) = host(Y0!8))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[36])).
% 0.19/0.48 tff(38,plain,
% 0.19/0.48 ((host(X!4) = host(Y0!8)) <=> (host(V0!7) = host(Y0!8))),
% 0.19/0.48 inference(symmetry,[status(thm)],[37])).
% 0.19/0.48 tff(39,plain,
% 0.19/0.48 ((~(host(X!4) = host(Y0!8))) <=> (~(host(V0!7) = host(Y0!8)))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[38])).
% 0.19/0.48 tff(40,plain,
% 0.19/0.48 (~(host(X!4) = host(Y0!8))),
% 0.19/0.48 inference(and_elim,[status(thm)],[34])).
% 0.19/0.48 tff(41,plain,
% 0.19/0.48 (~(host(V0!7) = host(Y0!8))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.48 tff(42,plain,
% 0.19/0.48 ((((~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7)))) <=> (host(V0!7) = host(Y0!8))) | ((~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7)))) | (host(V0!7) = host(Y0!8))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(43,plain,
% 0.19/0.48 ((~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[42, 41, 12])).
% 0.19/0.48 tff(44,plain,
% 0.19/0.48 (leq(s(zero), host(V0!7)) <=> leq(s(zero), host(X!4))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[36])).
% 0.19/0.48 tff(45,plain,
% 0.19/0.48 (leq(s(zero), host(X!4)) <=> leq(s(zero), host(V0!7))),
% 0.19/0.48 inference(symmetry,[status(thm)],[44])).
% 0.19/0.48 tff(46,plain,
% 0.19/0.48 (^[P: $i] : refl(leq(s(zero), host(P)) <=> leq(s(zero), host(P)))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(47,plain,
% 0.19/0.48 (![P: $i] : leq(s(zero), host(P)) <=> ![P: $i] : leq(s(zero), host(P))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.48 tff(48,plain,
% 0.19/0.48 (![P: $i] : leq(s(zero), host(P)) <=> ![P: $i] : leq(s(zero), host(P))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(49,axiom,(![P: $i] : leq(s(zero), host(P))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_02')).
% 0.19/0.48 tff(50,plain,
% 0.19/0.48 (![P: $i] : leq(s(zero), host(P))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.48 tff(51,plain,(
% 0.19/0.48 ![P: $i] : leq(s(zero), host(P))),
% 0.19/0.48 inference(skolemize,[status(sab)],[50])).
% 0.19/0.48 tff(52,plain,
% 0.19/0.48 (![P: $i] : leq(s(zero), host(P))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.19/0.48 tff(53,plain,
% 0.19/0.48 ((~![P: $i] : leq(s(zero), host(P))) | leq(s(zero), host(X!4))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(54,plain,
% 0.19/0.48 (leq(s(zero), host(X!4))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.19/0.48 tff(55,plain,
% 0.19/0.48 (leq(s(zero), host(V0!7))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[54, 45])).
% 0.19/0.48 tff(56,plain,
% 0.19/0.48 (index(status, host(X!4)) = elec_2),
% 0.19/0.48 inference(and_elim,[status(thm)],[34])).
% 0.19/0.48 tff(57,plain,
% 0.19/0.48 (index(status, host(V0!7)) = index(status, host(X!4))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[36])).
% 0.19/0.48 tff(58,plain,
% 0.19/0.48 (index(status, host(V0!7)) = elec_2),
% 0.19/0.48 inference(transitivity,[status(thm)],[57, 56])).
% 0.19/0.48 tff(59,plain,
% 0.19/0.48 (host(Y!3) = index(pendack, host(X!4))),
% 0.19/0.48 inference(and_elim,[status(thm)],[34])).
% 0.19/0.48 tff(60,plain,
% 0.19/0.48 (index(pendack, host(X!4)) = host(Y!3)),
% 0.19/0.48 inference(symmetry,[status(thm)],[59])).
% 0.19/0.48 tff(61,plain,
% 0.19/0.48 (index(pendack, host(V0!7)) = index(pendack, host(X!4))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[36])).
% 0.19/0.48 tff(62,plain,
% 0.19/0.48 (index(pendack, host(V0!7)) = host(Y!3)),
% 0.19/0.48 inference(transitivity,[status(thm)],[61, 60])).
% 0.19/0.48 tff(63,plain,
% 0.19/0.48 (leq(index(pendack, host(V0!7)), host(Y0!8)) <=> leq(host(Y!3), host(Y0!8))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[62])).
% 0.19/0.48 tff(64,plain,
% 0.19/0.48 (leq(host(Y!3), host(Y0!8)) <=> leq(index(pendack, host(V0!7)), host(Y0!8))),
% 0.19/0.48 inference(symmetry,[status(thm)],[63])).
% 0.19/0.48 tff(65,plain,
% 0.19/0.48 (((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) <=> (index(pendack, host(X!4)) = nbr_proc)))) <=> ((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) <=> (index(pendack, host(X!4)) = nbr_proc))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(66,plain,
% 0.19/0.48 ((~(((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) <=> (index(pendack, host(X!4)) = nbr_proc))) <=> (~(((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) <=> (index(pendack, host(X!4)) = nbr_proc)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(67,plain,
% 0.19/0.48 ((((~leq(index(pendack, host(X!4)), nbr_proc)) | (~leq(nbr_proc, index(pendack, host(X!4))))) <=> (index(pendack, host(X!4)) = nbr_proc)) <=> (((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) <=> (index(pendack, host(X!4)) = nbr_proc))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(68,plain,
% 0.19/0.48 ((~(((~leq(index(pendack, host(X!4)), nbr_proc)) | (~leq(nbr_proc, index(pendack, host(X!4))))) <=> (index(pendack, host(X!4)) = nbr_proc))) <=> (~(((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) <=> (index(pendack, host(X!4)) = nbr_proc)))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[67])).
% 0.19/0.48 tff(69,plain,
% 0.19/0.48 ((~(((~leq(index(pendack, host(X!4)), nbr_proc)) | (~leq(nbr_proc, index(pendack, host(X!4))))) <=> (index(pendack, host(X!4)) = nbr_proc))) <=> (~(((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) <=> (index(pendack, host(X!4)) = nbr_proc)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[68, 66])).
% 0.19/0.48 tff(70,plain,
% 0.19/0.48 (((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(index(pendack, host(X!4)), nbr_proc)) | (~leq(nbr_proc, index(pendack, host(X!4))))) <=> (index(pendack, host(X!4)) = nbr_proc)))) <=> ((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) <=> (index(pendack, host(X!4)) = nbr_proc))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[69])).
% 0.19/0.49 tff(71,plain,
% 0.19/0.49 (((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(index(pendack, host(X!4)), nbr_proc)) | (~leq(nbr_proc, index(pendack, host(X!4))))) <=> (index(pendack, host(X!4)) = nbr_proc)))) <=> ((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) <=> (index(pendack, host(X!4)) = nbr_proc))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[70, 65])).
% 0.19/0.49 tff(72,plain,
% 0.19/0.49 ((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(index(pendack, host(X!4)), nbr_proc)) | (~leq(nbr_proc, index(pendack, host(X!4))))) <=> (index(pendack, host(X!4)) = nbr_proc)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(73,plain,
% 0.19/0.49 ((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) <=> (index(pendack, host(X!4)) = nbr_proc)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.49 tff(74,plain,
% 0.19/0.49 (~(((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) <=> (index(pendack, host(X!4)) = nbr_proc))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[73, 10])).
% 0.19/0.49 tff(75,plain,
% 0.19/0.49 (leq(index(pendack, host(X!4)), nbr_proc) <=> leq(host(Y!3), nbr_proc)),
% 0.19/0.49 inference(monotonicity,[status(thm)],[60])).
% 0.19/0.49 tff(76,plain,
% 0.19/0.49 (leq(host(Y!3), nbr_proc) <=> leq(index(pendack, host(X!4)), nbr_proc)),
% 0.19/0.49 inference(symmetry,[status(thm)],[75])).
% 0.19/0.49 tff(77,plain,
% 0.19/0.49 (^[P: $i] : refl(leq(host(P), nbr_proc) <=> leq(host(P), nbr_proc))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(78,plain,
% 0.19/0.49 (![P: $i] : leq(host(P), nbr_proc) <=> ![P: $i] : leq(host(P), nbr_proc)),
% 0.19/0.49 inference(quant_intro,[status(thm)],[77])).
% 0.19/0.49 tff(79,plain,
% 0.19/0.49 (![P: $i] : leq(host(P), nbr_proc) <=> ![P: $i] : leq(host(P), nbr_proc)),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(80,axiom,(![P: $i] : leq(host(P), nbr_proc)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_04')).
% 0.19/0.49 tff(81,plain,
% 0.19/0.49 (![P: $i] : leq(host(P), nbr_proc)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.49 tff(82,plain,(
% 0.19/0.49 ![P: $i] : leq(host(P), nbr_proc)),
% 0.19/0.49 inference(skolemize,[status(sab)],[81])).
% 0.19/0.49 tff(83,plain,
% 0.19/0.49 (![P: $i] : leq(host(P), nbr_proc)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.19/0.49 tff(84,plain,
% 0.19/0.49 ((~![P: $i] : leq(host(P), nbr_proc)) | leq(host(Y!3), nbr_proc)),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(85,plain,
% 0.19/0.49 (leq(host(Y!3), nbr_proc)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.19/0.49 tff(86,plain,
% 0.19/0.49 (leq(index(pendack, host(X!4)), nbr_proc)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[85, 76])).
% 0.19/0.49 tff(87,plain,
% 0.19/0.49 (leq(nbr_proc, index(pendack, host(X!4)))),
% 0.19/0.49 inference(and_elim,[status(thm)],[34])).
% 0.19/0.49 tff(88,plain,
% 0.19/0.49 ((~((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc)))) | (~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(89,plain,
% 0.19/0.49 ((~((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc)))) | (~leq(index(pendack, host(X!4)), nbr_proc))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.19/0.49 tff(90,plain,
% 0.19/0.49 (~((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[89, 86])).
% 0.19/0.49 tff(91,plain,
% 0.19/0.49 ((((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) <=> (index(pendack, host(X!4)) = nbr_proc)) | ((~leq(nbr_proc, index(pendack, host(X!4)))) | (~leq(index(pendack, host(X!4)), nbr_proc))) | (index(pendack, host(X!4)) = nbr_proc)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(92,plain,
% 0.19/0.49 (index(pendack, host(X!4)) = nbr_proc),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[91, 90, 74])).
% 0.19/0.49 tff(93,plain,
% 0.19/0.49 (nbr_proc = index(pendack, host(X!4))),
% 0.19/0.49 inference(symmetry,[status(thm)],[92])).
% 0.19/0.49 tff(94,plain,
% 0.19/0.49 (((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc))) <=> (s(host(Y0!8)) = nbr_proc)))) <=> ((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc))) <=> (s(host(Y0!8)) = nbr_proc))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(95,plain,
% 0.19/0.49 ((~(((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc))) <=> (s(host(Y0!8)) = nbr_proc))) <=> (~(((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc))) <=> (s(host(Y0!8)) = nbr_proc)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(96,plain,
% 0.19/0.49 ((((~leq(s(host(Y0!8)), nbr_proc)) | (~leq(nbr_proc, s(host(Y0!8))))) <=> (s(host(Y0!8)) = nbr_proc)) <=> (((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc))) <=> (s(host(Y0!8)) = nbr_proc))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(97,plain,
% 0.19/0.49 ((~(((~leq(s(host(Y0!8)), nbr_proc)) | (~leq(nbr_proc, s(host(Y0!8))))) <=> (s(host(Y0!8)) = nbr_proc))) <=> (~(((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc))) <=> (s(host(Y0!8)) = nbr_proc)))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[96])).
% 0.19/0.49 tff(98,plain,
% 0.19/0.49 ((~(((~leq(s(host(Y0!8)), nbr_proc)) | (~leq(nbr_proc, s(host(Y0!8))))) <=> (s(host(Y0!8)) = nbr_proc))) <=> (~(((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc))) <=> (s(host(Y0!8)) = nbr_proc)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[97, 95])).
% 0.19/0.49 tff(99,plain,
% 0.19/0.49 (((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(s(host(Y0!8)), nbr_proc)) | (~leq(nbr_proc, s(host(Y0!8))))) <=> (s(host(Y0!8)) = nbr_proc)))) <=> ((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc))) <=> (s(host(Y0!8)) = nbr_proc))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[98])).
% 0.19/0.49 tff(100,plain,
% 0.19/0.49 (((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(s(host(Y0!8)), nbr_proc)) | (~leq(nbr_proc, s(host(Y0!8))))) <=> (s(host(Y0!8)) = nbr_proc)))) <=> ((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc))) <=> (s(host(Y0!8)) = nbr_proc))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[99, 94])).
% 0.19/0.49 tff(101,plain,
% 0.19/0.49 ((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(s(host(Y0!8)), nbr_proc)) | (~leq(nbr_proc, s(host(Y0!8))))) <=> (s(host(Y0!8)) = nbr_proc)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(102,plain,
% 0.19/0.49 ((~![X: $i, Y: $i] : (~(((~leq(X, Y)) | (~leq(Y, X))) <=> (X = Y)))) | (~(((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc))) <=> (s(host(Y0!8)) = nbr_proc)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.19/0.49 tff(103,plain,
% 0.19/0.49 (~(((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc))) <=> (s(host(Y0!8)) = nbr_proc))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[102, 10])).
% 0.19/0.49 tff(104,plain,
% 0.19/0.49 (host(W0!10) = s(host(Y0!8))),
% 0.19/0.49 inference(and_elim,[status(thm)],[34])).
% 0.19/0.49 tff(105,plain,
% 0.19/0.49 (s(host(Y0!8)) = host(W0!10)),
% 0.19/0.49 inference(symmetry,[status(thm)],[104])).
% 0.19/0.49 tff(106,plain,
% 0.19/0.49 (leq(s(host(Y0!8)), nbr_proc) <=> leq(host(W0!10), nbr_proc)),
% 0.19/0.49 inference(monotonicity,[status(thm)],[105])).
% 0.19/0.49 tff(107,plain,
% 0.19/0.49 (leq(host(W0!10), nbr_proc) <=> leq(s(host(Y0!8)), nbr_proc)),
% 0.19/0.49 inference(symmetry,[status(thm)],[106])).
% 0.19/0.49 tff(108,plain,
% 0.19/0.49 ((~![P: $i] : leq(host(P), nbr_proc)) | leq(host(W0!10), nbr_proc)),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(109,plain,
% 0.19/0.49 (leq(host(W0!10), nbr_proc)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[108, 83])).
% 0.19/0.49 tff(110,plain,
% 0.19/0.49 (leq(s(host(Y0!8)), nbr_proc)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[109, 107])).
% 0.19/0.49 tff(111,plain,
% 0.19/0.49 (leq(nbr_proc, s(host(Y0!8)))),
% 0.19/0.49 inference(and_elim,[status(thm)],[34])).
% 0.19/0.49 tff(112,plain,
% 0.19/0.49 ((~((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc)))) | (~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(113,plain,
% 0.19/0.49 ((~((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc)))) | (~leq(s(host(Y0!8)), nbr_proc))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.19/0.49 tff(114,plain,
% 0.19/0.49 (~((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[113, 110])).
% 0.19/0.49 tff(115,plain,
% 0.19/0.49 ((((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc))) <=> (s(host(Y0!8)) = nbr_proc)) | ((~leq(nbr_proc, s(host(Y0!8)))) | (~leq(s(host(Y0!8)), nbr_proc))) | (s(host(Y0!8)) = nbr_proc)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(116,plain,
% 0.19/0.49 (s(host(Y0!8)) = nbr_proc),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[115, 114, 103])).
% 0.19/0.49 tff(117,plain,
% 0.19/0.49 (host(W0!10) = host(Y!3)),
% 0.19/0.49 inference(transitivity,[status(thm)],[104, 116, 93, 60])).
% 0.19/0.49 tff(118,plain,
% 0.19/0.49 (leq(host(W0!10), host(Y0!8)) <=> leq(host(Y!3), host(Y0!8))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[117])).
% 0.19/0.49 tff(119,plain,
% 0.19/0.49 (leq(host(W0!10), host(Y0!8)) <=> leq(index(pendack, host(V0!7)), host(Y0!8))),
% 0.19/0.49 inference(transitivity,[status(thm)],[118, 64])).
% 0.19/0.49 tff(120,plain,
% 0.19/0.49 ((~leq(host(W0!10), host(Y0!8))) <=> (~leq(index(pendack, host(V0!7)), host(Y0!8)))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[119])).
% 0.19/0.49 tff(121,plain,
% 0.19/0.49 (leq(s(host(Y0!8)), host(Y0!8)) <=> leq(host(W0!10), host(Y0!8))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[105])).
% 0.19/0.49 tff(122,plain,
% 0.19/0.49 ((~leq(s(host(Y0!8)), host(Y0!8))) <=> (~leq(host(W0!10), host(Y0!8)))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[121])).
% 0.19/0.49 tff(123,plain,
% 0.19/0.49 (^[X: $i] : refl((~leq(s(X), X)) <=> (~leq(s(X), X)))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(124,plain,
% 0.19/0.49 (![X: $i] : (~leq(s(X), X)) <=> ![X: $i] : (~leq(s(X), X))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[123])).
% 0.19/0.49 tff(125,plain,
% 0.19/0.49 (![X: $i] : (~leq(s(X), X)) <=> ![X: $i] : (~leq(s(X), X))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(126,axiom,(![X: $i] : (~leq(s(X), X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_58')).
% 0.19/0.49 tff(127,plain,
% 0.19/0.49 (![X: $i] : (~leq(s(X), X))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.19/0.49 tff(128,plain,(
% 0.19/0.49 ![X: $i] : (~leq(s(X), X))),
% 0.19/0.49 inference(skolemize,[status(sab)],[127])).
% 0.19/0.49 tff(129,plain,
% 0.19/0.49 (![X: $i] : (~leq(s(X), X))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.19/0.49 tff(130,plain,
% 0.19/0.49 ((~![X: $i] : (~leq(s(X), X))) | (~leq(s(host(Y0!8)), host(Y0!8)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(131,plain,
% 0.19/0.49 (~leq(s(host(Y0!8)), host(Y0!8))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.19/0.49 tff(132,plain,
% 0.19/0.49 (~leq(host(W0!10), host(Y0!8))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[131, 122])).
% 0.19/0.49 tff(133,plain,
% 0.19/0.49 (~leq(index(pendack, host(V0!7)), host(Y0!8))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[132, 120])).
% 0.19/0.49 tff(134,plain,
% 0.19/0.49 (^[Z: $i, Pid0: $i] : refl(((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2))) <=> ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(135,plain,
% 0.19/0.49 (![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2))) <=> ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[134])).
% 0.19/0.49 tff(136,plain,
% 0.19/0.49 (^[Z: $i, Pid0: $i] : trans(monotonicity(trans(monotonicity(rewrite((setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2)) <=> (~((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2))))), ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) <=> (~(~((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2))))))), rewrite((~(~((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2))))) <=> ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))), ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) <=> ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2))))), (((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> (((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))))), rewrite((((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))), (((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(137,plain,
% 0.19/0.49 (![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[136])).
% 0.19/0.49 tff(138,plain,
% 0.19/0.49 (![Z: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & setIn(host(Pid0), index(down, host(Z))) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z)))),
% 0.19/0.49 inference(and_elim,[status(thm)],[34])).
% 0.19/0.49 tff(139,plain,
% 0.19/0.49 (![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.19/0.49 tff(140,plain,
% 0.19/0.49 (![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.19/0.49 tff(141,plain,
% 0.19/0.49 (setIn(Y0!8, alive)),
% 0.19/0.49 inference(and_elim,[status(thm)],[34])).
% 0.19/0.49 tff(142,plain,
% 0.19/0.49 (setIn(V0!7, alive)),
% 0.19/0.49 inference(and_elim,[status(thm)],[34])).
% 0.19/0.49 tff(143,plain,
% 0.19/0.49 (((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))) | ((~setIn(V0!7, alive)) | (~(index(status, host(V0!7)) = elec_2)) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(V0!7)), host(Y0!8)) | (~setIn(host(V0!7), index(down, host(Y0!8)))))) <=> ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))) | (~setIn(V0!7, alive)) | (~(index(status, host(V0!7)) = elec_2)) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(V0!7)), host(Y0!8)) | (~setIn(host(V0!7), index(down, host(Y0!8)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(144,plain,
% 0.19/0.49 (((~setIn(V0!7, alive)) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(V0!7)), host(Y0!8)) | (~setIn(host(V0!7), index(down, host(Y0!8)))) | (~(index(status, host(V0!7)) = elec_2))) <=> ((~setIn(V0!7, alive)) | (~(index(status, host(V0!7)) = elec_2)) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(V0!7)), host(Y0!8)) | (~setIn(host(V0!7), index(down, host(Y0!8)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(145,plain,
% 0.19/0.49 (((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))) | ((~setIn(V0!7, alive)) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(V0!7)), host(Y0!8)) | (~setIn(host(V0!7), index(down, host(Y0!8)))) | (~(index(status, host(V0!7)) = elec_2)))) <=> ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))) | ((~setIn(V0!7, alive)) | (~(index(status, host(V0!7)) = elec_2)) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(V0!7)), host(Y0!8)) | (~setIn(host(V0!7), index(down, host(Y0!8))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[144])).
% 0.19/0.49 tff(146,plain,
% 0.19/0.49 (((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))) | ((~setIn(V0!7, alive)) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(V0!7)), host(Y0!8)) | (~setIn(host(V0!7), index(down, host(Y0!8)))) | (~(index(status, host(V0!7)) = elec_2)))) <=> ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))) | (~setIn(V0!7, alive)) | (~(index(status, host(V0!7)) = elec_2)) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(V0!7)), host(Y0!8)) | (~setIn(host(V0!7), index(down, host(Y0!8)))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[145, 143])).
% 0.19/0.49 tff(147,plain,
% 0.19/0.49 ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))) | ((~setIn(V0!7, alive)) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(V0!7)), host(Y0!8)) | (~setIn(host(V0!7), index(down, host(Y0!8)))) | (~(index(status, host(V0!7)) = elec_2)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(148,plain,
% 0.19/0.49 ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~setIn(host(Pid0), index(down, host(Z)))) | (~(index(status, host(Pid0)) = elec_2)))) | (~setIn(V0!7, alive)) | (~(index(status, host(V0!7)) = elec_2)) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(V0!7)), host(Y0!8)) | (~setIn(host(V0!7), index(down, host(Y0!8))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.19/0.49 tff(149,plain,
% 0.19/0.49 ((~(index(status, host(V0!7)) = elec_2)) | leq(index(pendack, host(V0!7)), host(Y0!8)) | (~setIn(host(V0!7), index(down, host(Y0!8))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[148, 142, 141, 140])).
% 0.19/0.49 tff(150,plain,
% 0.19/0.49 (~setIn(host(V0!7), index(down, host(Y0!8)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[149, 133, 58])).
% 0.19/0.49 tff(151,plain,
% 0.19/0.49 ((host(X!4) = host(X0!9)) <=> (host(X0!9) = host(X!4))),
% 0.19/0.49 inference(commutativity,[status(thm)],[])).
% 0.19/0.49 tff(152,plain,
% 0.19/0.49 ((host(V0!7) = host(X0!9)) <=> (host(X!4) = host(X0!9))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[36])).
% 0.19/0.49 tff(153,plain,
% 0.19/0.49 ((host(V0!7) = host(X0!9)) <=> (host(X0!9) = host(X!4))),
% 0.19/0.49 inference(transitivity,[status(thm)],[152, 151])).
% 0.19/0.49 tff(154,plain,
% 0.19/0.49 ((host(X0!9) = host(X!4)) <=> (host(V0!7) = host(X0!9))),
% 0.19/0.49 inference(symmetry,[status(thm)],[153])).
% 0.19/0.49 tff(155,plain,
% 0.19/0.49 ((host(X!4) = host(X0!9)) <=> (host(V0!7) = host(X0!9))),
% 0.19/0.49 inference(transitivity,[status(thm)],[151, 154])).
% 0.19/0.49 tff(156,plain,
% 0.19/0.49 ((~(host(X!4) = host(X0!9))) <=> (~(host(V0!7) = host(X0!9)))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[155])).
% 0.19/0.49 tff(157,plain,
% 0.19/0.49 (leq(index(pendack, host(X!4)), host(Y0!8)) <=> leq(host(Y!3), host(Y0!8))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[60])).
% 0.19/0.49 tff(158,plain,
% 0.19/0.49 (leq(host(Y!3), host(Y0!8)) <=> leq(index(pendack, host(X!4)), host(Y0!8))),
% 0.19/0.49 inference(symmetry,[status(thm)],[157])).
% 0.19/0.49 tff(159,plain,
% 0.19/0.49 (leq(host(W0!10), host(Y0!8)) <=> leq(index(pendack, host(X!4)), host(Y0!8))),
% 0.19/0.49 inference(transitivity,[status(thm)],[118, 158])).
% 0.19/0.49 tff(160,plain,
% 0.19/0.49 ((~leq(host(W0!10), host(Y0!8))) <=> (~leq(index(pendack, host(X!4)), host(Y0!8)))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[159])).
% 0.19/0.49 tff(161,plain,
% 0.19/0.49 (~leq(index(pendack, host(X!4)), host(Y0!8))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[132, 160])).
% 0.19/0.49 tff(162,plain,
% 0.19/0.49 (^[Z: $i, Pid20: $i, Pid0: $i] : refl(((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z))))) <=> ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(163,plain,
% 0.19/0.49 (![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z))))) <=> ![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[162])).
% 0.19/0.49 tff(164,plain,
% 0.19/0.49 (^[Z: $i, Pid20: $i, Pid0: $i] : trans(monotonicity(trans(monotonicity(rewrite((setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2)) <=> (~((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z))))))), ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) <=> (~(~((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z))))))))), rewrite((~(~((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z))))))) <=> ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))), ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) <=> ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z))))))), (((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> (((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z))))) | leq(index(pendack, host(Pid0)), host(Z))))), rewrite((((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z))))) | leq(index(pendack, host(Pid0)), host(Z))) <=> ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))), (((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(165,plain,
% 0.19/0.50 (![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z))) <=> ![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[164])).
% 0.19/0.50 tff(166,plain,
% 0.19/0.50 (![Z: $i, Pid20: $i, Pid0: $i] : ((~(setIn(Z, alive) & setIn(Pid0, alive) & elem(m_Down(Pid20), queue(host(Z))) & (host(Pid0) = host(Pid20)) & (index(status, host(Pid0)) = elec_2))) | leq(index(pendack, host(Pid0)), host(Z)))),
% 0.19/0.50 inference(and_elim,[status(thm)],[34])).
% 0.19/0.50 tff(167,plain,
% 0.19/0.50 (![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.19/0.50 tff(168,plain,
% 0.19/0.50 (![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.19/0.50 tff(169,plain,
% 0.19/0.50 (elem(m_Down(X0!9), queue(host(Y0!8)))),
% 0.19/0.50 inference(and_elim,[status(thm)],[34])).
% 0.19/0.50 tff(170,plain,
% 0.19/0.50 (setIn(X!4, alive)),
% 0.19/0.50 inference(and_elim,[status(thm)],[34])).
% 0.19/0.50 tff(171,plain,
% 0.19/0.50 (((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | ((~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(host(X!4) = host(X0!9))))) <=> ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | (~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(host(X!4) = host(X0!9))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(172,plain,
% 0.19/0.50 (((~(host(X!4) = host(X0!9))) | (~setIn(X!4, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8))))) <=> ((~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(host(X!4) = host(X0!9))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(173,plain,
% 0.19/0.50 (((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | ((~(host(X!4) = host(X0!9))) | (~setIn(X!4, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))))) <=> ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | ((~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(host(X!4) = host(X0!9)))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[172])).
% 0.19/0.50 tff(174,plain,
% 0.19/0.50 (((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | ((~(host(X!4) = host(X0!9))) | (~setIn(X!4, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))))) <=> ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | (~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(host(X!4) = host(X0!9))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[173, 171])).
% 0.19/0.50 tff(175,plain,
% 0.19/0.50 ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | ((~(host(X!4) = host(X0!9))) | (~setIn(X!4, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(176,plain,
% 0.19/0.50 ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | (~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~(host(X!4) = host(X0!9)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.19/0.50 tff(177,plain,
% 0.19/0.50 (~(host(X!4) = host(X0!9))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[176, 170, 141, 169, 56, 168, 161])).
% 0.19/0.50 tff(178,plain,
% 0.19/0.50 (~(host(V0!7) = host(X0!9))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[177, 156])).
% 0.19/0.50 tff(179,plain,
% 0.19/0.50 (^[V1: $i] : refl(((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1))) <=> ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(180,plain,
% 0.19/0.50 (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1))) <=> ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[179])).
% 0.19/0.50 tff(181,plain,
% 0.19/0.50 (^[V1: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~leq(host(Y0!8), V1)) & leq(s(zero), V1)) <=> (~(leq(host(Y0!8), V1) | (~leq(s(zero), V1))))), ((~((~leq(host(Y0!8), V1)) & leq(s(zero), V1))) <=> (~(~(leq(host(Y0!8), V1) | (~leq(s(zero), V1))))))), rewrite((~(~(leq(host(Y0!8), V1) | (~leq(s(zero), V1))))) <=> (leq(host(Y0!8), V1) | (~leq(s(zero), V1)))), ((~((~leq(host(Y0!8), V1)) & leq(s(zero), V1))) <=> (leq(host(Y0!8), V1) | (~leq(s(zero), V1))))), (((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) <=> ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (leq(host(Y0!8), V1) | (~leq(s(zero), V1)))))), rewrite(((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (leq(host(Y0!8), V1) | (~leq(s(zero), V1)))) <=> ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))), (((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) <=> ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(182,plain,
% 0.19/0.50 (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1)))) <=> ![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[181])).
% 0.19/0.50 tff(183,plain,
% 0.19/0.50 (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | (~((~leq(host(Y0!8), V1)) & leq(s(zero), V1))))),
% 0.19/0.50 inference(and_elim,[status(thm)],[34])).
% 0.19/0.50 tff(184,plain,
% 0.19/0.50 (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.19/0.50 tff(185,plain,
% 0.19/0.50 (![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[184, 180])).
% 0.19/0.50 tff(186,plain,
% 0.19/0.50 (((~![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))) | (setIn(host(V0!7), index(down, host(Y0!8))) | leq(host(Y0!8), host(V0!7)) | (host(V0!7) = host(X0!9)) | (~leq(s(zero), host(V0!7))))) <=> ((~![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))) | setIn(host(V0!7), index(down, host(Y0!8))) | leq(host(Y0!8), host(V0!7)) | (host(V0!7) = host(X0!9)) | (~leq(s(zero), host(V0!7))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(187,plain,
% 0.19/0.50 (((host(V0!7) = host(X0!9)) | setIn(host(V0!7), index(down, host(Y0!8))) | leq(host(Y0!8), host(V0!7)) | (~leq(s(zero), host(V0!7)))) <=> (setIn(host(V0!7), index(down, host(Y0!8))) | leq(host(Y0!8), host(V0!7)) | (host(V0!7) = host(X0!9)) | (~leq(s(zero), host(V0!7))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(188,plain,
% 0.19/0.50 (((~![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))) | ((host(V0!7) = host(X0!9)) | setIn(host(V0!7), index(down, host(Y0!8))) | leq(host(Y0!8), host(V0!7)) | (~leq(s(zero), host(V0!7))))) <=> ((~![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))) | (setIn(host(V0!7), index(down, host(Y0!8))) | leq(host(Y0!8), host(V0!7)) | (host(V0!7) = host(X0!9)) | (~leq(s(zero), host(V0!7)))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[187])).
% 0.19/0.50 tff(189,plain,
% 0.19/0.50 (((~![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))) | ((host(V0!7) = host(X0!9)) | setIn(host(V0!7), index(down, host(Y0!8))) | leq(host(Y0!8), host(V0!7)) | (~leq(s(zero), host(V0!7))))) <=> ((~![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))) | setIn(host(V0!7), index(down, host(Y0!8))) | leq(host(Y0!8), host(V0!7)) | (host(V0!7) = host(X0!9)) | (~leq(s(zero), host(V0!7))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[188, 186])).
% 0.19/0.50 tff(190,plain,
% 0.19/0.50 ((~![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))) | ((host(V0!7) = host(X0!9)) | setIn(host(V0!7), index(down, host(Y0!8))) | leq(host(Y0!8), host(V0!7)) | (~leq(s(zero), host(V0!7))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(191,plain,
% 0.19/0.50 ((~![V1: $i] : ((V1 = host(X0!9)) | setIn(V1, index(down, host(Y0!8))) | leq(host(Y0!8), V1) | (~leq(s(zero), V1)))) | setIn(host(V0!7), index(down, host(Y0!8))) | leq(host(Y0!8), host(V0!7)) | (host(V0!7) = host(X0!9)) | (~leq(s(zero), host(V0!7)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.19/0.50 tff(192,plain,
% 0.19/0.50 (setIn(host(V0!7), index(down, host(Y0!8))) | leq(host(Y0!8), host(V0!7)) | (host(V0!7) = host(X0!9)) | (~leq(s(zero), host(V0!7)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[191, 185])).
% 0.19/0.50 tff(193,plain,
% 0.19/0.50 (leq(host(Y0!8), host(V0!7))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[192, 178, 150, 55])).
% 0.19/0.50 tff(194,plain,
% 0.19/0.50 (^[X: $i, Y: $i] : refl((leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y)))) <=> (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(195,plain,
% 0.19/0.50 (![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y)))) <=> ![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[194])).
% 0.19/0.50 tff(196,plain,
% 0.19/0.50 (![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y)))) <=> ![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(197,plain,
% 0.19/0.50 (^[X: $i, Y: $i] : rewrite((leq(X, s(Y)) <=> ((X = s(Y)) | leq(X, Y))) <=> (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(198,plain,
% 0.19/0.50 (![X: $i, Y: $i] : (leq(X, s(Y)) <=> ((X = s(Y)) | leq(X, Y))) <=> ![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[197])).
% 0.19/0.50 tff(199,axiom,(![X: $i, Y: $i] : (leq(X, s(Y)) <=> ((X = s(Y)) | leq(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_64')).
% 0.19/0.50 tff(200,plain,
% 0.19/0.50 (![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.19/0.50 tff(201,plain,
% 0.19/0.50 (![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[200, 196])).
% 0.19/0.50 tff(202,plain,(
% 0.19/0.50 ![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.19/0.50 inference(skolemize,[status(sab)],[201])).
% 0.19/0.50 tff(203,plain,
% 0.19/0.50 (![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[202, 195])).
% 0.19/0.50 tff(204,plain,
% 0.19/0.50 ((~![X: $i, Y: $i] : (leq(X, s(Y)) <=> (leq(X, Y) | (X = s(Y))))) | (leq(host(V0!7), s(host(Y0!8))) <=> (leq(host(V0!7), host(Y0!8)) | (host(V0!7) = s(host(Y0!8)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(205,plain,
% 0.19/0.50 (leq(host(V0!7), s(host(Y0!8))) <=> (leq(host(V0!7), host(Y0!8)) | (host(V0!7) = s(host(Y0!8))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[204, 203])).
% 0.19/0.50 tff(206,plain,
% 0.19/0.50 (leq(host(V0!7), s(host(Y0!8))) <=> leq(host(X!4), host(W0!10))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[36, 105])).
% 0.19/0.50 tff(207,plain,
% 0.19/0.50 (leq(host(X!4), host(W0!10)) <=> leq(host(V0!7), s(host(Y0!8)))),
% 0.19/0.50 inference(symmetry,[status(thm)],[206])).
% 0.19/0.50 tff(208,plain,
% 0.19/0.50 (nbr_proc = s(host(Y0!8))),
% 0.19/0.50 inference(symmetry,[status(thm)],[116])).
% 0.19/0.50 tff(209,plain,
% 0.19/0.50 (nbr_proc = host(W0!10)),
% 0.19/0.50 inference(transitivity,[status(thm)],[208, 105])).
% 0.19/0.50 tff(210,plain,
% 0.19/0.50 (leq(host(X!4), nbr_proc) <=> leq(host(X!4), host(W0!10))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[209])).
% 0.19/0.50 tff(211,plain,
% 0.19/0.50 (leq(host(X!4), nbr_proc) <=> leq(host(V0!7), s(host(Y0!8)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[210, 207])).
% 0.19/0.50 tff(212,plain,
% 0.19/0.50 ((~![P: $i] : leq(host(P), nbr_proc)) | leq(host(X!4), nbr_proc)),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(213,plain,
% 0.19/0.50 (leq(host(X!4), nbr_proc)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[212, 83])).
% 0.19/0.50 tff(214,plain,
% 0.19/0.50 (leq(host(V0!7), s(host(Y0!8)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[213, 211])).
% 0.19/0.50 tff(215,plain,
% 0.19/0.50 ((~(leq(host(V0!7), s(host(Y0!8))) <=> (leq(host(V0!7), host(Y0!8)) | (host(V0!7) = s(host(Y0!8)))))) | (~leq(host(V0!7), s(host(Y0!8)))) | (leq(host(V0!7), host(Y0!8)) | (host(V0!7) = s(host(Y0!8))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(216,plain,
% 0.19/0.50 ((~(leq(host(V0!7), s(host(Y0!8))) <=> (leq(host(V0!7), host(Y0!8)) | (host(V0!7) = s(host(Y0!8)))))) | (leq(host(V0!7), host(Y0!8)) | (host(V0!7) = s(host(Y0!8))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.19/0.50 tff(217,plain,
% 0.19/0.50 (leq(host(V0!7), host(Y0!8)) | (host(V0!7) = s(host(Y0!8)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[216, 205])).
% 0.19/0.50 tff(218,plain,
% 0.19/0.50 (s(host(Y0!8)) = host(Y!3)),
% 0.19/0.50 inference(transitivity,[status(thm)],[116, 93, 60])).
% 0.19/0.50 tff(219,plain,
% 0.19/0.50 ((host(V0!7) = s(host(Y0!8))) <=> (host(X!4) = host(Y!3))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[36, 218])).
% 0.19/0.50 tff(220,plain,
% 0.19/0.50 ((host(X!4) = host(Y!3)) <=> (host(V0!7) = s(host(Y0!8)))),
% 0.19/0.50 inference(symmetry,[status(thm)],[219])).
% 0.19/0.50 tff(221,plain,
% 0.19/0.50 ((~(host(X!4) = host(Y!3))) <=> (~(host(V0!7) = s(host(Y0!8))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[220])).
% 0.19/0.50 tff(222,plain,
% 0.19/0.50 ((host(X!4) = host(W0!10)) <=> (host(X!4) = host(Y!3))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[117])).
% 0.19/0.50 tff(223,plain,
% 0.19/0.50 ((~(host(X!4) = host(W0!10))) <=> (~(host(X!4) = host(Y!3)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[222])).
% 0.19/0.50 tff(224,plain,
% 0.19/0.50 (elem(m_Down(W0!10), queue(host(Y0!8)))),
% 0.19/0.50 inference(and_elim,[status(thm)],[34])).
% 0.19/0.50 tff(225,plain,
% 0.19/0.50 (((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | ((~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~(host(X!4) = host(W0!10))) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~elem(m_Down(W0!10), queue(host(Y0!8)))))) <=> ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | (~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~(host(X!4) = host(W0!10))) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~elem(m_Down(W0!10), queue(host(Y0!8)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(226,plain,
% 0.19/0.50 (((~(host(X!4) = host(W0!10))) | (~setIn(X!4, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(W0!10), queue(host(Y0!8))))) <=> ((~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~(host(X!4) = host(W0!10))) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~elem(m_Down(W0!10), queue(host(Y0!8)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(227,plain,
% 0.19/0.50 (((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | ((~(host(X!4) = host(W0!10))) | (~setIn(X!4, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(W0!10), queue(host(Y0!8)))))) <=> ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | ((~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~(host(X!4) = host(W0!10))) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~elem(m_Down(W0!10), queue(host(Y0!8))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[226])).
% 0.19/0.50 tff(228,plain,
% 0.19/0.50 (((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | ((~(host(X!4) = host(W0!10))) | (~setIn(X!4, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(W0!10), queue(host(Y0!8)))))) <=> ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | (~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~(host(X!4) = host(W0!10))) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~elem(m_Down(W0!10), queue(host(Y0!8)))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[227, 225])).
% 0.19/0.51 tff(229,plain,
% 0.19/0.51 ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | ((~(host(X!4) = host(W0!10))) | (~setIn(X!4, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~(index(status, host(X!4)) = elec_2)) | (~setIn(Y0!8, alive)) | (~elem(m_Down(W0!10), queue(host(Y0!8)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(230,plain,
% 0.19/0.51 ((~![Z: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid0, alive)) | leq(index(pendack, host(Pid0)), host(Z)) | (~(index(status, host(Pid0)) = elec_2)) | (~setIn(Z, alive)) | (~elem(m_Down(Pid20), queue(host(Z)))))) | (~setIn(X!4, alive)) | (~(index(status, host(X!4)) = elec_2)) | (~(host(X!4) = host(W0!10))) | (~setIn(Y0!8, alive)) | leq(index(pendack, host(X!4)), host(Y0!8)) | (~elem(m_Down(W0!10), queue(host(Y0!8))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.19/0.51 tff(231,plain,
% 0.19/0.51 (~(host(X!4) = host(W0!10))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[230, 170, 141, 224, 56, 168, 161])).
% 0.19/0.51 tff(232,plain,
% 0.19/0.51 (~(host(X!4) = host(Y!3))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[231, 223])).
% 0.19/0.51 tff(233,plain,
% 0.19/0.51 (~(host(V0!7) = s(host(Y0!8)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[232, 221])).
% 0.19/0.51 tff(234,plain,
% 0.19/0.51 ((~(leq(host(V0!7), host(Y0!8)) | (host(V0!7) = s(host(Y0!8))))) | leq(host(V0!7), host(Y0!8)) | (host(V0!7) = s(host(Y0!8)))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(235,plain,
% 0.19/0.51 (leq(host(V0!7), host(Y0!8))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[234, 233, 217])).
% 0.19/0.51 tff(236,plain,
% 0.19/0.51 ((~((~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7))))) | (~leq(host(V0!7), host(Y0!8))) | (~leq(host(Y0!8), host(V0!7)))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(237,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[236, 235, 193, 43])).
% 0.19/0.51 % SZS output end Proof
% 0.19/0.51 % E exiting
%------------------------------------------------------------------------------