TSTP Solution File: SWV282-2 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SWV282-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.br2nvdMaiY true
% Computer : n028.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 : Fri Sep 1 00:08:47 EDT 2023
% Result : Unsatisfiable 169.24s 24.81s
% Output : Refutation 169.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV282-2 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.br2nvdMaiY true
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 07:32:40 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.34 % Python version: Python 3.6.8
% 0.13/0.34 % Running in FO mode
% 0.19/0.63 % Total configuration time : 435
% 0.19/0.63 % Estimated wc time : 1092
% 0.19/0.63 % Estimated cpu time (7 cpus) : 156.0
% 0.19/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.19/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.19/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 1.02/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 1.02/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 1.20/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 1.20/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 169.24/24.81 % Solved by fo/fo5.sh.
% 169.24/24.81 % done 358 iterations in 24.051s
% 169.24/24.81 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 169.24/24.81 % SZS output start Refutation
% 169.24/24.81 thf(c_Message_Omsg_ONonce_type, type, c_Message_Omsg_ONonce: $i > $i).
% 169.24/24.81 thf(c_minus_type, type, c_minus: $i > $i > $i > $i).
% 169.24/24.81 thf(c_Event_Oused_type, type, c_Event_Oused: $i > $i).
% 169.24/24.81 thf(v_evs_type, type, v_evs: $i).
% 169.24/24.81 thf(v_evs_H_H_type, type, v_evs_H_H: $i).
% 169.24/24.81 thf(tc_nat_type, type, tc_nat: $i).
% 169.24/24.81 thf(c_Suc_type, type, c_Suc: $i > $i).
% 169.24/24.81 thf(v_sko__urX_type, type, v_sko__urX: $i > $i).
% 169.24/24.81 thf(c_lessequals_type, type, c_lessequals: $i > $i > $i > $o).
% 169.24/24.81 thf(c_1_type, type, c_1: $i).
% 169.24/24.81 thf(c_Binomial_Obinomial_type, type, c_Binomial_Obinomial: $i > $i > $i).
% 169.24/24.81 thf(v_evs_H_type, type, v_evs_H: $i).
% 169.24/24.81 thf(c_in_type, type, c_in: $i > $i > $i > $o).
% 169.24/24.81 thf(c_plus_type, type, c_plus: $i > $i > $i > $i).
% 169.24/24.81 thf(tc_Message_Omsg_type, type, tc_Message_Omsg: $i).
% 169.24/24.81 thf(c_less_type, type, c_less: $i > $i > $i > $o).
% 169.24/24.81 thf(c_0_type, type, c_0: $i).
% 169.24/24.81 thf(cls_Nat_OlessI_0, axiom, (c_less @ V_n @ ( c_Suc @ V_n ) @ tc_nat)).
% 169.24/24.81 thf(zip_derived_cl8, plain,
% 169.24/24.81 (![X0 : $i]: (c_less @ X0 @ (c_Suc @ X0) @ tc_nat)),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_OlessI_0])).
% 169.24/24.81 thf(cls_Nat_Ole__add1_0, axiom,
% 169.24/24.81 (c_lessequals @ V_n @ ( c_plus @ V_n @ V_m @ tc_nat ) @ tc_nat)).
% 169.24/24.81 thf(zip_derived_cl7, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (c_lessequals @ X0 @ (c_plus @ X0 @ X1 @ tc_nat) @ tc_nat)),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Ole__add1_0])).
% 169.24/24.81 thf(zip_derived_cl8, plain,
% 169.24/24.81 (![X0 : $i]: (c_less @ X0 @ (c_Suc @ X0) @ tc_nat)),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_OlessI_0])).
% 169.24/24.81 thf(zip_derived_cl7, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (c_lessequals @ X0 @ (c_plus @ X0 @ X1 @ tc_nat) @ tc_nat)),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Ole__add1_0])).
% 169.24/24.81 thf(cls_Nat_Odiff__self__eq__0_0, axiom,
% 169.24/24.81 (( c_minus @ V_m @ V_m @ tc_nat ) = ( c_0 ))).
% 169.24/24.81 thf(zip_derived_cl6, plain,
% 169.24/24.81 (![X0 : $i]: ((c_minus @ X0 @ X0 @ tc_nat) = (c_0))),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Odiff__self__eq__0_0])).
% 169.24/24.81 thf(cls_Nat_Odiff__is__0__eq_0, axiom,
% 169.24/24.81 (( ( c_minus @ V_m @ V_n @ tc_nat ) != ( c_0 ) ) |
% 169.24/24.81 ( c_lessequals @ V_m @ V_n @ tc_nat ))).
% 169.24/24.81 thf(zip_derived_cl5, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (((c_minus @ X0 @ X1 @ tc_nat) != (c_0))
% 169.24/24.81 | (c_lessequals @ X0 @ X1 @ tc_nat))),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Odiff__is__0__eq_0])).
% 169.24/24.81 thf(zip_derived_cl121, plain,
% 169.24/24.81 (![X0 : $i]: (((c_0) != (c_0)) | (c_lessequals @ X0 @ X0 @ tc_nat))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl6, zip_derived_cl5])).
% 169.24/24.81 thf(zip_derived_cl122, plain,
% 169.24/24.81 (![X0 : $i]: (c_lessequals @ X0 @ X0 @ tc_nat)),
% 169.24/24.81 inference('simplify', [status(thm)], [zip_derived_cl121])).
% 169.24/24.81 thf(cls_conjecture_0, conjecture,
% 169.24/24.81 (~( ( c_in @
% 169.24/24.81 ( c_Message_Omsg_ONonce @ V_U ) @ ( c_Event_Oused @ v_evs ) @
% 169.24/24.81 tc_Message_Omsg ) |
% 169.24/24.81 ( c_in @
% 169.24/24.81 ( c_Message_Omsg_ONonce @ V_V ) @ ( c_Event_Oused @ v_evs_H ) @
% 169.24/24.81 tc_Message_Omsg ) |
% 169.24/24.81 ( c_in @
% 169.24/24.81 ( c_Message_Omsg_ONonce @ V_W ) @ ( c_Event_Oused @ v_evs_H_H ) @
% 169.24/24.81 tc_Message_Omsg ) |
% 169.24/24.81 ( ( V_U ) = ( V_V ) ) | ( ( V_V ) = ( V_W ) ) | ( ( V_U ) = ( V_W ) ) ))).
% 169.24/24.81 thf(zf_stmt_0, negated_conjecture,
% 169.24/24.81 (( c_in @
% 169.24/24.81 ( c_Message_Omsg_ONonce @ V_U ) @ ( c_Event_Oused @ v_evs ) @
% 169.24/24.81 tc_Message_Omsg ) |
% 169.24/24.81 ( c_in @
% 169.24/24.81 ( c_Message_Omsg_ONonce @ V_V ) @ ( c_Event_Oused @ v_evs_H ) @
% 169.24/24.81 tc_Message_Omsg ) |
% 169.24/24.81 ( c_in @
% 169.24/24.81 ( c_Message_Omsg_ONonce @ V_W ) @ ( c_Event_Oused @ v_evs_H_H ) @
% 169.24/24.81 tc_Message_Omsg ) |
% 169.24/24.81 ( ( V_U ) = ( V_V ) ) | ( ( V_V ) = ( V_W ) ) | ( ( V_U ) = ( V_W ) )),
% 169.24/24.81 inference('cnf.neg', [status(esa)], [cls_conjecture_0])).
% 169.24/24.81 thf(zip_derived_cl0, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 169.24/24.81 ( (c_in @ (c_Message_Omsg_ONonce @ X0) @ (c_Event_Oused @ v_evs) @
% 169.24/24.81 tc_Message_Omsg)
% 169.24/24.81 | (c_in @ (c_Message_Omsg_ONonce @ X1) @
% 169.24/24.81 (c_Event_Oused @ v_evs_H) @ tc_Message_Omsg)
% 169.24/24.81 | (c_in @ (c_Message_Omsg_ONonce @ X2) @
% 169.24/24.81 (c_Event_Oused @ v_evs_H_H) @ tc_Message_Omsg)
% 169.24/24.81 | ((X0) = (X1))
% 169.24/24.81 | ((X1) = (X2))
% 169.24/24.81 | ((X0) = (X2)))),
% 169.24/24.81 inference('cnf', [status(esa)], [zf_stmt_0])).
% 169.24/24.81 thf(cls_Public_ONonce__supply__lemma_0, axiom,
% 169.24/24.81 (( ~( c_in @
% 169.24/24.81 ( c_Message_Omsg_ONonce @ V_U ) @ ( c_Event_Oused @ V_evs ) @
% 169.24/24.81 tc_Message_Omsg ) ) |
% 169.24/24.81 ( ~( c_lessequals @ ( v_sko__urX @ V_evs ) @ V_U @ tc_nat ) ))).
% 169.24/24.81 thf(zip_derived_cl12, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (~ (c_in @ (c_Message_Omsg_ONonce @ X0) @ (c_Event_Oused @ X1) @
% 169.24/24.81 tc_Message_Omsg)
% 169.24/24.81 | ~ (c_lessequals @ (v_sko__urX @ X1) @ X0 @ tc_nat))),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Public_ONonce__supply__lemma_0])).
% 169.24/24.81 thf(zip_derived_cl16, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 169.24/24.81 (((X0) = (X1))
% 169.24/24.81 | ((X2) = (X1))
% 169.24/24.81 | ((X0) = (X2))
% 169.24/24.81 | (c_in @ (c_Message_Omsg_ONonce @ X1) @
% 169.24/24.81 (c_Event_Oused @ v_evs_H_H) @ tc_Message_Omsg)
% 169.24/24.81 | (c_in @ (c_Message_Omsg_ONonce @ X2) @
% 169.24/24.81 (c_Event_Oused @ v_evs_H) @ tc_Message_Omsg)
% 169.24/24.81 | ~ (c_lessequals @ (v_sko__urX @ v_evs) @ X0 @ tc_nat))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl12])).
% 169.24/24.81 thf(zip_derived_cl150, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 ( (c_in @ (c_Message_Omsg_ONonce @ X0) @ (c_Event_Oused @ v_evs_H) @
% 169.24/24.81 tc_Message_Omsg)
% 169.24/24.81 | (c_in @ (c_Message_Omsg_ONonce @ X1) @
% 169.24/24.81 (c_Event_Oused @ v_evs_H_H) @ tc_Message_Omsg)
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (X0))
% 169.24/24.81 | ((X0) = (X1))
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (X1)))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl122, zip_derived_cl16])).
% 169.24/24.81 thf(zip_derived_cl12, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (~ (c_in @ (c_Message_Omsg_ONonce @ X0) @ (c_Event_Oused @ X1) @
% 169.24/24.81 tc_Message_Omsg)
% 169.24/24.81 | ~ (c_lessequals @ (v_sko__urX @ X1) @ X0 @ tc_nat))),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Public_ONonce__supply__lemma_0])).
% 169.24/24.81 thf(zip_derived_cl156, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (((v_sko__urX @ v_evs) = (X1))
% 169.24/24.81 | ((X0) = (X1))
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (X0))
% 169.24/24.81 | (c_in @ (c_Message_Omsg_ONonce @ X1) @
% 169.24/24.81 (c_Event_Oused @ v_evs_H_H) @ tc_Message_Omsg)
% 169.24/24.81 | ~ (c_lessequals @ (v_sko__urX @ v_evs_H) @ X0 @ tc_nat))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl150, zip_derived_cl12])).
% 169.24/24.81 thf(zip_derived_cl8, plain,
% 169.24/24.81 (![X0 : $i]: (c_less @ X0 @ (c_Suc @ X0) @ tc_nat)),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_OlessI_0])).
% 169.24/24.81 thf(zip_derived_cl8, plain,
% 169.24/24.81 (![X0 : $i]: (c_less @ X0 @ (c_Suc @ X0) @ tc_nat)),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_OlessI_0])).
% 169.24/24.81 thf(zip_derived_cl7, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (c_lessequals @ X0 @ (c_plus @ X0 @ X1 @ tc_nat) @ tc_nat)),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Ole__add1_0])).
% 169.24/24.81 thf(zip_derived_cl8, plain,
% 169.24/24.81 (![X0 : $i]: (c_less @ X0 @ (c_Suc @ X0) @ tc_nat)),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_OlessI_0])).
% 169.24/24.81 thf(zip_derived_cl7, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (c_lessequals @ X0 @ (c_plus @ X0 @ X1 @ tc_nat) @ tc_nat)),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Ole__add1_0])).
% 169.24/24.81 thf(zip_derived_cl122, plain,
% 169.24/24.81 (![X0 : $i]: (c_lessequals @ X0 @ X0 @ tc_nat)),
% 169.24/24.81 inference('simplify', [status(thm)], [zip_derived_cl121])).
% 169.24/24.81 thf(zip_derived_cl156, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (((v_sko__urX @ v_evs) = (X1))
% 169.24/24.81 | ((X0) = (X1))
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (X0))
% 169.24/24.81 | (c_in @ (c_Message_Omsg_ONonce @ X1) @
% 169.24/24.81 (c_Event_Oused @ v_evs_H_H) @ tc_Message_Omsg)
% 169.24/24.81 | ~ (c_lessequals @ (v_sko__urX @ v_evs_H) @ X0 @ tc_nat))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl150, zip_derived_cl12])).
% 169.24/24.81 thf(zip_derived_cl224, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 ( (c_in @ (c_Message_Omsg_ONonce @ X0) @
% 169.24/24.81 (c_Event_Oused @ v_evs_H_H) @ tc_Message_Omsg)
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H))
% 169.24/24.81 | ((v_sko__urX @ v_evs_H) = (X0))
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (X0)))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl122, zip_derived_cl156])).
% 169.24/24.81 thf(zip_derived_cl12, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (~ (c_in @ (c_Message_Omsg_ONonce @ X0) @ (c_Event_Oused @ X1) @
% 169.24/24.81 tc_Message_Omsg)
% 169.24/24.81 | ~ (c_lessequals @ (v_sko__urX @ X1) @ X0 @ tc_nat))),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Public_ONonce__supply__lemma_0])).
% 169.24/24.81 thf(zip_derived_cl226, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 (((v_sko__urX @ v_evs) = (X0))
% 169.24/24.81 | ((v_sko__urX @ v_evs_H) = (X0))
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H))
% 169.24/24.81 | ~ (c_lessequals @ (v_sko__urX @ v_evs_H_H) @ X0 @ tc_nat))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl224, zip_derived_cl12])).
% 169.24/24.81 thf(zip_derived_cl1096, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 (((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H))
% 169.24/24.81 | ((v_sko__urX @ v_evs_H)
% 169.24/24.81 = (c_plus @ (v_sko__urX @ v_evs_H_H) @ X0 @ tc_nat))
% 169.24/24.81 | ((v_sko__urX @ v_evs)
% 169.24/24.81 = (c_plus @ (v_sko__urX @ v_evs_H_H) @ X0 @ tc_nat)))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl226])).
% 169.24/24.81 thf(cls_Nat_Onot__add__less2_0, axiom,
% 169.24/24.81 (~( c_less @ ( c_plus @ V_j @ V_i @ tc_nat ) @ V_i @ tc_nat ))).
% 169.24/24.81 thf(zip_derived_cl11, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 ~ (c_less @ (c_plus @ X0 @ X1 @ tc_nat) @ X1 @ tc_nat)),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Onot__add__less2_0])).
% 169.24/24.81 thf(zip_derived_cl1336, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 (~ (c_less @ (v_sko__urX @ v_evs) @ X0 @ tc_nat)
% 169.24/24.81 | ((v_sko__urX @ v_evs_H)
% 169.24/24.81 = (c_plus @ (v_sko__urX @ v_evs_H_H) @ X0 @ tc_nat))
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H)))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl1096, zip_derived_cl11])).
% 169.24/24.81 thf(zip_derived_cl1340, plain,
% 169.24/24.81 ((((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H))
% 169.24/24.81 | ((v_sko__urX @ v_evs_H)
% 169.24/24.81 = (c_plus @ (v_sko__urX @ v_evs_H_H) @
% 169.24/24.81 (c_Suc @ (v_sko__urX @ v_evs)) @ tc_nat)))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl1336])).
% 169.24/24.81 thf(zip_derived_cl7, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (c_lessequals @ X0 @ (c_plus @ X0 @ X1 @ tc_nat) @ tc_nat)),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Ole__add1_0])).
% 169.24/24.81 thf(zip_derived_cl1343, plain,
% 169.24/24.81 (( (c_lessequals @ (v_sko__urX @ v_evs_H_H) @ (v_sko__urX @ v_evs_H) @
% 169.24/24.81 tc_nat)
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H)))),
% 169.24/24.81 inference('sup+', [status(thm)], [zip_derived_cl1340, zip_derived_cl7])).
% 169.24/24.81 thf(zip_derived_cl150, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 ( (c_in @ (c_Message_Omsg_ONonce @ X0) @ (c_Event_Oused @ v_evs_H) @
% 169.24/24.81 tc_Message_Omsg)
% 169.24/24.81 | (c_in @ (c_Message_Omsg_ONonce @ X1) @
% 169.24/24.81 (c_Event_Oused @ v_evs_H_H) @ tc_Message_Omsg)
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (X0))
% 169.24/24.81 | ((X0) = (X1))
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (X1)))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl122, zip_derived_cl16])).
% 169.24/24.81 thf(zip_derived_cl12, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (~ (c_in @ (c_Message_Omsg_ONonce @ X0) @ (c_Event_Oused @ X1) @
% 169.24/24.81 tc_Message_Omsg)
% 169.24/24.81 | ~ (c_lessequals @ (v_sko__urX @ X1) @ X0 @ tc_nat))),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Public_ONonce__supply__lemma_0])).
% 169.24/24.81 thf(zip_derived_cl157, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (((v_sko__urX @ v_evs) = (X0))
% 169.24/24.81 | ((X1) = (X0))
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (X1))
% 169.24/24.81 | (c_in @ (c_Message_Omsg_ONonce @ X1) @
% 169.24/24.81 (c_Event_Oused @ v_evs_H) @ tc_Message_Omsg)
% 169.24/24.81 | ~ (c_lessequals @ (v_sko__urX @ v_evs_H_H) @ X0 @ tc_nat))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl150, zip_derived_cl12])).
% 169.24/24.81 thf(zip_derived_cl1356, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 (((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H))
% 169.24/24.81 | (c_in @ (c_Message_Omsg_ONonce @ X0) @
% 169.24/24.81 (c_Event_Oused @ v_evs_H) @ tc_Message_Omsg)
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (X0))
% 169.24/24.81 | ((X0) = (v_sko__urX @ v_evs_H))
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H)))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl1343, zip_derived_cl157])).
% 169.24/24.81 thf(zip_derived_cl1358, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 (((X0) = (v_sko__urX @ v_evs_H))
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (X0))
% 169.24/24.81 | (c_in @ (c_Message_Omsg_ONonce @ X0) @
% 169.24/24.81 (c_Event_Oused @ v_evs_H) @ tc_Message_Omsg)
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H)))),
% 169.24/24.81 inference('simplify', [status(thm)], [zip_derived_cl1356])).
% 169.24/24.81 thf(zip_derived_cl12, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (~ (c_in @ (c_Message_Omsg_ONonce @ X0) @ (c_Event_Oused @ X1) @
% 169.24/24.81 tc_Message_Omsg)
% 169.24/24.81 | ~ (c_lessequals @ (v_sko__urX @ X1) @ X0 @ tc_nat))),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Public_ONonce__supply__lemma_0])).
% 169.24/24.81 thf(zip_derived_cl2707, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 (((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H))
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (X0))
% 169.24/24.81 | ((X0) = (v_sko__urX @ v_evs_H))
% 169.24/24.81 | ~ (c_lessequals @ (v_sko__urX @ v_evs_H) @ X0 @ tc_nat))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl1358, zip_derived_cl12])).
% 169.24/24.81 thf(zip_derived_cl2739, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 (((c_plus @ (v_sko__urX @ v_evs_H) @ X0 @ tc_nat)
% 169.24/24.81 = (v_sko__urX @ v_evs_H))
% 169.24/24.81 | ((v_sko__urX @ v_evs)
% 169.24/24.81 = (c_plus @ (v_sko__urX @ v_evs_H) @ X0 @ tc_nat))
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H)))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl2707])).
% 169.24/24.81 thf(zip_derived_cl11, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 ~ (c_less @ (c_plus @ X0 @ X1 @ tc_nat) @ X1 @ tc_nat)),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Onot__add__less2_0])).
% 169.24/24.81 thf(zip_derived_cl4548, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 (~ (c_less @ (v_sko__urX @ v_evs) @ X0 @ tc_nat)
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H))
% 169.24/24.81 | ((c_plus @ (v_sko__urX @ v_evs_H) @ X0 @ tc_nat)
% 169.24/24.81 = (v_sko__urX @ v_evs_H)))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl2739, zip_derived_cl11])).
% 169.24/24.81 thf(zip_derived_cl5130, plain,
% 169.24/24.81 ((((c_plus @ (v_sko__urX @ v_evs_H) @ (c_Suc @ (v_sko__urX @ v_evs)) @
% 169.24/24.81 tc_nat) = (v_sko__urX @ v_evs_H))
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H)))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl4548])).
% 169.24/24.81 thf(cls_Nat_Onat__add__left__cancel__le_0, axiom,
% 169.24/24.81 (( ~( c_lessequals @
% 169.24/24.81 ( c_plus @ V_k @ V_m @ tc_nat ) @ ( c_plus @ V_k @ V_n @ tc_nat ) @
% 169.24/24.81 tc_nat ) ) |
% 169.24/24.81 ( c_lessequals @ V_m @ V_n @ tc_nat ))).
% 169.24/24.81 thf(zip_derived_cl10, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 169.24/24.81 (~ (c_lessequals @ (c_plus @ X0 @ X1 @ tc_nat) @
% 169.24/24.81 (c_plus @ X0 @ X2 @ tc_nat) @ tc_nat)
% 169.24/24.81 | (c_lessequals @ X1 @ X2 @ tc_nat))),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Onat__add__left__cancel__le_0])).
% 169.24/24.81 thf(zip_derived_cl5469, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 (~ (c_lessequals @ (v_sko__urX @ v_evs_H) @
% 169.24/24.81 (c_plus @ (v_sko__urX @ v_evs_H) @ X0 @ tc_nat) @ tc_nat)
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H))
% 169.24/24.81 | (c_lessequals @ (c_Suc @ (v_sko__urX @ v_evs)) @ X0 @ tc_nat))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl5130, zip_derived_cl10])).
% 169.24/24.81 thf(zip_derived_cl7, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (c_lessequals @ X0 @ (c_plus @ X0 @ X1 @ tc_nat) @ tc_nat)),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Ole__add1_0])).
% 169.24/24.81 thf(zip_derived_cl5479, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 (((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H))
% 169.24/24.81 | (c_lessequals @ (c_Suc @ (v_sko__urX @ v_evs)) @ X0 @ tc_nat))),
% 169.24/24.81 inference('demod', [status(thm)], [zip_derived_cl5469, zip_derived_cl7])).
% 169.24/24.81 thf(cls_Nat_OOne__nat__def_0, axiom, (( c_1 ) = ( c_Suc @ c_0 ))).
% 169.24/24.81 thf(zip_derived_cl4, plain, (((c_1) = (c_Suc @ c_0))),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_OOne__nat__def_0])).
% 169.24/24.81 thf(cls_Binomial_Obinomial__Suc__Suc_0, axiom,
% 169.24/24.81 (( c_Binomial_Obinomial @ ( c_Suc @ V_n ) @ ( c_Suc @ V_k ) ) =
% 169.24/24.81 ( c_plus @
% 169.24/24.81 ( c_Binomial_Obinomial @ V_n @ V_k ) @
% 169.24/24.81 ( c_Binomial_Obinomial @ V_n @ ( c_Suc @ V_k ) ) @ tc_nat ))).
% 169.24/24.81 thf(zip_derived_cl2, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 ((c_Binomial_Obinomial @ (c_Suc @ X0) @ (c_Suc @ X1))
% 169.24/24.81 = (c_plus @ (c_Binomial_Obinomial @ X0 @ X1) @
% 169.24/24.81 (c_Binomial_Obinomial @ X0 @ (c_Suc @ X1)) @ tc_nat))),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Binomial_Obinomial__Suc__Suc_0])).
% 169.24/24.81 thf(zip_derived_cl258, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 ((c_Binomial_Obinomial @ (c_Suc @ X0) @ (c_Suc @ c_0))
% 169.24/24.81 = (c_plus @ (c_Binomial_Obinomial @ X0 @ c_0) @
% 169.24/24.81 (c_Binomial_Obinomial @ X0 @ c_1) @ tc_nat))),
% 169.24/24.81 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl2])).
% 169.24/24.81 thf(zip_derived_cl4, plain, (((c_1) = (c_Suc @ c_0))),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_OOne__nat__def_0])).
% 169.24/24.81 thf(cls_Binomial_Obinomial__1_0, axiom,
% 169.24/24.81 (( c_Binomial_Obinomial @ V_y @ ( c_Suc @ c_0 ) ) = ( V_y ))).
% 169.24/24.81 thf(zip_derived_cl1, plain,
% 169.24/24.81 (![X0 : $i]: ((c_Binomial_Obinomial @ X0 @ (c_Suc @ c_0)) = (X0))),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Binomial_Obinomial__1_0])).
% 169.24/24.81 thf(zip_derived_cl4, plain, (((c_1) = (c_Suc @ c_0))),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_OOne__nat__def_0])).
% 169.24/24.81 thf(zip_derived_cl14, plain,
% 169.24/24.81 (![X0 : $i]: ((c_Binomial_Obinomial @ X0 @ c_1) = (X0))),
% 169.24/24.81 inference('demod', [status(thm)], [zip_derived_cl1, zip_derived_cl4])).
% 169.24/24.81 thf(cls_Binomial_Obinomial__n__0_0, axiom,
% 169.24/24.81 (( c_Binomial_Obinomial @ V_n @ c_0 ) = ( c_1 ))).
% 169.24/24.81 thf(zip_derived_cl3, plain,
% 169.24/24.81 (![X0 : $i]: ((c_Binomial_Obinomial @ X0 @ c_0) = (c_1))),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Binomial_Obinomial__n__0_0])).
% 169.24/24.81 thf(zip_derived_cl14, plain,
% 169.24/24.81 (![X0 : $i]: ((c_Binomial_Obinomial @ X0 @ c_1) = (X0))),
% 169.24/24.81 inference('demod', [status(thm)], [zip_derived_cl1, zip_derived_cl4])).
% 169.24/24.81 thf(zip_derived_cl271, plain,
% 169.24/24.81 (![X0 : $i]: ((c_Suc @ X0) = (c_plus @ c_1 @ X0 @ tc_nat))),
% 169.24/24.81 inference('demod', [status(thm)],
% 169.24/24.81 [zip_derived_cl258, zip_derived_cl4, zip_derived_cl14,
% 169.24/24.81 zip_derived_cl3, zip_derived_cl14])).
% 169.24/24.81 thf(zip_derived_cl10, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 169.24/24.81 (~ (c_lessequals @ (c_plus @ X0 @ X1 @ tc_nat) @
% 169.24/24.81 (c_plus @ X0 @ X2 @ tc_nat) @ tc_nat)
% 169.24/24.81 | (c_lessequals @ X1 @ X2 @ tc_nat))),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Onat__add__left__cancel__le_0])).
% 169.24/24.81 thf(zip_derived_cl274, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (~ (c_lessequals @ (c_Suc @ X0) @ (c_plus @ c_1 @ X1 @ tc_nat) @
% 169.24/24.81 tc_nat)
% 169.24/24.81 | (c_lessequals @ X0 @ X1 @ tc_nat))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl271, zip_derived_cl10])).
% 169.24/24.81 thf(zip_derived_cl271, plain,
% 169.24/24.81 (![X0 : $i]: ((c_Suc @ X0) = (c_plus @ c_1 @ X0 @ tc_nat))),
% 169.24/24.81 inference('demod', [status(thm)],
% 169.24/24.81 [zip_derived_cl258, zip_derived_cl4, zip_derived_cl14,
% 169.24/24.81 zip_derived_cl3, zip_derived_cl14])).
% 169.24/24.81 thf(zip_derived_cl278, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (~ (c_lessequals @ (c_Suc @ X0) @ (c_Suc @ X1) @ tc_nat)
% 169.24/24.81 | (c_lessequals @ X0 @ X1 @ tc_nat))),
% 169.24/24.81 inference('demod', [status(thm)], [zip_derived_cl274, zip_derived_cl271])).
% 169.24/24.81 thf(zip_derived_cl5486, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 (((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H))
% 169.24/24.81 | (c_lessequals @ (v_sko__urX @ v_evs) @ X0 @ tc_nat))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl5479, zip_derived_cl278])).
% 169.24/24.81 thf(cls_Nat_Oless__Suc__eq__le_1, axiom,
% 169.24/24.81 (( ~( c_lessequals @ V_m @ V_n @ tc_nat ) ) |
% 169.24/24.81 ( c_less @ V_m @ ( c_Suc @ V_n ) @ tc_nat ))).
% 169.24/24.81 thf(zip_derived_cl9, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (~ (c_lessequals @ X0 @ X1 @ tc_nat)
% 169.24/24.81 | (c_less @ X0 @ (c_Suc @ X1) @ tc_nat))),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Oless__Suc__eq__le_1])).
% 169.24/24.81 thf(zip_derived_cl5495, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 (((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H))
% 169.24/24.81 | (c_less @ (v_sko__urX @ v_evs) @ (c_Suc @ X0) @ tc_nat))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl5486, zip_derived_cl9])).
% 169.24/24.81 thf(zip_derived_cl1336, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 (~ (c_less @ (v_sko__urX @ v_evs) @ X0 @ tc_nat)
% 169.24/24.81 | ((v_sko__urX @ v_evs_H)
% 169.24/24.81 = (c_plus @ (v_sko__urX @ v_evs_H_H) @ X0 @ tc_nat))
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H)))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl1096, zip_derived_cl11])).
% 169.24/24.81 thf(zip_derived_cl5506, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 (((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H))
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H))
% 169.24/24.81 | ((v_sko__urX @ v_evs_H)
% 169.24/24.81 = (c_plus @ (v_sko__urX @ v_evs_H_H) @ (c_Suc @ X0) @ tc_nat)))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl5495, zip_derived_cl1336])).
% 169.24/24.81 thf(zip_derived_cl5551, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 (((v_sko__urX @ v_evs_H)
% 169.24/24.81 = (c_plus @ (v_sko__urX @ v_evs_H_H) @ (c_Suc @ X0) @ tc_nat))
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H)))),
% 169.24/24.81 inference('simplify', [status(thm)], [zip_derived_cl5506])).
% 169.24/24.81 thf(zip_derived_cl11, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 ~ (c_less @ (c_plus @ X0 @ X1 @ tc_nat) @ X1 @ tc_nat)),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Onot__add__less2_0])).
% 169.24/24.81 thf(zip_derived_cl6983, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 (~ (c_less @ (v_sko__urX @ v_evs_H) @ (c_Suc @ X0) @ tc_nat)
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H)))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl5551, zip_derived_cl11])).
% 169.24/24.81 thf(zip_derived_cl7039, plain,
% 169.24/24.81 (((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl6983])).
% 169.24/24.81 thf(zip_derived_cl7039, plain,
% 169.24/24.81 (((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl6983])).
% 169.24/24.81 thf(zip_derived_cl7089, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (((v_sko__urX @ v_evs_H) = (X1))
% 169.24/24.81 | ((X0) = (X1))
% 169.24/24.81 | ((v_sko__urX @ v_evs_H) = (X0))
% 169.24/24.81 | (c_in @ (c_Message_Omsg_ONonce @ X1) @
% 169.24/24.81 (c_Event_Oused @ v_evs_H_H) @ tc_Message_Omsg)
% 169.24/24.81 | ~ (c_lessequals @ (v_sko__urX @ v_evs_H) @ X0 @ tc_nat))),
% 169.24/24.81 inference('demod', [status(thm)],
% 169.24/24.81 [zip_derived_cl156, zip_derived_cl7039, zip_derived_cl7039])).
% 169.24/24.81 thf(zip_derived_cl8, plain,
% 169.24/24.81 (![X0 : $i]: (c_less @ X0 @ (c_Suc @ X0) @ tc_nat)),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_OlessI_0])).
% 169.24/24.81 thf(zip_derived_cl7, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (c_lessequals @ X0 @ (c_plus @ X0 @ X1 @ tc_nat) @ tc_nat)),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Ole__add1_0])).
% 169.24/24.81 thf(zip_derived_cl122, plain,
% 169.24/24.81 (![X0 : $i]: (c_lessequals @ X0 @ X0 @ tc_nat)),
% 169.24/24.81 inference('simplify', [status(thm)], [zip_derived_cl121])).
% 169.24/24.81 thf(zip_derived_cl157, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (((v_sko__urX @ v_evs) = (X0))
% 169.24/24.81 | ((X1) = (X0))
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (X1))
% 169.24/24.81 | (c_in @ (c_Message_Omsg_ONonce @ X1) @
% 169.24/24.81 (c_Event_Oused @ v_evs_H) @ tc_Message_Omsg)
% 169.24/24.81 | ~ (c_lessequals @ (v_sko__urX @ v_evs_H_H) @ X0 @ tc_nat))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl150, zip_derived_cl12])).
% 169.24/24.81 thf(zip_derived_cl1099, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 ( (c_in @ (c_Message_Omsg_ONonce @ X0) @ (c_Event_Oused @ v_evs_H) @
% 169.24/24.81 tc_Message_Omsg)
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (X0))
% 169.24/24.81 | ((X0) = (v_sko__urX @ v_evs_H_H))
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H_H)))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl122, zip_derived_cl157])).
% 169.24/24.81 thf(zip_derived_cl12, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (~ (c_in @ (c_Message_Omsg_ONonce @ X0) @ (c_Event_Oused @ X1) @
% 169.24/24.81 tc_Message_Omsg)
% 169.24/24.81 | ~ (c_lessequals @ (v_sko__urX @ X1) @ X0 @ tc_nat))),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Public_ONonce__supply__lemma_0])).
% 169.24/24.81 thf(zip_derived_cl1101, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 (((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H_H))
% 169.24/24.81 | ((X0) = (v_sko__urX @ v_evs_H_H))
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (X0))
% 169.24/24.81 | ~ (c_lessequals @ (v_sko__urX @ v_evs_H) @ X0 @ tc_nat))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl1099, zip_derived_cl12])).
% 169.24/24.81 thf(zip_derived_cl1121, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 (((v_sko__urX @ v_evs)
% 169.24/24.81 = (c_plus @ (v_sko__urX @ v_evs_H) @ X0 @ tc_nat))
% 169.24/24.81 | ((c_plus @ (v_sko__urX @ v_evs_H) @ X0 @ tc_nat)
% 169.24/24.81 = (v_sko__urX @ v_evs_H_H))
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H_H)))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl1101])).
% 169.24/24.81 thf(zip_derived_cl11, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 ~ (c_less @ (c_plus @ X0 @ X1 @ tc_nat) @ X1 @ tc_nat)),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Onot__add__less2_0])).
% 169.24/24.81 thf(zip_derived_cl4277, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 (~ (c_less @ (v_sko__urX @ v_evs) @ X0 @ tc_nat)
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H_H))
% 169.24/24.81 | ((c_plus @ (v_sko__urX @ v_evs_H) @ X0 @ tc_nat)
% 169.24/24.81 = (v_sko__urX @ v_evs_H_H)))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl1121, zip_derived_cl11])).
% 169.24/24.81 thf(zip_derived_cl4282, plain,
% 169.24/24.81 ((((c_plus @ (v_sko__urX @ v_evs_H) @ (c_Suc @ (v_sko__urX @ v_evs)) @
% 169.24/24.81 tc_nat) = (v_sko__urX @ v_evs_H_H))
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H_H)))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl4277])).
% 169.24/24.81 thf(zip_derived_cl7, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (c_lessequals @ X0 @ (c_plus @ X0 @ X1 @ tc_nat) @ tc_nat)),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Ole__add1_0])).
% 169.24/24.81 thf(zip_derived_cl9, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (~ (c_lessequals @ X0 @ X1 @ tc_nat)
% 169.24/24.81 | (c_less @ X0 @ (c_Suc @ X1) @ tc_nat))),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Oless__Suc__eq__le_1])).
% 169.24/24.81 thf(zip_derived_cl124, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (c_less @ X1 @ (c_Suc @ (c_plus @ X1 @ X0 @ tc_nat)) @ tc_nat)),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 169.24/24.81 thf(zip_derived_cl4291, plain,
% 169.24/24.81 (( (c_less @ (v_sko__urX @ v_evs_H) @
% 169.24/24.81 (c_Suc @ (v_sko__urX @ v_evs_H_H)) @ tc_nat)
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H_H)))),
% 169.24/24.81 inference('sup+', [status(thm)], [zip_derived_cl4282, zip_derived_cl124])).
% 169.24/24.81 thf(zip_derived_cl7039, plain,
% 169.24/24.81 (((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl6983])).
% 169.24/24.81 thf(zip_derived_cl7100, plain,
% 169.24/24.81 (( (c_less @ (v_sko__urX @ v_evs_H) @
% 169.24/24.81 (c_Suc @ (v_sko__urX @ v_evs_H_H)) @ tc_nat)
% 169.24/24.81 | ((v_sko__urX @ v_evs_H) = (v_sko__urX @ v_evs_H_H)))),
% 169.24/24.81 inference('demod', [status(thm)],
% 169.24/24.81 [zip_derived_cl4291, zip_derived_cl7039])).
% 169.24/24.81 thf(zip_derived_cl4277, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 (~ (c_less @ (v_sko__urX @ v_evs) @ X0 @ tc_nat)
% 169.24/24.81 | ((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H_H))
% 169.24/24.81 | ((c_plus @ (v_sko__urX @ v_evs_H) @ X0 @ tc_nat)
% 169.24/24.81 = (v_sko__urX @ v_evs_H_H)))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl1121, zip_derived_cl11])).
% 169.24/24.81 thf(zip_derived_cl7039, plain,
% 169.24/24.81 (((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl6983])).
% 169.24/24.81 thf(zip_derived_cl7039, plain,
% 169.24/24.81 (((v_sko__urX @ v_evs) = (v_sko__urX @ v_evs_H))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl6983])).
% 169.24/24.81 thf(zip_derived_cl7094, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 (~ (c_less @ (v_sko__urX @ v_evs_H) @ X0 @ tc_nat)
% 169.24/24.81 | ((v_sko__urX @ v_evs_H) = (v_sko__urX @ v_evs_H_H))
% 169.24/24.81 | ((c_plus @ (v_sko__urX @ v_evs_H) @ X0 @ tc_nat)
% 169.24/24.81 = (v_sko__urX @ v_evs_H_H)))),
% 169.24/24.81 inference('demod', [status(thm)],
% 169.24/24.81 [zip_derived_cl4277, zip_derived_cl7039, zip_derived_cl7039])).
% 169.24/24.81 thf(zip_derived_cl10726, plain,
% 169.24/24.81 ((((v_sko__urX @ v_evs_H) = (v_sko__urX @ v_evs_H_H))
% 169.24/24.81 | ((c_plus @ (v_sko__urX @ v_evs_H) @
% 169.24/24.81 (c_Suc @ (v_sko__urX @ v_evs_H_H)) @ tc_nat)
% 169.24/24.81 = (v_sko__urX @ v_evs_H_H))
% 169.24/24.81 | ((v_sko__urX @ v_evs_H) = (v_sko__urX @ v_evs_H_H)))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl7100, zip_derived_cl7094])).
% 169.24/24.81 thf(zip_derived_cl10727, plain,
% 169.24/24.81 ((((c_plus @ (v_sko__urX @ v_evs_H) @
% 169.24/24.81 (c_Suc @ (v_sko__urX @ v_evs_H_H)) @ tc_nat)
% 169.24/24.81 = (v_sko__urX @ v_evs_H_H))
% 169.24/24.81 | ((v_sko__urX @ v_evs_H) = (v_sko__urX @ v_evs_H_H)))),
% 169.24/24.81 inference('simplify', [status(thm)], [zip_derived_cl10726])).
% 169.24/24.81 thf(zip_derived_cl11, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 ~ (c_less @ (c_plus @ X0 @ X1 @ tc_nat) @ X1 @ tc_nat)),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Onot__add__less2_0])).
% 169.24/24.81 thf(zip_derived_cl11383, plain,
% 169.24/24.81 ((~ (c_less @ (v_sko__urX @ v_evs_H_H) @
% 169.24/24.81 (c_Suc @ (v_sko__urX @ v_evs_H_H)) @ tc_nat)
% 169.24/24.81 | ((v_sko__urX @ v_evs_H) = (v_sko__urX @ v_evs_H_H)))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl10727, zip_derived_cl11])).
% 169.24/24.81 thf(zip_derived_cl8, plain,
% 169.24/24.81 (![X0 : $i]: (c_less @ X0 @ (c_Suc @ X0) @ tc_nat)),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_OlessI_0])).
% 169.24/24.81 thf(zip_derived_cl11391, plain,
% 169.24/24.81 (((v_sko__urX @ v_evs_H) = (v_sko__urX @ v_evs_H_H))),
% 169.24/24.81 inference('demod', [status(thm)], [zip_derived_cl11383, zip_derived_cl8])).
% 169.24/24.81 thf(zip_derived_cl11391, plain,
% 169.24/24.81 (((v_sko__urX @ v_evs_H) = (v_sko__urX @ v_evs_H_H))),
% 169.24/24.81 inference('demod', [status(thm)], [zip_derived_cl11383, zip_derived_cl8])).
% 169.24/24.81 thf(zip_derived_cl11391, plain,
% 169.24/24.81 (((v_sko__urX @ v_evs_H) = (v_sko__urX @ v_evs_H_H))),
% 169.24/24.81 inference('demod', [status(thm)], [zip_derived_cl11383, zip_derived_cl8])).
% 169.24/24.81 thf(zip_derived_cl13630, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (((v_sko__urX @ v_evs_H_H) = (X1))
% 169.24/24.81 | ((X0) = (X1))
% 169.24/24.81 | ((v_sko__urX @ v_evs_H_H) = (X0))
% 169.24/24.81 | (c_in @ (c_Message_Omsg_ONonce @ X1) @
% 169.24/24.81 (c_Event_Oused @ v_evs_H_H) @ tc_Message_Omsg)
% 169.24/24.81 | ~ (c_lessequals @ (v_sko__urX @ v_evs_H_H) @ X0 @ tc_nat))),
% 169.24/24.81 inference('demod', [status(thm)],
% 169.24/24.81 [zip_derived_cl7089, zip_derived_cl11391, zip_derived_cl11391,
% 169.24/24.81 zip_derived_cl11391])).
% 169.24/24.81 thf(zip_derived_cl13633, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 ( (c_in @ (c_Message_Omsg_ONonce @ X1) @
% 169.24/24.81 (c_Event_Oused @ v_evs_H_H) @ tc_Message_Omsg)
% 169.24/24.81 | ((v_sko__urX @ v_evs_H_H)
% 169.24/24.81 = (c_plus @ (v_sko__urX @ v_evs_H_H) @ X0 @ tc_nat))
% 169.24/24.81 | ((c_plus @ (v_sko__urX @ v_evs_H_H) @ X0 @ tc_nat) = (X1))
% 169.24/24.81 | ((v_sko__urX @ v_evs_H_H) = (X1)))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl13630])).
% 169.24/24.81 thf(zip_derived_cl11, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 ~ (c_less @ (c_plus @ X0 @ X1 @ tc_nat) @ X1 @ tc_nat)),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Onot__add__less2_0])).
% 169.24/24.81 thf(zip_derived_cl21927, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (~ (c_less @ X0 @ X1 @ tc_nat)
% 169.24/24.81 | ((v_sko__urX @ v_evs_H_H) = (X0))
% 169.24/24.81 | ((v_sko__urX @ v_evs_H_H)
% 169.24/24.81 = (c_plus @ (v_sko__urX @ v_evs_H_H) @ X1 @ tc_nat))
% 169.24/24.81 | (c_in @ (c_Message_Omsg_ONonce @ X0) @
% 169.24/24.81 (c_Event_Oused @ v_evs_H_H) @ tc_Message_Omsg))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl13633, zip_derived_cl11])).
% 169.24/24.81 thf(zip_derived_cl22072, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 ( (c_in @ (c_Message_Omsg_ONonce @ X0) @
% 169.24/24.81 (c_Event_Oused @ v_evs_H_H) @ tc_Message_Omsg)
% 169.24/24.81 | ((v_sko__urX @ v_evs_H_H)
% 169.24/24.81 = (c_plus @ (v_sko__urX @ v_evs_H_H) @ (c_Suc @ X0) @ tc_nat))
% 169.24/24.81 | ((v_sko__urX @ v_evs_H_H) = (X0)))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl8, zip_derived_cl21927])).
% 169.24/24.81 thf(zip_derived_cl12, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (~ (c_in @ (c_Message_Omsg_ONonce @ X0) @ (c_Event_Oused @ X1) @
% 169.24/24.81 tc_Message_Omsg)
% 169.24/24.81 | ~ (c_lessequals @ (v_sko__urX @ X1) @ X0 @ tc_nat))),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Public_ONonce__supply__lemma_0])).
% 169.24/24.81 thf(zip_derived_cl22087, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 (((v_sko__urX @ v_evs_H_H) = (X0))
% 169.24/24.81 | ((v_sko__urX @ v_evs_H_H)
% 169.24/24.81 = (c_plus @ (v_sko__urX @ v_evs_H_H) @ (c_Suc @ X0) @ tc_nat))
% 169.24/24.81 | ~ (c_lessequals @ (v_sko__urX @ v_evs_H_H) @ X0 @ tc_nat))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl22072, zip_derived_cl12])).
% 169.24/24.81 thf(zip_derived_cl24082, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 (((v_sko__urX @ v_evs_H_H)
% 169.24/24.81 = (c_plus @ (v_sko__urX @ v_evs_H_H) @
% 169.24/24.81 (c_Suc @ (c_plus @ (v_sko__urX @ v_evs_H_H) @ X0 @ tc_nat)) @
% 169.24/24.81 tc_nat))
% 169.24/24.81 | ((v_sko__urX @ v_evs_H_H)
% 169.24/24.81 = (c_plus @ (v_sko__urX @ v_evs_H_H) @ X0 @ tc_nat)))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl22087])).
% 169.24/24.81 thf(zip_derived_cl11, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 ~ (c_less @ (c_plus @ X0 @ X1 @ tc_nat) @ X1 @ tc_nat)),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Onot__add__less2_0])).
% 169.24/24.81 thf(zip_derived_cl24853, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 (~ (c_less @ (v_sko__urX @ v_evs_H_H) @
% 169.24/24.81 (c_Suc @ (c_plus @ (v_sko__urX @ v_evs_H_H) @ X0 @ tc_nat)) @
% 169.24/24.81 tc_nat)
% 169.24/24.81 | ((v_sko__urX @ v_evs_H_H)
% 169.24/24.81 = (c_plus @ (v_sko__urX @ v_evs_H_H) @ X0 @ tc_nat)))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl24082, zip_derived_cl11])).
% 169.24/24.81 thf(zip_derived_cl124, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (c_less @ X1 @ (c_Suc @ (c_plus @ X1 @ X0 @ tc_nat)) @ tc_nat)),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 169.24/24.81 thf(zip_derived_cl25047, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 ((v_sko__urX @ v_evs_H_H)
% 169.24/24.81 = (c_plus @ (v_sko__urX @ v_evs_H_H) @ X0 @ tc_nat))),
% 169.24/24.81 inference('demod', [status(thm)],
% 169.24/24.81 [zip_derived_cl24853, zip_derived_cl124])).
% 169.24/24.81 thf(zip_derived_cl271, plain,
% 169.24/24.81 (![X0 : $i]: ((c_Suc @ X0) = (c_plus @ c_1 @ X0 @ tc_nat))),
% 169.24/24.81 inference('demod', [status(thm)],
% 169.24/24.81 [zip_derived_cl258, zip_derived_cl4, zip_derived_cl14,
% 169.24/24.81 zip_derived_cl3, zip_derived_cl14])).
% 169.24/24.81 thf(zip_derived_cl124, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (c_less @ X1 @ (c_Suc @ (c_plus @ X1 @ X0 @ tc_nat)) @ tc_nat)),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl9])).
% 169.24/24.81 thf(zip_derived_cl277, plain,
% 169.24/24.81 (![X0 : $i]: (c_less @ c_1 @ (c_Suc @ (c_Suc @ X0)) @ tc_nat)),
% 169.24/24.81 inference('sup+', [status(thm)], [zip_derived_cl271, zip_derived_cl124])).
% 169.24/24.81 thf(zip_derived_cl21927, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (~ (c_less @ X0 @ X1 @ tc_nat)
% 169.24/24.81 | ((v_sko__urX @ v_evs_H_H) = (X0))
% 169.24/24.81 | ((v_sko__urX @ v_evs_H_H)
% 169.24/24.81 = (c_plus @ (v_sko__urX @ v_evs_H_H) @ X1 @ tc_nat))
% 169.24/24.81 | (c_in @ (c_Message_Omsg_ONonce @ X0) @
% 169.24/24.81 (c_Event_Oused @ v_evs_H_H) @ tc_Message_Omsg))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl13633, zip_derived_cl11])).
% 169.24/24.81 thf(zip_derived_cl22085, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 ( (c_in @ (c_Message_Omsg_ONonce @ c_1) @
% 169.24/24.81 (c_Event_Oused @ v_evs_H_H) @ tc_Message_Omsg)
% 169.24/24.81 | ((v_sko__urX @ v_evs_H_H)
% 169.24/24.81 = (c_plus @ (v_sko__urX @ v_evs_H_H) @ (c_Suc @ (c_Suc @ X0)) @
% 169.24/24.81 tc_nat))
% 169.24/24.81 | ((v_sko__urX @ v_evs_H_H) = (c_1)))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl277, zip_derived_cl21927])).
% 169.24/24.81 thf(zip_derived_cl10, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 169.24/24.81 (~ (c_lessequals @ (c_plus @ X0 @ X1 @ tc_nat) @
% 169.24/24.81 (c_plus @ X0 @ X2 @ tc_nat) @ tc_nat)
% 169.24/24.81 | (c_lessequals @ X1 @ X2 @ tc_nat))),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Onat__add__left__cancel__le_0])).
% 169.24/24.81 thf(zip_derived_cl22176, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (~ (c_lessequals @ (v_sko__urX @ v_evs_H_H) @
% 169.24/24.81 (c_plus @ (v_sko__urX @ v_evs_H_H) @ X0 @ tc_nat) @ tc_nat)
% 169.24/24.81 | ((v_sko__urX @ v_evs_H_H) = (c_1))
% 169.24/24.81 | (c_in @ (c_Message_Omsg_ONonce @ c_1) @
% 169.24/24.81 (c_Event_Oused @ v_evs_H_H) @ tc_Message_Omsg)
% 169.24/24.81 | (c_lessequals @ (c_Suc @ (c_Suc @ X1)) @ X0 @ tc_nat))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl22085, zip_derived_cl10])).
% 169.24/24.81 thf(zip_derived_cl7, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (c_lessequals @ X0 @ (c_plus @ X0 @ X1 @ tc_nat) @ tc_nat)),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Ole__add1_0])).
% 169.24/24.81 thf(zip_derived_cl22351, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (((v_sko__urX @ v_evs_H_H) = (c_1))
% 169.24/24.81 | (c_in @ (c_Message_Omsg_ONonce @ c_1) @
% 169.24/24.81 (c_Event_Oused @ v_evs_H_H) @ tc_Message_Omsg)
% 169.24/24.81 | (c_lessequals @ (c_Suc @ (c_Suc @ X1)) @ X0 @ tc_nat))),
% 169.24/24.81 inference('demod', [status(thm)], [zip_derived_cl22176, zip_derived_cl7])).
% 169.24/24.81 thf(zip_derived_cl278, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (~ (c_lessequals @ (c_Suc @ X0) @ (c_Suc @ X1) @ tc_nat)
% 169.24/24.81 | (c_lessequals @ X0 @ X1 @ tc_nat))),
% 169.24/24.81 inference('demod', [status(thm)], [zip_derived_cl274, zip_derived_cl271])).
% 169.24/24.81 thf(zip_derived_cl24088, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 ( (c_in @ (c_Message_Omsg_ONonce @ c_1) @
% 169.24/24.81 (c_Event_Oused @ v_evs_H_H) @ tc_Message_Omsg)
% 169.24/24.81 | ((v_sko__urX @ v_evs_H_H) = (c_1))
% 169.24/24.81 | (c_lessequals @ (c_Suc @ X1) @ X0 @ tc_nat))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl22351, zip_derived_cl278])).
% 169.24/24.81 thf(zip_derived_cl278, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (~ (c_lessequals @ (c_Suc @ X0) @ (c_Suc @ X1) @ tc_nat)
% 169.24/24.81 | (c_lessequals @ X0 @ X1 @ tc_nat))),
% 169.24/24.81 inference('demod', [status(thm)], [zip_derived_cl274, zip_derived_cl271])).
% 169.24/24.81 thf(zip_derived_cl24265, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (((v_sko__urX @ v_evs_H_H) = (c_1))
% 169.24/24.81 | (c_in @ (c_Message_Omsg_ONonce @ c_1) @
% 169.24/24.81 (c_Event_Oused @ v_evs_H_H) @ tc_Message_Omsg)
% 169.24/24.81 | (c_lessequals @ X1 @ X0 @ tc_nat))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl24088, zip_derived_cl278])).
% 169.24/24.81 thf(zip_derived_cl9, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (~ (c_lessequals @ X0 @ X1 @ tc_nat)
% 169.24/24.81 | (c_less @ X0 @ (c_Suc @ X1) @ tc_nat))),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Oless__Suc__eq__le_1])).
% 169.24/24.81 thf(zip_derived_cl24355, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 ( (c_in @ (c_Message_Omsg_ONonce @ c_1) @
% 169.24/24.81 (c_Event_Oused @ v_evs_H_H) @ tc_Message_Omsg)
% 169.24/24.81 | ((v_sko__urX @ v_evs_H_H) = (c_1))
% 169.24/24.81 | (c_less @ X1 @ (c_Suc @ X0) @ tc_nat))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl24265, zip_derived_cl9])).
% 169.24/24.81 thf(zip_derived_cl271, plain,
% 169.24/24.81 (![X0 : $i]: ((c_Suc @ X0) = (c_plus @ c_1 @ X0 @ tc_nat))),
% 169.24/24.81 inference('demod', [status(thm)],
% 169.24/24.81 [zip_derived_cl258, zip_derived_cl4, zip_derived_cl14,
% 169.24/24.81 zip_derived_cl3, zip_derived_cl14])).
% 169.24/24.81 thf(zip_derived_cl11, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 ~ (c_less @ (c_plus @ X0 @ X1 @ tc_nat) @ X1 @ tc_nat)),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Onot__add__less2_0])).
% 169.24/24.81 thf(zip_derived_cl275, plain,
% 169.24/24.81 (![X0 : $i]: ~ (c_less @ (c_Suc @ X0) @ X0 @ tc_nat)),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl271, zip_derived_cl11])).
% 169.24/24.81 thf(zip_derived_cl24756, plain,
% 169.24/24.81 ((((v_sko__urX @ v_evs_H_H) = (c_1))
% 169.24/24.81 | (c_in @ (c_Message_Omsg_ONonce @ c_1) @
% 169.24/24.81 (c_Event_Oused @ v_evs_H_H) @ tc_Message_Omsg))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl24355, zip_derived_cl275])).
% 169.24/24.81 thf(zip_derived_cl12, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (~ (c_in @ (c_Message_Omsg_ONonce @ X0) @ (c_Event_Oused @ X1) @
% 169.24/24.81 tc_Message_Omsg)
% 169.24/24.81 | ~ (c_lessequals @ (v_sko__urX @ X1) @ X0 @ tc_nat))),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Public_ONonce__supply__lemma_0])).
% 169.24/24.81 thf(zip_derived_cl24850, plain,
% 169.24/24.81 ((((v_sko__urX @ v_evs_H_H) = (c_1))
% 169.24/24.81 | ~ (c_lessequals @ (v_sko__urX @ v_evs_H_H) @ c_1 @ tc_nat))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl24756, zip_derived_cl12])).
% 169.24/24.81 thf(zip_derived_cl25047, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 ((v_sko__urX @ v_evs_H_H)
% 169.24/24.81 = (c_plus @ (v_sko__urX @ v_evs_H_H) @ X0 @ tc_nat))),
% 169.24/24.81 inference('demod', [status(thm)],
% 169.24/24.81 [zip_derived_cl24853, zip_derived_cl124])).
% 169.24/24.81 thf(zip_derived_cl10, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i, X2 : $i]:
% 169.24/24.81 (~ (c_lessequals @ (c_plus @ X0 @ X1 @ tc_nat) @
% 169.24/24.81 (c_plus @ X0 @ X2 @ tc_nat) @ tc_nat)
% 169.24/24.81 | (c_lessequals @ X1 @ X2 @ tc_nat))),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Onat__add__left__cancel__le_0])).
% 169.24/24.81 thf(zip_derived_cl25051, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 (~ (c_lessequals @ (v_sko__urX @ v_evs_H_H) @
% 169.24/24.81 (c_plus @ (v_sko__urX @ v_evs_H_H) @ X0 @ tc_nat) @ tc_nat)
% 169.24/24.81 | (c_lessequals @ X1 @ X0 @ tc_nat))),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl25047, zip_derived_cl10])).
% 169.24/24.81 thf(zip_derived_cl25047, plain,
% 169.24/24.81 (![X0 : $i]:
% 169.24/24.81 ((v_sko__urX @ v_evs_H_H)
% 169.24/24.81 = (c_plus @ (v_sko__urX @ v_evs_H_H) @ X0 @ tc_nat))),
% 169.24/24.81 inference('demod', [status(thm)],
% 169.24/24.81 [zip_derived_cl24853, zip_derived_cl124])).
% 169.24/24.81 thf(zip_derived_cl122, plain,
% 169.24/24.81 (![X0 : $i]: (c_lessequals @ X0 @ X0 @ tc_nat)),
% 169.24/24.81 inference('simplify', [status(thm)], [zip_derived_cl121])).
% 169.24/24.81 thf(zip_derived_cl25062, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]: (c_lessequals @ X1 @ X0 @ tc_nat)),
% 169.24/24.81 inference('demod', [status(thm)],
% 169.24/24.81 [zip_derived_cl25051, zip_derived_cl25047, zip_derived_cl122])).
% 169.24/24.81 thf(zip_derived_cl25080, plain, (((v_sko__urX @ v_evs_H_H) = (c_1))),
% 169.24/24.81 inference('demod', [status(thm)],
% 169.24/24.81 [zip_derived_cl24850, zip_derived_cl25062])).
% 169.24/24.81 thf(zip_derived_cl25080, plain, (((v_sko__urX @ v_evs_H_H) = (c_1))),
% 169.24/24.81 inference('demod', [status(thm)],
% 169.24/24.81 [zip_derived_cl24850, zip_derived_cl25062])).
% 169.24/24.81 thf(zip_derived_cl271, plain,
% 169.24/24.81 (![X0 : $i]: ((c_Suc @ X0) = (c_plus @ c_1 @ X0 @ tc_nat))),
% 169.24/24.81 inference('demod', [status(thm)],
% 169.24/24.81 [zip_derived_cl258, zip_derived_cl4, zip_derived_cl14,
% 169.24/24.81 zip_derived_cl3, zip_derived_cl14])).
% 169.24/24.81 thf(zip_derived_cl25090, plain, (![X0 : $i]: ((c_1) = (c_Suc @ X0))),
% 169.24/24.81 inference('demod', [status(thm)],
% 169.24/24.81 [zip_derived_cl25047, zip_derived_cl25080,
% 169.24/24.81 zip_derived_cl25080, zip_derived_cl271])).
% 169.24/24.81 thf(zip_derived_cl26267, plain, (![X0 : $i]: (c_less @ X0 @ c_1 @ tc_nat)),
% 169.24/24.81 inference('demod', [status(thm)], [zip_derived_cl8, zip_derived_cl25090])).
% 169.24/24.81 thf(zip_derived_cl11, plain,
% 169.24/24.81 (![X0 : $i, X1 : $i]:
% 169.24/24.81 ~ (c_less @ (c_plus @ X0 @ X1 @ tc_nat) @ X1 @ tc_nat)),
% 169.24/24.81 inference('cnf', [status(esa)], [cls_Nat_Onot__add__less2_0])).
% 169.24/24.81 thf(zip_derived_cl27897, plain, ($false),
% 169.24/24.81 inference('sup-', [status(thm)], [zip_derived_cl26267, zip_derived_cl11])).
% 169.24/24.81
% 169.24/24.81 % SZS output end Refutation
% 169.24/24.81
% 169.24/24.81
% 169.24/24.81 % Terminating...
% 169.60/24.90 % Runner terminated.
% 169.60/24.91 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------