%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV455+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:34:05 AM UTC 2025
% Result : Theorem 14.12s 14.33s
% Output : Proof 14.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV455+1 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.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 09:51:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 14.12/14.33 % SZS status Theorem
% 14.12/14.33 % SZS output start Proof
% 14.12/14.33 tff(host_type, type, (
% 14.12/14.33 host: $i > $i)).
% 14.12/14.33 tff(tptp_fun_X0_8_type, type, (
% 14.12/14.33 tptp_fun_X0_8: $i)).
% 14.12/14.33 tff(tptp_fun_Z_7_type, type, (
% 14.12/14.33 tptp_fun_Z_7: $i)).
% 14.12/14.33 tff(tptp_fun_Y0_10_type, type, (
% 14.12/14.33 tptp_fun_Y0_10: $i)).
% 14.12/14.33 tff(tptp_fun_W0_9_type, type, (
% 14.12/14.33 tptp_fun_W0_9: $i)).
% 14.12/14.33 tff(setIn_type, type, (
% 14.12/14.33 setIn: ( $i * $i ) > $o)).
% 14.12/14.33 tff(alive_type, type, (
% 14.12/14.33 alive: $i)).
% 14.12/14.33 tff(elem_type, type, (
% 14.12/14.33 elem: ( $i * $i ) > $o)).
% 14.12/14.33 tff(queue_type, type, (
% 14.12/14.33 queue: $i > $i)).
% 14.12/14.33 tff(m_Down_type, type, (
% 14.12/14.33 m_Down: $i > $i)).
% 14.12/14.33 tff(tptp_fun_V_5_type, type, (
% 14.12/14.33 tptp_fun_V_5: $i)).
% 14.12/14.33 tff(tptp_fun_X_4_type, type, (
% 14.12/14.33 tptp_fun_X_4: $i)).
% 14.12/14.33 tff(cons_type, type, (
% 14.12/14.33 cons: ( $i * $i ) > $i)).
% 14.12/14.33 tff(tptp_fun_Y_3_type, type, (
% 14.12/14.33 tptp_fun_Y_3: $i)).
% 14.12/14.33 tff(leq_type, type, (
% 14.12/14.33 leq: ( $i * $i ) > $o)).
% 14.12/14.33 tff(m_Ack_type, type, (
% 14.12/14.33 m_Ack: ( $i * $i ) > $i)).
% 14.12/14.33 tff(m_Halt_type, type, (
% 14.12/14.33 m_Halt: $i > $i)).
% 14.12/14.33 tff(elec_1_type, type, (
% 14.12/14.33 elec_1: $i)).
% 14.12/14.33 tff(index_type, type, (
% 14.12/14.33 index: ( $i * $i ) > $i)).
% 14.12/14.33 tff(status_type, type, (
% 14.12/14.33 status: $i)).
% 14.12/14.33 tff(tptp_fun_Z_6_type, type, (
% 14.12/14.33 tptp_fun_Z_6: $i)).
% 14.12/14.33 tff(s_type, type, (
% 14.12/14.33 s: $i > $i)).
% 14.12/14.33 tff(zero_type, type, (
% 14.12/14.33 zero: $i)).
% 14.12/14.33 tff(down_type, type, (
% 14.12/14.33 down: $i)).
% 14.12/14.33 tff(norm_type, type, (
% 14.12/14.33 norm: $i)).
% 14.12/14.33 tff(ldr_type, type, (
% 14.12/14.33 ldr: $i)).
% 14.12/14.33 tff(elid_type, type, (
% 14.12/14.33 elid: $i)).
% 14.12/14.33 tff(wait_type, type, (
% 14.12/14.33 wait: $i)).
% 14.12/14.33 tff(1,plain,
% 14.12/14.33 ((host(Z!7) = host(X0!8)) <=> (host(X0!8) = host(Z!7))),
% 14.12/14.33 inference(commutativity,[status(thm)],[])).
% 14.12/14.33 tff(2,plain,
% 14.12/14.33 ((host(X0!8) = host(Z!7)) <=> (host(Z!7) = host(X0!8))),
% 14.12/14.33 inference(symmetry,[status(thm)],[1])).
% 14.12/14.33 tff(3,plain,
% 14.12/14.33 ((~(host(X0!8) = host(Z!7))) <=> (~(host(Z!7) = host(X0!8)))),
% 14.12/14.33 inference(monotonicity,[status(thm)],[2])).
% 14.12/14.33 tff(4,plain,
% 14.12/14.33 (((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~((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!6 = host(Y!3)) | setIn(Z!6, index(down, host(X!4))) | (~((~leq(host(X!4), Z!6)) & leq(s(zero), Z!6))))) | (~(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))) & ((~(host(X!4) = host(Z!7))) & (host(X!4) = host(X0!8)) & (~((~(elem(m_Down(W0!9), V!5) & elem(m_Down(Y0!10), queue(host(Z!7))))) | (~((~(host(X0!8) = host(Z!7))) & setIn(Z!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(Z!7)) & (host(Y0!10) = host(X0!8)))))))) <=> ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~((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!6 = host(Y!3)) | setIn(Z!6, index(down, host(X!4))) | (~((~leq(host(X!4), Z!6)) & leq(s(zero), Z!6))))) | (~(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)) & (~(host(X!4) = host(Z!7))) & (host(X!4) = host(X0!8)) & (~((~(elem(m_Down(W0!9), V!5) & elem(m_Down(Y0!10), queue(host(Z!7))))) | (~((~(host(X0!8) = host(Z!7))) & setIn(Z!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(Z!7)) & (host(Y0!10) = host(X0!8)))))))),
% 14.12/14.33 inference(rewrite,[status(thm)],[])).
% 14.12/14.33 tff(5,plain,
% 14.12/14.33 (((~(host(X!4) = host(Z!7))) & ((host(X!4) = host(X0!8)) & (~((~(elem(m_Down(W0!9), V!5) & elem(m_Down(Y0!10), queue(host(Z!7))))) | (~((~(host(X0!8) = host(Z!7))) & setIn(Z!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(Z!7)) & (host(Y0!10) = host(X0!8)))))))) <=> ((~(host(X!4) = host(Z!7))) & (host(X!4) = host(X0!8)) & (~((~(elem(m_Down(W0!9), V!5) & elem(m_Down(Y0!10), queue(host(Z!7))))) | (~((~(host(X0!8) = host(Z!7))) & setIn(Z!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(Z!7)) & (host(Y0!10) = host(X0!8)))))))),
% 14.12/14.33 inference(rewrite,[status(thm)],[])).
% 14.12/14.33 tff(6,plain,
% 14.12/14.33 ((![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)))),
% 14.12/14.33 inference(rewrite,[status(thm)],[])).
% 14.12/14.33 tff(7,plain,
% 14.12/14.33 (((~((Z!6 = host(Y!3)) | setIn(Z!6, index(down, host(X!4))) | (~((~leq(host(X!4), Z!6)) & leq(s(zero), Z!6))))) | (~(index(status, host(X!4)) = elec_1))) <=> ((~((Z!6 = host(Y!3)) | setIn(Z!6, index(down, host(X!4))) | (~((~leq(host(X!4), Z!6)) & leq(s(zero), Z!6))))) | (~(index(status, host(X!4)) = elec_1)))),
% 14.12/14.33 inference(rewrite,[status(thm)],[])).
% 14.12/14.33 tff(8,plain,
% 14.12/14.33 ((~((Z!6 = host(Y!3)) | setIn(Z!6, index(down, host(X!4))) | (~((~leq(host(X!4), Z!6)) & leq(s(zero), Z!6))))) <=> (~((Z!6 = host(Y!3)) | setIn(Z!6, index(down, host(X!4))) | (~((~leq(host(X!4), Z!6)) & leq(s(zero), Z!6)))))),
% 14.12/14.33 inference(rewrite,[status(thm)],[])).
% 14.12/14.33 tff(9,plain,
% 14.12/14.33 (((~((Z!6 = host(Y!3)) | setIn(Z!6, index(down, host(X!4))) | (~((~leq(host(X!4), Z!6)) & leq(s(zero), Z!6))))) | (~(index(status, host(X!4)) = elec_1))) <=> ((~((Z!6 = host(Y!3)) | setIn(Z!6, index(down, host(X!4))) | (~((~leq(host(X!4), Z!6)) & leq(s(zero), Z!6))))) | (~(index(status, host(X!4)) = elec_1)))),
% 14.12/14.33 inference(monotonicity,[status(thm)],[8])).
% 14.12/14.33 tff(10,plain,
% 14.12/14.33 (((~((Z!6 = host(Y!3)) | setIn(Z!6, index(down, host(X!4))) | (~((~leq(host(X!4), Z!6)) & leq(s(zero), Z!6))))) | (~(index(status, host(X!4)) = elec_1))) <=> ((~((Z!6 = host(Y!3)) | setIn(Z!6, index(down, host(X!4))) | (~((~leq(host(X!4), Z!6)) & leq(s(zero), Z!6))))) | (~(index(status, host(X!4)) = elec_1)))),
% 14.12/14.33 inference(transitivity,[status(thm)],[9, 7])).
% 14.12/14.33 tff(11,plain,
% 14.12/14.33 (((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~((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!6 = host(Y!3)) | setIn(Z!6, index(down, host(X!4))) | (~((~leq(host(X!4), Z!6)) & leq(s(zero), Z!6))))) | (~(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))) & ((~(host(X!4) = host(Z!7))) & ((host(X!4) = host(X0!8)) & (~((~(elem(m_Down(W0!9), V!5) & elem(m_Down(Y0!10), queue(host(Z!7))))) | (~((~(host(X0!8) = host(Z!7))) & setIn(Z!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(Z!7)) & (host(Y0!10) = host(X0!8))))))))) <=> ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~((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!6 = host(Y!3)) | setIn(Z!6, index(down, host(X!4))) | (~((~leq(host(X!4), Z!6)) & leq(s(zero), Z!6))))) | (~(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))) & ((~(host(X!4) = host(Z!7))) & (host(X!4) = host(X0!8)) & (~((~(elem(m_Down(W0!9), V!5) & elem(m_Down(Y0!10), queue(host(Z!7))))) | (~((~(host(X0!8) = host(Z!7))) & setIn(Z!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(Z!7)) & (host(Y0!10) = host(X0!8))))))))),
% 14.12/14.34 inference(monotonicity,[status(thm)],[10, 6, 5])).
% 14.12/14.34 tff(12,plain,
% 14.12/14.34 (((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~((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!6 = host(Y!3)) | setIn(Z!6, index(down, host(X!4))) | (~((~leq(host(X!4), Z!6)) & leq(s(zero), Z!6))))) | (~(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))) & ((~(host(X!4) = host(Z!7))) & ((host(X!4) = host(X0!8)) & (~((~(elem(m_Down(W0!9), V!5) & elem(m_Down(Y0!10), queue(host(Z!7))))) | (~((~(host(X0!8) = host(Z!7))) & setIn(Z!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(Z!7)) & (host(Y0!10) = host(X0!8))))))))) <=> ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~((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!6 = host(Y!3)) | setIn(Z!6, index(down, host(X!4))) | (~((~leq(host(X!4), Z!6)) & leq(s(zero), Z!6))))) | (~(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)) & (~(host(X!4) = host(Z!7))) & (host(X!4) = host(X0!8)) & (~((~(elem(m_Down(W0!9), V!5) & elem(m_Down(Y0!10), queue(host(Z!7))))) | (~((~(host(X0!8) = host(Z!7))) & setIn(Z!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(Z!7)) & (host(Y0!10) = host(X0!8)))))))),
% 14.12/14.34 inference(transitivity,[status(thm)],[11, 4])).
% 14.12/14.34 tff(13,plain,
% 14.12/14.34 ((~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((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] : ((host(X) = host(Z)) | ![W0: $i, X0: $i] : ((~(host(X) = host(X0))) | ![Y0: $i] : ((~(elem(m_Down(W0), V) & elem(m_Down(Y0), queue(host(Z))))) | (~((~(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)) | ((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] : ((host(X) = host(Z)) | ![W0: $i, X0: $i] : ((~(host(X) = host(X0))) | ![Y0: $i] : ((~(elem(m_Down(W0), V) & elem(m_Down(Y0), queue(host(Z))))) | (~((~(host(X0) = host(Z))) & setIn(Z, alive) & setIn(X0, alive) & (host(W0) = host(Z)) & (host(Y0) = host(X0)))))))))),
% 14.12/14.34 inference(rewrite,[status(thm)],[])).
% 14.12/14.34 tff(14,plain,
% 14.12/14.34 ((~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((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] : ((host(X) = host(Z)) | ![W0: $i, X0: $i] : ((~(host(X) = host(X0))) | ![Y0: $i] : ((~(elem(m_Down(W0), V) & elem(m_Down(Y0), queue(host(Z))))) | (~((~(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)) | ((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] : ((host(X) = host(Z)) | ![W0: $i, X0: $i] : ((~(host(X) = host(X0))) | ![Y0: $i] : ((~(elem(m_Down(W0), V) & elem(m_Down(Y0), queue(host(Z))))) | (~((~(host(X0) = host(Z))) & setIn(Z, alive) & setIn(X0, alive) & (host(W0) = host(Z)) & (host(Y0) = host(X0)))))))))),
% 14.12/14.34 inference(rewrite,[status(thm)],[])).
% 14.12/14.34 tff(15,plain,
% 14.12/14.34 ((~![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))) => ![Z: $i] : ((~(host(X) = host(Z))) => ![W0: $i, X0: $i] : ((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(W0), V) & elem(m_Down(Y0), queue(host(Z)))))))))))))) <=> (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((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] : ((host(X) = host(Z)) | ![W0: $i, X0: $i] : ((~(host(X) = host(X0))) | ![Y0: $i] : ((~(elem(m_Down(W0), V) & elem(m_Down(Y0), queue(host(Z))))) | (~((~(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))))))),
% 14.12/14.34 inference(rewrite,[status(thm)],[])).
% 14.12/14.34 tff(16,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))) => ![Z: $i] : ((~(host(X) = host(Z))) => ![W0: $i, X0: $i] : ((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(W0), V) & elem(m_Down(Y0), queue(host(Z)))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj')).
% 14.12/14.34 tff(17,plain,
% 14.12/14.34 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((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] : ((host(X) = host(Z)) | ![W0: $i, X0: $i] : ((~(host(X) = host(X0))) | ![Y0: $i] : ((~(elem(m_Down(W0), V) & elem(m_Down(Y0), queue(host(Z))))) | (~((~(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)))))),
% 14.12/14.34 inference(modus_ponens,[status(thm)],[16, 15])).
% 14.12/14.34 tff(18,plain,
% 14.12/14.34 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((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] : ((host(X) = host(Z)) | ![W0: $i, X0: $i] : ((~(host(X) = host(X0))) | ![Y0: $i] : ((~(elem(m_Down(W0), V) & elem(m_Down(Y0), queue(host(Z))))) | (~((~(host(X0) = host(Z))) & setIn(Z, alive) & setIn(X0, alive) & (host(W0) = host(Z)) & (host(Y0) = host(X0))))))))),
% 14.12/14.34 inference(modus_ponens,[status(thm)],[17, 14])).
% 14.12/14.34 tff(19,plain,
% 14.12/14.34 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((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] : ((host(X) = host(Z)) | ![W0: $i, X0: $i] : ((~(host(X) = host(X0))) | ![Y0: $i] : ((~(elem(m_Down(W0), V) & elem(m_Down(Y0), queue(host(Z))))) | (~((~(host(X0) = host(Z))) & setIn(Z, alive) & setIn(X0, alive) & (host(W0) = host(Z)) & (host(Y0) = host(X0))))))))),
% 14.12/14.34 inference(modus_ponens,[status(thm)],[18, 13])).
% 14.20/14.34 tff(20,plain,
% 14.20/14.34 (~![V: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | ((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] : ((host(X) = host(Z)) | ![W0: $i, X0: $i] : ((~(host(X) = host(X0))) | ![Y0: $i] : ((~(elem(m_Down(W0), V) & elem(m_Down(Y0), queue(host(Z))))) | (~((~(host(X0) = host(Z))) & setIn(Z, alive) & setIn(X0, alive) & (host(W0) = host(Z)) & (host(Y0) = host(X0))))))))),
% 14.20/14.34 inference(modus_ponens,[status(thm)],[19, 13])).
% 14.20/14.34 tff(21,plain,
% 14.20/14.34 ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~((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!6 = host(Y!3)) | setIn(Z!6, index(down, host(X!4))) | (~((~leq(host(X!4), Z!6)) & leq(s(zero), Z!6))))) | (~(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)) & (~(host(X!4) = host(Z!7))) & (host(X!4) = host(X0!8)) & (~((~(elem(m_Down(W0!9), V!5) & elem(m_Down(Y0!10), queue(host(Z!7))))) | (~((~(host(X0!8) = host(Z!7))) & setIn(Z!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(Z!7)) & (host(Y0!10) = host(X0!8))))))),
% 14.20/14.34 inference(modus_ponens,[status(thm)],[20, 12])).
% 14.20/14.34 tff(22,plain,
% 14.20/14.34 (~((~(elem(m_Down(W0!9), V!5) & elem(m_Down(Y0!10), queue(host(Z!7))))) | (~((~(host(X0!8) = host(Z!7))) & setIn(Z!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(Z!7)) & (host(Y0!10) = host(X0!8)))))),
% 14.20/14.34 inference(and_elim,[status(thm)],[21])).
% 14.20/14.34 tff(23,plain,
% 14.20/14.34 ((~(host(X0!8) = host(Z!7))) & setIn(Z!7, alive) & setIn(X0!8, alive) & (host(W0!9) = host(Z!7)) & (host(Y0!10) = host(X0!8))),
% 14.20/14.34 inference(or_elim,[status(thm)],[22])).
% 14.20/14.34 tff(24,plain,
% 14.20/14.34 (~(host(X0!8) = host(Z!7))),
% 14.20/14.34 inference(and_elim,[status(thm)],[23])).
% 14.20/14.34 tff(25,plain,
% 14.20/14.34 (~(host(Z!7) = host(X0!8))),
% 14.20/14.34 inference(modus_ponens,[status(thm)],[24, 3])).
% 14.20/14.34 tff(26,plain,
% 14.20/14.34 (host(X!4) = host(X0!8)),
% 14.20/14.34 inference(and_elim,[status(thm)],[21])).
% 14.20/14.34 tff(27,plain,
% 14.20/14.34 (host(X0!8) = host(X!4)),
% 14.20/14.34 inference(symmetry,[status(thm)],[26])).
% 14.20/14.34 tff(28,plain,
% 14.20/14.34 (queue(host(X0!8)) = queue(host(X!4))),
% 14.20/14.34 inference(monotonicity,[status(thm)],[27])).
% 14.20/14.34 tff(29,plain,
% 14.20/14.34 (elem(m_Down(W0!9), queue(host(X0!8))) <=> elem(m_Down(W0!9), queue(host(X!4)))),
% 14.20/14.34 inference(monotonicity,[status(thm)],[28])).
% 14.20/14.34 tff(30,plain,
% 14.20/14.34 (elem(m_Down(W0!9), queue(host(X!4))) <=> elem(m_Down(W0!9), queue(host(X0!8)))),
% 14.20/14.34 inference(symmetry,[status(thm)],[29])).
% 14.20/14.34 tff(31,plain,
% 14.20/14.34 (queue(host(X!4)) = cons(m_Down(Y!3), V!5)),
% 14.20/14.34 inference(and_elim,[status(thm)],[21])).
% 14.20/14.34 tff(32,plain,
% 14.20/14.34 (cons(m_Down(Y!3), V!5) = queue(host(X!4))),
% 14.20/14.34 inference(symmetry,[status(thm)],[31])).
% 14.20/14.34 tff(33,plain,
% 14.20/14.34 (elem(m_Down(W0!9), cons(m_Down(Y!3), V!5)) <=> elem(m_Down(W0!9), queue(host(X!4)))),
% 14.20/14.34 inference(monotonicity,[status(thm)],[32])).
% 14.20/14.34 tff(34,plain,
% 14.20/14.34 (elem(m_Down(W0!9), queue(host(X!4))) <=> elem(m_Down(W0!9), cons(m_Down(Y!3), V!5))),
% 14.20/14.34 inference(symmetry,[status(thm)],[33])).
% 14.20/14.34 tff(35,plain,
% 14.20/14.34 ((~elem(m_Down(W0!9), queue(host(X!4)))) <=> (~elem(m_Down(W0!9), cons(m_Down(Y!3), V!5)))),
% 14.20/14.34 inference(monotonicity,[status(thm)],[34])).
% 14.20/14.34 tff(36,assumption,(~elem(m_Down(W0!9), queue(host(X!4)))), introduced(assumption)).
% 14.20/14.34 tff(37,plain,
% 14.20/14.34 (~elem(m_Down(W0!9), cons(m_Down(Y!3), V!5))),
% 14.20/14.34 inference(modus_ponens,[status(thm)],[36, 35])).
% 14.20/14.34 tff(38,plain,
% 14.20/14.34 (^[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))))),
% 14.20/14.34 inference(bind,[status(th)],[])).
% 14.20/14.34 tff(39,plain,
% 14.20/14.34 (![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)))),
% 14.20/14.34 inference(quant_intro,[status(thm)],[38])).
% 14.20/14.34 tff(40,plain,
% 14.20/14.34 (![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)))),
% 14.20/14.34 inference(rewrite,[status(thm)],[])).
% 14.20/14.34 tff(41,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')).
% 14.20/14.34 tff(42,plain,
% 14.20/14.34 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 14.20/14.34 inference(modus_ponens,[status(thm)],[41, 40])).
% 14.20/14.34 tff(43,plain,(
% 14.20/14.34 ![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 14.20/14.34 inference(skolemize,[status(sab)],[42])).
% 14.20/14.34 tff(44,plain,
% 14.20/14.34 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 14.20/14.34 inference(modus_ponens,[status(thm)],[43, 39])).
% 14.20/14.34 tff(45,plain,
% 14.20/14.34 ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(W0!9), cons(m_Down(Y!3), V!5)) <=> ((m_Down(W0!9) = m_Down(Y!3)) | elem(m_Down(W0!9), V!5)))),
% 14.20/14.34 inference(quant_inst,[status(thm)],[])).
% 14.20/14.34 tff(46,plain,
% 14.20/14.34 (elem(m_Down(W0!9), cons(m_Down(Y!3), V!5)) <=> ((m_Down(W0!9) = m_Down(Y!3)) | elem(m_Down(W0!9), V!5))),
% 14.20/14.34 inference(unit_resolution,[status(thm)],[45, 44])).
% 14.20/14.34 tff(47,plain,
% 14.20/14.34 (elem(m_Down(W0!9), V!5) & elem(m_Down(Y0!10), queue(host(Z!7)))),
% 14.20/14.34 inference(or_elim,[status(thm)],[22])).
% 14.20/14.34 tff(48,plain,
% 14.20/14.34 (elem(m_Down(W0!9), V!5)),
% 14.20/14.34 inference(and_elim,[status(thm)],[47])).
% 14.20/14.34 tff(49,plain,
% 14.20/14.34 (((m_Down(W0!9) = m_Down(Y!3)) | elem(m_Down(W0!9), V!5)) | (~elem(m_Down(W0!9), V!5))),
% 14.20/14.34 inference(tautology,[status(thm)],[])).
% 14.20/14.34 tff(50,plain,
% 14.20/14.34 ((m_Down(W0!9) = m_Down(Y!3)) | elem(m_Down(W0!9), V!5)),
% 14.20/14.34 inference(unit_resolution,[status(thm)],[49, 48])).
% 14.20/14.34 tff(51,plain,
% 14.20/14.34 ((~(elem(m_Down(W0!9), cons(m_Down(Y!3), V!5)) <=> ((m_Down(W0!9) = m_Down(Y!3)) | elem(m_Down(W0!9), V!5)))) | elem(m_Down(W0!9), cons(m_Down(Y!3), V!5)) | (~((m_Down(W0!9) = m_Down(Y!3)) | elem(m_Down(W0!9), V!5)))),
% 14.20/14.34 inference(tautology,[status(thm)],[])).
% 14.20/14.34 tff(52,plain,
% 14.20/14.34 ((~(elem(m_Down(W0!9), cons(m_Down(Y!3), V!5)) <=> ((m_Down(W0!9) = m_Down(Y!3)) | elem(m_Down(W0!9), V!5)))) | elem(m_Down(W0!9), cons(m_Down(Y!3), V!5))),
% 14.20/14.34 inference(unit_resolution,[status(thm)],[51, 50])).
% 14.20/14.35 tff(53,plain,
% 14.20/14.35 (elem(m_Down(W0!9), cons(m_Down(Y!3), V!5))),
% 14.20/14.35 inference(unit_resolution,[status(thm)],[52, 46])).
% 14.20/14.35 tff(54,plain,
% 14.20/14.35 ($false),
% 14.20/14.35 inference(unit_resolution,[status(thm)],[53, 37])).
% 14.20/14.35 tff(55,plain,(elem(m_Down(W0!9), queue(host(X!4)))), inference(lemma,lemma(discharge,[]))).
% 14.20/14.35 tff(56,plain,
% 14.20/14.35 (elem(m_Down(W0!9), queue(host(X0!8)))),
% 14.20/14.35 inference(modus_ponens,[status(thm)],[55, 30])).
% 14.20/14.35 tff(57,plain,
% 14.20/14.35 (host(Y0!10) = host(X0!8)),
% 14.20/14.35 inference(and_elim,[status(thm)],[23])).
% 14.20/14.35 tff(58,plain,
% 14.20/14.35 (host(W0!9) = host(Z!7)),
% 14.20/14.35 inference(and_elim,[status(thm)],[23])).
% 14.20/14.35 tff(59,plain,
% 14.20/14.35 (setIn(X0!8, alive)),
% 14.20/14.35 inference(and_elim,[status(thm)],[23])).
% 14.20/14.35 tff(60,plain,
% 14.20/14.35 (setIn(Z!7, alive)),
% 14.20/14.35 inference(and_elim,[status(thm)],[23])).
% 14.20/14.35 tff(61,plain,
% 14.20/14.35 (elem(m_Down(Y0!10), queue(host(Z!7)))),
% 14.20/14.35 inference(and_elim,[status(thm)],[47])).
% 14.20/14.35 tff(62,plain,
% 14.20/14.35 (^[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)))))),
% 14.20/14.35 inference(bind,[status(th)],[])).
% 14.20/14.35 tff(63,plain,
% 14.20/14.35 (![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))))),
% 14.20/14.35 inference(quant_intro,[status(thm)],[62])).
% 14.20/14.35 tff(64,plain,
% 14.20/14.35 (^[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))))))),
% 14.20/14.35 inference(bind,[status(th)],[])).
% 14.20/14.35 tff(65,plain,
% 14.20/14.35 (![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))))),
% 14.20/14.35 inference(quant_intro,[status(thm)],[64])).
% 14.20/14.35 tff(66,plain,
% 14.20/14.35 (![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)))))),
% 14.20/14.35 inference(and_elim,[status(thm)],[21])).
% 14.20/14.35 tff(67,plain,
% 14.20/14.35 (![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))))),
% 14.20/14.35 inference(modus_ponens,[status(thm)],[66, 65])).
% 14.20/14.35 tff(68,plain,
% 14.20/14.35 (![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))))),
% 14.20/14.35 inference(modus_ponens,[status(thm)],[67, 63])).
% 14.20/14.35 tff(69,plain,
% 14.20/14.35 (((~![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))))) | ((~setIn(X0!8, alive)) | (~setIn(Z!7, alive)) | (~(host(W0!9) = host(Z!7))) | (~(host(Y0!10) = host(X0!8))) | (~elem(m_Down(W0!9), queue(host(X0!8)))) | (~elem(m_Down(Y0!10), queue(host(Z!7)))) | (host(Z!7) = host(X0!8)))) <=> ((~![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))))) | (~setIn(X0!8, alive)) | (~setIn(Z!7, alive)) | (~(host(W0!9) = host(Z!7))) | (~(host(Y0!10) = host(X0!8))) | (~elem(m_Down(W0!9), queue(host(X0!8)))) | (~elem(m_Down(Y0!10), queue(host(Z!7)))) | (host(Z!7) = host(X0!8)))),
% 14.20/14.35 inference(rewrite,[status(thm)],[])).
% 14.20/14.35 tff(70,plain,
% 14.20/14.35 (((~(host(W0!9) = host(Z!7))) | (~setIn(Z!7, alive)) | (host(Z!7) = host(X0!8)) | (~elem(m_Down(W0!9), queue(host(X0!8)))) | (~elem(m_Down(Y0!10), queue(host(Z!7)))) | (~setIn(X0!8, alive)) | (~(host(Y0!10) = host(X0!8)))) <=> ((~setIn(X0!8, alive)) | (~setIn(Z!7, alive)) | (~(host(W0!9) = host(Z!7))) | (~(host(Y0!10) = host(X0!8))) | (~elem(m_Down(W0!9), queue(host(X0!8)))) | (~elem(m_Down(Y0!10), queue(host(Z!7)))) | (host(Z!7) = host(X0!8)))),
% 14.20/14.37 inference(rewrite,[status(thm)],[])).
% 14.20/14.37 tff(71,plain,
% 14.20/14.37 (((~![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(W0!9) = host(Z!7))) | (~setIn(Z!7, alive)) | (host(Z!7) = host(X0!8)) | (~elem(m_Down(W0!9), queue(host(X0!8)))) | (~elem(m_Down(Y0!10), queue(host(Z!7)))) | (~setIn(X0!8, alive)) | (~(host(Y0!10) = host(X0!8))))) <=> ((~![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))))) | ((~setIn(X0!8, alive)) | (~setIn(Z!7, alive)) | (~(host(W0!9) = host(Z!7))) | (~(host(Y0!10) = host(X0!8))) | (~elem(m_Down(W0!9), queue(host(X0!8)))) | (~elem(m_Down(Y0!10), queue(host(Z!7)))) | (host(Z!7) = host(X0!8))))),
% 14.20/14.37 inference(monotonicity,[status(thm)],[70])).
% 14.20/14.37 tff(72,plain,
% 14.20/14.37 (((~![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(W0!9) = host(Z!7))) | (~setIn(Z!7, alive)) | (host(Z!7) = host(X0!8)) | (~elem(m_Down(W0!9), queue(host(X0!8)))) | (~elem(m_Down(Y0!10), queue(host(Z!7)))) | (~setIn(X0!8, alive)) | (~(host(Y0!10) = host(X0!8))))) <=> ((~![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))))) | (~setIn(X0!8, alive)) | (~setIn(Z!7, alive)) | (~(host(W0!9) = host(Z!7))) | (~(host(Y0!10) = host(X0!8))) | (~elem(m_Down(W0!9), queue(host(X0!8)))) | (~elem(m_Down(Y0!10), queue(host(Z!7)))) | (host(Z!7) = host(X0!8)))),
% 14.20/14.37 inference(transitivity,[status(thm)],[71, 69])).
% 14.20/14.37 tff(73,plain,
% 14.20/14.37 ((~![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(W0!9) = host(Z!7))) | (~setIn(Z!7, alive)) | (host(Z!7) = host(X0!8)) | (~elem(m_Down(W0!9), queue(host(X0!8)))) | (~elem(m_Down(Y0!10), queue(host(Z!7)))) | (~setIn(X0!8, alive)) | (~(host(Y0!10) = host(X0!8))))),
% 14.20/14.37 inference(quant_inst,[status(thm)],[])).
% 14.20/14.37 tff(74,plain,
% 14.20/14.37 ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))) | (~setIn(X0!8, alive)) | (~setIn(Z!7, alive)) | (~(host(W0!9) = host(Z!7))) | (~(host(Y0!10) = host(X0!8))) | (~elem(m_Down(W0!9), queue(host(X0!8)))) | (~elem(m_Down(Y0!10), queue(host(Z!7)))) | (host(Z!7) = host(X0!8))),
% 14.20/14.37 inference(modus_ponens,[status(thm)],[73, 72])).
% 14.20/14.37 tff(75,plain,
% 14.20/14.37 ($false),
% 14.20/14.37 inference(unit_resolution,[status(thm)],[74, 68, 61, 60, 59, 58, 57, 56, 25])).
% 14.20/14.37 % SZS output end Proof
% 14.20/14.37 % E exiting
%------------------------------------------------------------------------------