%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV451+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:34:05 AM UTC 2025
% Result : Theorem 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV451+1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 09:51:54 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 tff(host_type, type, (
% 0.21/0.40 host: $i > $i)).
% 0.21/0.40 tff(tptp_fun_Z_6_type, type, (
% 0.21/0.40 tptp_fun_Z_6: $i)).
% 0.21/0.40 tff(tptp_fun_Y_3_type, type, (
% 0.21/0.40 tptp_fun_Y_3: $i)).
% 0.21/0.40 tff(tptp_fun_W_4_type, type, (
% 0.21/0.40 tptp_fun_W_4: $i)).
% 0.21/0.40 tff(setIn_type, type, (
% 0.21/0.40 setIn: ( $i * $i ) > $o)).
% 0.21/0.40 tff(alive_type, type, (
% 0.21/0.40 alive: $i)).
% 0.21/0.40 tff(tptp_fun_Y0_7_type, type, (
% 0.21/0.40 tptp_fun_Y0_7: $i)).
% 0.21/0.40 tff(s_type, type, (
% 0.21/0.40 s: $i > $i)).
% 0.21/0.40 tff(tptp_fun_Z0_9_type, type, (
% 0.21/0.40 tptp_fun_Z0_9: $i)).
% 0.21/0.40 tff(tptp_fun_X0_8_type, type, (
% 0.21/0.40 tptp_fun_X0_8: $i)).
% 0.21/0.40 tff(elem_type, type, (
% 0.21/0.40 elem: ( $i * $i ) > $o)).
% 0.21/0.40 tff(snoc_type, type, (
% 0.21/0.40 snoc: ( $i * $i ) > $i)).
% 0.21/0.40 tff(m_Halt_type, type, (
% 0.21/0.40 m_Halt: $i > $i)).
% 0.21/0.40 tff(queue_type, type, (
% 0.21/0.40 queue: $i > $i)).
% 0.21/0.40 tff(m_Down_type, type, (
% 0.21/0.40 m_Down: $i > $i)).
% 0.21/0.40 tff(tptp_fun_V_5_type, type, (
% 0.21/0.40 tptp_fun_V_5: $i)).
% 0.21/0.40 tff(cons_type, type, (
% 0.21/0.40 cons: ( $i * $i ) > $i)).
% 0.21/0.40 tff(m_NotNorm_type, type, (
% 0.21/0.40 m_NotNorm: $i > $i)).
% 0.21/0.40 tff(index_type, type, (
% 0.21/0.40 index: ( $i * $i ) > $i)).
% 0.21/0.40 tff(elid_type, type, (
% 0.21/0.40 elid: $i)).
% 0.21/0.40 tff(leq_type, type, (
% 0.21/0.40 leq: ( $i * $i ) > $o)).
% 0.21/0.40 tff(nbr_proc_type, type, (
% 0.21/0.40 nbr_proc: $i)).
% 0.21/0.40 tff(zero_type, type, (
% 0.21/0.40 zero: $i)).
% 0.21/0.40 tff(norm_type, type, (
% 0.21/0.40 norm: $i)).
% 0.21/0.40 tff(status_type, type, (
% 0.21/0.40 status: $i)).
% 0.21/0.40 tff(ldr_type, type, (
% 0.21/0.40 ldr: $i)).
% 0.21/0.40 tff(m_Ack_type, type, (
% 0.21/0.40 m_Ack: ( $i * $i ) > $i)).
% 0.21/0.40 tff(pids_type, type, (
% 0.21/0.40 pids: $i)).
% 0.21/0.40 tff(1,plain,
% 0.21/0.40 ((host(Z!6) = host(Y!3)) <=> (host(Y!3) = host(Z!6))),
% 0.21/0.40 inference(commutativity,[status(thm)],[])).
% 0.21/0.40 tff(2,plain,
% 0.21/0.40 (((~setIn(W!4, pids)) & setIn(Y!3, alive) & (host(Y!3) = host(W!4)) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z)))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & (index(ldr, host(Y!3)) = host(Y!3)) & (index(status, host(Y!3)) = norm) & ![Z: $i] : ((~(host(Y!3) = host(Z))) | leq(Z, W!4)) & (host(W!4) = s(zero)) & (~leq(nbr_proc, host(W!4))) & (queue(host(Y!3)) = cons(m_NotNorm(index(elid, host(Y!3))), V!5)) & ((~(host(Y!3) = host(Z!6))) & (s(host(W!4)) = host(Z!6)) & (host(Y!3) = host(Y0!7)) & (~((~(elem(m_Down(X0!8), V!5) & elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4))))) | (~(((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) & (((~(Y0!7 = Y!3)) & setIn(Y0!7, alive)) | (Y0!7 = W!4)) & (~(host(Y0!7) = host(Z!6))) & (host(X0!8) = host(Z!6)) & (host(Z0!9) = host(Y0!7)))))) & (~(s(host(W!4)) = host(Y0!7))))) <=> ((~setIn(W!4, pids)) & setIn(Y!3, alive) & (host(Y!3) = host(W!4)) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z)))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & (index(ldr, host(Y!3)) = host(Y!3)) & (index(status, host(Y!3)) = norm) & ![Z: $i] : ((~(host(Y!3) = host(Z))) | leq(Z, W!4)) & (host(W!4) = s(zero)) & (~leq(nbr_proc, host(W!4))) & (queue(host(Y!3)) = cons(m_NotNorm(index(elid, host(Y!3))), V!5)) & (~(host(Y!3) = host(Z!6))) & (s(host(W!4)) = host(Z!6)) & (host(Y!3) = host(Y0!7)) & (~((~(elem(m_Down(X0!8), V!5) & elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4))))) | (~(((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) & (((~(Y0!7 = Y!3)) & setIn(Y0!7, alive)) | (Y0!7 = W!4)) & (~(host(Y0!7) = host(Z!6))) & (host(X0!8) = host(Z!6)) & (host(Z0!9) = host(Y0!7)))))) & (~(s(host(W!4)) = host(Y0!7))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(3,plain,
% 0.21/0.41 (((~(host(Y!3) = host(Z!6))) & (s(host(W!4)) = host(Z!6)) & ((host(Y!3) = host(Y0!7)) & (~((~(elem(m_Down(X0!8), V!5) & elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4))))) | (~(((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) & (((~(Y0!7 = Y!3)) & setIn(Y0!7, alive)) | (Y0!7 = W!4)) & (~(host(Y0!7) = host(Z!6))) & (host(X0!8) = host(Z!6)) & (host(Z0!9) = host(Y0!7)))))) & (~(s(host(W!4)) = host(Y0!7))))) <=> ((~(host(Y!3) = host(Z!6))) & (s(host(W!4)) = host(Z!6)) & (host(Y!3) = host(Y0!7)) & (~((~(elem(m_Down(X0!8), V!5) & elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4))))) | (~(((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) & (((~(Y0!7 = Y!3)) & setIn(Y0!7, alive)) | (Y0!7 = W!4)) & (~(host(Y0!7) = host(Z!6))) & (host(X0!8) = host(Z!6)) & (host(Z0!9) = host(Y0!7)))))) & (~(s(host(W!4)) = host(Y0!7))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(4,plain,
% 0.21/0.41 ((((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) & (((~(Y0!7 = Y!3)) & setIn(Y0!7, alive)) | (Y0!7 = W!4)) & (~(host(Y0!7) = host(Z!6))) & (host(X0!8) = host(Z!6)) & (host(Z0!9) = host(Y0!7))) <=> (((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) & (((~(Y0!7 = Y!3)) & setIn(Y0!7, alive)) | (Y0!7 = W!4)) & (~(host(Y0!7) = host(Z!6))) & (host(X0!8) = host(Z!6)) & (host(Z0!9) = host(Y0!7)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(5,plain,
% 0.21/0.41 ((~(((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) & (((~(Y0!7 = Y!3)) & setIn(Y0!7, alive)) | (Y0!7 = W!4)) & (~(host(Y0!7) = host(Z!6))) & (host(X0!8) = host(Z!6)) & (host(Z0!9) = host(Y0!7)))) <=> (~(((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) & (((~(Y0!7 = Y!3)) & setIn(Y0!7, alive)) | (Y0!7 = W!4)) & (~(host(Y0!7) = host(Z!6))) & (host(X0!8) = host(Z!6)) & (host(Z0!9) = host(Y0!7))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[4])).
% 0.21/0.41 tff(6,plain,
% 0.21/0.41 (((~(elem(m_Down(X0!8), V!5) & elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4))))) | (~(((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) & (((~(Y0!7 = Y!3)) & setIn(Y0!7, alive)) | (Y0!7 = W!4)) & (~(host(Y0!7) = host(Z!6))) & (host(X0!8) = host(Z!6)) & (host(Z0!9) = host(Y0!7))))) <=> ((~(elem(m_Down(X0!8), V!5) & elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4))))) | (~(((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) & (((~(Y0!7 = Y!3)) & setIn(Y0!7, alive)) | (Y0!7 = W!4)) & (~(host(Y0!7) = host(Z!6))) & (host(X0!8) = host(Z!6)) & (host(Z0!9) = host(Y0!7)))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[5])).
% 0.21/0.41 tff(7,plain,
% 0.21/0.41 ((~((~(elem(m_Down(X0!8), V!5) & elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4))))) | (~(((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) & (((~(Y0!7 = Y!3)) & setIn(Y0!7, alive)) | (Y0!7 = W!4)) & (~(host(Y0!7) = host(Z!6))) & (host(X0!8) = host(Z!6)) & (host(Z0!9) = host(Y0!7)))))) <=> (~((~(elem(m_Down(X0!8), V!5) & elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4))))) | (~(((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) & (((~(Y0!7 = Y!3)) & setIn(Y0!7, alive)) | (Y0!7 = W!4)) & (~(host(Y0!7) = host(Z!6))) & (host(X0!8) = host(Z!6)) & (host(Z0!9) = host(Y0!7))))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[6])).
% 0.21/0.41 tff(8,plain,
% 0.21/0.41 (((host(Y!3) = host(Y0!7)) & (~((~(elem(m_Down(X0!8), V!5) & elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4))))) | (~(((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) & (((~(Y0!7 = Y!3)) & setIn(Y0!7, alive)) | (Y0!7 = W!4)) & (~(host(Y0!7) = host(Z!6))) & (host(X0!8) = host(Z!6)) & (host(Z0!9) = host(Y0!7)))))) & (~(s(host(W!4)) = host(Y0!7)))) <=> ((host(Y!3) = host(Y0!7)) & (~((~(elem(m_Down(X0!8), V!5) & elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4))))) | (~(((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) & (((~(Y0!7 = Y!3)) & setIn(Y0!7, alive)) | (Y0!7 = W!4)) & (~(host(Y0!7) = host(Z!6))) & (host(X0!8) = host(Z!6)) & (host(Z0!9) = host(Y0!7)))))) & (~(s(host(W!4)) = host(Y0!7))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[7])).
% 0.21/0.41 tff(9,plain,
% 0.21/0.41 (((~(host(Y!3) = host(Z!6))) & (s(host(W!4)) = host(Z!6)) & ((host(Y!3) = host(Y0!7)) & (~((~(elem(m_Down(X0!8), V!5) & elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4))))) | (~(((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) & (((~(Y0!7 = Y!3)) & setIn(Y0!7, alive)) | (Y0!7 = W!4)) & (~(host(Y0!7) = host(Z!6))) & (host(X0!8) = host(Z!6)) & (host(Z0!9) = host(Y0!7)))))) & (~(s(host(W!4)) = host(Y0!7))))) <=> ((~(host(Y!3) = host(Z!6))) & (s(host(W!4)) = host(Z!6)) & ((host(Y!3) = host(Y0!7)) & (~((~(elem(m_Down(X0!8), V!5) & elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4))))) | (~(((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) & (((~(Y0!7 = Y!3)) & setIn(Y0!7, alive)) | (Y0!7 = W!4)) & (~(host(Y0!7) = host(Z!6))) & (host(X0!8) = host(Z!6)) & (host(Z0!9) = host(Y0!7)))))) & (~(s(host(W!4)) = host(Y0!7)))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[8])).
% 0.21/0.41 tff(10,plain,
% 0.21/0.41 (((~(host(Y!3) = host(Z!6))) & (s(host(W!4)) = host(Z!6)) & ((host(Y!3) = host(Y0!7)) & (~((~(elem(m_Down(X0!8), V!5) & elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4))))) | (~(((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) & (((~(Y0!7 = Y!3)) & setIn(Y0!7, alive)) | (Y0!7 = W!4)) & (~(host(Y0!7) = host(Z!6))) & (host(X0!8) = host(Z!6)) & (host(Z0!9) = host(Y0!7)))))) & (~(s(host(W!4)) = host(Y0!7))))) <=> ((~(host(Y!3) = host(Z!6))) & (s(host(W!4)) = host(Z!6)) & (host(Y!3) = host(Y0!7)) & (~((~(elem(m_Down(X0!8), V!5) & elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4))))) | (~(((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) & (((~(Y0!7 = Y!3)) & setIn(Y0!7, alive)) | (Y0!7 = W!4)) & (~(host(Y0!7) = host(Z!6))) & (host(X0!8) = host(Z!6)) & (host(Z0!9) = host(Y0!7)))))) & (~(s(host(W!4)) = host(Y0!7))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[9, 3])).
% 0.21/0.41 tff(11,plain,
% 0.21/0.41 (((~setIn(W!4, pids)) & setIn(Y!3, alive) & (host(Y!3) = host(W!4)) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z)))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & (index(ldr, host(Y!3)) = host(Y!3)) & (index(status, host(Y!3)) = norm) & ![Z: $i] : ((~(host(Y!3) = host(Z))) | leq(Z, W!4)) & (host(W!4) = s(zero)) & (~leq(nbr_proc, host(W!4))) & (queue(host(Y!3)) = cons(m_NotNorm(index(elid, host(Y!3))), V!5)) & ((~(host(Y!3) = host(Z!6))) & (s(host(W!4)) = host(Z!6)) & ((host(Y!3) = host(Y0!7)) & (~((~(elem(m_Down(X0!8), V!5) & elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4))))) | (~(((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) & (((~(Y0!7 = Y!3)) & setIn(Y0!7, alive)) | (Y0!7 = W!4)) & (~(host(Y0!7) = host(Z!6))) & (host(X0!8) = host(Z!6)) & (host(Z0!9) = host(Y0!7)))))) & (~(s(host(W!4)) = host(Y0!7)))))) <=> ((~setIn(W!4, pids)) & setIn(Y!3, alive) & (host(Y!3) = host(W!4)) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z)))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & (index(ldr, host(Y!3)) = host(Y!3)) & (index(status, host(Y!3)) = norm) & ![Z: $i] : ((~(host(Y!3) = host(Z))) | leq(Z, W!4)) & (host(W!4) = s(zero)) & (~leq(nbr_proc, host(W!4))) & (queue(host(Y!3)) = cons(m_NotNorm(index(elid, host(Y!3))), V!5)) & ((~(host(Y!3) = host(Z!6))) & (s(host(W!4)) = host(Z!6)) & (host(Y!3) = host(Y0!7)) & (~((~(elem(m_Down(X0!8), V!5) & elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4))))) | (~(((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) & (((~(Y0!7 = Y!3)) & setIn(Y0!7, alive)) | (Y0!7 = W!4)) & (~(host(Y0!7) = host(Z!6))) & (host(X0!8) = host(Z!6)) & (host(Z0!9) = host(Y0!7)))))) & (~(s(host(W!4)) = host(Y0!7)))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[10])).
% 0.21/0.42 tff(12,plain,
% 0.21/0.42 (((~setIn(W!4, pids)) & setIn(Y!3, alive) & (host(Y!3) = host(W!4)) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z)))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & (index(ldr, host(Y!3)) = host(Y!3)) & (index(status, host(Y!3)) = norm) & ![Z: $i] : ((~(host(Y!3) = host(Z))) | leq(Z, W!4)) & (host(W!4) = s(zero)) & (~leq(nbr_proc, host(W!4))) & (queue(host(Y!3)) = cons(m_NotNorm(index(elid, host(Y!3))), V!5)) & ((~(host(Y!3) = host(Z!6))) & (s(host(W!4)) = host(Z!6)) & ((host(Y!3) = host(Y0!7)) & (~((~(elem(m_Down(X0!8), V!5) & elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4))))) | (~(((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) & (((~(Y0!7 = Y!3)) & setIn(Y0!7, alive)) | (Y0!7 = W!4)) & (~(host(Y0!7) = host(Z!6))) & (host(X0!8) = host(Z!6)) & (host(Z0!9) = host(Y0!7)))))) & (~(s(host(W!4)) = host(Y0!7)))))) <=> ((~setIn(W!4, pids)) & setIn(Y!3, alive) & (host(Y!3) = host(W!4)) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z)))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & (index(ldr, host(Y!3)) = host(Y!3)) & (index(status, host(Y!3)) = norm) & ![Z: $i] : ((~(host(Y!3) = host(Z))) | leq(Z, W!4)) & (host(W!4) = s(zero)) & (~leq(nbr_proc, host(W!4))) & (queue(host(Y!3)) = cons(m_NotNorm(index(elid, host(Y!3))), V!5)) & (~(host(Y!3) = host(Z!6))) & (s(host(W!4)) = host(Z!6)) & (host(Y!3) = host(Y0!7)) & (~((~(elem(m_Down(X0!8), V!5) & elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4))))) | (~(((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) & (((~(Y0!7 = Y!3)) & setIn(Y0!7, alive)) | (Y0!7 = W!4)) & (~(host(Y0!7) = host(Z!6))) & (host(X0!8) = host(Z!6)) & (host(Z0!9) = host(Y0!7)))))) & (~(s(host(W!4)) = host(Y0!7))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[11, 2])).
% 0.21/0.42 tff(13,plain,
% 0.21/0.42 ((~![V: $i, W: $i, Y: $i] : (setIn(W, pids) | (~setIn(Y, alive)) | (~(host(Y) = host(W))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive)))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z))))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z)))))) | (~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20)))))) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~![Z: $i] : ((~(host(Y) = host(Z))) | leq(Z, W))) | (~(host(W) = s(zero))) | leq(nbr_proc, host(W)) | (~(queue(host(Y)) = cons(m_NotNorm(index(elid, host(Y))), V))) | ![Z: $i] : ((host(Y) = host(Z)) | (~(s(host(W)) = host(Z))) | ![X0: $i, Y0: $i] : ((~(host(Y) = host(Y0))) | ![Z0: $i] : ((~(elem(m_Down(X0), V) & elem(m_Down(Z0), snoc(queue(host(Z)), m_Halt(W))))) | (~(((Z = W) | ((~(Z = Y)) & setIn(Z, alive))) & (((~(Y0 = Y)) & setIn(Y0, alive)) | (Y0 = W)) & (~(host(Y0) = host(Z))) & (host(X0) = host(Z)) & (host(Z0) = host(Y0))))) | (s(host(W)) = host(Y0)))))) <=> (~![V: $i, W: $i, Y: $i] : (setIn(W, pids) | (~setIn(Y, alive)) | (~(host(Y) = host(W))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive)))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z))))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z)))))) | (~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20)))))) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~![Z: $i] : ((~(host(Y) = host(Z))) | leq(Z, W))) | (~(host(W) = s(zero))) | leq(nbr_proc, host(W)) | (~(queue(host(Y)) = cons(m_NotNorm(index(elid, host(Y))), V))) | ![Z: $i] : ((host(Y) = host(Z)) | (~(s(host(W)) = host(Z))) | ![X0: $i, Y0: $i] : ((~(host(Y) = host(Y0))) | ![Z0: $i] : ((~(elem(m_Down(X0), V) & elem(m_Down(Z0), snoc(queue(host(Z)), m_Halt(W))))) | (~(((Z = W) | ((~(Z = Y)) & setIn(Z, alive))) & (((~(Y0 = Y)) & setIn(Y0, alive)) | (Y0 = W)) & (~(host(Y0) = host(Z))) & (host(X0) = host(Z)) & (host(Z0) = host(Y0))))) | (s(host(W)) = host(Y0))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(14,plain,
% 0.21/0.42 ((~![V: $i, W: $i, X: $i, Y: $i] : (((((((((![Z: $i, Pid0: $i] : (setIn(Pid0, alive) => (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : (elem(m_Down(Pid0), queue(host(Z))) => (~setIn(Pid0, alive)))) & ![Z: $i, Pid0: $i] : (elem(m_Down(Pid0), queue(host(Z))) => (~(host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : (elem(m_Halt(Pid0), queue(host(Z))) => (~leq(host(Z), host(Pid0))))) & ![Z: $i, Pid20: $i, Pid0: $i] : (elem(m_Ack(Pid0, Z), queue(host(Pid20))) => (~leq(host(Z), host(Pid0))))) & ![Z: $i, Pid0: $i] : ((((~setIn(Z, alive)) & leq(Pid0, Z)) & (host(Pid0) = host(Z))) => (~setIn(Pid0, alive)))) & ![Z: $i, Pid0: $i] : (((~(Pid0 = Z)) & (host(Pid0) = host(Z))) => ((~setIn(Z, alive)) | (~setIn(Pid0, alive))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((((((~(host(Pid20) = host(Z))) & setIn(Z, alive)) & setIn(Pid20, alive)) & (host(Pid30) = host(Z))) & (host(Pid0) = host(Pid20))) => (~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))))) & (queue(host(Y)) = cons(m_NotNorm(X), V))) => (setIn(Y, alive) => ((((index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm)) & (index(elid, host(Y)) = X)) => (((![Z: $i] : ((host(Y) = host(Z)) => leq(Z, W)) & (~setIn(W, pids))) & (host(Y) = host(W))) => ((host(W) = s(zero)) => ((~leq(nbr_proc, host(W))) => ![Z: $i] : ((s(host(W)) = host(Z)) => ((~(host(Y) = host(Z))) => ![X0: $i, Y0: $i] : ((~(s(host(W)) = host(Y0))) => ((host(Y) = host(Y0)) => ![Z0: $i] : ((((((((~(Z = Y)) & setIn(Z, alive)) | (Z = W)) & (((~(Y0 = Y)) & setIn(Y0, alive)) | (Y0 = W))) & (~(host(Y0) = host(Z)))) & (host(X0) = host(Z))) & (host(Z0) = host(Y0))) => (~(elem(m_Down(X0), V) & elem(m_Down(Z0), snoc(queue(host(Z)), m_Halt(W))))))))))))))))) <=> (~![V: $i, W: $i, Y: $i] : (setIn(W, pids) | (~setIn(Y, alive)) | (~(host(Y) = host(W))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive)))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z))))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z)))))) | (~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20)))))) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~![Z: $i] : ((~(host(Y) = host(Z))) | leq(Z, W))) | (~(host(W) = s(zero))) | leq(nbr_proc, host(W)) | (~(queue(host(Y)) = cons(m_NotNorm(index(elid, host(Y))), V))) | ![Z: $i] : ((host(Y) = host(Z)) | (~(s(host(W)) = host(Z))) | ![X0: $i, Y0: $i] : ((~(host(Y) = host(Y0))) | ![Z0: $i] : ((~(elem(m_Down(X0), V) & elem(m_Down(Z0), snoc(queue(host(Z)), m_Halt(W))))) | (~(((Z = W) | ((~(Z = Y)) & setIn(Z, alive))) & (((~(Y0 = Y)) & setIn(Y0, alive)) | (Y0 = W)) & (~(host(Y0) = host(Z))) & (host(X0) = host(Z)) & (host(Z0) = host(Y0))))) | (s(host(W)) = host(Y0))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(15,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(Y)) = cons(m_NotNorm(X), V))) => (setIn(Y, alive) => ((((index(ldr, host(Y)) = host(Y)) & (index(status, host(Y)) = norm)) & (index(elid, host(Y)) = X)) => (((![Z: $i] : ((host(Y) = host(Z)) => leq(Z, W)) & (~setIn(W, pids))) & (host(Y) = host(W))) => ((host(W) = s(zero)) => ((~leq(nbr_proc, host(W))) => ![Z: $i] : ((s(host(W)) = host(Z)) => ((~(host(Y) = host(Z))) => ![X0: $i, Y0: $i] : ((~(s(host(W)) = host(Y0))) => ((host(Y) = host(Y0)) => ![Z0: $i] : ((((((((~(Z = Y)) & setIn(Z, alive)) | (Z = W)) & (((~(Y0 = Y)) & setIn(Y0, alive)) | (Y0 = W))) & (~(host(Y0) = host(Z)))) & (host(X0) = host(Z))) & (host(Z0) = host(Y0))) => (~(elem(m_Down(X0), V) & elem(m_Down(Z0), snoc(queue(host(Z)), m_Halt(W))))))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj')).
% 0.21/0.43 tff(16,plain,
% 0.21/0.43 (~![V: $i, W: $i, Y: $i] : (setIn(W, pids) | (~setIn(Y, alive)) | (~(host(Y) = host(W))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive)))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z))))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z)))))) | (~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20)))))) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~![Z: $i] : ((~(host(Y) = host(Z))) | leq(Z, W))) | (~(host(W) = s(zero))) | leq(nbr_proc, host(W)) | (~(queue(host(Y)) = cons(m_NotNorm(index(elid, host(Y))), V))) | ![Z: $i] : ((host(Y) = host(Z)) | (~(s(host(W)) = host(Z))) | ![X0: $i, Y0: $i] : ((~(host(Y) = host(Y0))) | ![Z0: $i] : ((~(elem(m_Down(X0), V) & elem(m_Down(Z0), snoc(queue(host(Z)), m_Halt(W))))) | (~(((Z = W) | ((~(Z = Y)) & setIn(Z, alive))) & (((~(Y0 = Y)) & setIn(Y0, alive)) | (Y0 = W)) & (~(host(Y0) = host(Z))) & (host(X0) = host(Z)) & (host(Z0) = host(Y0))))) | (s(host(W)) = host(Y0)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.21/0.43 tff(17,plain,
% 0.21/0.43 (~![V: $i, W: $i, Y: $i] : (setIn(W, pids) | (~setIn(Y, alive)) | (~(host(Y) = host(W))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive)))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z))))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z)))))) | (~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20)))))) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~![Z: $i] : ((~(host(Y) = host(Z))) | leq(Z, W))) | (~(host(W) = s(zero))) | leq(nbr_proc, host(W)) | (~(queue(host(Y)) = cons(m_NotNorm(index(elid, host(Y))), V))) | ![Z: $i] : ((host(Y) = host(Z)) | (~(s(host(W)) = host(Z))) | ![X0: $i, Y0: $i] : ((~(host(Y) = host(Y0))) | ![Z0: $i] : ((~(elem(m_Down(X0), V) & elem(m_Down(Z0), snoc(queue(host(Z)), m_Halt(W))))) | (~(((Z = W) | ((~(Z = Y)) & setIn(Z, alive))) & (((~(Y0 = Y)) & setIn(Y0, alive)) | (Y0 = W)) & (~(host(Y0) = host(Z))) & (host(X0) = host(Z)) & (host(Z0) = host(Y0))))) | (s(host(W)) = host(Y0)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.21/0.43 tff(18,plain,
% 0.21/0.43 (~![V: $i, W: $i, Y: $i] : (setIn(W, pids) | (~setIn(Y, alive)) | (~(host(Y) = host(W))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive)))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z))))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z)))))) | (~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20)))))) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~![Z: $i] : ((~(host(Y) = host(Z))) | leq(Z, W))) | (~(host(W) = s(zero))) | leq(nbr_proc, host(W)) | (~(queue(host(Y)) = cons(m_NotNorm(index(elid, host(Y))), V))) | ![Z: $i] : ((host(Y) = host(Z)) | (~(s(host(W)) = host(Z))) | ![X0: $i, Y0: $i] : ((~(host(Y) = host(Y0))) | ![Z0: $i] : ((~(elem(m_Down(X0), V) & elem(m_Down(Z0), snoc(queue(host(Z)), m_Halt(W))))) | (~(((Z = W) | ((~(Z = Y)) & setIn(Z, alive))) & (((~(Y0 = Y)) & setIn(Y0, alive)) | (Y0 = W)) & (~(host(Y0) = host(Z))) & (host(X0) = host(Z)) & (host(Z0) = host(Y0))))) | (s(host(W)) = host(Y0)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.21/0.43 tff(19,plain,
% 0.21/0.43 (~![V: $i, W: $i, Y: $i] : (setIn(W, pids) | (~setIn(Y, alive)) | (~(host(Y) = host(W))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive)))) | (~![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z))))) | (~![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z)))))) | (~![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z)))))) | (~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z)))))) | (~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20)))))) | (~(index(ldr, host(Y)) = host(Y))) | (~(index(status, host(Y)) = norm)) | (~![Z: $i] : ((~(host(Y) = host(Z))) | leq(Z, W))) | (~(host(W) = s(zero))) | leq(nbr_proc, host(W)) | (~(queue(host(Y)) = cons(m_NotNorm(index(elid, host(Y))), V))) | ![Z: $i] : ((host(Y) = host(Z)) | (~(s(host(W)) = host(Z))) | ![X0: $i, Y0: $i] : ((~(host(Y) = host(Y0))) | ![Z0: $i] : ((~(elem(m_Down(X0), V) & elem(m_Down(Z0), snoc(queue(host(Z)), m_Halt(W))))) | (~(((Z = W) | ((~(Z = Y)) & setIn(Z, alive))) & (((~(Y0 = Y)) & setIn(Y0, alive)) | (Y0 = W)) & (~(host(Y0) = host(Z))) & (host(X0) = host(Z)) & (host(Z0) = host(Y0))))) | (s(host(W)) = host(Y0)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.21/0.43 tff(20,plain,
% 0.21/0.43 ((~setIn(W!4, pids)) & setIn(Y!3, alive) & (host(Y!3) = host(W!4)) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z)))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & (index(ldr, host(Y!3)) = host(Y!3)) & (index(status, host(Y!3)) = norm) & ![Z: $i] : ((~(host(Y!3) = host(Z))) | leq(Z, W!4)) & (host(W!4) = s(zero)) & (~leq(nbr_proc, host(W!4))) & (queue(host(Y!3)) = cons(m_NotNorm(index(elid, host(Y!3))), V!5)) & (~(host(Y!3) = host(Z!6))) & (s(host(W!4)) = host(Z!6)) & (host(Y!3) = host(Y0!7)) & (~((~(elem(m_Down(X0!8), V!5) & elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4))))) | (~(((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) & (((~(Y0!7 = Y!3)) & setIn(Y0!7, alive)) | (Y0!7 = W!4)) & (~(host(Y0!7) = host(Z!6))) & (host(X0!8) = host(Z!6)) & (host(Z0!9) = host(Y0!7)))))) & (~(s(host(W!4)) = host(Y0!7)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.21/0.43 tff(21,plain,
% 0.21/0.43 (host(Y!3) = host(W!4)),
% 0.21/0.43 inference(and_elim,[status(thm)],[20])).
% 0.21/0.43 tff(22,plain,
% 0.21/0.43 (host(W!4) = host(Y!3)),
% 0.21/0.43 inference(symmetry,[status(thm)],[21])).
% 0.21/0.43 tff(23,plain,
% 0.21/0.43 ((host(Z!6) = host(W!4)) <=> (host(Z!6) = host(Y!3))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[22])).
% 0.21/0.43 tff(24,plain,
% 0.21/0.43 ((host(Z!6) = host(W!4)) <=> (host(Y!3) = host(Z!6))),
% 0.21/0.43 inference(transitivity,[status(thm)],[23, 1])).
% 0.21/0.43 tff(25,plain,
% 0.21/0.43 ((host(Y!3) = host(Z!6)) <=> (host(Z!6) = host(W!4))),
% 0.21/0.43 inference(symmetry,[status(thm)],[24])).
% 0.21/0.43 tff(26,plain,
% 0.21/0.43 ((~(host(Y!3) = host(Z!6))) <=> (~(host(Z!6) = host(W!4)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[25])).
% 0.21/0.43 tff(27,plain,
% 0.21/0.43 (~(host(Y!3) = host(Z!6))),
% 0.21/0.43 inference(and_elim,[status(thm)],[20])).
% 0.21/0.43 tff(28,plain,
% 0.21/0.43 (~(host(Z!6) = host(W!4))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.21/0.43 tff(29,plain,
% 0.21/0.43 (^[X: $i, Y: $i, Q: $i] : refl((elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))) <=> (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(30,plain,
% 0.21/0.43 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))) <=> ![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[29])).
% 0.21/0.43 tff(31,plain,
% 0.21/0.43 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q))) <=> ![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(32,axiom,(![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV011+0.ax','axiom_47')).
% 0.21/0.44 tff(33,plain,
% 0.21/0.44 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.21/0.44 tff(34,plain,(
% 0.21/0.44 ![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[33])).
% 0.21/0.44 tff(35,plain,
% 0.21/0.44 (![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.21/0.44 tff(36,plain,
% 0.21/0.44 ((~![X: $i, Y: $i, Q: $i] : (elem(X, snoc(Q, Y)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4))) <=> ((m_Down(Z0!9) = m_Halt(W!4)) | elem(m_Down(Z0!9), queue(host(Z!6)))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(37,plain,
% 0.21/0.44 (elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4))) <=> ((m_Down(Z0!9) = m_Halt(W!4)) | elem(m_Down(Z0!9), queue(host(Z!6))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.21/0.44 tff(38,plain,
% 0.21/0.44 (~((~(elem(m_Down(X0!8), V!5) & elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4))))) | (~(((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) & (((~(Y0!7 = Y!3)) & setIn(Y0!7, alive)) | (Y0!7 = W!4)) & (~(host(Y0!7) = host(Z!6))) & (host(X0!8) = host(Z!6)) & (host(Z0!9) = host(Y0!7)))))),
% 0.21/0.44 inference(and_elim,[status(thm)],[20])).
% 0.21/0.44 tff(39,plain,
% 0.21/0.44 (elem(m_Down(X0!8), V!5) & elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4)))),
% 0.21/0.44 inference(or_elim,[status(thm)],[38])).
% 0.21/0.44 tff(40,plain,
% 0.21/0.44 (elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4)))),
% 0.21/0.44 inference(and_elim,[status(thm)],[39])).
% 0.21/0.44 tff(41,plain,
% 0.21/0.44 ((~(elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4))) <=> ((m_Down(Z0!9) = m_Halt(W!4)) | elem(m_Down(Z0!9), queue(host(Z!6)))))) | (~elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4)))) | ((m_Down(Z0!9) = m_Halt(W!4)) | elem(m_Down(Z0!9), queue(host(Z!6))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(42,plain,
% 0.21/0.44 ((~(elem(m_Down(Z0!9), snoc(queue(host(Z!6)), m_Halt(W!4))) <=> ((m_Down(Z0!9) = m_Halt(W!4)) | elem(m_Down(Z0!9), queue(host(Z!6)))))) | ((m_Down(Z0!9) = m_Halt(W!4)) | elem(m_Down(Z0!9), queue(host(Z!6))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.21/0.44 tff(43,plain,
% 0.21/0.44 ((m_Down(Z0!9) = m_Halt(W!4)) | elem(m_Down(Z0!9), queue(host(Z!6)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[42, 37])).
% 0.21/0.44 tff(44,plain,
% 0.21/0.44 (^[X: $i, Y: $i] : refl((~(m_Down(X) = m_Halt(Y))) <=> (~(m_Down(X) = m_Halt(Y))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(45,plain,
% 0.21/0.44 (![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y))) <=> ![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.44 tff(46,plain,
% 0.21/0.44 (![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y))) <=> ![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(47,axiom,(![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV011+0.ax','axiom_17')).
% 0.21/0.44 tff(48,plain,
% 0.21/0.44 (![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.21/0.44 tff(49,plain,(
% 0.21/0.44 ![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[48])).
% 0.21/0.44 tff(50,plain,
% 0.21/0.44 (![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.21/0.44 tff(51,plain,
% 0.21/0.44 ((~![X: $i, Y: $i] : (~(m_Down(X) = m_Halt(Y)))) | (~(m_Down(Z0!9) = m_Halt(W!4)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(52,plain,
% 0.21/0.44 (~(m_Down(Z0!9) = m_Halt(W!4))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.21/0.44 tff(53,plain,
% 0.21/0.44 ((~((m_Down(Z0!9) = m_Halt(W!4)) | elem(m_Down(Z0!9), queue(host(Z!6))))) | (m_Down(Z0!9) = m_Halt(W!4)) | elem(m_Down(Z0!9), queue(host(Z!6)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(54,plain,
% 0.21/0.44 ((~((m_Down(Z0!9) = m_Halt(W!4)) | elem(m_Down(Z0!9), queue(host(Z!6))))) | elem(m_Down(Z0!9), queue(host(Z!6)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.21/0.44 tff(55,plain,
% 0.21/0.44 (elem(m_Down(Z0!9), queue(host(Z!6)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[54, 43])).
% 0.21/0.44 tff(56,plain,
% 0.21/0.44 (queue(host(W!4)) = queue(host(Y!3))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[22])).
% 0.21/0.44 tff(57,plain,
% 0.21/0.44 (elem(m_Down(X0!8), queue(host(W!4))) <=> elem(m_Down(X0!8), queue(host(Y!3)))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[56])).
% 0.21/0.44 tff(58,plain,
% 0.21/0.44 (elem(m_Down(X0!8), queue(host(Y!3))) <=> elem(m_Down(X0!8), queue(host(W!4)))),
% 0.21/0.44 inference(symmetry,[status(thm)],[57])).
% 0.21/0.44 tff(59,plain,
% 0.21/0.44 (queue(host(Y!3)) = cons(m_NotNorm(index(elid, host(Y!3))), V!5)),
% 0.21/0.44 inference(and_elim,[status(thm)],[20])).
% 0.21/0.44 tff(60,plain,
% 0.21/0.44 (cons(m_NotNorm(index(elid, host(Y!3))), V!5) = queue(host(Y!3))),
% 0.21/0.44 inference(symmetry,[status(thm)],[59])).
% 0.21/0.44 tff(61,plain,
% 0.21/0.44 (elem(m_Down(X0!8), cons(m_NotNorm(index(elid, host(Y!3))), V!5)) <=> elem(m_Down(X0!8), queue(host(Y!3)))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[60])).
% 0.21/0.44 tff(62,plain,
% 0.21/0.44 (elem(m_Down(X0!8), queue(host(Y!3))) <=> elem(m_Down(X0!8), cons(m_NotNorm(index(elid, host(Y!3))), V!5))),
% 0.21/0.44 inference(symmetry,[status(thm)],[61])).
% 0.21/0.44 tff(63,plain,
% 0.21/0.44 ((~elem(m_Down(X0!8), queue(host(Y!3)))) <=> (~elem(m_Down(X0!8), cons(m_NotNorm(index(elid, host(Y!3))), V!5)))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[62])).
% 0.21/0.44 tff(64,assumption,(~elem(m_Down(X0!8), queue(host(Y!3)))), introduced(assumption)).
% 0.21/0.44 tff(65,plain,
% 0.21/0.44 (~elem(m_Down(X0!8), cons(m_NotNorm(index(elid, host(Y!3))), V!5))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.44 tff(66,plain,
% 0.21/0.44 (^[X: $i, Y: $i, Q: $i] : refl((elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q))) <=> (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(67,plain,
% 0.21/0.44 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q))) <=> ![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[66])).
% 0.21/0.44 tff(68,plain,
% 0.21/0.44 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q))) <=> ![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(69,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')).
% 0.21/0.44 tff(70,plain,
% 0.21/0.44 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.21/0.44 tff(71,plain,(
% 0.21/0.44 ![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[70])).
% 0.21/0.44 tff(72,plain,
% 0.21/0.44 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.21/0.44 tff(73,plain,
% 0.21/0.44 (((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(X0!8), cons(m_NotNorm(index(elid, host(Y!3))), V!5)) <=> (elem(m_Down(X0!8), V!5) | (m_Down(X0!8) = m_NotNorm(index(elid, host(Y!3))))))) <=> ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(X0!8), cons(m_NotNorm(index(elid, host(Y!3))), V!5)) <=> (elem(m_Down(X0!8), V!5) | (m_Down(X0!8) = m_NotNorm(index(elid, host(Y!3)))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(74,plain,
% 0.21/0.44 ((elem(m_Down(X0!8), cons(m_NotNorm(index(elid, host(Y!3))), V!5)) <=> ((m_Down(X0!8) = m_NotNorm(index(elid, host(Y!3)))) | elem(m_Down(X0!8), V!5))) <=> (elem(m_Down(X0!8), cons(m_NotNorm(index(elid, host(Y!3))), V!5)) <=> (elem(m_Down(X0!8), V!5) | (m_Down(X0!8) = m_NotNorm(index(elid, host(Y!3))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(75,plain,
% 0.21/0.44 (((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(X0!8), cons(m_NotNorm(index(elid, host(Y!3))), V!5)) <=> ((m_Down(X0!8) = m_NotNorm(index(elid, host(Y!3)))) | elem(m_Down(X0!8), V!5)))) <=> ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(X0!8), cons(m_NotNorm(index(elid, host(Y!3))), V!5)) <=> (elem(m_Down(X0!8), V!5) | (m_Down(X0!8) = m_NotNorm(index(elid, host(Y!3)))))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[74])).
% 0.21/0.44 tff(76,plain,
% 0.21/0.44 (((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(X0!8), cons(m_NotNorm(index(elid, host(Y!3))), V!5)) <=> ((m_Down(X0!8) = m_NotNorm(index(elid, host(Y!3)))) | elem(m_Down(X0!8), V!5)))) <=> ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(X0!8), cons(m_NotNorm(index(elid, host(Y!3))), V!5)) <=> (elem(m_Down(X0!8), V!5) | (m_Down(X0!8) = m_NotNorm(index(elid, host(Y!3)))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[75, 73])).
% 0.21/0.44 tff(77,plain,
% 0.21/0.44 ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(X0!8), cons(m_NotNorm(index(elid, host(Y!3))), V!5)) <=> ((m_Down(X0!8) = m_NotNorm(index(elid, host(Y!3)))) | elem(m_Down(X0!8), V!5)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(78,plain,
% 0.21/0.44 ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(X0!8), cons(m_NotNorm(index(elid, host(Y!3))), V!5)) <=> (elem(m_Down(X0!8), V!5) | (m_Down(X0!8) = m_NotNorm(index(elid, host(Y!3))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.21/0.44 tff(79,plain,
% 0.21/0.44 (elem(m_Down(X0!8), cons(m_NotNorm(index(elid, host(Y!3))), V!5)) <=> (elem(m_Down(X0!8), V!5) | (m_Down(X0!8) = m_NotNorm(index(elid, host(Y!3)))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[78, 72])).
% 0.21/0.44 tff(80,plain,
% 0.21/0.44 (elem(m_Down(X0!8), V!5)),
% 0.21/0.44 inference(and_elim,[status(thm)],[39])).
% 0.21/0.44 tff(81,plain,
% 0.21/0.44 ((elem(m_Down(X0!8), V!5) | (m_Down(X0!8) = m_NotNorm(index(elid, host(Y!3))))) | (~elem(m_Down(X0!8), V!5))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(82,plain,
% 0.21/0.44 (elem(m_Down(X0!8), V!5) | (m_Down(X0!8) = m_NotNorm(index(elid, host(Y!3))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.21/0.44 tff(83,plain,
% 0.21/0.44 ((~(elem(m_Down(X0!8), cons(m_NotNorm(index(elid, host(Y!3))), V!5)) <=> (elem(m_Down(X0!8), V!5) | (m_Down(X0!8) = m_NotNorm(index(elid, host(Y!3))))))) | elem(m_Down(X0!8), cons(m_NotNorm(index(elid, host(Y!3))), V!5)) | (~(elem(m_Down(X0!8), V!5) | (m_Down(X0!8) = m_NotNorm(index(elid, host(Y!3))))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(84,plain,
% 0.21/0.44 ((~(elem(m_Down(X0!8), cons(m_NotNorm(index(elid, host(Y!3))), V!5)) <=> (elem(m_Down(X0!8), V!5) | (m_Down(X0!8) = m_NotNorm(index(elid, host(Y!3))))))) | elem(m_Down(X0!8), cons(m_NotNorm(index(elid, host(Y!3))), V!5))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.21/0.44 tff(85,plain,
% 0.21/0.44 (elem(m_Down(X0!8), cons(m_NotNorm(index(elid, host(Y!3))), V!5))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[84, 79])).
% 0.21/0.44 tff(86,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[85, 65])).
% 0.21/0.44 tff(87,plain,(elem(m_Down(X0!8), queue(host(Y!3)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(88,plain,
% 0.21/0.44 (elem(m_Down(X0!8), queue(host(W!4)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[87, 58])).
% 0.21/0.44 tff(89,plain,
% 0.21/0.44 (host(Y!3) = host(Y0!7)),
% 0.21/0.44 inference(and_elim,[status(thm)],[20])).
% 0.21/0.44 tff(90,plain,
% 0.21/0.44 (host(Y0!7) = host(Y!3)),
% 0.21/0.44 inference(symmetry,[status(thm)],[89])).
% 0.21/0.44 tff(91,plain,
% 0.21/0.44 (((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) & (((~(Y0!7 = Y!3)) & setIn(Y0!7, alive)) | (Y0!7 = W!4)) & (~(host(Y0!7) = host(Z!6))) & (host(X0!8) = host(Z!6)) & (host(Z0!9) = host(Y0!7))),
% 0.21/0.44 inference(or_elim,[status(thm)],[38])).
% 0.21/0.44 tff(92,plain,
% 0.21/0.44 (host(Z0!9) = host(Y0!7)),
% 0.21/0.44 inference(and_elim,[status(thm)],[91])).
% 0.21/0.44 tff(93,plain,
% 0.21/0.44 (host(Z0!9) = host(W!4)),
% 0.21/0.44 inference(transitivity,[status(thm)],[92, 90, 21])).
% 0.21/0.44 tff(94,plain,
% 0.21/0.44 (^[Z: $i] : refl(((~(host(Y!3) = host(Z))) | leq(Z, W!4)) <=> ((~(host(Y!3) = host(Z))) | leq(Z, W!4)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(95,plain,
% 0.21/0.44 (![Z: $i] : ((~(host(Y!3) = host(Z))) | leq(Z, W!4)) <=> ![Z: $i] : ((~(host(Y!3) = host(Z))) | leq(Z, W!4))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[94])).
% 0.21/0.44 tff(96,plain,
% 0.21/0.44 (![Z: $i] : ((~(host(Y!3) = host(Z))) | leq(Z, W!4))),
% 0.21/0.44 inference(and_elim,[status(thm)],[20])).
% 0.21/0.44 tff(97,plain,
% 0.21/0.44 (![Z: $i] : ((~(host(Y!3) = host(Z))) | leq(Z, W!4))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.21/0.44 tff(98,plain,
% 0.21/0.45 (((~![Z: $i] : ((~(host(Y!3) = host(Z))) | leq(Z, W!4))) | leq(Y!3, W!4)) <=> ((~![Z: $i] : ((~(host(Y!3) = host(Z))) | leq(Z, W!4))) | leq(Y!3, W!4))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(99,plain,
% 0.21/0.45 (($false | leq(Y!3, W!4)) <=> leq(Y!3, W!4)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(100,plain,
% 0.21/0.45 ((~$true) <=> $false),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(101,plain,
% 0.21/0.45 ((host(Y!3) = host(Y!3)) <=> $true),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(102,plain,
% 0.21/0.45 ((~(host(Y!3) = host(Y!3))) <=> (~$true)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[101])).
% 0.21/0.45 tff(103,plain,
% 0.21/0.45 ((~(host(Y!3) = host(Y!3))) <=> $false),
% 0.21/0.45 inference(transitivity,[status(thm)],[102, 100])).
% 0.21/0.45 tff(104,plain,
% 0.21/0.45 (((~(host(Y!3) = host(Y!3))) | leq(Y!3, W!4)) <=> ($false | leq(Y!3, W!4))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[103])).
% 0.21/0.45 tff(105,plain,
% 0.21/0.45 (((~(host(Y!3) = host(Y!3))) | leq(Y!3, W!4)) <=> leq(Y!3, W!4)),
% 0.21/0.45 inference(transitivity,[status(thm)],[104, 99])).
% 0.21/0.45 tff(106,plain,
% 0.21/0.45 (((~![Z: $i] : ((~(host(Y!3) = host(Z))) | leq(Z, W!4))) | ((~(host(Y!3) = host(Y!3))) | leq(Y!3, W!4))) <=> ((~![Z: $i] : ((~(host(Y!3) = host(Z))) | leq(Z, W!4))) | leq(Y!3, W!4))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[105])).
% 0.21/0.45 tff(107,plain,
% 0.21/0.45 (((~![Z: $i] : ((~(host(Y!3) = host(Z))) | leq(Z, W!4))) | ((~(host(Y!3) = host(Y!3))) | leq(Y!3, W!4))) <=> ((~![Z: $i] : ((~(host(Y!3) = host(Z))) | leq(Z, W!4))) | leq(Y!3, W!4))),
% 0.21/0.45 inference(transitivity,[status(thm)],[106, 98])).
% 0.21/0.45 tff(108,plain,
% 0.21/0.45 ((~![Z: $i] : ((~(host(Y!3) = host(Z))) | leq(Z, W!4))) | ((~(host(Y!3) = host(Y!3))) | leq(Y!3, W!4))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(109,plain,
% 0.21/0.45 ((~![Z: $i] : ((~(host(Y!3) = host(Z))) | leq(Z, W!4))) | leq(Y!3, W!4)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.21/0.45 tff(110,plain,
% 0.21/0.45 (leq(Y!3, W!4)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[109, 97])).
% 0.21/0.45 tff(111,plain,
% 0.21/0.45 (^[Z: $i, Pid0: $i] : refl(((~setIn(Pid0, alive)) | (~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z))) <=> ((~setIn(Pid0, alive)) | (~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(112,plain,
% 0.21/0.45 (![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z))) <=> ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[111])).
% 0.21/0.45 tff(113,plain,
% 0.21/0.45 (^[Z: $i, Pid0: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z))) <=> (~((~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z))))), ((~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z)))) <=> (~(~((~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z))))))), rewrite((~(~((~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z))))) <=> ((~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z)))), ((~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z)))) <=> ((~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z))))), (((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) <=> ((~setIn(Pid0, alive)) | ((~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z)))))), rewrite(((~setIn(Pid0, alive)) | ((~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z)))) <=> ((~setIn(Pid0, alive)) | (~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z)))), (((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) <=> ((~setIn(Pid0, alive)) | (~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(114,plain,
% 0.21/0.45 (![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) <=> ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[113])).
% 0.21/0.45 tff(115,plain,
% 0.21/0.45 (![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z)))))),
% 0.21/0.45 inference(and_elim,[status(thm)],[20])).
% 0.21/0.45 tff(116,plain,
% 0.21/0.45 (![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.21/0.45 tff(117,plain,
% 0.21/0.45 (![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.21/0.45 tff(118,plain,
% 0.21/0.45 (setIn(Y!3, alive)),
% 0.21/0.45 inference(and_elim,[status(thm)],[20])).
% 0.21/0.45 tff(119,plain,
% 0.21/0.45 (((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z)))) | ((~(host(Y!3) = host(W!4))) | (~setIn(Y!3, alive)) | setIn(W!4, alive) | (~leq(Y!3, W!4)))) <=> ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z)))) | (~(host(Y!3) = host(W!4))) | (~setIn(Y!3, alive)) | setIn(W!4, alive) | (~leq(Y!3, W!4)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(120,plain,
% 0.21/0.45 (((~setIn(Y!3, alive)) | (~(host(Y!3) = host(W!4))) | setIn(W!4, alive) | (~leq(Y!3, W!4))) <=> ((~(host(Y!3) = host(W!4))) | (~setIn(Y!3, alive)) | setIn(W!4, alive) | (~leq(Y!3, W!4)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(121,plain,
% 0.21/0.45 (((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z)))) | ((~setIn(Y!3, alive)) | (~(host(Y!3) = host(W!4))) | setIn(W!4, alive) | (~leq(Y!3, W!4)))) <=> ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z)))) | ((~(host(Y!3) = host(W!4))) | (~setIn(Y!3, alive)) | setIn(W!4, alive) | (~leq(Y!3, W!4))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[120])).
% 0.21/0.45 tff(122,plain,
% 0.21/0.45 (((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z)))) | ((~setIn(Y!3, alive)) | (~(host(Y!3) = host(W!4))) | setIn(W!4, alive) | (~leq(Y!3, W!4)))) <=> ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z)))) | (~(host(Y!3) = host(W!4))) | (~setIn(Y!3, alive)) | setIn(W!4, alive) | (~leq(Y!3, W!4)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[121, 119])).
% 0.21/0.45 tff(123,plain,
% 0.21/0.45 ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z)))) | ((~setIn(Y!3, alive)) | (~(host(Y!3) = host(W!4))) | setIn(W!4, alive) | (~leq(Y!3, W!4)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(124,plain,
% 0.21/0.45 ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z)))) | (~(host(Y!3) = host(W!4))) | (~setIn(Y!3, alive)) | setIn(W!4, alive) | (~leq(Y!3, W!4))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.21/0.45 tff(125,plain,
% 0.21/0.45 (setIn(W!4, alive)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[124, 118, 21, 117, 110])).
% 0.21/0.45 tff(126,plain,
% 0.21/0.45 (host(X0!8) = host(Z!6)),
% 0.21/0.45 inference(and_elim,[status(thm)],[91])).
% 0.21/0.45 tff(127,plain,
% 0.21/0.45 (^[Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : refl(((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z)))) <=> ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(128,plain,
% 0.21/0.45 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z)))) <=> ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[127])).
% 0.21/0.45 tff(129,plain,
% 0.21/0.45 (^[Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : trans(monotonicity(trans(monotonicity(rewrite((elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20)))) <=> (~((~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20))))))), ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) <=> (~(~((~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20))))))))), rewrite((~(~((~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20))))))) <=> ((~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))))), ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) <=> ((~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20))))))), trans(monotonicity(rewrite(((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))) <=> (~((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z)))))), ((~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20)))) <=> (~(~((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z)))))))), rewrite((~(~((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z)))))) <=> ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))), ((~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20)))) <=> ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z)))))), (((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) <=> (((~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20))))) | ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))))), rewrite((((~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20))))) | ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))) <=> ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))), (((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) <=> ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(130,plain,
% 0.21/0.45 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) <=> ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[129])).
% 0.21/0.45 tff(131,plain,
% 0.21/0.45 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20)))))),
% 0.21/0.45 inference(and_elim,[status(thm)],[20])).
% 0.21/0.45 tff(132,plain,
% 0.21/0.45 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.21/0.45 tff(133,plain,
% 0.21/0.45 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.21/0.45 tff(134,plain,
% 0.21/0.45 (((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))) | ((~setIn(Z!6, alive)) | (~setIn(W!4, alive)) | (~(host(X0!8) = host(Z!6))) | (~(host(Z0!9) = host(W!4))) | (~elem(m_Down(X0!8), queue(host(W!4)))) | (~elem(m_Down(Z0!9), queue(host(Z!6)))) | (host(Z!6) = host(W!4)))) <=> ((~![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(Z!6, alive)) | (~setIn(W!4, alive)) | (~(host(X0!8) = host(Z!6))) | (~(host(Z0!9) = host(W!4))) | (~elem(m_Down(X0!8), queue(host(W!4)))) | (~elem(m_Down(Z0!9), queue(host(Z!6)))) | (host(Z!6) = host(W!4)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(135,plain,
% 0.21/0.45 (((~(host(X0!8) = host(Z!6))) | (~setIn(Z!6, alive)) | (host(Z!6) = host(W!4)) | (~elem(m_Down(X0!8), queue(host(W!4)))) | (~elem(m_Down(Z0!9), queue(host(Z!6)))) | (~setIn(W!4, alive)) | (~(host(Z0!9) = host(W!4)))) <=> ((~setIn(Z!6, alive)) | (~setIn(W!4, alive)) | (~(host(X0!8) = host(Z!6))) | (~(host(Z0!9) = host(W!4))) | (~elem(m_Down(X0!8), queue(host(W!4)))) | (~elem(m_Down(Z0!9), queue(host(Z!6)))) | (host(Z!6) = host(W!4)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(136,plain,
% 0.21/0.45 (((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))) | ((~(host(X0!8) = host(Z!6))) | (~setIn(Z!6, alive)) | (host(Z!6) = host(W!4)) | (~elem(m_Down(X0!8), queue(host(W!4)))) | (~elem(m_Down(Z0!9), queue(host(Z!6)))) | (~setIn(W!4, alive)) | (~(host(Z0!9) = host(W!4))))) <=> ((~![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(Z!6, alive)) | (~setIn(W!4, alive)) | (~(host(X0!8) = host(Z!6))) | (~(host(Z0!9) = host(W!4))) | (~elem(m_Down(X0!8), queue(host(W!4)))) | (~elem(m_Down(Z0!9), queue(host(Z!6)))) | (host(Z!6) = host(W!4))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[135])).
% 0.21/0.45 tff(137,plain,
% 0.21/0.45 (((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))) | ((~(host(X0!8) = host(Z!6))) | (~setIn(Z!6, alive)) | (host(Z!6) = host(W!4)) | (~elem(m_Down(X0!8), queue(host(W!4)))) | (~elem(m_Down(Z0!9), queue(host(Z!6)))) | (~setIn(W!4, alive)) | (~(host(Z0!9) = host(W!4))))) <=> ((~![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(Z!6, alive)) | (~setIn(W!4, alive)) | (~(host(X0!8) = host(Z!6))) | (~(host(Z0!9) = host(W!4))) | (~elem(m_Down(X0!8), queue(host(W!4)))) | (~elem(m_Down(Z0!9), queue(host(Z!6)))) | (host(Z!6) = host(W!4)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[136, 134])).
% 0.21/0.46 tff(138,plain,
% 0.21/0.46 ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))) | ((~(host(X0!8) = host(Z!6))) | (~setIn(Z!6, alive)) | (host(Z!6) = host(W!4)) | (~elem(m_Down(X0!8), queue(host(W!4)))) | (~elem(m_Down(Z0!9), queue(host(Z!6)))) | (~setIn(W!4, alive)) | (~(host(Z0!9) = host(W!4))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(139,plain,
% 0.21/0.46 ((~![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(Z!6, alive)) | (~setIn(W!4, alive)) | (~(host(X0!8) = host(Z!6))) | (~(host(Z0!9) = host(W!4))) | (~elem(m_Down(X0!8), queue(host(W!4)))) | (~elem(m_Down(Z0!9), queue(host(Z!6)))) | (host(Z!6) = host(W!4))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.21/0.46 tff(140,plain,
% 0.21/0.46 ((~setIn(Z!6, alive)) | (host(Z!6) = host(W!4))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[139, 133, 126, 125, 93, 88, 55])).
% 0.21/0.46 tff(141,plain,
% 0.21/0.46 (~setIn(Z!6, alive)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[140, 28])).
% 0.21/0.46 tff(142,plain,
% 0.21/0.46 (((Z!6 = Y!3) | (~setIn(Z!6, alive))) | setIn(Z!6, alive)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(143,plain,
% 0.21/0.46 ((Z!6 = Y!3) | (~setIn(Z!6, alive))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.21/0.46 tff(144,plain,
% 0.21/0.46 (((Z!6 = W!4) | (~((Z!6 = Y!3) | (~setIn(Z!6, alive))))) <=> ((Z!6 = W!4) | (~((Z!6 = Y!3) | (~setIn(Z!6, alive)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(145,plain,
% 0.21/0.46 (((~(Z!6 = Y!3)) & setIn(Z!6, alive)) <=> (~((Z!6 = Y!3) | (~setIn(Z!6, alive))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(146,plain,
% 0.21/0.46 (((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) <=> ((Z!6 = W!4) | (~((Z!6 = Y!3) | (~setIn(Z!6, alive)))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[145])).
% 0.21/0.46 tff(147,plain,
% 0.21/0.46 (((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))) <=> ((Z!6 = W!4) | (~((Z!6 = Y!3) | (~setIn(Z!6, alive)))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[146, 144])).
% 0.21/0.46 tff(148,plain,
% 0.21/0.46 ((Z!6 = W!4) | ((~(Z!6 = Y!3)) & setIn(Z!6, alive))),
% 0.21/0.46 inference(and_elim,[status(thm)],[91])).
% 0.21/0.46 tff(149,plain,
% 0.21/0.46 ((Z!6 = W!4) | (~((Z!6 = Y!3) | (~setIn(Z!6, alive))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.21/0.46 tff(150,plain,
% 0.21/0.46 (Z!6 = W!4),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[149, 143])).
% 0.21/0.46 tff(151,plain,
% 0.21/0.46 (host(Z!6) = host(W!4)),
% 0.21/0.46 inference(monotonicity,[status(thm)],[150])).
% 0.21/0.46 tff(152,plain,
% 0.21/0.46 (host(W!4) = host(Z!6)),
% 0.21/0.46 inference(symmetry,[status(thm)],[151])).
% 0.21/0.46 tff(153,plain,
% 0.21/0.46 (host(Y!3) = host(Z!6)),
% 0.21/0.46 inference(transitivity,[status(thm)],[21, 152])).
% 0.21/0.46 tff(154,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[27, 153])).
% 0.21/0.46 % SZS output end Proof
% 0.21/0.46 % E exiting
%------------------------------------------------------------------------------