TSTP Solution File: SWV284-2 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV284-2 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n029.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 : Wed May 29 18:05:00 EDT 2024
% Result : Unsatisfiable 10.38s 10.58s
% Output : Proof 10.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWV284-2 : TPTP v8.2.0. Released v3.2.0.
% 0.04/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n029.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun May 26 23:13:09 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.50 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.33/10.54 --- Run --no-e-matching --full-saturate-quant at 5...
% 10.38/10.58 % SZS status Unsatisfiable for /export/starexec/sandbox/tmp/tmp.cuDo8302J3/cvc5---1.0.5_13028.smt2
% 10.38/10.58 % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.cuDo8302J3/cvc5---1.0.5_13028.smt2
% 10.38/10.59 (assume a0 (forall ((V_U $$unsorted)) (tptp.c_lessequals V_U (tptp.v_x V_U) tptp.tc_nat)))
% 10.38/10.59 (assume a1 (forall ((V_U $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_U) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N V_U tptp.tc_nat)))))
% 10.38/10.59 (assume a2 (forall ((V_U $$unsorted)) (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x V_U)) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x V_U)) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))))
% 10.38/10.59 (assume a3 (forall ((V_U $$unsorted) (V_msg $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_U) (tptp.c_Message_Oparts (tptp.c_insert V_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX V_msg) V_U tptp.tc_nat)))))
% 10.38/10.59 (assume a4 (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals V_k V_n tptp.tc_nat))))
% 10.38/10.59 (assume a5 (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals V_m V_n tptp.tc_nat))))
% 10.38/10.59 (step t1 (cl (=> (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals V_k V_n tptp.tc_nat))) (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals V_k V_n tptp.tc_nat)))) :rule implies_neg1)
% 10.38/10.59 (anchor :step t2)
% 10.38/10.59 (assume t2.a0 (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals V_k V_n tptp.tc_nat))))
% 10.38/10.59 (step t2.t1 (cl (or (not (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals V_k V_n tptp.tc_nat)))) (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) :rule forall_inst :args ((:= V_m tptp.v_N) (:= V_k (tptp.v_sko__upX tptp.v_msg)) (:= V_n (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)))))
% 10.38/10.59 (step t2.t2 (cl (not (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals V_k V_n tptp.tc_nat)))) (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) :rule or :premises (t2.t1))
% 10.38/10.59 (step t2.t3 (cl (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) :rule resolution :premises (t2.t2 t2.a0))
% 10.38/10.59 (step t2 (cl (not (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals V_k V_n tptp.tc_nat)))) (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) :rule subproof :discharge (t2.a0))
% 10.38/10.59 (step t3 (cl (=> (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals V_k V_n tptp.tc_nat))) (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) :rule resolution :premises (t1 t2))
% 10.38/10.59 (step t4 (cl (=> (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals V_k V_n tptp.tc_nat))) (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) (not (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) :rule implies_neg2)
% 10.38/10.59 (step t5 (cl (=> (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals V_k V_n tptp.tc_nat))) (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) (=> (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals V_k V_n tptp.tc_nat))) (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) :rule resolution :premises (t3 t4))
% 10.38/10.59 (step t6 (cl (=> (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals V_k V_n tptp.tc_nat))) (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) :rule contraction :premises (t5))
% 10.38/10.59 (step t7 (cl (not (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals V_k V_n tptp.tc_nat)))) (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) :rule implies :premises (t6))
% 10.38/10.59 (step t8 (cl (not (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) :rule or_pos)
% 10.38/10.59 (step t9 (cl (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat) (not (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) :rule reordering :premises (t8))
% 10.38/10.59 (step t10 (cl (=> (forall ((V_U $$unsorted)) (tptp.c_lessequals V_U (tptp.v_x V_U) tptp.tc_nat)) (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (forall ((V_U $$unsorted)) (tptp.c_lessequals V_U (tptp.v_x V_U) tptp.tc_nat))) :rule implies_neg1)
% 10.38/10.59 (anchor :step t11)
% 10.38/10.59 (assume t11.a0 (forall ((V_U $$unsorted)) (tptp.c_lessequals V_U (tptp.v_x V_U) tptp.tc_nat)))
% 10.38/10.59 (step t11.t1 (cl (or (not (forall ((V_U $$unsorted)) (tptp.c_lessequals V_U (tptp.v_x V_U) tptp.tc_nat))) (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) :rule forall_inst :args ((:= V_U (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))))
% 10.38/10.59 (step t11.t2 (cl (not (forall ((V_U $$unsorted)) (tptp.c_lessequals V_U (tptp.v_x V_U) tptp.tc_nat))) (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) :rule or :premises (t11.t1))
% 10.38/10.59 (step t11.t3 (cl (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) :rule resolution :premises (t11.t2 t11.a0))
% 10.38/10.59 (step t11 (cl (not (forall ((V_U $$unsorted)) (tptp.c_lessequals V_U (tptp.v_x V_U) tptp.tc_nat))) (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) :rule subproof :discharge (t11.a0))
% 10.38/10.59 (step t12 (cl (=> (forall ((V_U $$unsorted)) (tptp.c_lessequals V_U (tptp.v_x V_U) tptp.tc_nat)) (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) :rule resolution :premises (t10 t11))
% 10.38/10.59 (step t13 (cl (=> (forall ((V_U $$unsorted)) (tptp.c_lessequals V_U (tptp.v_x V_U) tptp.tc_nat)) (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) :rule implies_neg2)
% 10.38/10.59 (step t14 (cl (=> (forall ((V_U $$unsorted)) (tptp.c_lessequals V_U (tptp.v_x V_U) tptp.tc_nat)) (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (=> (forall ((V_U $$unsorted)) (tptp.c_lessequals V_U (tptp.v_x V_U) tptp.tc_nat)) (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) :rule resolution :premises (t12 t13))
% 10.38/10.59 (step t15 (cl (=> (forall ((V_U $$unsorted)) (tptp.c_lessequals V_U (tptp.v_x V_U) tptp.tc_nat)) (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) :rule contraction :premises (t14))
% 10.38/10.59 (step t16 (cl (not (forall ((V_U $$unsorted)) (tptp.c_lessequals V_U (tptp.v_x V_U) tptp.tc_nat))) (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) :rule implies :premises (t15))
% 10.38/10.59 (step t17 (cl (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) :rule resolution :premises (t16 a0))
% 10.38/10.59 (step t18 (cl (not (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) :rule or_pos)
% 10.38/10.59 (step t19 (cl (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (not (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))))) :rule reordering :premises (t18))
% 10.38/10.59 (step t20 (cl (not (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) :rule or_pos)
% 10.38/10.59 (step t21 (cl (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg) (not (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))) :rule reordering :premises (t20))
% 10.38/10.59 (step t22 (cl (not (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) :rule or_pos)
% 10.38/10.59 (step t23 (cl (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (not (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))))) :rule reordering :premises (t22))
% 10.38/10.59 (step t24 (cl (not (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) :rule or_pos)
% 10.38/10.59 (step t25 (cl (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat) (not (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) :rule reordering :premises (t24))
% 10.38/10.59 (step t26 (cl (=> (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals V_m V_n tptp.tc_nat)))) :rule implies_neg1)
% 10.38/10.59 (anchor :step t27)
% 10.38/10.59 (assume t27.a0 (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals V_m V_n tptp.tc_nat))))
% 10.38/10.59 (step t27.t1 (cl (or (not (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) :rule forall_inst :args ((:= V_m tptp.v_N) (:= V_k (tptp.v_sko__upX tptp.v_msg)) (:= V_n (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)))))
% 10.38/10.59 (step t27.t2 (cl (not (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) :rule or :premises (t27.t1))
% 10.38/10.59 (step t27.t3 (cl (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) :rule resolution :premises (t27.t2 t27.a0))
% 10.38/10.59 (step t27 (cl (not (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) :rule subproof :discharge (t27.a0))
% 10.38/10.59 (step t28 (cl (=> (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) :rule resolution :premises (t26 t27))
% 10.38/10.59 (step t29 (cl (=> (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) (not (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) :rule implies_neg2)
% 10.38/10.59 (step t30 (cl (=> (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) (=> (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) :rule resolution :premises (t28 t29))
% 10.38/10.59 (step t31 (cl (=> (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) :rule contraction :premises (t30))
% 10.38/10.59 (step t32 (cl (not (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals (tptp.c_plus V_m V_k tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) :rule implies :premises (t31))
% 10.38/10.59 (step t33 (cl (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) :rule resolution :premises (t32 a5))
% 10.38/10.59 (step t34 (cl (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) :rule resolution :premises (t25 t17 t33))
% 10.38/10.59 (step t35 (cl (=> (forall ((V_U $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_U) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N V_U tptp.tc_nat)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) (forall ((V_U $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_U) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N V_U tptp.tc_nat))))) :rule implies_neg1)
% 10.38/10.59 (anchor :step t36)
% 10.38/10.59 (assume t36.a0 (forall ((V_U $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_U) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N V_U tptp.tc_nat)))))
% 10.38/10.59 (step t36.t1 (cl (or (not (forall ((V_U $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_U) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N V_U tptp.tc_nat))))) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))))) :rule forall_inst :args ((:= V_U (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)))))
% 10.38/10.59 (step t36.t2 (cl (not (forall ((V_U $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_U) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N V_U tptp.tc_nat))))) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) :rule or :premises (t36.t1))
% 10.38/10.59 (step t36.t3 (cl (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) :rule resolution :premises (t36.t2 t36.a0))
% 10.38/10.59 (step t36 (cl (not (forall ((V_U $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_U) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N V_U tptp.tc_nat))))) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) :rule subproof :discharge (t36.a0))
% 10.38/10.59 (step t37 (cl (=> (forall ((V_U $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_U) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N V_U tptp.tc_nat)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) :rule resolution :premises (t35 t36))
% 10.38/10.59 (step t38 (cl (=> (forall ((V_U $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_U) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N V_U tptp.tc_nat)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) (not (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))))) :rule implies_neg2)
% 10.38/10.59 (step t39 (cl (=> (forall ((V_U $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_U) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N V_U tptp.tc_nat)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) (=> (forall ((V_U $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_U) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N V_U tptp.tc_nat)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))))) :rule resolution :premises (t37 t38))
% 10.38/10.59 (step t40 (cl (=> (forall ((V_U $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_U) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N V_U tptp.tc_nat)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))))) :rule contraction :premises (t39))
% 10.38/10.59 (step t41 (cl (not (forall ((V_U $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_U) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N V_U tptp.tc_nat))))) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) :rule implies :premises (t40))
% 10.38/10.59 (step t42 (cl (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals tptp.v_N (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) :rule resolution :premises (t41 a1))
% 10.38/10.59 (step t43 (cl (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg))) :rule resolution :premises (t23 t34 t42))
% 10.38/10.59 (step t44 (cl (=> (forall ((V_U $$unsorted)) (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x V_U)) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x V_U)) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))) (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))) (forall ((V_U $$unsorted)) (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x V_U)) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x V_U)) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))) :rule implies_neg1)
% 10.38/10.59 (anchor :step t45)
% 10.38/10.59 (assume t45.a0 (forall ((V_U $$unsorted)) (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x V_U)) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x V_U)) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))))
% 10.38/10.59 (step t45.t1 (cl (or (not (forall ((V_U $$unsorted)) (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x V_U)) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x V_U)) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))) (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))) :rule forall_inst :args ((:= V_U (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))))
% 10.38/10.59 (step t45.t2 (cl (not (forall ((V_U $$unsorted)) (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x V_U)) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x V_U)) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))) (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))) :rule or :premises (t45.t1))
% 10.38/10.59 (step t45.t3 (cl (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))) :rule resolution :premises (t45.t2 t45.a0))
% 10.38/10.59 (step t45 (cl (not (forall ((V_U $$unsorted)) (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x V_U)) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x V_U)) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))) (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))) :rule subproof :discharge (t45.a0))
% 10.38/10.59 (step t46 (cl (=> (forall ((V_U $$unsorted)) (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x V_U)) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x V_U)) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))) (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))) (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))) :rule resolution :premises (t44 t45))
% 10.38/10.59 (step t47 (cl (=> (forall ((V_U $$unsorted)) (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x V_U)) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x V_U)) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))) (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))) (not (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))) :rule implies_neg2)
% 10.38/10.59 (step t48 (cl (=> (forall ((V_U $$unsorted)) (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x V_U)) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x V_U)) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))) (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))) (=> (forall ((V_U $$unsorted)) (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x V_U)) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x V_U)) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))) (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))) :rule resolution :premises (t46 t47))
% 10.38/10.59 (step t49 (cl (=> (forall ((V_U $$unsorted)) (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x V_U)) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x V_U)) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))) (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))) :rule contraction :premises (t48))
% 10.38/10.59 (step t50 (cl (not (forall ((V_U $$unsorted)) (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x V_U)) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x V_U)) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)))) (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))) :rule implies :premises (t49))
% 10.38/10.59 (step t51 (cl (or (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Event_Oused tptp.v_list) tptp.tc_Message_Omsg) (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg))) :rule resolution :premises (t50 a2))
% 10.38/10.59 (step t52 (cl (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) :rule resolution :premises (t21 t43 t51))
% 10.38/10.59 (step t53 (cl (=> (forall ((V_U $$unsorted) (V_msg $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_U) (tptp.c_Message_Oparts (tptp.c_insert V_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX V_msg) V_U tptp.tc_nat)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) (forall ((V_U $$unsorted) (V_msg $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_U) (tptp.c_Message_Oparts (tptp.c_insert V_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX V_msg) V_U tptp.tc_nat))))) :rule implies_neg1)
% 10.38/10.59 (anchor :step t54)
% 10.38/10.59 (assume t54.a0 (forall ((V_U $$unsorted) (V_msg $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_U) (tptp.c_Message_Oparts (tptp.c_insert V_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX V_msg) V_U tptp.tc_nat)))))
% 10.38/10.59 (step t54.t1 (cl (or (not (forall ((V_U $$unsorted) (V_msg $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_U) (tptp.c_Message_Oparts (tptp.c_insert V_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX V_msg) V_U tptp.tc_nat))))) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))))) :rule forall_inst :args ((:= V_U (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (:= V_msg tptp.v_msg)))
% 10.38/10.59 (step t54.t2 (cl (not (forall ((V_U $$unsorted) (V_msg $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_U) (tptp.c_Message_Oparts (tptp.c_insert V_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX V_msg) V_U tptp.tc_nat))))) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) :rule or :premises (t54.t1))
% 10.38/10.59 (step t54.t3 (cl (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) :rule resolution :premises (t54.t2 t54.a0))
% 10.38/10.59 (step t54 (cl (not (forall ((V_U $$unsorted) (V_msg $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_U) (tptp.c_Message_Oparts (tptp.c_insert V_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX V_msg) V_U tptp.tc_nat))))) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) :rule subproof :discharge (t54.a0))
% 10.38/10.59 (step t55 (cl (=> (forall ((V_U $$unsorted) (V_msg $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_U) (tptp.c_Message_Oparts (tptp.c_insert V_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX V_msg) V_U tptp.tc_nat)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) :rule resolution :premises (t53 t54))
% 10.38/10.59 (step t56 (cl (=> (forall ((V_U $$unsorted) (V_msg $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_U) (tptp.c_Message_Oparts (tptp.c_insert V_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX V_msg) V_U tptp.tc_nat)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) (not (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))))) :rule implies_neg2)
% 10.38/10.59 (step t57 (cl (=> (forall ((V_U $$unsorted) (V_msg $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_U) (tptp.c_Message_Oparts (tptp.c_insert V_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX V_msg) V_U tptp.tc_nat)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) (=> (forall ((V_U $$unsorted) (V_msg $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_U) (tptp.c_Message_Oparts (tptp.c_insert V_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX V_msg) V_U tptp.tc_nat)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))))) :rule resolution :premises (t55 t56))
% 10.38/10.59 (step t58 (cl (=> (forall ((V_U $$unsorted) (V_msg $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_U) (tptp.c_Message_Oparts (tptp.c_insert V_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX V_msg) V_U tptp.tc_nat)))) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))))) :rule contraction :premises (t57))
% 10.38/10.59 (step t59 (cl (not (forall ((V_U $$unsorted) (V_msg $$unsorted)) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce V_U) (tptp.c_Message_Oparts (tptp.c_insert V_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX V_msg) V_U tptp.tc_nat))))) (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) :rule implies :premises (t58))
% 10.38/10.59 (step t60 (cl (or (not (tptp.c_in (tptp.c_Message_Omsg_ONonce (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat))) (tptp.c_Message_Oparts (tptp.c_insert tptp.v_msg tptp.c_emptyset tptp.tc_Message_Omsg)) tptp.tc_Message_Omsg)) (not (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) :rule resolution :premises (t59 a3))
% 10.38/10.59 (step t61 (cl (not (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat))) :rule resolution :premises (t19 t52 t60))
% 10.38/10.59 (step t62 (cl (not (or (not (tptp.c_lessequals (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)) (tptp.c_lessequals (tptp.v_sko__upX tptp.v_msg) (tptp.v_x (tptp.c_plus tptp.v_N (tptp.v_sko__upX tptp.v_msg) tptp.tc_nat)) tptp.tc_nat)))) :rule resolution :premises (t9 t17 t61))
% 10.38/10.59 (step t63 (cl) :rule resolution :premises (t7 t62 a4))
% 10.38/10.59
% 10.38/10.59 % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.cuDo8302J3/cvc5---1.0.5_13028.smt2
% 10.38/10.59 % cvc5---1.0.5 exiting
% 10.38/10.60 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------