%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV452+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 0.48s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV452+1 : TPTP v9.0.0. Released v4.0.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.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 09:53:17 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.48 % SZS status Theorem
% 0.21/0.48 % SZS output start Proof
% 0.21/0.48 tff(host_type, type, (
% 0.21/0.48 host: $i > $i)).
% 0.21/0.48 tff(tptp_fun_W_5_type, type, (
% 0.21/0.48 tptp_fun_W_5: $i)).
% 0.21/0.48 tff(tptp_fun_Y0_8_type, type, (
% 0.21/0.48 tptp_fun_Y0_8: $i)).
% 0.21/0.48 tff(tptp_fun_Z_7_type, type, (
% 0.21/0.48 tptp_fun_Z_7: $i)).
% 0.21/0.48 tff(tptp_fun_X_4_type, type, (
% 0.21/0.48 tptp_fun_X_4: $i)).
% 0.21/0.48 tff(cons_type, type, (
% 0.21/0.48 cons: ( $i * $i ) > $i)).
% 0.21/0.48 tff(tptp_fun_V_6_type, type, (
% 0.21/0.48 tptp_fun_V_6: $i)).
% 0.21/0.48 tff(m_Down_type, type, (
% 0.21/0.48 m_Down: $i > $i)).
% 0.21/0.48 tff(tptp_fun_Y_3_type, type, (
% 0.21/0.48 tptp_fun_Y_3: $i)).
% 0.21/0.48 tff(queue_type, type, (
% 0.21/0.48 queue: $i > $i)).
% 0.21/0.48 tff(setIn_type, type, (
% 0.21/0.48 setIn: ( $i * $i ) > $o)).
% 0.21/0.48 tff(alive_type, type, (
% 0.21/0.48 alive: $i)).
% 0.21/0.48 tff(elem_type, type, (
% 0.21/0.48 elem: ( $i * $i ) > $o)).
% 0.21/0.48 tff(leq_type, type, (
% 0.21/0.48 leq: ( $i * $i ) > $o)).
% 0.21/0.48 tff(m_Ack_type, type, (
% 0.21/0.48 m_Ack: ( $i * $i ) > $i)).
% 0.21/0.48 tff(m_Halt_type, type, (
% 0.21/0.48 m_Halt: $i > $i)).
% 0.21/0.48 tff(index_type, type, (
% 0.21/0.48 index: ( $i * $i ) > $i)).
% 0.21/0.48 tff(elid_type, type, (
% 0.21/0.48 elid: $i)).
% 0.21/0.48 tff(wait_type, type, (
% 0.21/0.48 wait: $i)).
% 0.21/0.48 tff(status_type, type, (
% 0.21/0.48 status: $i)).
% 0.21/0.48 tff(norm_type, type, (
% 0.21/0.48 norm: $i)).
% 0.21/0.48 tff(ldr_type, type, (
% 0.21/0.48 ldr: $i)).
% 0.21/0.48 tff(pids_type, type, (
% 0.21/0.48 pids: $i)).
% 0.21/0.48 tff(tptp_fun_Z0_10_type, type, (
% 0.21/0.48 tptp_fun_Z0_10: $i)).
% 0.21/0.48 tff(tptp_fun_X0_9_type, type, (
% 0.21/0.48 tptp_fun_X0_9: $i)).
% 0.21/0.48 tff(s_type, type, (
% 0.21/0.48 s: $i > $i)).
% 0.21/0.48 tff(zero_type, type, (
% 0.21/0.48 zero: $i)).
% 0.21/0.48 tff(1,plain,
% 0.21/0.48 (((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~(host(W!5) = s(zero))) & ((host(X!4) = host(Z!7)) & (~(host(X!4) = host(Y0!8))) & (~((~(elem(m_Down(Z0!10), V!6) & elem(m_Down(X0!9), queue(host(Y0!8))))) | (~((((~(Z!7 = X!4)) & setIn(Z!7, alive)) | (Z!7 = W!5)) & ((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) & (~(host(Y0!8) = host(Z!7))) & (host(X0!9) = host(Z!7)) & (host(Z0!10) = host(Y0!8))))))) & (![Z: $i] : ((~(host(X!4) = host(Z))) | leq(Z, W!5)) & (~setIn(W!5, pids)) & (host(X!4) = host(W!5))) & (((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm)) | ((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z)))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!6)))) <=> ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~(host(W!5) = s(zero))) & (host(X!4) = host(Z!7)) & (~(host(X!4) = host(Y0!8))) & (~((~(elem(m_Down(Z0!10), V!6) & elem(m_Down(X0!9), queue(host(Y0!8))))) | (~((((~(Z!7 = X!4)) & setIn(Z!7, alive)) | (Z!7 = W!5)) & ((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) & (~(host(Y0!8) = host(Z!7))) & (host(X0!9) = host(Z!7)) & (host(Z0!10) = host(Y0!8)))))) & ![Z: $i] : ((~(host(X!4) = host(Z))) | leq(Z, W!5)) & (~setIn(W!5, pids)) & (host(X!4) = host(W!5)) & (((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm)) | ((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z)))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!6)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(2,plain,
% 0.21/0.49 ((![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!6))) <=> (![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!6)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(3,plain,
% 0.21/0.49 ((![Z: $i] : ((~(host(X!4) = host(Z))) | leq(Z, W!5)) & (~setIn(W!5, pids)) & (host(X!4) = host(W!5))) <=> (![Z: $i] : ((~(host(X!4) = host(Z))) | leq(Z, W!5)) & (~setIn(W!5, pids)) & (host(X!4) = host(W!5)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(4,plain,
% 0.21/0.49 (((host(X!4) = host(Z!7)) & ((~(host(X!4) = host(Y0!8))) & (~((~(elem(m_Down(Z0!10), V!6) & elem(m_Down(X0!9), queue(host(Y0!8))))) | (~((((~(Z!7 = X!4)) & setIn(Z!7, alive)) | (Z!7 = W!5)) & ((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) & (~(host(Y0!8) = host(Z!7))) & (host(X0!9) = host(Z!7)) & (host(Z0!10) = host(Y0!8)))))))) <=> ((host(X!4) = host(Z!7)) & (~(host(X!4) = host(Y0!8))) & (~((~(elem(m_Down(Z0!10), V!6) & elem(m_Down(X0!9), queue(host(Y0!8))))) | (~((((~(Z!7 = X!4)) & setIn(Z!7, alive)) | (Z!7 = W!5)) & ((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) & (~(host(Y0!8) = host(Z!7))) & (host(X0!9) = host(Z!7)) & (host(Z0!10) = host(Y0!8)))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(5,plain,
% 0.21/0.49 (((((~(Z!7 = X!4)) & setIn(Z!7, alive)) | (Z!7 = W!5)) & ((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) & (~(host(Y0!8) = host(Z!7))) & (host(X0!9) = host(Z!7)) & (host(Z0!10) = host(Y0!8))) <=> ((((~(Z!7 = X!4)) & setIn(Z!7, alive)) | (Z!7 = W!5)) & ((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) & (~(host(Y0!8) = host(Z!7))) & (host(X0!9) = host(Z!7)) & (host(Z0!10) = host(Y0!8)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(6,plain,
% 0.21/0.49 ((~((((~(Z!7 = X!4)) & setIn(Z!7, alive)) | (Z!7 = W!5)) & ((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) & (~(host(Y0!8) = host(Z!7))) & (host(X0!9) = host(Z!7)) & (host(Z0!10) = host(Y0!8)))) <=> (~((((~(Z!7 = X!4)) & setIn(Z!7, alive)) | (Z!7 = W!5)) & ((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) & (~(host(Y0!8) = host(Z!7))) & (host(X0!9) = host(Z!7)) & (host(Z0!10) = host(Y0!8))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[5])).
% 0.21/0.49 tff(7,plain,
% 0.21/0.49 (((~(elem(m_Down(Z0!10), V!6) & elem(m_Down(X0!9), queue(host(Y0!8))))) | (~((((~(Z!7 = X!4)) & setIn(Z!7, alive)) | (Z!7 = W!5)) & ((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) & (~(host(Y0!8) = host(Z!7))) & (host(X0!9) = host(Z!7)) & (host(Z0!10) = host(Y0!8))))) <=> ((~(elem(m_Down(Z0!10), V!6) & elem(m_Down(X0!9), queue(host(Y0!8))))) | (~((((~(Z!7 = X!4)) & setIn(Z!7, alive)) | (Z!7 = W!5)) & ((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) & (~(host(Y0!8) = host(Z!7))) & (host(X0!9) = host(Z!7)) & (host(Z0!10) = host(Y0!8)))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[6])).
% 0.21/0.49 tff(8,plain,
% 0.21/0.49 ((~((~(elem(m_Down(Z0!10), V!6) & elem(m_Down(X0!9), queue(host(Y0!8))))) | (~((((~(Z!7 = X!4)) & setIn(Z!7, alive)) | (Z!7 = W!5)) & ((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) & (~(host(Y0!8) = host(Z!7))) & (host(X0!9) = host(Z!7)) & (host(Z0!10) = host(Y0!8)))))) <=> (~((~(elem(m_Down(Z0!10), V!6) & elem(m_Down(X0!9), queue(host(Y0!8))))) | (~((((~(Z!7 = X!4)) & setIn(Z!7, alive)) | (Z!7 = W!5)) & ((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) & (~(host(Y0!8) = host(Z!7))) & (host(X0!9) = host(Z!7)) & (host(Z0!10) = host(Y0!8))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[7])).
% 0.21/0.49 tff(9,plain,
% 0.21/0.49 (((~(host(X!4) = host(Y0!8))) & (~((~(elem(m_Down(Z0!10), V!6) & elem(m_Down(X0!9), queue(host(Y0!8))))) | (~((((~(Z!7 = X!4)) & setIn(Z!7, alive)) | (Z!7 = W!5)) & ((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) & (~(host(Y0!8) = host(Z!7))) & (host(X0!9) = host(Z!7)) & (host(Z0!10) = host(Y0!8))))))) <=> ((~(host(X!4) = host(Y0!8))) & (~((~(elem(m_Down(Z0!10), V!6) & elem(m_Down(X0!9), queue(host(Y0!8))))) | (~((((~(Z!7 = X!4)) & setIn(Z!7, alive)) | (Z!7 = W!5)) & ((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) & (~(host(Y0!8) = host(Z!7))) & (host(X0!9) = host(Z!7)) & (host(Z0!10) = host(Y0!8)))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[8])).
% 0.21/0.49 tff(10,plain,
% 0.21/0.49 (((host(X!4) = host(Z!7)) & ((~(host(X!4) = host(Y0!8))) & (~((~(elem(m_Down(Z0!10), V!6) & elem(m_Down(X0!9), queue(host(Y0!8))))) | (~((((~(Z!7 = X!4)) & setIn(Z!7, alive)) | (Z!7 = W!5)) & ((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) & (~(host(Y0!8) = host(Z!7))) & (host(X0!9) = host(Z!7)) & (host(Z0!10) = host(Y0!8)))))))) <=> ((host(X!4) = host(Z!7)) & ((~(host(X!4) = host(Y0!8))) & (~((~(elem(m_Down(Z0!10), V!6) & elem(m_Down(X0!9), queue(host(Y0!8))))) | (~((((~(Z!7 = X!4)) & setIn(Z!7, alive)) | (Z!7 = W!5)) & ((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) & (~(host(Y0!8) = host(Z!7))) & (host(X0!9) = host(Z!7)) & (host(Z0!10) = host(Y0!8))))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[9])).
% 0.21/0.49 tff(11,plain,
% 0.21/0.49 (((host(X!4) = host(Z!7)) & ((~(host(X!4) = host(Y0!8))) & (~((~(elem(m_Down(Z0!10), V!6) & elem(m_Down(X0!9), queue(host(Y0!8))))) | (~((((~(Z!7 = X!4)) & setIn(Z!7, alive)) | (Z!7 = W!5)) & ((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) & (~(host(Y0!8) = host(Z!7))) & (host(X0!9) = host(Z!7)) & (host(Z0!10) = host(Y0!8)))))))) <=> ((host(X!4) = host(Z!7)) & (~(host(X!4) = host(Y0!8))) & (~((~(elem(m_Down(Z0!10), V!6) & elem(m_Down(X0!9), queue(host(Y0!8))))) | (~((((~(Z!7 = X!4)) & setIn(Z!7, alive)) | (Z!7 = W!5)) & ((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) & (~(host(Y0!8) = host(Z!7))) & (host(X0!9) = host(Z!7)) & (host(Z0!10) = host(Y0!8)))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[10, 4])).
% 0.21/0.49 tff(12,plain,
% 0.21/0.49 (((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~(host(W!5) = s(zero))) & ((host(X!4) = host(Z!7)) & ((~(host(X!4) = host(Y0!8))) & (~((~(elem(m_Down(Z0!10), V!6) & elem(m_Down(X0!9), queue(host(Y0!8))))) | (~((((~(Z!7 = X!4)) & setIn(Z!7, alive)) | (Z!7 = W!5)) & ((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) & (~(host(Y0!8) = host(Z!7))) & (host(X0!9) = host(Z!7)) & (host(Z0!10) = host(Y0!8)))))))) & (![Z: $i] : ((~(host(X!4) = host(Z))) | leq(Z, W!5)) & (~setIn(W!5, pids)) & (host(X!4) = host(W!5))) & (((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm)) | ((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z)))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!6)))) <=> ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~(host(W!5) = s(zero))) & ((host(X!4) = host(Z!7)) & (~(host(X!4) = host(Y0!8))) & (~((~(elem(m_Down(Z0!10), V!6) & elem(m_Down(X0!9), queue(host(Y0!8))))) | (~((((~(Z!7 = X!4)) & setIn(Z!7, alive)) | (Z!7 = W!5)) & ((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) & (~(host(Y0!8) = host(Z!7))) & (host(X0!9) = host(Z!7)) & (host(Z0!10) = host(Y0!8))))))) & (![Z: $i] : ((~(host(X!4) = host(Z))) | leq(Z, W!5)) & (~setIn(W!5, pids)) & (host(X!4) = host(W!5))) & (((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm)) | ((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z)))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!6))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[11, 3, 2])).
% 0.21/0.49 tff(13,plain,
% 0.21/0.49 (((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~(host(W!5) = s(zero))) & ((host(X!4) = host(Z!7)) & ((~(host(X!4) = host(Y0!8))) & (~((~(elem(m_Down(Z0!10), V!6) & elem(m_Down(X0!9), queue(host(Y0!8))))) | (~((((~(Z!7 = X!4)) & setIn(Z!7, alive)) | (Z!7 = W!5)) & ((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) & (~(host(Y0!8) = host(Z!7))) & (host(X0!9) = host(Z!7)) & (host(Z0!10) = host(Y0!8)))))))) & (![Z: $i] : ((~(host(X!4) = host(Z))) | leq(Z, W!5)) & (~setIn(W!5, pids)) & (host(X!4) = host(W!5))) & (((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm)) | ((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & (![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z)))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!6)))) <=> ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~(host(W!5) = s(zero))) & (host(X!4) = host(Z!7)) & (~(host(X!4) = host(Y0!8))) & (~((~(elem(m_Down(Z0!10), V!6) & elem(m_Down(X0!9), queue(host(Y0!8))))) | (~((((~(Z!7 = X!4)) & setIn(Z!7, alive)) | (Z!7 = W!5)) & ((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) & (~(host(Y0!8) = host(Z!7))) & (host(X0!9) = host(Z!7)) & (host(Z0!10) = host(Y0!8)))))) & ![Z: $i] : ((~(host(X!4) = host(Z))) | leq(Z, W!5)) & (~setIn(W!5, pids)) & (host(X!4) = host(W!5)) & (((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm)) | ((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z)))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!6)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[12, 1])).
% 0.21/0.49 tff(14,plain,
% 0.21/0.49 ((~![V: $i, W: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | (host(W) = s(zero)) | ![Z: $i] : ((~(host(X) = host(Z))) | ![X0: $i, Y0: $i] : ((host(X) = host(Y0)) | ![Z0: $i] : ((~(elem(m_Down(Z0), V) & elem(m_Down(X0), queue(host(Y0))))) | (~((((~(Z = X)) & setIn(Z, alive)) | (Z = W)) & ((Y0 = W) | ((~(Y0 = X)) & setIn(Y0, alive))) & (~(host(Y0) = host(Z))) & (host(X0) = host(Z)) & (host(Z0) = host(Y0))))))) | (~(![Z: $i] : ((~(host(X) = host(Z))) | leq(Z, W)) & (~setIn(W, pids)) & (host(X) = host(W)))) | (~(((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, 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, W: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | (host(W) = s(zero)) | ![Z: $i] : ((~(host(X) = host(Z))) | ![X0: $i, Y0: $i] : ((host(X) = host(Y0)) | ![Z0: $i] : ((~(elem(m_Down(Z0), V) & elem(m_Down(X0), queue(host(Y0))))) | (~((((~(Z = X)) & setIn(Z, alive)) | (Z = W)) & ((Y0 = W) | ((~(Y0 = X)) & setIn(Y0, alive))) & (~(host(Y0) = host(Z))) & (host(X0) = host(Z)) & (host(Z0) = host(Y0))))))) | (~(![Z: $i] : ((~(host(X) = host(Z))) | leq(Z, W)) & (~setIn(W, pids)) & (host(X) = host(W)))) | (~(((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, 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))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(15,plain,
% 0.21/0.50 ((~![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] : ((host(X) = host(Z)) => leq(Z, W)) & (~setIn(W, pids))) & (host(X) = host(W))) => ((~(host(W) = s(zero))) => ![Z: $i] : ((host(X) = host(Z)) => ![X0: $i, Y0: $i] : ((~(host(X) = host(Y0))) => ![Z0: $i] : ((((((((~(Z = X)) & setIn(Z, alive)) | (Z = W)) & (((~(Y0 = X)) & setIn(Y0, alive)) | (Y0 = W))) & (~(host(Y0) = host(Z)))) & (host(X0) = host(Z))) & (host(Z0) = host(Y0))) => (~(elem(m_Down(Z0), V) & elem(m_Down(X0), queue(host(Y0))))))))))))))) <=> (~![V: $i, W: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | (host(W) = s(zero)) | ![Z: $i] : ((~(host(X) = host(Z))) | ![X0: $i, Y0: $i] : ((host(X) = host(Y0)) | ![Z0: $i] : ((~(elem(m_Down(Z0), V) & elem(m_Down(X0), queue(host(Y0))))) | (~((((~(Z = X)) & setIn(Z, alive)) | (Z = W)) & ((Y0 = W) | ((~(Y0 = X)) & setIn(Y0, alive))) & (~(host(Y0) = host(Z))) & (host(X0) = host(Z)) & (host(Z0) = host(Y0))))))) | (~(![Z: $i] : ((~(host(X) = host(Z))) | leq(Z, W)) & (~setIn(W, pids)) & (host(X) = host(W)))) | (~(((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, 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))))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 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] : ((host(X) = host(Z)) => leq(Z, W)) & (~setIn(W, pids))) & (host(X) = host(W))) => ((~(host(W) = s(zero))) => ![Z: $i] : ((host(X) = host(Z)) => ![X0: $i, Y0: $i] : ((~(host(X) = host(Y0))) => ![Z0: $i] : ((((((((~(Z = X)) & setIn(Z, alive)) | (Z = W)) & (((~(Y0 = X)) & setIn(Y0, alive)) | (Y0 = W))) & (~(host(Y0) = host(Z)))) & (host(X0) = host(Z))) & (host(Z0) = host(Y0))) => (~(elem(m_Down(Z0), V) & elem(m_Down(X0), queue(host(Y0))))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj')).
% 0.21/0.50 tff(17,plain,
% 0.21/0.50 (~![V: $i, W: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | (host(W) = s(zero)) | ![Z: $i] : ((~(host(X) = host(Z))) | ![X0: $i, Y0: $i] : ((host(X) = host(Y0)) | ![Z0: $i] : ((~(elem(m_Down(Z0), V) & elem(m_Down(X0), queue(host(Y0))))) | (~((((~(Z = X)) & setIn(Z, alive)) | (Z = W)) & ((Y0 = W) | ((~(Y0 = X)) & setIn(Y0, alive))) & (~(host(Y0) = host(Z))) & (host(X0) = host(Z)) & (host(Z0) = host(Y0))))))) | (~(![Z: $i] : ((~(host(X) = host(Z))) | leq(Z, W)) & (~setIn(W, pids)) & (host(X) = host(W)))) | (~(((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, 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)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.50 tff(18,plain,
% 0.21/0.50 (~![V: $i, W: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | (host(W) = s(zero)) | ![Z: $i] : ((~(host(X) = host(Z))) | ![X0: $i, Y0: $i] : ((host(X) = host(Y0)) | ![Z0: $i] : ((~(elem(m_Down(Z0), V) & elem(m_Down(X0), queue(host(Y0))))) | (~((((~(Z = X)) & setIn(Z, alive)) | (Z = W)) & ((Y0 = W) | ((~(Y0 = X)) & setIn(Y0, alive))) & (~(host(Y0) = host(Z))) & (host(X0) = host(Z)) & (host(Z0) = host(Y0))))))) | (~(![Z: $i] : ((~(host(X) = host(Z))) | leq(Z, W)) & (~setIn(W, pids)) & (host(X) = host(W)))) | (~(((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, 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)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.21/0.50 tff(19,plain,
% 0.21/0.50 (~![V: $i, W: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | (host(W) = s(zero)) | ![Z: $i] : ((~(host(X) = host(Z))) | ![X0: $i, Y0: $i] : ((host(X) = host(Y0)) | ![Z0: $i] : ((~(elem(m_Down(Z0), V) & elem(m_Down(X0), queue(host(Y0))))) | (~((((~(Z = X)) & setIn(Z, alive)) | (Z = W)) & ((Y0 = W) | ((~(Y0 = X)) & setIn(Y0, alive))) & (~(host(Y0) = host(Z))) & (host(X0) = host(Z)) & (host(Z0) = host(Y0))))))) | (~(![Z: $i] : ((~(host(X) = host(Z))) | leq(Z, W)) & (~setIn(W, pids)) & (host(X) = host(W)))) | (~(((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, 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)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.50 tff(20,plain,
% 0.21/0.50 (~![V: $i, W: $i, X: $i, Y: $i] : (leq(host(X), host(Y)) | (~setIn(X, alive)) | (host(W) = s(zero)) | ![Z: $i] : ((~(host(X) = host(Z))) | ![X0: $i, Y0: $i] : ((host(X) = host(Y0)) | ![Z0: $i] : ((~(elem(m_Down(Z0), V) & elem(m_Down(X0), queue(host(Y0))))) | (~((((~(Z = X)) & setIn(Z, alive)) | (Z = W)) & ((Y0 = W) | ((~(Y0 = X)) & setIn(Y0, alive))) & (~(host(Y0) = host(Z))) & (host(X0) = host(Z)) & (host(Z0) = host(Y0))))))) | (~(![Z: $i] : ((~(host(X) = host(Z))) | leq(Z, W)) & (~setIn(W, pids)) & (host(X) = host(W)))) | (~(((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, 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)))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.21/0.50 tff(21,plain,
% 0.21/0.50 ((~leq(host(X!4), host(Y!3))) & setIn(X!4, alive) & (~(host(W!5) = s(zero))) & (host(X!4) = host(Z!7)) & (~(host(X!4) = host(Y0!8))) & (~((~(elem(m_Down(Z0!10), V!6) & elem(m_Down(X0!9), queue(host(Y0!8))))) | (~((((~(Z!7 = X!4)) & setIn(Z!7, alive)) | (Z!7 = W!5)) & ((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) & (~(host(Y0!8) = host(Z!7))) & (host(X0!9) = host(Z!7)) & (host(Z0!10) = host(Y0!8)))))) & ![Z: $i] : ((~(host(X!4) = host(Z))) | leq(Z, W!5)) & (~setIn(W!5, pids)) & (host(X!4) = host(W!5)) & (((index(ldr, host(X!4)) = host(Y!3)) & (index(status, host(X!4)) = norm)) | ((index(status, host(X!4)) = wait) & (host(Y!3) = host(index(elid, host(X!4)))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~elem(m_Down(Pid0), queue(host(Z))))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~setIn(Pid0, alive))) & ![Z: $i, Pid0: $i] : ((~elem(m_Down(Pid0), queue(host(Z)))) | (~(host(Pid0) = host(Z)))) & ![Z: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Halt(Pid0), queue(host(Z))))) & ![Z: $i, Pid20: $i, Pid0: $i] : ((~leq(host(Z), host(Pid0))) | (~elem(m_Ack(Pid0, Z), queue(host(Pid20))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~setIn(Z, alive)) | (~((~(Pid0 = Z)) & (host(Pid0) = host(Z))))) & ![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(elem(m_Down(Pid0), queue(host(Z))) & elem(m_Down(Pid30), queue(host(Pid20))))) | (~((~(host(Pid20) = host(Z))) & setIn(Z, alive) & setIn(Pid20, alive) & (host(Pid30) = host(Z)) & (host(Pid0) = host(Pid20))))) & (queue(host(X!4)) = cons(m_Down(Y!3), V!6))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.21/0.50 tff(22,plain,
% 0.21/0.50 (host(X!4) = host(Z!7)),
% 0.21/0.50 inference(and_elim,[status(thm)],[21])).
% 0.21/0.50 tff(23,plain,
% 0.21/0.50 (host(X!4) = host(W!5)),
% 0.21/0.50 inference(and_elim,[status(thm)],[21])).
% 0.21/0.50 tff(24,plain,
% 0.21/0.50 (host(W!5) = host(X!4)),
% 0.21/0.50 inference(symmetry,[status(thm)],[23])).
% 0.21/0.50 tff(25,plain,
% 0.21/0.50 (host(W!5) = host(Z!7)),
% 0.21/0.50 inference(transitivity,[status(thm)],[24, 22])).
% 0.21/0.50 tff(26,plain,
% 0.21/0.50 ((host(Y0!8) = host(W!5)) <=> (host(Y0!8) = host(Z!7))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[25])).
% 0.21/0.50 tff(27,plain,
% 0.21/0.50 ((host(Y0!8) = host(Z!7)) <=> (host(Y0!8) = host(W!5))),
% 0.21/0.50 inference(symmetry,[status(thm)],[26])).
% 0.21/0.50 tff(28,plain,
% 0.21/0.50 ((~(host(Y0!8) = host(Z!7))) <=> (~(host(Y0!8) = host(W!5)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[27])).
% 0.21/0.50 tff(29,plain,
% 0.21/0.50 (~((~(elem(m_Down(Z0!10), V!6) & elem(m_Down(X0!9), queue(host(Y0!8))))) | (~((((~(Z!7 = X!4)) & setIn(Z!7, alive)) | (Z!7 = W!5)) & ((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) & (~(host(Y0!8) = host(Z!7))) & (host(X0!9) = host(Z!7)) & (host(Z0!10) = host(Y0!8)))))),
% 0.21/0.50 inference(and_elim,[status(thm)],[21])).
% 0.21/0.50 tff(30,plain,
% 0.21/0.50 ((((~(Z!7 = X!4)) & setIn(Z!7, alive)) | (Z!7 = W!5)) & ((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) & (~(host(Y0!8) = host(Z!7))) & (host(X0!9) = host(Z!7)) & (host(Z0!10) = host(Y0!8))),
% 0.21/0.50 inference(or_elim,[status(thm)],[29])).
% 0.21/0.50 tff(31,plain,
% 0.21/0.50 (~(host(Y0!8) = host(Z!7))),
% 0.21/0.50 inference(and_elim,[status(thm)],[30])).
% 0.21/0.50 tff(32,plain,
% 0.21/0.50 (~(host(Y0!8) = host(W!5))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[31, 28])).
% 0.21/0.50 tff(33,plain,
% 0.21/0.50 (queue(host(W!5)) = queue(host(X!4))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[24])).
% 0.21/0.50 tff(34,plain,
% 0.21/0.50 (elem(m_Down(Z0!10), queue(host(W!5))) <=> elem(m_Down(Z0!10), queue(host(X!4)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[33])).
% 0.21/0.50 tff(35,plain,
% 0.21/0.50 (elem(m_Down(Z0!10), queue(host(X!4))) <=> elem(m_Down(Z0!10), queue(host(W!5)))),
% 0.21/0.50 inference(symmetry,[status(thm)],[34])).
% 0.21/0.50 tff(36,plain,
% 0.21/0.50 (queue(host(X!4)) = cons(m_Down(Y!3), V!6)),
% 0.21/0.50 inference(and_elim,[status(thm)],[21])).
% 0.21/0.50 tff(37,plain,
% 0.21/0.50 (cons(m_Down(Y!3), V!6) = queue(host(X!4))),
% 0.21/0.50 inference(symmetry,[status(thm)],[36])).
% 0.21/0.50 tff(38,plain,
% 0.21/0.50 (elem(m_Down(Z0!10), cons(m_Down(Y!3), V!6)) <=> elem(m_Down(Z0!10), queue(host(X!4)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[37])).
% 0.21/0.50 tff(39,plain,
% 0.21/0.50 (elem(m_Down(Z0!10), queue(host(X!4))) <=> elem(m_Down(Z0!10), cons(m_Down(Y!3), V!6))),
% 0.21/0.50 inference(symmetry,[status(thm)],[38])).
% 0.21/0.50 tff(40,plain,
% 0.21/0.50 ((~elem(m_Down(Z0!10), queue(host(X!4)))) <=> (~elem(m_Down(Z0!10), cons(m_Down(Y!3), V!6)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[39])).
% 0.21/0.50 tff(41,assumption,(~elem(m_Down(Z0!10), queue(host(X!4)))), introduced(assumption)).
% 0.21/0.50 tff(42,plain,
% 0.21/0.50 (~elem(m_Down(Z0!10), cons(m_Down(Y!3), V!6))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.21/0.50 tff(43,plain,
% 0.21/0.50 (^[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))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(44,plain,
% 0.21/0.50 (![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)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[43])).
% 0.21/0.50 tff(45,plain,
% 0.21/0.50 (![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)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(46,axiom,(![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV011+0.ax','axiom_46')).
% 0.21/0.50 tff(47,plain,
% 0.21/0.50 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.50 tff(48,plain,(
% 0.21/0.50 ![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[47])).
% 0.21/0.50 tff(49,plain,
% 0.21/0.50 (![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.21/0.50 tff(50,plain,
% 0.21/0.50 ((~![X: $i, Y: $i, Q: $i] : (elem(X, cons(Y, Q)) <=> ((X = Y) | elem(X, Q)))) | (elem(m_Down(Z0!10), cons(m_Down(Y!3), V!6)) <=> ((m_Down(Z0!10) = m_Down(Y!3)) | elem(m_Down(Z0!10), V!6)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(51,plain,
% 0.21/0.50 (elem(m_Down(Z0!10), cons(m_Down(Y!3), V!6)) <=> ((m_Down(Z0!10) = m_Down(Y!3)) | elem(m_Down(Z0!10), V!6))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.21/0.50 tff(52,plain,
% 0.21/0.50 (elem(m_Down(Z0!10), V!6) & elem(m_Down(X0!9), queue(host(Y0!8)))),
% 0.21/0.50 inference(or_elim,[status(thm)],[29])).
% 0.21/0.50 tff(53,plain,
% 0.21/0.50 (elem(m_Down(Z0!10), V!6)),
% 0.21/0.50 inference(and_elim,[status(thm)],[52])).
% 0.21/0.50 tff(54,plain,
% 0.21/0.50 (((m_Down(Z0!10) = m_Down(Y!3)) | elem(m_Down(Z0!10), V!6)) | (~elem(m_Down(Z0!10), V!6))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(55,plain,
% 0.21/0.50 ((m_Down(Z0!10) = m_Down(Y!3)) | elem(m_Down(Z0!10), V!6)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.21/0.50 tff(56,plain,
% 0.21/0.50 ((~(elem(m_Down(Z0!10), cons(m_Down(Y!3), V!6)) <=> ((m_Down(Z0!10) = m_Down(Y!3)) | elem(m_Down(Z0!10), V!6)))) | elem(m_Down(Z0!10), cons(m_Down(Y!3), V!6)) | (~((m_Down(Z0!10) = m_Down(Y!3)) | elem(m_Down(Z0!10), V!6)))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(57,plain,
% 0.21/0.50 ((~(elem(m_Down(Z0!10), cons(m_Down(Y!3), V!6)) <=> ((m_Down(Z0!10) = m_Down(Y!3)) | elem(m_Down(Z0!10), V!6)))) | elem(m_Down(Z0!10), cons(m_Down(Y!3), V!6))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.21/0.50 tff(58,plain,
% 0.21/0.50 (elem(m_Down(Z0!10), cons(m_Down(Y!3), V!6))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[57, 51])).
% 0.21/0.50 tff(59,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[58, 42])).
% 0.21/0.50 tff(60,plain,(elem(m_Down(Z0!10), queue(host(X!4)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(61,plain,
% 0.21/0.50 (elem(m_Down(Z0!10), queue(host(W!5)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[60, 35])).
% 0.21/0.50 tff(62,plain,
% 0.21/0.50 (host(Z!7) = host(X!4)),
% 0.21/0.50 inference(symmetry,[status(thm)],[22])).
% 0.21/0.50 tff(63,plain,
% 0.21/0.50 (host(X0!9) = host(Z!7)),
% 0.21/0.50 inference(and_elim,[status(thm)],[30])).
% 0.21/0.50 tff(64,plain,
% 0.21/0.50 (host(X0!9) = host(W!5)),
% 0.21/0.50 inference(transitivity,[status(thm)],[63, 62, 23])).
% 0.21/0.50 tff(65,plain,
% 0.21/0.50 (^[Z: $i] : refl(((~(host(X!4) = host(Z))) | leq(Z, W!5)) <=> ((~(host(X!4) = host(Z))) | leq(Z, W!5)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(66,plain,
% 0.21/0.50 (![Z: $i] : ((~(host(X!4) = host(Z))) | leq(Z, W!5)) <=> ![Z: $i] : ((~(host(X!4) = host(Z))) | leq(Z, W!5))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[65])).
% 0.21/0.50 tff(67,plain,
% 0.21/0.50 (![Z: $i] : ((~(host(X!4) = host(Z))) | leq(Z, W!5))),
% 0.21/0.50 inference(and_elim,[status(thm)],[21])).
% 0.21/0.50 tff(68,plain,
% 0.21/0.50 (![Z: $i] : ((~(host(X!4) = host(Z))) | leq(Z, W!5))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.21/0.50 tff(69,plain,
% 0.21/0.50 (((~![Z: $i] : ((~(host(X!4) = host(Z))) | leq(Z, W!5))) | leq(X!4, W!5)) <=> ((~![Z: $i] : ((~(host(X!4) = host(Z))) | leq(Z, W!5))) | leq(X!4, W!5))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(70,plain,
% 0.21/0.50 (($false | leq(X!4, W!5)) <=> leq(X!4, W!5)),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(71,plain,
% 0.21/0.50 ((~$true) <=> $false),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(72,plain,
% 0.21/0.50 ((host(X!4) = host(X!4)) <=> $true),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(73,plain,
% 0.21/0.50 ((~(host(X!4) = host(X!4))) <=> (~$true)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[72])).
% 0.21/0.50 tff(74,plain,
% 0.21/0.50 ((~(host(X!4) = host(X!4))) <=> $false),
% 0.21/0.50 inference(transitivity,[status(thm)],[73, 71])).
% 0.21/0.50 tff(75,plain,
% 0.21/0.50 (((~(host(X!4) = host(X!4))) | leq(X!4, W!5)) <=> ($false | leq(X!4, W!5))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[74])).
% 0.21/0.50 tff(76,plain,
% 0.21/0.50 (((~(host(X!4) = host(X!4))) | leq(X!4, W!5)) <=> leq(X!4, W!5)),
% 0.21/0.50 inference(transitivity,[status(thm)],[75, 70])).
% 0.21/0.50 tff(77,plain,
% 0.21/0.50 (((~![Z: $i] : ((~(host(X!4) = host(Z))) | leq(Z, W!5))) | ((~(host(X!4) = host(X!4))) | leq(X!4, W!5))) <=> ((~![Z: $i] : ((~(host(X!4) = host(Z))) | leq(Z, W!5))) | leq(X!4, W!5))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[76])).
% 0.21/0.50 tff(78,plain,
% 0.21/0.50 (((~![Z: $i] : ((~(host(X!4) = host(Z))) | leq(Z, W!5))) | ((~(host(X!4) = host(X!4))) | leq(X!4, W!5))) <=> ((~![Z: $i] : ((~(host(X!4) = host(Z))) | leq(Z, W!5))) | leq(X!4, W!5))),
% 0.21/0.50 inference(transitivity,[status(thm)],[77, 69])).
% 0.21/0.50 tff(79,plain,
% 0.21/0.50 ((~![Z: $i] : ((~(host(X!4) = host(Z))) | leq(Z, W!5))) | ((~(host(X!4) = host(X!4))) | leq(X!4, W!5))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(80,plain,
% 0.21/0.50 ((~![Z: $i] : ((~(host(X!4) = host(Z))) | leq(Z, W!5))) | leq(X!4, W!5)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.21/0.51 tff(81,plain,
% 0.21/0.51 (leq(X!4, W!5)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[80, 68])).
% 0.21/0.51 tff(82,plain,
% 0.21/0.51 (^[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))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(83,plain,
% 0.21/0.51 (![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)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[82])).
% 0.21/0.51 tff(84,plain,
% 0.21/0.51 (^[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)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(85,plain,
% 0.21/0.51 (![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)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[84])).
% 0.21/0.51 tff(86,plain,
% 0.21/0.51 (![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~((~setIn(Z, alive)) & leq(Pid0, Z) & (host(Pid0) = host(Z)))))),
% 0.21/0.51 inference(and_elim,[status(thm)],[21])).
% 0.21/0.51 tff(87,plain,
% 0.21/0.51 (![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.21/0.51 tff(88,plain,
% 0.21/0.51 (![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.21/0.51 tff(89,plain,
% 0.21/0.51 (setIn(X!4, alive)),
% 0.21/0.51 inference(and_elim,[status(thm)],[21])).
% 0.21/0.51 tff(90,plain,
% 0.21/0.51 (((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z)))) | ((~setIn(X!4, alive)) | (~(host(X!4) = host(W!5))) | setIn(W!5, alive) | (~leq(X!4, W!5)))) <=> ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z)))) | (~setIn(X!4, alive)) | (~(host(X!4) = host(W!5))) | setIn(W!5, alive) | (~leq(X!4, W!5)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(91,plain,
% 0.21/0.51 ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z)))) | ((~setIn(X!4, alive)) | (~(host(X!4) = host(W!5))) | setIn(W!5, alive) | (~leq(X!4, W!5)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(92,plain,
% 0.21/0.51 ((~![Z: $i, Pid0: $i] : ((~setIn(Pid0, alive)) | (~(host(Pid0) = host(Z))) | setIn(Z, alive) | (~leq(Pid0, Z)))) | (~setIn(X!4, alive)) | (~(host(X!4) = host(W!5))) | setIn(W!5, alive) | (~leq(X!4, W!5))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.21/0.51 tff(93,plain,
% 0.21/0.51 (setIn(W!5, alive)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[92, 89, 23, 88, 81])).
% 0.21/0.51 tff(94,plain,
% 0.21/0.51 (^[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)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(95,plain,
% 0.21/0.51 (![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))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[94])).
% 0.21/0.51 tff(96,plain,
% 0.21/0.51 (^[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))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(97,plain,
% 0.21/0.51 (![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))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[96])).
% 0.21/0.51 tff(98,plain,
% 0.21/0.51 (![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)))))),
% 0.21/0.51 inference(and_elim,[status(thm)],[21])).
% 0.21/0.51 tff(99,plain,
% 0.21/0.51 (![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))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.21/0.51 tff(100,plain,
% 0.21/0.51 (![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.21/0.51 tff(101,plain,
% 0.21/0.51 (host(Z0!10) = host(Y0!8)),
% 0.21/0.51 inference(and_elim,[status(thm)],[30])).
% 0.21/0.51 tff(102,assumption,(Y0!8 = W!5), introduced(assumption)).
% 0.21/0.51 tff(103,plain,
% 0.21/0.51 (host(Y0!8) = host(W!5)),
% 0.21/0.51 inference(monotonicity,[status(thm)],[102])).
% 0.21/0.51 tff(104,plain,
% 0.21/0.51 (host(Y0!8) = host(Z!7)),
% 0.21/0.51 inference(transitivity,[status(thm)],[103, 24, 22])).
% 0.21/0.51 tff(105,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[31, 104])).
% 0.21/0.51 tff(106,plain,(~(Y0!8 = W!5)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(107,plain,
% 0.21/0.51 (((Y0!8 = W!5) | (~((Y0!8 = X!4) | (~setIn(Y0!8, alive))))) <=> ((Y0!8 = W!5) | (~((Y0!8 = X!4) | (~setIn(Y0!8, alive)))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(108,plain,
% 0.21/0.51 (((~(Y0!8 = X!4)) & setIn(Y0!8, alive)) <=> (~((Y0!8 = X!4) | (~setIn(Y0!8, alive))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(109,plain,
% 0.21/0.51 (((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) <=> ((Y0!8 = W!5) | (~((Y0!8 = X!4) | (~setIn(Y0!8, alive)))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[108])).
% 0.21/0.51 tff(110,plain,
% 0.21/0.51 (((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))) <=> ((Y0!8 = W!5) | (~((Y0!8 = X!4) | (~setIn(Y0!8, alive)))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[109, 107])).
% 0.21/0.51 tff(111,plain,
% 0.21/0.51 ((Y0!8 = W!5) | ((~(Y0!8 = X!4)) & setIn(Y0!8, alive))),
% 0.21/0.51 inference(and_elim,[status(thm)],[30])).
% 0.21/0.51 tff(112,plain,
% 0.21/0.51 ((Y0!8 = W!5) | (~((Y0!8 = X!4) | (~setIn(Y0!8, alive))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.21/0.51 tff(113,plain,
% 0.21/0.51 (~((Y0!8 = X!4) | (~setIn(Y0!8, alive)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[112, 106])).
% 0.21/0.51 tff(114,plain,
% 0.21/0.51 (((Y0!8 = X!4) | (~setIn(Y0!8, alive))) | setIn(Y0!8, alive)),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(115,plain,
% 0.21/0.51 (setIn(Y0!8, alive)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.21/0.51 tff(116,plain,
% 0.21/0.51 (elem(m_Down(X0!9), queue(host(Y0!8)))),
% 0.21/0.51 inference(and_elim,[status(thm)],[52])).
% 0.21/0.51 tff(117,plain,
% 0.21/0.51 (((~![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(Y0!8, alive)) | (~setIn(W!5, alive)) | (~(host(X0!9) = host(W!5))) | (~(host(Z0!10) = host(Y0!8))) | (~elem(m_Down(Z0!10), queue(host(W!5)))) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (host(Y0!8) = host(W!5)))) <=> ((~![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(Y0!8, alive)) | (~setIn(W!5, alive)) | (~(host(X0!9) = host(W!5))) | (~(host(Z0!10) = host(Y0!8))) | (~elem(m_Down(Z0!10), queue(host(W!5)))) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (host(Y0!8) = host(W!5)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(118,plain,
% 0.21/0.51 (((~(host(Z0!10) = host(Y0!8))) | (~setIn(Y0!8, alive)) | (host(Y0!8) = host(W!5)) | (~elem(m_Down(Z0!10), queue(host(W!5)))) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~setIn(W!5, alive)) | (~(host(X0!9) = host(W!5)))) <=> ((~setIn(Y0!8, alive)) | (~setIn(W!5, alive)) | (~(host(X0!9) = host(W!5))) | (~(host(Z0!10) = host(Y0!8))) | (~elem(m_Down(Z0!10), queue(host(W!5)))) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (host(Y0!8) = host(W!5)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(119,plain,
% 0.21/0.51 (((~![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(Z0!10) = host(Y0!8))) | (~setIn(Y0!8, alive)) | (host(Y0!8) = host(W!5)) | (~elem(m_Down(Z0!10), queue(host(W!5)))) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~setIn(W!5, alive)) | (~(host(X0!9) = host(W!5))))) <=> ((~![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(Y0!8, alive)) | (~setIn(W!5, alive)) | (~(host(X0!9) = host(W!5))) | (~(host(Z0!10) = host(Y0!8))) | (~elem(m_Down(Z0!10), queue(host(W!5)))) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (host(Y0!8) = host(W!5))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[118])).
% 0.21/0.51 tff(120,plain,
% 0.21/0.51 (((~![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(Z0!10) = host(Y0!8))) | (~setIn(Y0!8, alive)) | (host(Y0!8) = host(W!5)) | (~elem(m_Down(Z0!10), queue(host(W!5)))) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~setIn(W!5, alive)) | (~(host(X0!9) = host(W!5))))) <=> ((~![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(Y0!8, alive)) | (~setIn(W!5, alive)) | (~(host(X0!9) = host(W!5))) | (~(host(Z0!10) = host(Y0!8))) | (~elem(m_Down(Z0!10), queue(host(W!5)))) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (host(Y0!8) = host(W!5)))),
% 0.21/0.51 inference(transitivity,[status(thm)],[119, 117])).
% 0.21/0.51 tff(121,plain,
% 0.21/0.51 ((~![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(Z0!10) = host(Y0!8))) | (~setIn(Y0!8, alive)) | (host(Y0!8) = host(W!5)) | (~elem(m_Down(Z0!10), queue(host(W!5)))) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (~setIn(W!5, alive)) | (~(host(X0!9) = host(W!5))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(122,plain,
% 0.21/0.51 ((~![Z: $i, Pid30: $i, Pid20: $i, Pid0: $i] : ((~(host(Pid0) = host(Pid20))) | (~setIn(Pid20, alive)) | (host(Pid20) = host(Z)) | (~elem(m_Down(Pid0), queue(host(Z)))) | (~elem(m_Down(Pid30), queue(host(Pid20)))) | (~setIn(Z, alive)) | (~(host(Pid30) = host(Z))))) | (~setIn(Y0!8, alive)) | (~setIn(W!5, alive)) | (~(host(X0!9) = host(W!5))) | (~(host(Z0!10) = host(Y0!8))) | (~elem(m_Down(Z0!10), queue(host(W!5)))) | (~elem(m_Down(X0!9), queue(host(Y0!8)))) | (host(Y0!8) = host(W!5))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.21/0.51 tff(123,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[122, 116, 115, 101, 100, 93, 64, 61, 32])).
% 0.21/0.51 % SZS output end Proof
% 0.21/0.51 % E exiting
%------------------------------------------------------------------------------