%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV449+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:34:05 AM UTC 2025
% Result : Theorem 0.18s 0.41s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV449+1 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 09:51:33 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.41 % SZS status Theorem
% 0.18/0.41 % SZS output start Proof
% 0.18/0.41 tff(elem_type, type, (
% 0.18/0.41 elem: ( $i * $i ) > $o)).
% 0.18/0.41 tff(queue_type, type, (
% 0.18/0.41 queue: $i > $i)).
% 0.18/0.41 tff(host_type, type, (
% 0.18/0.41 host: $i > $i)).
% 0.18/0.41 tff(tptp_fun_V0_7_type, type, (
% 0.18/0.41 tptp_fun_V0_7: $i)).
% 0.18/0.41 tff(m_Down_type, type, (
% 0.18/0.41 m_Down: $i > $i)).
% 0.18/0.41 tff(tptp_fun_Y0_10_type, type, (
% 0.18/0.41 tptp_fun_Y0_10: $i)).
% 0.18/0.41 tff(tptp_fun_X_4_type, type, (
% 0.18/0.41 tptp_fun_X_4: $i)).
% 0.18/0.41 tff(cons_type, type, (
% 0.18/0.41 cons: ( $i * $i ) > $i)).
% 0.18/0.41 tff(tptp_fun_V_5_type, type, (
% 0.18/0.41 tptp_fun_V_5: $i)).
% 0.18/0.41 tff(m_Ack_type, type, (
% 0.18/0.41 m_Ack: ( $i * $i ) > $i)).
% 0.18/0.41 tff(tptp_fun_Y_3_type, type, (
% 0.18/0.41 tptp_fun_Y_3: $i)).
% 0.18/0.41 tff(index_type, type, (
% 0.18/0.41 index: ( $i * $i ) > $i)).
% 0.18/0.41 tff(elid_type, type, (
% 0.18/0.41 elid: $i)).
% 0.18/0.41 tff(tptp_fun_X0_8_type, type, (
% 0.18/0.41 tptp_fun_X0_8: $i)).
% 0.18/0.41 tff(tptp_fun_W0_9_type, type, (
% 0.18/0.41 tptp_fun_W0_9: $i)).
% 0.18/0.41 tff(setIn_type, type, (
% 0.18/0.41 setIn: ( $i * $i ) > $o)).
% 0.18/0.41 tff(alive_type, type, (
% 0.18/0.41 alive: $i)).
% 0.18/0.41 tff(snoc_type, type, (
% 0.18/0.41 snoc: ( $i * $i ) > $i)).
% 0.18/0.41 tff(m_Ldr_type, type, (
% 0.18/0.41 m_Ldr: $i > $i)).
% 0.18/0.41 tff(tptp_fun_Z_6_type, type, (
% 0.18/0.41 tptp_fun_Z_6: $i)).
% 0.18/0.41 tff(acks_type, type, (
% 0.18/0.41 acks: $i)).
% 0.18/0.41 tff(pendack_type, type, (
% 0.18/0.41 pendack: $i)).
% 0.18/0.41 tff(elec_2_type, type, (
% 0.18/0.41 elec_2: $i)).
% 0.18/0.41 tff(status_type, type, (
% 0.18/0.41 status: $i)).
% 0.18/0.41 tff(leq_type, type, (
% 0.18/0.41 leq: ( $i * $i ) > $o)).
% 0.18/0.41 tff(m_Halt_type, type, (
% 0.18/0.41 m_Halt: $i > $i)).
% 0.18/0.41 tff(nbr_proc_type, type, (
% 0.18/0.41 nbr_proc: $i)).
% 0.18/0.41 tff(1,plain,
% 0.18/0.41 ((setIn(X!4, alive) & leq(nbr_proc, index(pendack, host(X!4))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z)))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = 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))))) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))) & (((host(Z!6) = host(Y!3)) | setIn(host(Z!6), index(acks, host(X!4)))) & (host(Z!6) = host(V0!7)) & (host(X!4) = host(V0!7)) & (~(host(Z!6) = host(X0!8))) & (~(host(X!4) = host(X0!8))) & (~((~(elem(m_Down(W0!9), queue(host(X0!8))) & elem(m_Down(Y0!10), snoc(V!5, m_Ldr(X!4))))) | (~((~(host(X0!8) = host(V0!7))) & setIn(V0!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(V0!7)) & (host(Y0!10) = host(X0!8))))))) & (queue(host(X!4)) = cons(m_Ack(index(elid, host(X!4)), Y!3), V!5))) <=> (setIn(X!4, alive) & leq(nbr_proc, index(pendack, host(X!4))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z)))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = 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))))) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))) & ((host(Z!6) = host(Y!3)) | setIn(host(Z!6), index(acks, host(X!4)))) & (host(Z!6) = host(V0!7)) & (host(X!4) = host(V0!7)) & (~(host(Z!6) = host(X0!8))) & (~(host(X!4) = host(X0!8))) & (~((~(elem(m_Down(W0!9), queue(host(X0!8))) & elem(m_Down(Y0!10), snoc(V!5, m_Ldr(X!4))))) | (~((~(host(X0!8) = host(V0!7))) & setIn(V0!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(V0!7)) & (host(Y0!10) = host(X0!8)))))) & (queue(host(X!4)) = cons(m_Ack(index(elid, host(X!4)), Y!3), V!5)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(2,plain,
% 0.18/0.41 ((((host(Z!6) = host(Y!3)) | setIn(host(Z!6), index(acks, host(X!4)))) & ((host(Z!6) = host(V0!7)) & (host(X!4) = host(V0!7)) & (~(host(Z!6) = host(X0!8))) & (~(host(X!4) = host(X0!8))) & (~((~(elem(m_Down(W0!9), queue(host(X0!8))) & elem(m_Down(Y0!10), snoc(V!5, m_Ldr(X!4))))) | (~((~(host(X0!8) = host(V0!7))) & setIn(V0!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(V0!7)) & (host(Y0!10) = host(X0!8)))))))) <=> (((host(Z!6) = host(Y!3)) | setIn(host(Z!6), index(acks, host(X!4)))) & (host(Z!6) = host(V0!7)) & (host(X!4) = host(V0!7)) & (~(host(Z!6) = host(X0!8))) & (~(host(X!4) = host(X0!8))) & (~((~(elem(m_Down(W0!9), queue(host(X0!8))) & elem(m_Down(Y0!10), snoc(V!5, m_Ldr(X!4))))) | (~((~(host(X0!8) = host(V0!7))) & setIn(V0!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(V0!7)) & (host(Y0!10) = host(X0!8)))))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(3,plain,
% 0.18/0.41 (((host(Z!6) = host(V0!7)) & (host(X!4) = host(V0!7)) & ((~(host(Z!6) = host(X0!8))) & (~(host(X!4) = host(X0!8))) & (~((~(elem(m_Down(W0!9), queue(host(X0!8))) & elem(m_Down(Y0!10), snoc(V!5, m_Ldr(X!4))))) | (~((~(host(X0!8) = host(V0!7))) & setIn(V0!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(V0!7)) & (host(Y0!10) = host(X0!8)))))))) <=> ((host(Z!6) = host(V0!7)) & (host(X!4) = host(V0!7)) & (~(host(Z!6) = host(X0!8))) & (~(host(X!4) = host(X0!8))) & (~((~(elem(m_Down(W0!9), queue(host(X0!8))) & elem(m_Down(Y0!10), snoc(V!5, m_Ldr(X!4))))) | (~((~(host(X0!8) = host(V0!7))) & setIn(V0!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(V0!7)) & (host(Y0!10) = host(X0!8)))))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(4,plain,
% 0.18/0.41 ((((host(Z!6) = host(Y!3)) | setIn(host(Z!6), index(acks, host(X!4)))) & ((host(Z!6) = host(V0!7)) & (host(X!4) = host(V0!7)) & ((~(host(Z!6) = host(X0!8))) & (~(host(X!4) = host(X0!8))) & (~((~(elem(m_Down(W0!9), queue(host(X0!8))) & elem(m_Down(Y0!10), snoc(V!5, m_Ldr(X!4))))) | (~((~(host(X0!8) = host(V0!7))) & setIn(V0!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(V0!7)) & (host(Y0!10) = host(X0!8))))))))) <=> (((host(Z!6) = host(Y!3)) | setIn(host(Z!6), index(acks, host(X!4)))) & ((host(Z!6) = host(V0!7)) & (host(X!4) = host(V0!7)) & (~(host(Z!6) = host(X0!8))) & (~(host(X!4) = host(X0!8))) & (~((~(elem(m_Down(W0!9), queue(host(X0!8))) & elem(m_Down(Y0!10), snoc(V!5, m_Ldr(X!4))))) | (~((~(host(X0!8) = host(V0!7))) & setIn(V0!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(V0!7)) & (host(Y0!10) = host(X0!8))))))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[3])).
% 0.18/0.41 tff(5,plain,
% 0.18/0.41 ((((host(Z!6) = host(Y!3)) | setIn(host(Z!6), index(acks, host(X!4)))) & ((host(Z!6) = host(V0!7)) & (host(X!4) = host(V0!7)) & ((~(host(Z!6) = host(X0!8))) & (~(host(X!4) = host(X0!8))) & (~((~(elem(m_Down(W0!9), queue(host(X0!8))) & elem(m_Down(Y0!10), snoc(V!5, m_Ldr(X!4))))) | (~((~(host(X0!8) = host(V0!7))) & setIn(V0!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(V0!7)) & (host(Y0!10) = host(X0!8))))))))) <=> (((host(Z!6) = host(Y!3)) | setIn(host(Z!6), index(acks, host(X!4)))) & (host(Z!6) = host(V0!7)) & (host(X!4) = host(V0!7)) & (~(host(Z!6) = host(X0!8))) & (~(host(X!4) = host(X0!8))) & (~((~(elem(m_Down(W0!9), queue(host(X0!8))) & elem(m_Down(Y0!10), snoc(V!5, m_Ldr(X!4))))) | (~((~(host(X0!8) = host(V0!7))) & setIn(V0!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(V0!7)) & (host(Y0!10) = host(X0!8)))))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[4, 2])).
% 0.18/0.41 tff(6,plain,
% 0.18/0.41 ((setIn(X!4, alive) & leq(nbr_proc, index(pendack, host(X!4))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z)))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = 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))))) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))) & (((host(Z!6) = host(Y!3)) | setIn(host(Z!6), index(acks, host(X!4)))) & ((host(Z!6) = host(V0!7)) & (host(X!4) = host(V0!7)) & ((~(host(Z!6) = host(X0!8))) & (~(host(X!4) = host(X0!8))) & (~((~(elem(m_Down(W0!9), queue(host(X0!8))) & elem(m_Down(Y0!10), snoc(V!5, m_Ldr(X!4))))) | (~((~(host(X0!8) = host(V0!7))) & setIn(V0!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(V0!7)) & (host(Y0!10) = host(X0!8))))))))) & (queue(host(X!4)) = cons(m_Ack(index(elid, host(X!4)), Y!3), V!5))) <=> (setIn(X!4, alive) & leq(nbr_proc, index(pendack, host(X!4))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z)))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = 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))))) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))) & (((host(Z!6) = host(Y!3)) | setIn(host(Z!6), index(acks, host(X!4)))) & (host(Z!6) = host(V0!7)) & (host(X!4) = host(V0!7)) & (~(host(Z!6) = host(X0!8))) & (~(host(X!4) = host(X0!8))) & (~((~(elem(m_Down(W0!9), queue(host(X0!8))) & elem(m_Down(Y0!10), snoc(V!5, m_Ldr(X!4))))) | (~((~(host(X0!8) = host(V0!7))) & setIn(V0!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(V0!7)) & (host(Y0!10) = host(X0!8))))))) & (queue(host(X!4)) = cons(m_Ack(index(elid, host(X!4)), Y!3), V!5)))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[5])).
% 0.18/0.42 tff(7,plain,
% 0.18/0.42 ((setIn(X!4, alive) & leq(nbr_proc, index(pendack, host(X!4))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z)))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = 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))))) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))) & (((host(Z!6) = host(Y!3)) | setIn(host(Z!6), index(acks, host(X!4)))) & ((host(Z!6) = host(V0!7)) & (host(X!4) = host(V0!7)) & ((~(host(Z!6) = host(X0!8))) & (~(host(X!4) = host(X0!8))) & (~((~(elem(m_Down(W0!9), queue(host(X0!8))) & elem(m_Down(Y0!10), snoc(V!5, m_Ldr(X!4))))) | (~((~(host(X0!8) = host(V0!7))) & setIn(V0!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(V0!7)) & (host(Y0!10) = host(X0!8))))))))) & (queue(host(X!4)) = cons(m_Ack(index(elid, host(X!4)), Y!3), V!5))) <=> (setIn(X!4, alive) & leq(nbr_proc, index(pendack, host(X!4))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z)))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = 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))))) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))) & ((host(Z!6) = host(Y!3)) | setIn(host(Z!6), index(acks, host(X!4)))) & (host(Z!6) = host(V0!7)) & (host(X!4) = host(V0!7)) & (~(host(Z!6) = host(X0!8))) & (~(host(X!4) = host(X0!8))) & (~((~(elem(m_Down(W0!9), queue(host(X0!8))) & elem(m_Down(Y0!10), snoc(V!5, m_Ldr(X!4))))) | (~((~(host(X0!8) = host(V0!7))) & setIn(V0!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(V0!7)) & (host(Y0!10) = host(X0!8)))))) & (queue(host(X!4)) = cons(m_Ack(index(elid, host(X!4)), Y!3), V!5)))),
% 0.18/0.42 inference(transitivity,[status(thm)],[6, 1])).
% 0.18/0.42 tff(8,plain,
% 0.18/0.42 ((~![V: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | (~leq(nbr_proc, index(pendack, host(X)))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive)))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z))))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = 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)))))) | (~(index(status, host(X)) = elec_2)) | (~(host(Y) = index(pendack, host(X)))) | ![Z: $i] : ((~((host(Z) = host(Y)) | setIn(host(Z), index(acks, host(X))))) | ![V0: $i] : ((~(host(Z) = host(V0))) | (~(host(X) = host(V0))) | ![W0: $i, X0: $i] : ((host(Z) = host(X0)) | (host(X) = host(X0)) | ![Y0: $i] : ((~(elem(m_Down(W0), queue(host(X0))) & elem(m_Down(Y0), snoc(V, m_Ldr(X))))) | (~((~(host(X0) = host(V0))) & setIn(V0, alive) & setIn(X0, alive) & (host(W0) = host(V0)) & (host(Y0) = host(X0)))))))) | (~(queue(host(X)) = cons(m_Ack(index(elid, host(X)), Y), V))))) <=> (~![V: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | (~leq(nbr_proc, index(pendack, host(X)))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive)))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z))))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = 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)))))) | (~(index(status, host(X)) = elec_2)) | (~(host(Y) = index(pendack, host(X)))) | ![Z: $i] : ((~((host(Z) = host(Y)) | setIn(host(Z), index(acks, host(X))))) | ![V0: $i] : ((~(host(Z) = host(V0))) | (~(host(X) = host(V0))) | ![W0: $i, X0: $i] : ((host(Z) = host(X0)) | (host(X) = host(X0)) | ![Y0: $i] : ((~(elem(m_Down(W0), queue(host(X0))) & elem(m_Down(Y0), snoc(V, m_Ldr(X))))) | (~((~(host(X0) = host(V0))) & setIn(V0, alive) & setIn(X0, alive) & (host(W0) = host(V0)) & (host(Y0) = host(X0)))))))) | (~(queue(host(X)) = cons(m_Ack(index(elid, host(X)), Y), V)))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(9,plain,
% 0.18/0.42 ((~![V: $i, W: $i, X: $i, Y: $i] : (((((((((![Z: $i, Pid0: $i] : (setIn(Pid0, alive) => (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : (elem(m_Down(Pid0), queue(host(Z))) => (~setIn(Pid0, alive)))) & ![Z: $i, Pid0: $i] : (elem(m_Down(Pid0), queue(host(Z))) => (~(host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : (elem(m_Halt(Pid0), queue(host(Z))) => (~leq(host(Z), host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (elem(m_Ack(Pid0, Z), queue(host(Pid20))) => (~leq(host(Z), host(Pid0))))) & ![Z: $i, Pid0: $i] : ((((~setIn(Z, alive)) & leq(Pid0, Z)) & (host(Pid0) = host(Z))) => (~setIn(Pid0, alive)))) & ![Z: $i, Pid0: $i] : (((~(Pid0 = Z)) & (host(Pid0) = host(Z))) => ((~setIn(Z, alive)) | (~setIn(Pid0, alive))))) & ![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))))))) & (queue(host(X)) = cons(m_Ack(W, Y), V))) => (setIn(X, alive) => ((((index(elid, host(X)) = W) & (index(status, host(X)) = elec_2)) & (host(Y) = index(pendack, host(X)))) => (leq(nbr_proc, index(pendack, host(X))) => ![Z: $i] : ((setIn(host(Z), index(acks, host(X))) | (host(Z) = host(Y))) => ![V0: $i] : ((host(Z) = host(V0)) => ((host(X) = host(V0)) => ![W0: $i, X0: $i] : ((~(host(Z) = host(X0))) => ((~(host(X) = host(X0))) => ![Y0: $i] : ((((((~(host(X0) = host(V0))) & setIn(V0, alive)) & setIn(X0, alive)) & (host(W0) = host(V0))) & (host(Y0) = host(X0))) => (~(elem(m_Down(W0), queue(host(X0))) & elem(m_Down(Y0), snoc(V, m_Ldr(X)))))))))))))))) <=> (~![V: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | (~leq(nbr_proc, index(pendack, host(X)))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive)))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z))))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = 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)))))) | (~(index(status, host(X)) = elec_2)) | (~(host(Y) = index(pendack, host(X)))) | ![Z: $i] : ((~((host(Z) = host(Y)) | setIn(host(Z), index(acks, host(X))))) | ![V0: $i] : ((~(host(Z) = host(V0))) | (~(host(X) = host(V0))) | ![W0: $i, X0: $i] : ((host(Z) = host(X0)) | (host(X) = host(X0)) | ![Y0: $i] : ((~(elem(m_Down(W0), queue(host(X0))) & elem(m_Down(Y0), snoc(V, m_Ldr(X))))) | (~((~(host(X0) = host(V0))) & setIn(V0, alive) & setIn(X0, alive) & (host(W0) = host(V0)) & (host(Y0) = host(X0)))))))) | (~(queue(host(X)) = cons(m_Ack(index(elid, host(X)), Y), V)))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(10,axiom,(~![V: $i, W: $i, X: $i, Y: $i] : (((((((((![Z: $i, Pid0: $i] : (setIn(Pid0, alive) => (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : (elem(m_Down(Pid0), queue(host(Z))) => (~setIn(Pid0, alive)))) & ![Z: $i, Pid0: $i] : (elem(m_Down(Pid0), queue(host(Z))) => (~(host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : (elem(m_Halt(Pid0), queue(host(Z))) => (~leq(host(Z), host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (elem(m_Ack(Pid0, Z), queue(host(Pid20))) => (~leq(host(Z), host(Pid0))))) & ![Z: $i, Pid0: $i] : ((((~setIn(Z, alive)) & leq(Pid0, Z)) & (host(Pid0) = host(Z))) => (~setIn(Pid0, alive)))) & ![Z: $i, Pid0: $i] : (((~(Pid0 = Z)) & (host(Pid0) = host(Z))) => ((~setIn(Z, alive)) | (~setIn(Pid0, alive))))) & ![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))))))) & (queue(host(X)) = cons(m_Ack(W, Y), V))) => (setIn(X, alive) => ((((index(elid, host(X)) = W) & (index(status, host(X)) = elec_2)) & (host(Y) = index(pendack, host(X)))) => (leq(nbr_proc, index(pendack, host(X))) => ![Z: $i] : ((setIn(host(Z), index(acks, host(X))) | (host(Z) = host(Y))) => ![V0: $i] : ((host(Z) = host(V0)) => ((host(X) = host(V0)) => ![W0: $i, X0: $i] : ((~(host(Z) = host(X0))) => ((~(host(X) = host(X0))) => ![Y0: $i] : ((((((~(host(X0) = host(V0))) & setIn(V0, alive)) & setIn(X0, alive)) & (host(W0) = host(V0))) & (host(Y0) = host(X0))) => (~(elem(m_Down(W0), queue(host(X0))) & elem(m_Down(Y0), snoc(V, m_Ldr(X)))))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj')).
% 0.18/0.43 tff(11,plain,
% 0.18/0.43 (~![V: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | (~leq(nbr_proc, index(pendack, host(X)))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive)))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z))))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = 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)))))) | (~(index(status, host(X)) = elec_2)) | (~(host(Y) = index(pendack, host(X)))) | ![Z: $i] : ((~((host(Z) = host(Y)) | setIn(host(Z), index(acks, host(X))))) | ![V0: $i] : ((~(host(Z) = host(V0))) | (~(host(X) = host(V0))) | ![W0: $i, X0: $i] : ((host(Z) = host(X0)) | (host(X) = host(X0)) | ![Y0: $i] : ((~(elem(m_Down(W0), queue(host(X0))) & elem(m_Down(Y0), snoc(V, m_Ldr(X))))) | (~((~(host(X0) = host(V0))) & setIn(V0, alive) & setIn(X0, alive) & (host(W0) = host(V0)) & (host(Y0) = host(X0)))))))) | (~(queue(host(X)) = cons(m_Ack(index(elid, host(X)), Y), V))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.18/0.43 tff(12,plain,
% 0.18/0.43 (~![V: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | (~leq(nbr_proc, index(pendack, host(X)))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive)))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z))))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = 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)))))) | (~(index(status, host(X)) = elec_2)) | (~(host(Y) = index(pendack, host(X)))) | ![Z: $i] : ((~((host(Z) = host(Y)) | setIn(host(Z), index(acks, host(X))))) | ![V0: $i] : ((~(host(Z) = host(V0))) | (~(host(X) = host(V0))) | ![W0: $i, X0: $i] : ((host(Z) = host(X0)) | (host(X) = host(X0)) | ![Y0: $i] : ((~(elem(m_Down(W0), queue(host(X0))) & elem(m_Down(Y0), snoc(V, m_Ldr(X))))) | (~((~(host(X0) = host(V0))) & setIn(V0, alive) & setIn(X0, alive) & (host(W0) = host(V0)) & (host(Y0) = host(X0)))))))) | (~(queue(host(X)) = cons(m_Ack(index(elid, host(X)), Y), V))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.18/0.43 tff(13,plain,
% 0.18/0.43 (~![V: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | (~leq(nbr_proc, index(pendack, host(X)))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive)))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z))))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = 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)))))) | (~(index(status, host(X)) = elec_2)) | (~(host(Y) = index(pendack, host(X)))) | ![Z: $i] : ((~((host(Z) = host(Y)) | setIn(host(Z), index(acks, host(X))))) | ![V0: $i] : ((~(host(Z) = host(V0))) | (~(host(X) = host(V0))) | ![W0: $i, X0: $i] : ((host(Z) = host(X0)) | (host(X) = host(X0)) | ![Y0: $i] : ((~(elem(m_Down(W0), queue(host(X0))) & elem(m_Down(Y0), snoc(V, m_Ldr(X))))) | (~((~(host(X0) = host(V0))) & setIn(V0, alive) & setIn(X0, alive) & (host(W0) = host(V0)) & (host(Y0) = host(X0)))))))) | (~(queue(host(X)) = cons(m_Ack(index(elid, host(X)), Y), V))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.18/0.43 tff(14,plain,
% 0.18/0.43 (~![V: $i, X: $i, Y: $i] : ((~setIn(X, alive)) | (~leq(nbr_proc, index(pendack, host(X)))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive)))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z))))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = 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)))))) | (~(index(status, host(X)) = elec_2)) | (~(host(Y) = index(pendack, host(X)))) | ![Z: $i] : ((~((host(Z) = host(Y)) | setIn(host(Z), index(acks, host(X))))) | ![V0: $i] : ((~(host(Z) = host(V0))) | (~(host(X) = host(V0))) | ![W0: $i, X0: $i] : ((host(Z) = host(X0)) | (host(X) = host(X0)) | ![Y0: $i] : ((~(elem(m_Down(W0), queue(host(X0))) & elem(m_Down(Y0), snoc(V, m_Ldr(X))))) | (~((~(host(X0) = host(V0))) & setIn(V0, alive) & setIn(X0, alive) & (host(W0) = host(V0)) & (host(Y0) = host(X0)))))))) | (~(queue(host(X)) = cons(m_Ack(index(elid, host(X)), Y), V))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[13, 8])).
% 0.18/0.43 tff(15,plain,
% 0.18/0.43 (setIn(X!4, alive) & leq(nbr_proc, index(pendack, host(X!4))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z)))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = 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))))) & (index(status, host(X!4)) = elec_2) & (host(Y!3) = index(pendack, host(X!4))) & ((host(Z!6) = host(Y!3)) | setIn(host(Z!6), index(acks, host(X!4)))) & (host(Z!6) = host(V0!7)) & (host(X!4) = host(V0!7)) & (~(host(Z!6) = host(X0!8))) & (~(host(X!4) = host(X0!8))) & (~((~(elem(m_Down(W0!9), queue(host(X0!8))) & elem(m_Down(Y0!10), snoc(V!5, m_Ldr(X!4))))) | (~((~(host(X0!8) = host(V0!7))) & setIn(V0!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(V0!7)) & (host(Y0!10) = host(X0!8)))))) & (queue(host(X!4)) = cons(m_Ack(index(elid, host(X!4)), Y!3), V!5))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.18/0.43 tff(16,plain,
% 0.18/0.43 (host(X!4) = host(V0!7)),
% 0.18/0.43 inference(and_elim,[status(thm)],[15])).
% 0.18/0.43 tff(17,plain,
% 0.18/0.43 (host(V0!7) = host(X!4)),
% 0.18/0.43 inference(symmetry,[status(thm)],[16])).
% 0.18/0.43 tff(18,plain,
% 0.18/0.43 (queue(host(V0!7)) = queue(host(X!4))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[17])).
% 0.18/0.43 tff(19,plain,
% 0.18/0.43 (elem(m_Down(Y0!10), queue(host(V0!7))) <=> elem(m_Down(Y0!10), queue(host(X!4)))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[18])).
% 0.18/0.43 tff(20,plain,
% 0.18/0.43 (elem(m_Down(Y0!10), queue(host(X!4))) <=> elem(m_Down(Y0!10), queue(host(V0!7)))),
% 0.18/0.43 inference(symmetry,[status(thm)],[19])).
% 0.18/0.43 tff(21,plain,
% 0.18/0.43 (queue(host(X!4)) = cons(m_Ack(index(elid, host(X!4)), Y!3), V!5)),
% 0.18/0.43 inference(and_elim,[status(thm)],[15])).
% 0.18/0.43 tff(22,plain,
% 0.18/0.43 (cons(m_Ack(index(elid, host(X!4)), Y!3), V!5) = queue(host(X!4))),
% 0.18/0.43 inference(symmetry,[status(thm)],[21])).
% 0.18/0.43 tff(23,plain,
% 0.18/0.43 (elem(m_Down(Y0!10), cons(m_Ack(index(elid, host(X!4)), Y!3), V!5)) <=> elem(m_Down(Y0!10), queue(host(X!4)))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[22])).
% 0.18/0.43 tff(24,plain,
% 0.18/0.43 (elem(m_Down(Y0!10), queue(host(X!4))) <=> elem(m_Down(Y0!10), cons(m_Ack(index(elid, host(X!4)), Y!3), V!5))),
% 0.18/0.43 inference(symmetry,[status(thm)],[23])).
% 0.18/0.43 tff(25,plain,
% 0.18/0.43 ((~elem(m_Down(Y0!10), queue(host(X!4)))) <=> (~elem(m_Down(Y0!10), cons(m_Ack(index(elid, host(X!4)), Y!3), V!5)))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[24])).
% 0.18/0.44 tff(26,assumption,(~elem(m_Down(Y0!10), queue(host(X!4)))), introduced(assumption)).
% 0.18/0.44 tff(27,plain,
% 0.18/0.44 (~elem(m_Down(Y0!10), cons(m_Ack(index(elid, host(X!4)), Y!3), V!5))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.18/0.44 tff(28,plain,
% 0.18/0.44 (^[X: $i, Y: $i, Q: $i] : refl((elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q))) <=> (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(29,plain,
% 0.18/0.44 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q))) <=> ![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[28])).
% 0.18/0.44 tff(30,plain,
% 0.18/0.44 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q))) <=> ![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(31,axiom,(![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_46')).
% 0.18/0.44 tff(32,plain,
% 0.18/0.44 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.18/0.44 tff(33,plain,(
% 0.18/0.44 ![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.18/0.44 inference(skolemize,[status(sab)],[32])).
% 0.18/0.44 tff(34,plain,
% 0.18/0.44 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.18/0.44 tff(35,plain,
% 0.18/0.44 (((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(Y0!10), cons(m_Ack(index(elid, host(X!4)), Y!3), V!5)) <=> (elem(m_Down(Y0!10), V!5) | (m_Down(Y0!10) = m_Ack(index(elid, host(X!4)), Y!3))))) <=> ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(Y0!10), cons(m_Ack(index(elid, host(X!4)), Y!3), V!5)) <=> (elem(m_Down(Y0!10), V!5) | (m_Down(Y0!10) = m_Ack(index(elid, host(X!4)), Y!3)))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(36,plain,
% 0.18/0.44 ((elem(m_Down(Y0!10), cons(m_Ack(index(elid, host(X!4)), Y!3), V!5)) <=> ((m_Down(Y0!10) = m_Ack(index(elid, host(X!4)), Y!3)) | elem(m_Down(Y0!10), V!5))) <=> (elem(m_Down(Y0!10), cons(m_Ack(index(elid, host(X!4)), Y!3), V!5)) <=> (elem(m_Down(Y0!10), V!5) | (m_Down(Y0!10) = m_Ack(index(elid, host(X!4)), Y!3))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(37,plain,
% 0.18/0.44 (((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(Y0!10), cons(m_Ack(index(elid, host(X!4)), Y!3), V!5)) <=> ((m_Down(Y0!10) = m_Ack(index(elid, host(X!4)), Y!3)) | elem(m_Down(Y0!10), V!5)))) <=> ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(Y0!10), cons(m_Ack(index(elid, host(X!4)), Y!3), V!5)) <=> (elem(m_Down(Y0!10), V!5) | (m_Down(Y0!10) = m_Ack(index(elid, host(X!4)), Y!3)))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[36])).
% 0.18/0.44 tff(38,plain,
% 0.18/0.44 (((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(Y0!10), cons(m_Ack(index(elid, host(X!4)), Y!3), V!5)) <=> ((m_Down(Y0!10) = m_Ack(index(elid, host(X!4)), Y!3)) | elem(m_Down(Y0!10), V!5)))) <=> ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(Y0!10), cons(m_Ack(index(elid, host(X!4)), Y!3), V!5)) <=> (elem(m_Down(Y0!10), V!5) | (m_Down(Y0!10) = m_Ack(index(elid, host(X!4)), Y!3)))))),
% 0.18/0.44 inference(transitivity,[status(thm)],[37, 35])).
% 0.18/0.44 tff(39,plain,
% 0.18/0.44 ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(Y0!10), cons(m_Ack(index(elid, host(X!4)), Y!3), V!5)) <=> ((m_Down(Y0!10) = m_Ack(index(elid, host(X!4)), Y!3)) | elem(m_Down(Y0!10), V!5)))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(40,plain,
% 0.18/0.44 ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(Y0!10), cons(m_Ack(index(elid, host(X!4)), Y!3), V!5)) <=> (elem(m_Down(Y0!10), V!5) | (m_Down(Y0!10) = m_Ack(index(elid, host(X!4)), Y!3))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.18/0.44 tff(41,plain,
% 0.18/0.44 (elem(m_Down(Y0!10), cons(m_Ack(index(elid, host(X!4)), Y!3), V!5)) <=> (elem(m_Down(Y0!10), V!5) | (m_Down(Y0!10) = m_Ack(index(elid, host(X!4)), Y!3)))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[40, 34])).
% 0.18/0.44 tff(42,plain,
% 0.18/0.44 (^[X: $i, Y: $i, Q: $i] : refl((elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))) <=> (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(43,plain,
% 0.18/0.44 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))) <=> ![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[42])).
% 0.18/0.44 tff(44,plain,
% 0.18/0.44 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))) <=> ![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(45,axiom,(![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_47')).
% 0.18/0.44 tff(46,plain,
% 0.18/0.44 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.18/0.44 tff(47,plain,(
% 0.18/0.44 ![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.18/0.44 inference(skolemize,[status(sab)],[46])).
% 0.18/0.44 tff(48,plain,
% 0.18/0.44 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.18/0.44 tff(49,plain,
% 0.18/0.44 ((~![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(Y0!10), snoc(V!5, m_Ldr(X!4))) <=> ((m_Down(Y0!10) = m_Ldr(X!4)) | elem(m_Down(Y0!10), V!5)))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(50,plain,
% 0.18/0.44 (elem(m_Down(Y0!10), snoc(V!5, m_Ldr(X!4))) <=> ((m_Down(Y0!10) = m_Ldr(X!4)) | elem(m_Down(Y0!10), V!5))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.18/0.44 tff(51,plain,
% 0.18/0.44 (~((~(elem(m_Down(W0!9), queue(host(X0!8))) & elem(m_Down(Y0!10), snoc(V!5, m_Ldr(X!4))))) | (~((~(host(X0!8) = host(V0!7))) & setIn(V0!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(V0!7)) & (host(Y0!10) = host(X0!8)))))),
% 0.18/0.44 inference(and_elim,[status(thm)],[15])).
% 0.18/0.44 tff(52,plain,
% 0.18/0.44 (elem(m_Down(W0!9), queue(host(X0!8))) & elem(m_Down(Y0!10), snoc(V!5, m_Ldr(X!4)))),
% 0.18/0.44 inference(or_elim,[status(thm)],[51])).
% 0.18/0.44 tff(53,plain,
% 0.18/0.44 (elem(m_Down(Y0!10), snoc(V!5, m_Ldr(X!4)))),
% 0.18/0.44 inference(and_elim,[status(thm)],[52])).
% 0.18/0.44 tff(54,plain,
% 0.18/0.44 ((~(elem(m_Down(Y0!10), snoc(V!5, m_Ldr(X!4))) <=> ((m_Down(Y0!10) = m_Ldr(X!4)) | elem(m_Down(Y0!10), V!5)))) | (~elem(m_Down(Y0!10), snoc(V!5, m_Ldr(X!4)))) | ((m_Down(Y0!10) = m_Ldr(X!4)) | elem(m_Down(Y0!10), V!5))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(55,plain,
% 0.18/0.44 ((~(elem(m_Down(Y0!10), snoc(V!5, m_Ldr(X!4))) <=> ((m_Down(Y0!10) = m_Ldr(X!4)) | elem(m_Down(Y0!10), V!5)))) | ((m_Down(Y0!10) = m_Ldr(X!4)) | elem(m_Down(Y0!10), V!5))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.18/0.44 tff(56,plain,
% 0.18/0.44 ((m_Down(Y0!10) = m_Ldr(X!4)) | elem(m_Down(Y0!10), V!5)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[55, 50])).
% 0.18/0.44 tff(57,plain,
% 0.18/0.44 (^[X: $i, Y: $i] : refl((~(m_Down(X) = m_Ldr(Y))) <=> (~(m_Down(X) = m_Ldr(Y))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(58,plain,
% 0.18/0.44 (![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y))) <=> ![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[57])).
% 0.18/0.44 tff(59,plain,
% 0.18/0.44 (![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y))) <=> ![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(60,axiom,(![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_18')).
% 0.18/0.44 tff(61,plain,
% 0.18/0.44 (![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.18/0.44 tff(62,plain,(
% 0.18/0.44 ![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))),
% 0.18/0.44 inference(skolemize,[status(sab)],[61])).
% 0.18/0.44 tff(63,plain,
% 0.18/0.44 (![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.18/0.44 tff(64,plain,
% 0.18/0.44 ((~![X: $i, Y: $i] : (~(m_Down(X) = m_Ldr(Y)))) | (~(m_Down(Y0!10) = m_Ldr(X!4)))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(65,plain,
% 0.18/0.44 (~(m_Down(Y0!10) = m_Ldr(X!4))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.18/0.44 tff(66,plain,
% 0.18/0.44 ((~((m_Down(Y0!10) = m_Ldr(X!4)) | elem(m_Down(Y0!10), V!5))) | (m_Down(Y0!10) = m_Ldr(X!4)) | elem(m_Down(Y0!10), V!5)),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(67,plain,
% 0.18/0.44 ((~((m_Down(Y0!10) = m_Ldr(X!4)) | elem(m_Down(Y0!10), V!5))) | elem(m_Down(Y0!10), V!5)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.18/0.44 tff(68,plain,
% 0.18/0.44 (elem(m_Down(Y0!10), V!5)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[67, 56])).
% 0.18/0.44 tff(69,plain,
% 0.18/0.44 ((elem(m_Down(Y0!10), V!5) | (m_Down(Y0!10) = m_Ack(index(elid, host(X!4)), Y!3))) | (~elem(m_Down(Y0!10), V!5))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(70,plain,
% 0.18/0.44 (elem(m_Down(Y0!10), V!5) | (m_Down(Y0!10) = m_Ack(index(elid, host(X!4)), Y!3))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.18/0.44 tff(71,plain,
% 0.18/0.44 ((~(elem(m_Down(Y0!10), cons(m_Ack(index(elid, host(X!4)), Y!3), V!5)) <=> (elem(m_Down(Y0!10), V!5) | (m_Down(Y0!10) = m_Ack(index(elid, host(X!4)), Y!3))))) | elem(m_Down(Y0!10), cons(m_Ack(index(elid, host(X!4)), Y!3), V!5)) | (~(elem(m_Down(Y0!10), V!5) | (m_Down(Y0!10) = m_Ack(index(elid, host(X!4)), Y!3))))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(72,plain,
% 0.18/0.44 ((~(elem(m_Down(Y0!10), cons(m_Ack(index(elid, host(X!4)), Y!3), V!5)) <=> (elem(m_Down(Y0!10), V!5) | (m_Down(Y0!10) = m_Ack(index(elid, host(X!4)), Y!3))))) | elem(m_Down(Y0!10), cons(m_Ack(index(elid, host(X!4)), Y!3), V!5))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.18/0.44 tff(73,plain,
% 0.18/0.44 (elem(m_Down(Y0!10), cons(m_Ack(index(elid, host(X!4)), Y!3), V!5))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[72, 41])).
% 0.18/0.44 tff(74,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[73, 27])).
% 0.18/0.44 tff(75,plain,(elem(m_Down(Y0!10), queue(host(X!4)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.44 tff(76,plain,
% 0.18/0.44 (elem(m_Down(Y0!10), queue(host(V0!7)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[75, 20])).
% 0.18/0.44 tff(77,plain,
% 0.18/0.44 ((~(host(X0!8) = host(V0!7))) & setIn(V0!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(V0!7)) & (host(Y0!10) = host(X0!8))),
% 0.18/0.44 inference(or_elim,[status(thm)],[51])).
% 0.18/0.44 tff(78,plain,
% 0.18/0.44 (host(Y0!10) = host(X0!8)),
% 0.18/0.44 inference(and_elim,[status(thm)],[77])).
% 0.18/0.44 tff(79,plain,
% 0.18/0.44 (host(W0!9) = host(V0!7)),
% 0.18/0.44 inference(and_elim,[status(thm)],[77])).
% 0.18/0.44 tff(80,plain,
% 0.18/0.44 (setIn(X0!8, alive)),
% 0.18/0.44 inference(and_elim,[status(thm)],[77])).
% 0.18/0.44 tff(81,plain,
% 0.18/0.44 (setIn(V0!7, alive)),
% 0.18/0.44 inference(and_elim,[status(thm)],[77])).
% 0.18/0.44 tff(82,plain,
% 0.18/0.44 (~(host(X0!8) = host(V0!7))),
% 0.18/0.44 inference(and_elim,[status(thm)],[77])).
% 0.18/0.44 tff(83,plain,
% 0.18/0.44 (elem(m_Down(W0!9), queue(host(X0!8)))),
% 0.18/0.44 inference(and_elim,[status(thm)],[52])).
% 0.18/0.44 tff(84,plain,
% 0.18/0.44 (^[Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : refl(((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z)))) <=> ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z)))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(85,plain,
% 0.18/0.44 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z)))) <=> ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[84])).
% 0.18/0.44 tff(86,plain,
% 0.18/0.44 (^[Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : trans(monotonicity(trans(monotonicity(rewrite((elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20)))) <=> (~((~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20))))))), ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) <=> (~(~((~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20))))))))), rewrite((~(~((~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20))))))) <=> ((~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))))), ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) <=> ((~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20))))))), trans(monotonicity(rewrite(((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))) <=> (~((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z)))))), ((~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20)))) <=> (~(~((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z)))))))), rewrite((~(~((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z)))))) <=> ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))), ((~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20)))) <=> ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z)))))), (((~(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))))) <=> (((~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20))))) | ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))))), rewrite((((~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20))))) | ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))) <=> ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))), (((~(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))))) <=> ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(87,plain,
% 0.18/0.44 (![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] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[86])).
% 0.18/0.44 tff(88,plain,
% 0.18/0.44 (![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)))))),
% 0.18/0.44 inference(and_elim,[status(thm)],[15])).
% 0.18/0.44 tff(89,plain,
% 0.18/0.44 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.18/0.44 tff(90,plain,
% 0.18/0.44 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.18/0.44 tff(91,plain,
% 0.18/0.44 (((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))) | ((host(X0!8) = host(V0!7)) | (~setIn(V0!7, alive)) | (~setIn(X0!8, alive)) | (~(host(W0!9) = host(V0!7))) | (~(host(Y0!10) = host(X0!8))) | (~elem(m_Down(W0!9), queue(host(X0!8)))) | (~elem(m_Down(Y0!10), queue(host(V0!7)))))) <=> ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))) | (host(X0!8) = host(V0!7)) | (~setIn(V0!7, alive)) | (~setIn(X0!8, alive)) | (~(host(W0!9) = host(V0!7))) | (~(host(Y0!10) = host(X0!8))) | (~elem(m_Down(W0!9), queue(host(X0!8)))) | (~elem(m_Down(Y0!10), queue(host(V0!7)))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(92,plain,
% 0.18/0.44 (((~(host(Y0!10) = host(X0!8))) | (~setIn(X0!8, alive)) | (host(X0!8) = host(V0!7)) | (~elem(m_Down(Y0!10), queue(host(V0!7)))) | (~elem(m_Down(W0!9), queue(host(X0!8)))) | (~setIn(V0!7, alive)) | (~(host(W0!9) = host(V0!7)))) <=> ((host(X0!8) = host(V0!7)) | (~setIn(V0!7, alive)) | (~setIn(X0!8, alive)) | (~(host(W0!9) = host(V0!7))) | (~(host(Y0!10) = host(X0!8))) | (~elem(m_Down(W0!9), queue(host(X0!8)))) | (~elem(m_Down(Y0!10), queue(host(V0!7)))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(93,plain,
% 0.18/0.44 (((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))) | ((~(host(Y0!10) = host(X0!8))) | (~setIn(X0!8, alive)) | (host(X0!8) = host(V0!7)) | (~elem(m_Down(Y0!10), queue(host(V0!7)))) | (~elem(m_Down(W0!9), queue(host(X0!8)))) | (~setIn(V0!7, alive)) | (~(host(W0!9) = host(V0!7))))) <=> ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))) | ((host(X0!8) = host(V0!7)) | (~setIn(V0!7, alive)) | (~setIn(X0!8, alive)) | (~(host(W0!9) = host(V0!7))) | (~(host(Y0!10) = host(X0!8))) | (~elem(m_Down(W0!9), queue(host(X0!8)))) | (~elem(m_Down(Y0!10), queue(host(V0!7))))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[92])).
% 0.18/0.44 tff(94,plain,
% 0.18/0.44 (((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))) | ((~(host(Y0!10) = host(X0!8))) | (~setIn(X0!8, alive)) | (host(X0!8) = host(V0!7)) | (~elem(m_Down(Y0!10), queue(host(V0!7)))) | (~elem(m_Down(W0!9), queue(host(X0!8)))) | (~setIn(V0!7, alive)) | (~(host(W0!9) = host(V0!7))))) <=> ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))) | (host(X0!8) = host(V0!7)) | (~setIn(V0!7, alive)) | (~setIn(X0!8, alive)) | (~(host(W0!9) = host(V0!7))) | (~(host(Y0!10) = host(X0!8))) | (~elem(m_Down(W0!9), queue(host(X0!8)))) | (~elem(m_Down(Y0!10), queue(host(V0!7)))))),
% 0.18/0.45 inference(transitivity,[status(thm)],[93, 91])).
% 0.18/0.45 tff(95,plain,
% 0.18/0.45 ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))) | ((~(host(Y0!10) = host(X0!8))) | (~setIn(X0!8, alive)) | (host(X0!8) = host(V0!7)) | (~elem(m_Down(Y0!10), queue(host(V0!7)))) | (~elem(m_Down(W0!9), queue(host(X0!8)))) | (~setIn(V0!7, alive)) | (~(host(W0!9) = host(V0!7))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(96,plain,
% 0.18/0.45 ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))) | (host(X0!8) = host(V0!7)) | (~setIn(V0!7, alive)) | (~setIn(X0!8, alive)) | (~(host(W0!9) = host(V0!7))) | (~(host(Y0!10) = host(X0!8))) | (~elem(m_Down(W0!9), queue(host(X0!8)))) | (~elem(m_Down(Y0!10), queue(host(V0!7))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.18/0.45 tff(97,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[96, 90, 83, 82, 81, 80, 79, 78, 76])).
% 0.18/0.45 % SZS output end Proof
% 0.18/0.45 % E exiting
%------------------------------------------------------------------------------