%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV454+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 23.45s 23.67s
% Output : Proof 23.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV454+1 : TPTP v9.0.0. Released v4.0.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:51:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 23.45/23.67 % SZS status Theorem
% 23.45/23.67 % SZS output start Proof
% 23.45/23.67 tff(elem_type, type, (
% 23.45/23.67 elem: ( $i * $i ) > $o)).
% 23.45/23.67 tff(queue_type, type, (
% 23.45/23.67 queue: $i > $i)).
% 23.45/23.67 tff(host_type, type, (
% 23.45/23.67 host: $i > $i)).
% 23.45/23.67 tff(tptp_fun_Z_6_type, type, (
% 23.45/23.67 tptp_fun_Z_6: $i)).
% 23.45/23.67 tff(m_Down_type, type, (
% 23.45/23.67 m_Down: $i > $i)).
% 23.45/23.67 tff(tptp_fun_Y0_9_type, type, (
% 23.45/23.67 tptp_fun_Y0_9: $i)).
% 23.45/23.67 tff(tptp_fun_X_4_type, type, (
% 23.45/23.67 tptp_fun_X_4: $i)).
% 23.45/23.67 tff(tptp_fun_X0_7_type, type, (
% 23.45/23.67 tptp_fun_X0_7: $i)).
% 23.45/23.67 tff(tptp_fun_W0_8_type, type, (
% 23.45/23.67 tptp_fun_W0_8: $i)).
% 23.45/23.67 tff(setIn_type, type, (
% 23.45/23.67 setIn: ( $i * $i ) > $o)).
% 23.45/23.67 tff(alive_type, type, (
% 23.45/23.67 alive: $i)).
% 23.45/23.67 tff(tptp_fun_V_5_type, type, (
% 23.45/23.67 tptp_fun_V_5: $i)).
% 23.45/23.67 tff(s_type, type, (
% 23.45/23.67 s: $i > $i)).
% 23.45/23.67 tff(cons_type, type, (
% 23.45/23.67 cons: ( $i * $i ) > $i)).
% 23.45/23.67 tff(tptp_fun_Y_3_type, type, (
% 23.45/23.67 tptp_fun_Y_3: $i)).
% 23.45/23.67 tff(leq_type, type, (
% 23.45/23.67 leq: ( $i * $i ) > $o)).
% 23.45/23.67 tff(m_Ack_type, type, (
% 23.45/23.67 m_Ack: ( $i * $i ) > $i)).
% 23.45/23.67 tff(m_Halt_type, type, (
% 23.45/23.67 m_Halt: $i > $i)).
% 23.45/23.67 tff(elec_1_type, type, (
% 23.45/23.67 elec_1: $i)).
% 23.45/23.67 tff(index_type, type, (
% 23.45/23.67 index: ( $i * $i ) > $i)).
% 23.45/23.67 tff(status_type, type, (
% 23.45/23.67 status: $i)).
% 23.45/23.67 tff(zero_type, type, (
% 23.45/23.67 zero: $i)).
% 23.45/23.67 tff(down_type, type, (
% 23.45/23.67 down: $i)).
% 23.45/23.67 tff(norm_type, type, (
% 23.45/23.67 norm: $i)).
% 23.45/23.67 tff(ldr_type, type, (
% 23.45/23.67 ldr: $i)).
% 23.45/23.67 tff(elid_type, type, (
% 23.45/23.67 elid: $i)).
% 23.45/23.67 tff(wait_type, type, (
% 23.45/23.67 wait: $i)).
% 23.45/23.67 tff(nbr_proc_type, type, (
% 23.45/23.67 nbr_proc: $i)).
% 23.45/23.67 tff(1,plain,
% 23.45/23.67 (((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~leq(nbr_proc, host(X!4))) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1)) & (![Z: $i, Pid0: $i] : ((~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))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5))) & ((~(s(host(X!4)) = host(Z!6))) & (host(X!4) = host(Z!6)) & (~(s(host(X!4)) = host(X0!7))) & (~(host(X!4) = host(X0!7))) & (~((~(elem(m_Down(Y0!9), V!5) & elem(m_Down(W0!8), queue(host(X0!7))))) | (~((~(host(X0!7) = host(Z!6))) & setIn(Z!6, alive) & setIn(X0!7, alive) & (host(W0!8) = host(Z!6)) & (host(Y0!9) = host(X0!7)))))))) <=> ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~leq(nbr_proc, host(X!4))) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & ![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1) & ![Z: $i, Pid0: $i] : ((~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))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)) & (~(s(host(X!4)) = host(Z!6))) & (host(X!4) = host(Z!6)) & (~(s(host(X!4)) = host(X0!7))) & (~(host(X!4) = host(X0!7))) & (~((~(elem(m_Down(Y0!9), V!5) & elem(m_Down(W0!8), queue(host(X0!7))))) | (~((~(host(X0!7) = host(Z!6))) & setIn(Z!6, alive) & setIn(X0!7, alive) & (host(W0!8) = host(Z!6)) & (host(Y0!9) = host(X0!7)))))))),
% 23.45/23.67 inference(rewrite,[status(thm)],[])).
% 23.45/23.67 tff(2,plain,
% 23.45/23.67 (((~(s(host(X!4)) = host(Z!6))) & (host(X!4) = host(Z!6)) & ((~(s(host(X!4)) = host(X0!7))) & (~(host(X!4) = host(X0!7))) & (~((~(elem(m_Down(Y0!9), V!5) & elem(m_Down(W0!8), queue(host(X0!7))))) | (~((~(host(X0!7) = host(Z!6))) & setIn(Z!6, alive) & setIn(X0!7, alive) & (host(W0!8) = host(Z!6)) & (host(Y0!9) = host(X0!7)))))))) <=> ((~(s(host(X!4)) = host(Z!6))) & (host(X!4) = host(Z!6)) & (~(s(host(X!4)) = host(X0!7))) & (~(host(X!4) = host(X0!7))) & (~((~(elem(m_Down(Y0!9), V!5) & elem(m_Down(W0!8), queue(host(X0!7))))) | (~((~(host(X0!7) = host(Z!6))) & setIn(Z!6, alive) & setIn(X0!7, alive) & (host(W0!8) = host(Z!6)) & (host(Y0!9) = host(X0!7)))))))),
% 23.45/23.67 inference(rewrite,[status(thm)],[])).
% 23.45/23.67 tff(3,plain,
% 23.45/23.67 ((![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))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5))) <=> (![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))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)))),
% 23.45/23.67 inference(rewrite,[status(thm)],[])).
% 23.45/23.67 tff(4,plain,
% 23.45/23.67 ((![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1)) <=> (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1))),
% 23.45/23.67 inference(rewrite,[status(thm)],[])).
% 23.45/23.67 tff(5,plain,
% 23.45/23.67 (((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~leq(nbr_proc, host(X!4))) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1)) & (![Z: $i, Pid0: $i] : ((~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))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5))) & ((~(s(host(X!4)) = host(Z!6))) & (host(X!4) = host(Z!6)) & ((~(s(host(X!4)) = host(X0!7))) & (~(host(X!4) = host(X0!7))) & (~((~(elem(m_Down(Y0!9), V!5) & elem(m_Down(W0!8), queue(host(X0!7))))) | (~((~(host(X0!7) = host(Z!6))) & setIn(Z!6, alive) & setIn(X0!7, alive) & (host(W0!8) = host(Z!6)) & (host(Y0!9) = host(X0!7))))))))) <=> ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~leq(nbr_proc, host(X!4))) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1)) & (![Z: $i, Pid0: $i] : ((~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))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5))) & ((~(s(host(X!4)) = host(Z!6))) & (host(X!4) = host(Z!6)) & (~(s(host(X!4)) = host(X0!7))) & (~(host(X!4) = host(X0!7))) & (~((~(elem(m_Down(Y0!9), V!5) & elem(m_Down(W0!8), queue(host(X0!7))))) | (~((~(host(X0!7) = host(Z!6))) & setIn(Z!6, alive) & setIn(X0!7, alive) & (host(W0!8) = host(Z!6)) & (host(Y0!9) = host(X0!7))))))))),
% 23.45/23.68 inference(monotonicity,[status(thm)],[4, 3, 2])).
% 23.45/23.68 tff(6,plain,
% 23.45/23.68 (((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~leq(nbr_proc, host(X!4))) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & (![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1)) & (![Z: $i, Pid0: $i] : ((~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))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5))) & ((~(s(host(X!4)) = host(Z!6))) & (host(X!4) = host(Z!6)) & ((~(s(host(X!4)) = host(X0!7))) & (~(host(X!4) = host(X0!7))) & (~((~(elem(m_Down(Y0!9), V!5) & elem(m_Down(W0!8), queue(host(X0!7))))) | (~((~(host(X0!7) = host(Z!6))) & setIn(Z!6, alive) & setIn(X0!7, alive) & (host(W0!8) = host(Z!6)) & (host(Y0!9) = host(X0!7))))))))) <=> ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~leq(nbr_proc, host(X!4))) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & ![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1) & ![Z: $i, Pid0: $i] : ((~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))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)) & (~(s(host(X!4)) = host(Z!6))) & (host(X!4) = host(Z!6)) & (~(s(host(X!4)) = host(X0!7))) & (~(host(X!4) = host(X0!7))) & (~((~(elem(m_Down(Y0!9), V!5) & elem(m_Down(W0!8), queue(host(X0!7))))) | (~((~(host(X0!7) = host(Z!6))) & setIn(Z!6, alive) & setIn(X0!7, alive) & (host(W0!8) = host(Z!6)) & (host(Y0!9) = host(X0!7)))))))),
% 23.45/23.68 inference(transitivity,[status(thm)],[5, 1])).
% 23.45/23.68 tff(7,plain,
% 23.45/23.68 ((~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | leq(nbr_proc, host(X)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i, Pid0: $i] : ((~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))))) & (queue(host(X)) = cons(m_Down(Y), V)))) | ![Z: $i] : ((s(host(X)) = host(Z)) | (~(host(X) = host(Z))) | ![W0: $i, X0: $i] : ((s(host(X)) = host(X0)) | (host(X) = host(X0)) | ![Y0: $i] : ((~(elem(m_Down(Y0), V) & elem(m_Down(W0), queue(host(X0))))) | (~((~(host(X0) = host(Z))) & setIn(Z, alive) & setIn(X0, alive) & (host(W0) = host(Z)) & (host(Y0) = host(X0))))))))) <=> (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | leq(nbr_proc, host(X)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i, Pid0: $i] : ((~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))))) & (queue(host(X)) = cons(m_Down(Y), V)))) | ![Z: $i] : ((s(host(X)) = host(Z)) | (~(host(X) = host(Z))) | ![W0: $i, X0: $i] : ((s(host(X)) = host(X0)) | (host(X) = host(X0)) | ![Y0: $i] : ((~(elem(m_Down(Y0), V) & elem(m_Down(W0), queue(host(X0))))) | (~((~(host(X0) = host(Z))) & setIn(Z, alive) & setIn(X0, alive) & (host(W0) = host(Z)) & (host(Y0) = host(X0)))))))))),
% 23.45/23.68 inference(rewrite,[status(thm)],[])).
% 23.45/23.68 tff(8,plain,
% 23.45/23.68 ((~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | leq(nbr_proc, host(X)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | ![Z: $i] : ((s(host(X)) = host(Z)) | (~(host(X) = host(Z))) | ![W0: $i, X0: $i] : ((s(host(X)) = host(X0)) | (host(X) = host(X0)) | ![Y0: $i] : ((~(elem(m_Down(Y0), V) & elem(m_Down(W0), queue(host(X0))))) | (~((~(host(X0) = host(Z))) & setIn(Z, alive) & setIn(X0, alive) & (host(W0) = host(Z)) & (host(Y0) = host(X0))))))) | (~(![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))))) & (queue(host(X)) = cons(m_Down(Y), V)))))) <=> (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | leq(nbr_proc, host(X)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i, Pid0: $i] : ((~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))))) & (queue(host(X)) = cons(m_Down(Y), V)))) | ![Z: $i] : ((s(host(X)) = host(Z)) | (~(host(X) = host(Z))) | ![W0: $i, X0: $i] : ((s(host(X)) = host(X0)) | (host(X) = host(X0)) | ![Y0: $i] : ((~(elem(m_Down(Y0), V) & elem(m_Down(W0), queue(host(X0))))) | (~((~(host(X0) = host(Z))) & setIn(Z, alive) & setIn(X0, alive) & (host(W0) = host(Z)) & (host(Y0) = host(X0)))))))))),
% 23.45/23.68 inference(rewrite,[status(thm)],[])).
% 23.45/23.68 tff(9,plain,
% 23.45/23.68 ((~![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_Down(Y), V))) => (setIn(X, alive) => ((~leq(host(X), host(Y))) => ((~(((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))))) => ((![Z: $i] : (((~leq(host(X), Z)) & leq(s(zero), Z)) => (setIn(Z, index(down, host(X))) | (Z = host(Y)))) & (index(status, host(X)) = elec_1)) => ((~leq(nbr_proc, host(X))) => ![Z: $i] : ((~(s(host(X)) = host(Z))) => ((host(X) = host(Z)) => ![W0: $i, X0: $i] : ((~(s(host(X)) = host(X0))) => ((~(host(X) = host(X0))) => ![Y0: $i] : ((((((~(host(X0) = host(Z))) & setIn(Z, alive)) & setIn(X0, alive)) & (host(W0) = host(Z))) & (host(Y0) = host(X0))) => (~(elem(m_Down(Y0), V) & elem(m_Down(W0), queue(host(X0))))))))))))))))) <=> (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | leq(nbr_proc, host(X)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | ![Z: $i] : ((s(host(X)) = host(Z)) | (~(host(X) = host(Z))) | ![W0: $i, X0: $i] : ((s(host(X)) = host(X0)) | (host(X) = host(X0)) | ![Y0: $i] : ((~(elem(m_Down(Y0), V) & elem(m_Down(W0), queue(host(X0))))) | (~((~(host(X0) = host(Z))) & setIn(Z, alive) & setIn(X0, alive) & (host(W0) = host(Z)) & (host(Y0) = host(X0))))))) | (~(![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))))) & (queue(host(X)) = cons(m_Down(Y), V))))))),
% 23.53/23.68 inference(rewrite,[status(thm)],[])).
% 23.53/23.68 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_Down(Y), V))) => (setIn(X, alive) => ((~leq(host(X), host(Y))) => ((~(((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))))) => ((![Z: $i] : (((~leq(host(X), Z)) & leq(s(zero), Z)) => (setIn(Z, index(down, host(X))) | (Z = host(Y)))) & (index(status, host(X)) = elec_1)) => ((~leq(nbr_proc, host(X))) => ![Z: $i] : ((~(s(host(X)) = host(Z))) => ((host(X) = host(Z)) => ![W0: $i, X0: $i] : ((~(s(host(X)) = host(X0))) => ((~(host(X) = host(X0))) => ![Y0: $i] : ((((((~(host(X0) = host(Z))) & setIn(Z, alive)) & setIn(X0, alive)) & (host(W0) = host(Z))) & (host(Y0) = host(X0))) => (~(elem(m_Down(Y0), V) & elem(m_Down(W0), queue(host(X0))))))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj')).
% 23.53/23.68 tff(11,plain,
% 23.53/23.68 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | leq(nbr_proc, host(X)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | ![Z: $i] : ((s(host(X)) = host(Z)) | (~(host(X) = host(Z))) | ![W0: $i, X0: $i] : ((s(host(X)) = host(X0)) | (host(X) = host(X0)) | ![Y0: $i] : ((~(elem(m_Down(Y0), V) & elem(m_Down(W0), queue(host(X0))))) | (~((~(host(X0) = host(Z))) & setIn(Z, alive) & setIn(X0, alive) & (host(W0) = host(Z)) & (host(Y0) = host(X0))))))) | (~(![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))))) & (queue(host(X)) = cons(m_Down(Y), V)))))),
% 23.53/23.68 inference(modus_ponens,[status(thm)],[10, 9])).
% 23.53/23.68 tff(12,plain,
% 23.53/23.68 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | leq(nbr_proc, host(X)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i, Pid0: $i] : ((~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))))) & (queue(host(X)) = cons(m_Down(Y), V)))) | ![Z: $i] : ((s(host(X)) = host(Z)) | (~(host(X) = host(Z))) | ![W0: $i, X0: $i] : ((s(host(X)) = host(X0)) | (host(X) = host(X0)) | ![Y0: $i] : ((~(elem(m_Down(Y0), V) & elem(m_Down(W0), queue(host(X0))))) | (~((~(host(X0) = host(Z))) & setIn(Z, alive) & setIn(X0, alive) & (host(W0) = host(Z)) & (host(Y0) = host(X0))))))))),
% 23.53/23.68 inference(modus_ponens,[status(thm)],[11, 8])).
% 23.53/23.68 tff(13,plain,
% 23.53/23.68 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | leq(nbr_proc, host(X)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i, Pid0: $i] : ((~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))))) & (queue(host(X)) = cons(m_Down(Y), V)))) | ![Z: $i] : ((s(host(X)) = host(Z)) | (~(host(X) = host(Z))) | ![W0: $i, X0: $i] : ((s(host(X)) = host(X0)) | (host(X) = host(X0)) | ![Y0: $i] : ((~(elem(m_Down(Y0), V) & elem(m_Down(W0), queue(host(X0))))) | (~((~(host(X0) = host(Z))) & setIn(Z, alive) & setIn(X0, alive) & (host(W0) = host(Z)) & (host(Y0) = host(X0))))))))),
% 23.53/23.68 inference(modus_ponens,[status(thm)],[12, 7])).
% 23.53/23.68 tff(14,plain,
% 23.53/23.68 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | leq(nbr_proc, host(X)) | ((index(status, host(X)) = wait) & (host(Y) = host(index(elid, host(X))))) | ((index(ldr, host(X)) = host(Y)) & (index(status, host(X)) = norm)) | (~(![Z: $i] : ((Z = host(Y)) | setIn(Z, index(down, host(X))) | (~((~leq(host(X), Z)) & leq(s(zero), Z)))) & (index(status, host(X)) = elec_1))) | (~(![Z: $i, Pid0: $i] : ((~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))))) & (queue(host(X)) = cons(m_Down(Y), V)))) | ![Z: $i] : ((s(host(X)) = host(Z)) | (~(host(X) = host(Z))) | ![W0: $i, X0: $i] : ((s(host(X)) = host(X0)) | (host(X) = host(X0)) | ![Y0: $i] : ((~(elem(m_Down(Y0), V) & elem(m_Down(W0), queue(host(X0))))) | (~((~(host(X0) = host(Z))) & setIn(Z, alive) & setIn(X0, alive) & (host(W0) = host(Z)) & (host(Y0) = host(X0))))))))),
% 23.53/23.68 inference(modus_ponens,[status(thm)],[13, 7])).
% 23.53/23.68 tff(15,plain,
% 23.53/23.68 ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~leq(nbr_proc, host(X!4))) & (~((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (~((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm))) & ![Z: $i] : ((Z = host(Y!3)) | setIn(Z, index(down, host(X!4))) | (~((~leq(host(X!4), Z)) & leq(s(zero), Z)))) & (index(status, host(X!4)) = elec_1) & ![Z: $i, Pid0: $i] : ((~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))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!5)) & (~(s(host(X!4)) = host(Z!6))) & (host(X!4) = host(Z!6)) & (~(s(host(X!4)) = host(X0!7))) & (~(host(X!4) = host(X0!7))) & (~((~(elem(m_Down(Y0!9), V!5) & elem(m_Down(W0!8), queue(host(X0!7))))) | (~((~(host(X0!7) = host(Z!6))) & setIn(Z!6, alive) & setIn(X0!7, alive) & (host(W0!8) = host(Z!6)) & (host(Y0!9) = host(X0!7))))))),
% 23.53/23.68 inference(modus_ponens,[status(thm)],[14, 6])).
% 23.53/23.68 tff(16,plain,
% 23.53/23.68 (host(X!4) = host(Z!6)),
% 23.53/23.68 inference(and_elim,[status(thm)],[15])).
% 23.53/23.68 tff(17,plain,
% 23.53/23.68 (host(Z!6) = host(X!4)),
% 23.53/23.68 inference(symmetry,[status(thm)],[16])).
% 23.53/23.68 tff(18,plain,
% 23.53/23.68 (queue(host(Z!6)) = queue(host(X!4))),
% 23.53/23.68 inference(monotonicity,[status(thm)],[17])).
% 23.53/23.68 tff(19,plain,
% 23.53/23.68 (elem(m_Down(Y0!9), queue(host(Z!6))) <=> elem(m_Down(Y0!9), queue(host(X!4)))),
% 23.53/23.68 inference(monotonicity,[status(thm)],[18])).
% 23.53/23.69 tff(20,plain,
% 23.53/23.69 (elem(m_Down(Y0!9), queue(host(X!4))) <=> elem(m_Down(Y0!9), queue(host(Z!6)))),
% 23.53/23.69 inference(symmetry,[status(thm)],[19])).
% 23.53/23.69 tff(21,plain,
% 23.53/23.69 (queue(host(X!4)) = cons(m_Down(Y!3), V!5)),
% 23.53/23.69 inference(and_elim,[status(thm)],[15])).
% 23.53/23.69 tff(22,plain,
% 23.53/23.69 (cons(m_Down(Y!3), V!5) = queue(host(X!4))),
% 23.53/23.69 inference(symmetry,[status(thm)],[21])).
% 23.53/23.69 tff(23,plain,
% 23.53/23.69 (elem(m_Down(Y0!9), cons(m_Down(Y!3), V!5)) <=> elem(m_Down(Y0!9), queue(host(X!4)))),
% 23.53/23.69 inference(monotonicity,[status(thm)],[22])).
% 23.53/23.69 tff(24,plain,
% 23.53/23.69 (elem(m_Down(Y0!9), queue(host(X!4))) <=> elem(m_Down(Y0!9), cons(m_Down(Y!3), V!5))),
% 23.53/23.69 inference(symmetry,[status(thm)],[23])).
% 23.53/23.69 tff(25,plain,
% 23.53/23.69 ((~elem(m_Down(Y0!9), queue(host(X!4)))) <=> (~elem(m_Down(Y0!9), cons(m_Down(Y!3), V!5)))),
% 23.53/23.69 inference(monotonicity,[status(thm)],[24])).
% 23.53/23.69 tff(26,assumption,(~elem(m_Down(Y0!9), queue(host(X!4)))), introduced(assumption)).
% 23.53/23.69 tff(27,plain,
% 23.53/23.69 (~elem(m_Down(Y0!9), cons(m_Down(Y!3), V!5))),
% 23.53/23.69 inference(modus_ponens,[status(thm)],[26, 25])).
% 23.53/23.69 tff(28,plain,
% 23.53/23.69 (^[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))))),
% 23.53/23.69 inference(bind,[status(th)],[])).
% 23.53/23.69 tff(29,plain,
% 23.53/23.69 (![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)))),
% 23.53/23.69 inference(quant_intro,[status(thm)],[28])).
% 23.53/23.69 tff(30,plain,
% 23.53/23.69 (![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)))),
% 23.53/23.69 inference(rewrite,[status(thm)],[])).
% 23.53/23.69 tff(31,axiom,(![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV011+0.ax','axiom_46')).
% 23.53/23.69 tff(32,plain,
% 23.53/23.69 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 23.53/23.69 inference(modus_ponens,[status(thm)],[31, 30])).
% 23.53/23.69 tff(33,plain,(
% 23.53/23.69 ![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 23.53/23.69 inference(skolemize,[status(sab)],[32])).
% 23.53/23.69 tff(34,plain,
% 23.53/23.69 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 23.53/23.69 inference(modus_ponens,[status(thm)],[33, 29])).
% 23.53/23.69 tff(35,plain,
% 23.53/23.69 ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(Y0!9), cons(m_Down(Y!3), V!5)) <=> ((m_Down(Y0!9) = m_Down(Y!3)) | elem(m_Down(Y0!9), V!5)))),
% 23.53/23.69 inference(quant_inst,[status(thm)],[])).
% 23.53/23.69 tff(36,plain,
% 23.53/23.69 (elem(m_Down(Y0!9), cons(m_Down(Y!3), V!5)) <=> ((m_Down(Y0!9) = m_Down(Y!3)) | elem(m_Down(Y0!9), V!5))),
% 23.53/23.69 inference(unit_resolution,[status(thm)],[35, 34])).
% 23.53/23.69 tff(37,plain,
% 23.53/23.69 (~((~(elem(m_Down(Y0!9), V!5) & elem(m_Down(W0!8), queue(host(X0!7))))) | (~((~(host(X0!7) = host(Z!6))) & setIn(Z!6, alive) & setIn(X0!7, alive) & (host(W0!8) = host(Z!6)) & (host(Y0!9) = host(X0!7)))))),
% 23.53/23.69 inference(and_elim,[status(thm)],[15])).
% 23.53/23.69 tff(38,plain,
% 23.53/23.69 (elem(m_Down(Y0!9), V!5) & elem(m_Down(W0!8), queue(host(X0!7)))),
% 23.53/23.69 inference(or_elim,[status(thm)],[37])).
% 23.53/23.69 tff(39,plain,
% 23.53/23.69 (elem(m_Down(Y0!9), V!5)),
% 23.53/23.69 inference(and_elim,[status(thm)],[38])).
% 23.53/23.69 tff(40,plain,
% 23.53/23.69 (((m_Down(Y0!9) = m_Down(Y!3)) | elem(m_Down(Y0!9), V!5)) | (~elem(m_Down(Y0!9), V!5))),
% 23.53/23.69 inference(tautology,[status(thm)],[])).
% 23.53/23.69 tff(41,plain,
% 23.53/23.69 ((m_Down(Y0!9) = m_Down(Y!3)) | elem(m_Down(Y0!9), V!5)),
% 23.53/23.69 inference(unit_resolution,[status(thm)],[40, 39])).
% 23.53/23.69 tff(42,plain,
% 23.53/23.69 ((~(elem(m_Down(Y0!9), cons(m_Down(Y!3), V!5)) <=> ((m_Down(Y0!9) = m_Down(Y!3)) | elem(m_Down(Y0!9), V!5)))) | elem(m_Down(Y0!9), cons(m_Down(Y!3), V!5)) | (~((m_Down(Y0!9) = m_Down(Y!3)) | elem(m_Down(Y0!9), V!5)))),
% 23.53/23.69 inference(tautology,[status(thm)],[])).
% 23.53/23.69 tff(43,plain,
% 23.53/23.69 ((~(elem(m_Down(Y0!9), cons(m_Down(Y!3), V!5)) <=> ((m_Down(Y0!9) = m_Down(Y!3)) | elem(m_Down(Y0!9), V!5)))) | elem(m_Down(Y0!9), cons(m_Down(Y!3), V!5))),
% 23.53/23.69 inference(unit_resolution,[status(thm)],[42, 41])).
% 23.53/23.69 tff(44,plain,
% 23.53/23.69 (elem(m_Down(Y0!9), cons(m_Down(Y!3), V!5))),
% 23.53/23.69 inference(unit_resolution,[status(thm)],[43, 36])).
% 23.53/23.69 tff(45,plain,
% 23.53/23.69 ($false),
% 23.53/23.69 inference(unit_resolution,[status(thm)],[44, 27])).
% 23.53/23.69 tff(46,plain,(elem(m_Down(Y0!9), queue(host(X!4)))), inference(lemma,lemma(discharge,[]))).
% 23.53/23.69 tff(47,plain,
% 23.53/23.69 (elem(m_Down(Y0!9), queue(host(Z!6)))),
% 23.53/23.69 inference(modus_ponens,[status(thm)],[46, 20])).
% 23.53/23.69 tff(48,plain,
% 23.53/23.69 ((~(host(X0!7) = host(Z!6))) & setIn(Z!6, alive) & setIn(X0!7, alive) & (host(W0!8) = host(Z!6)) & (host(Y0!9) = host(X0!7))),
% 23.53/23.69 inference(or_elim,[status(thm)],[37])).
% 23.53/23.69 tff(49,plain,
% 23.53/23.69 (host(Y0!9) = host(X0!7)),
% 23.53/23.69 inference(and_elim,[status(thm)],[48])).
% 23.53/23.69 tff(50,plain,
% 23.53/23.69 (host(W0!8) = host(Z!6)),
% 23.53/23.69 inference(and_elim,[status(thm)],[48])).
% 23.53/23.69 tff(51,plain,
% 23.53/23.69 (setIn(X0!7, alive)),
% 23.53/23.69 inference(and_elim,[status(thm)],[48])).
% 23.53/23.69 tff(52,plain,
% 23.53/23.69 (setIn(Z!6, alive)),
% 23.53/23.69 inference(and_elim,[status(thm)],[48])).
% 23.53/23.69 tff(53,plain,
% 23.53/23.69 (~(host(X0!7) = host(Z!6))),
% 23.53/23.69 inference(and_elim,[status(thm)],[48])).
% 23.53/23.69 tff(54,plain,
% 23.53/23.69 (elem(m_Down(W0!8), queue(host(X0!7)))),
% 23.53/23.69 inference(and_elim,[status(thm)],[38])).
% 23.53/23.69 tff(55,plain,
% 23.53/23.69 (^[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)))))),
% 23.53/23.69 inference(bind,[status(th)],[])).
% 23.53/23.69 tff(56,plain,
% 23.53/23.69 (![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))))),
% 23.53/23.69 inference(quant_intro,[status(thm)],[55])).
% 23.53/23.69 tff(57,plain,
% 23.53/23.69 (^[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))))))),
% 23.53/23.69 inference(bind,[status(th)],[])).
% 23.53/23.69 tff(58,plain,
% 23.53/23.69 (![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))))),
% 23.53/23.69 inference(quant_intro,[status(thm)],[57])).
% 23.53/23.69 tff(59,plain,
% 23.53/23.69 (![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)))))),
% 23.53/23.69 inference(and_elim,[status(thm)],[15])).
% 23.53/23.69 tff(60,plain,
% 23.53/23.69 (![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))))),
% 23.53/23.69 inference(modus_ponens,[status(thm)],[59, 58])).
% 23.53/23.69 tff(61,plain,
% 23.53/23.69 (![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))))),
% 23.53/23.69 inference(modus_ponens,[status(thm)],[60, 56])).
% 23.53/23.69 tff(62,plain,
% 23.53/23.69 (((~![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!7) = host(Z!6)) | (~setIn(Z!6, alive)) | (~setIn(X0!7, alive)) | (~(host(W0!8) = host(Z!6))) | (~(host(Y0!9) = host(X0!7))) | (~elem(m_Down(Y0!9), queue(host(Z!6)))) | (~elem(m_Down(W0!8), queue(host(X0!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!7) = host(Z!6)) | (~setIn(Z!6, alive)) | (~setIn(X0!7, alive)) | (~(host(W0!8) = host(Z!6))) | (~(host(Y0!9) = host(X0!7))) | (~elem(m_Down(Y0!9), queue(host(Z!6)))) | (~elem(m_Down(W0!8), queue(host(X0!7)))))),
% 23.53/23.69 inference(rewrite,[status(thm)],[])).
% 23.53/23.69 tff(63,plain,
% 23.53/23.69 (((~(host(Y0!9) = host(X0!7))) | (~setIn(X0!7, alive)) | (host(X0!7) = host(Z!6)) | (~elem(m_Down(Y0!9), queue(host(Z!6)))) | (~elem(m_Down(W0!8), queue(host(X0!7)))) | (~setIn(Z!6, alive)) | (~(host(W0!8) = host(Z!6)))) <=> ((host(X0!7) = host(Z!6)) | (~setIn(Z!6, alive)) | (~setIn(X0!7, alive)) | (~(host(W0!8) = host(Z!6))) | (~(host(Y0!9) = host(X0!7))) | (~elem(m_Down(Y0!9), queue(host(Z!6)))) | (~elem(m_Down(W0!8), queue(host(X0!7)))))),
% 23.53/23.70 inference(rewrite,[status(thm)],[])).
% 23.53/23.70 tff(64,plain,
% 23.53/23.70 (((~![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!9) = host(X0!7))) | (~setIn(X0!7, alive)) | (host(X0!7) = host(Z!6)) | (~elem(m_Down(Y0!9), queue(host(Z!6)))) | (~elem(m_Down(W0!8), queue(host(X0!7)))) | (~setIn(Z!6, alive)) | (~(host(W0!8) = host(Z!6))))) <=> ((~![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!7) = host(Z!6)) | (~setIn(Z!6, alive)) | (~setIn(X0!7, alive)) | (~(host(W0!8) = host(Z!6))) | (~(host(Y0!9) = host(X0!7))) | (~elem(m_Down(Y0!9), queue(host(Z!6)))) | (~elem(m_Down(W0!8), queue(host(X0!7))))))),
% 23.53/23.70 inference(monotonicity,[status(thm)],[63])).
% 23.53/23.70 tff(65,plain,
% 23.53/23.70 (((~![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!9) = host(X0!7))) | (~setIn(X0!7, alive)) | (host(X0!7) = host(Z!6)) | (~elem(m_Down(Y0!9), queue(host(Z!6)))) | (~elem(m_Down(W0!8), queue(host(X0!7)))) | (~setIn(Z!6, alive)) | (~(host(W0!8) = host(Z!6))))) <=> ((~![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!7) = host(Z!6)) | (~setIn(Z!6, alive)) | (~setIn(X0!7, alive)) | (~(host(W0!8) = host(Z!6))) | (~(host(Y0!9) = host(X0!7))) | (~elem(m_Down(Y0!9), queue(host(Z!6)))) | (~elem(m_Down(W0!8), queue(host(X0!7)))))),
% 23.53/23.70 inference(transitivity,[status(thm)],[64, 62])).
% 23.53/23.70 tff(66,plain,
% 23.53/23.70 ((~![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!9) = host(X0!7))) | (~setIn(X0!7, alive)) | (host(X0!7) = host(Z!6)) | (~elem(m_Down(Y0!9), queue(host(Z!6)))) | (~elem(m_Down(W0!8), queue(host(X0!7)))) | (~setIn(Z!6, alive)) | (~(host(W0!8) = host(Z!6))))),
% 23.53/23.70 inference(quant_inst,[status(thm)],[])).
% 23.53/23.70 tff(67,plain,
% 23.53/23.70 ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))) | (host(X0!7) = host(Z!6)) | (~setIn(Z!6, alive)) | (~setIn(X0!7, alive)) | (~(host(W0!8) = host(Z!6))) | (~(host(Y0!9) = host(X0!7))) | (~elem(m_Down(Y0!9), queue(host(Z!6)))) | (~elem(m_Down(W0!8), queue(host(X0!7))))),
% 23.53/23.70 inference(modus_ponens,[status(thm)],[66, 65])).
% 23.53/23.70 tff(68,plain,
% 23.53/23.70 ($false),
% 23.53/23.70 inference(unit_resolution,[status(thm)],[67, 61, 54, 53, 52, 51, 50, 49, 47])).
% 23.53/23.70 % SZS output end Proof
% 23.53/23.71 % E exiting
%------------------------------------------------------------------------------