%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEV656+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n021.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 : Tue May 5 06:56:03 PM UTC 2026
% Result : Theorem 15.86s 16.11s
% Output : Proof 16.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV656+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.15/0.32 % Computer : n021.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 07:36:12 EDT 2026
% 0.15/0.32 % CPUTime :
% 15.86/16.11 % SZS status Theorem
% 15.86/16.11 % SZS output start Proof
% 15.86/16.11 tff(cCoq_2eInit_2eDatatypes_2ebool___24t_type, type, (
% 15.86/16.11 cCoq_2eInit_2eDatatypes_2ebool___24t: $i > $o)).
% 15.86/16.11 tff(cMaplists_2eMapLists_2ead__list__stutters___24a1_type, type, (
% 15.86/16.11 cMaplists_2eMapLists_2ead__list__stutters___24a1: $i > $i)).
% 15.86/16.11 tff(tptp_fun_V0__l_1722_type, type, (
% 15.86/16.11 tptp_fun_V0__l_1722: $i)).
% 15.86/16.11 tff(happ_type, type, (
% 15.86/16.11 happ: ( $i * $i ) > $i)).
% 15.86/16.11 tff(cCoq_2eInit_2eDatatypes_2econs___24a3_type, type, (
% 15.86/16.11 cCoq_2eInit_2eDatatypes_2econs___24a3: ( $i * $i * $i ) > $i)).
% 15.86/16.11 tff(tptp_fun_Vvar__2___24Anonymous__783_649_type, type, (
% 15.86/16.11 tptp_fun_Vvar__2___24Anonymous__783_649: $i > $i)).
% 15.86/16.11 tff(tptp_fun_Vvar__1___24Anonymous__782_648_type, type, (
% 15.86/16.11 tptp_fun_Vvar__1___24Anonymous__782_648: $i > $i)).
% 15.86/16.11 tff(cIntMap_2eMap_2ead_type, type, (
% 15.86/16.11 cIntMap_2eMap_2ead: $i)).
% 15.86/16.11 tff(cMaplists_2eMapLists_2ead__list__stutters_type, type, (
% 15.86/16.11 cMaplists_2eMapLists_2ead__list__stutters: $i)).
% 15.86/16.11 tff(cCoq_2eInit_2eDatatypes_2eorb___24a2_type, type, (
% 15.86/16.11 cCoq_2eInit_2eDatatypes_2eorb___24a2: ( $i * $i ) > $i)).
% 15.86/16.11 tff(cMaplists_2eMapLists_2ead__in__list___24a2_type, type, (
% 15.86/16.11 cMaplists_2eMapLists_2ead__in__list___24a2: ( $i * $i ) > $i)).
% 15.86/16.11 tff(cCoq_2eInit_2eDatatypes_2elist___24t_type, type, (
% 15.86/16.11 cCoq_2eInit_2eDatatypes_2elist___24t: ( $i * $i ) > $o)).
% 15.86/16.11 tff(cIntMap_2eMap_2ead___24t_type, type, (
% 15.86/16.11 cIntMap_2eMap_2ead___24t: $i > $o)).
% 15.86/16.11 tff(cCoq_2eInit_2eDatatypes_2enil___24a1_type, type, (
% 15.86/16.11 cCoq_2eInit_2eDatatypes_2enil___24a1: $i > $i)).
% 15.86/16.11 tff(cCoq_2eInit_2eDatatypes_2efalse_type, type, (
% 15.86/16.11 cCoq_2eInit_2eDatatypes_2efalse: $i)).
% 15.86/16.11 tff(cCoq_2eInit_2eDatatypes_2eapp___24a3_type, type, (
% 15.86/16.11 cCoq_2eInit_2eDatatypes_2eapp___24a3: ( $i * $i * $i ) > $i)).
% 15.86/16.11 tff(tptp_fun_V1__l_27_1723_type, type, (
% 15.86/16.11 tptp_fun_V1__l_27_1723: $i)).
% 15.86/16.11 tff(c_24__type__785___24t_type, type, (
% 15.86/16.11 c_24__type__785___24t: $i > $o)).
% 15.86/16.11 tff(tptp_fun_Vv__CANONICAL__0_1581_type, type, (
% 15.86/16.11 tptp_fun_Vv__CANONICAL__0_1581: $i > $i)).
% 15.86/16.11 tff(cCoq_2eInit_2eDatatypes_2enegb___24a1_type, type, (
% 15.86/16.11 cCoq_2eInit_2eDatatypes_2enegb___24a1: $i > $i)).
% 15.86/16.11 tff(cCoq_2eInit_2eDatatypes_2etrue_type, type, (
% 15.86/16.11 cCoq_2eInit_2eDatatypes_2etrue: $i)).
% 15.86/16.11 tff(1,plain,
% 15.86/16.11 ((~((cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2efalse) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27!1723)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27!1723)) = cCoq_2eInit_2eDatatypes_2efalse)))) <=> (~((cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2efalse) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27!1723)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27!1723)) = cCoq_2eInit_2eDatatypes_2efalse))))),
% 15.86/16.11 inference(rewrite,[status(thm)],[])).
% 15.86/16.11 tff(2,plain,
% 15.86/16.11 ((cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l!1722) & (~((cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2efalse) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27!1723)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27!1723)) = cCoq_2eInit_2eDatatypes_2efalse))))) <=> (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l!1722) & (~((cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2efalse) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27!1723)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27!1723)) = cCoq_2eInit_2eDatatypes_2efalse)))))),
% 15.86/16.11 inference(monotonicity,[status(thm)],[1])).
% 15.86/16.11 tff(3,plain,
% 15.86/16.11 ((~![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2efalse) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2efalse))))) <=> (~![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2efalse) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2efalse)))))),
% 15.86/16.11 inference(rewrite,[status(thm)],[])).
% 15.86/16.11 tff(4,plain,
% 15.86/16.11 ((~![V0__l: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l) => ![V1__l_27: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27) => ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2efalse) => (cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2efalse))))) <=> (~![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2efalse) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2efalse)))))),
% 15.86/16.11 inference(rewrite,[status(thm)],[])).
% 15.86/16.11 tff(5,axiom,(~![V0__l: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l) => ![V1__l_27: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27) => ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2efalse) => (cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2efalse))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''_HAMMER_GOAL'')).
% 15.86/16.11 tff(6,plain,
% 15.86/16.11 (~![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2efalse) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2efalse))))),
% 15.86/16.11 inference(modus_ponens,[status(thm)],[5, 4])).
% 15.86/16.11 tff(7,plain,
% 15.86/16.11 (~![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2efalse) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2efalse))))),
% 15.86/16.11 inference(modus_ponens,[status(thm)],[6, 3])).
% 15.86/16.11 tff(8,plain,
% 15.86/16.11 (~![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2efalse) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2efalse))))),
% 15.86/16.11 inference(modus_ponens,[status(thm)],[7, 3])).
% 15.86/16.11 tff(9,plain,
% 15.86/16.11 (~![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2efalse) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2efalse))))),
% 15.86/16.11 inference(modus_ponens,[status(thm)],[8, 3])).
% 15.86/16.11 tff(10,plain,
% 15.86/16.11 (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l!1722) & (~((cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2efalse) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27!1723)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27!1723)) = cCoq_2eInit_2eDatatypes_2efalse))))),
% 15.86/16.11 inference(modus_ponens,[status(thm)],[9, 2])).
% 15.86/16.11 tff(11,plain,
% 15.86/16.11 (~((cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2efalse) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27!1723)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27!1723)) = cCoq_2eInit_2eDatatypes_2efalse)))),
% 15.86/16.11 inference(and_elim,[status(thm)],[10])).
% 15.86/16.11 tff(12,plain,
% 15.86/16.11 (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2efalse)),
% 15.86/16.11 inference(or_elim,[status(thm)],[11])).
% 15.86/16.11 tff(13,plain,
% 15.86/16.11 (((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(V0__l!1722 = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)))) | (cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2efalse)),
% 15.86/16.11 inference(tautology,[status(thm)],[])).
% 15.86/16.11 tff(14,plain,
% 15.86/16.11 ((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(V0__l!1722 = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)))),
% 15.86/16.11 inference(unit_resolution,[status(thm)],[13, 12])).
% 15.86/16.11 tff(15,plain,
% 15.86/16.11 (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l!1722)),
% 15.86/16.11 inference(and_elim,[status(thm)],[10])).
% 15.86/16.11 tff(16,plain,
% 15.86/16.11 (^[V1__l: $i] : refl(((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead))))) | (~((~cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) | (~(V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))))))) <=> ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead))))) | (~((~cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) | (~(V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))))))))),
% 15.86/16.11 inference(bind,[status(th)],[])).
% 15.86/16.11 tff(17,plain,
% 15.86/16.11 (![V1__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead))))) | (~((~cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) | (~(V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))))))) <=> ![V1__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead))))) | (~((~cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) | (~(V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))))))))),
% 15.86/16.11 inference(quant_intro,[status(thm)],[16])).
% 15.86/16.11 tff(18,plain,
% 15.86/16.11 (^[V1__l: $i] : trans(monotonicity(rewrite(((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) <=> (~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)))))), rewrite((cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l)) & cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))))) <=> (~((~cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) | (~(V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))))))), ((((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l)) & cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))))) <=> ((~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead))))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (~((~cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) | (~(V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))))))))), rewrite(((~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead))))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (~((~cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) | (~(V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))))))) <=> ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead))))) | (~((~cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) | (~(V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))))))))), ((((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l)) & cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))))) <=> ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead))))) | (~((~cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) | (~(V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))))))))))),
% 15.86/16.11 inference(bind,[status(th)],[])).
% 15.86/16.11 tff(19,plain,
% 15.86/16.11 (![V1__l: $i] : (((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l)) & cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))))) <=> ![V1__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead))))) | (~((~cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) | (~(V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))))))))),
% 15.86/16.11 inference(quant_intro,[status(thm)],[18])).
% 15.86/16.11 tff(20,plain,
% 15.86/16.11 (^[V1__l: $i] : trans(monotonicity(rewrite((cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l)) & (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))))) <=> (cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l)) & cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))))), ((((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l)) & (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))))))) <=> (((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l)) & cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))))))), rewrite((((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l)) & cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))))) <=> (((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l)) & cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))))))), ((((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l)) & (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))))))) <=> (((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l)) & cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))))))))),
% 15.86/16.11 inference(bind,[status(th)],[])).
% 15.86/16.11 tff(21,plain,
% 15.86/16.11 (![V1__l: $i] : (((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l)) & (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))))))) <=> ![V1__l: $i] : (((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l)) & cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))))))),
% 15.86/16.11 inference(quant_intro,[status(thm)],[20])).
% 15.86/16.11 tff(22,plain,
% 15.86/16.11 (![V1__l: $i] : (((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | ?[Vvar__1___24Anonymous__782: $i] : (cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__782) & ?[Vvar__2___24Anonymous__783: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vvar__2___24Anonymous__783) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783), cMaplists_2eMapLists_2ead__list__stutters___24a1(Vvar__2___24Anonymous__783)))))) <=> ![V1__l: $i] : (((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | ?[Vvar__1___24Anonymous__782: $i] : (cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__782) & ?[Vvar__2___24Anonymous__783: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vvar__2___24Anonymous__783) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783), cMaplists_2eMapLists_2ead__list__stutters___24a1(Vvar__2___24Anonymous__783))))))),
% 15.86/16.11 inference(rewrite,[status(thm)],[])).
% 15.86/16.11 tff(23,plain,
% 15.86/16.11 (^[V1__l: $i] : trans(monotonicity(rewrite((((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | ?[Vvar__1___24Anonymous__782: $i] : (cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__782) & ?[Vvar__2___24Anonymous__783: $i] : ((cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vvar__2___24Anonymous__783) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783))) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783), cMaplists_2eMapLists_2ead__list__stutters___24a1(Vvar__2___24Anonymous__783)))))) <=> (((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | ?[Vvar__1___24Anonymous__782: $i] : (cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__782) & ?[Vvar__2___24Anonymous__783: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vvar__2___24Anonymous__783) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783), cMaplists_2eMapLists_2ead__list__stutters___24a1(Vvar__2___24Anonymous__783))))))), ((cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l) => (((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | ?[Vvar__1___24Anonymous__782: $i] : (cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__782) & ?[Vvar__2___24Anonymous__783: $i] : ((cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vvar__2___24Anonymous__783) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783))) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783), cMaplists_2eMapLists_2ead__list__stutters___24a1(Vvar__2___24Anonymous__783))))))) <=> (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l) => (((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | ?[Vvar__1___24Anonymous__782: $i] : (cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__782) & ?[Vvar__2___24Anonymous__783: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vvar__2___24Anonymous__783) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783), cMaplists_2eMapLists_2ead__list__stutters___24a1(Vvar__2___24Anonymous__783))))))))), rewrite((cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l) => (((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | ?[Vvar__1___24Anonymous__782: $i] : (cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__782) & ?[Vvar__2___24Anonymous__783: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vvar__2___24Anonymous__783) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783), cMaplists_2eMapLists_2ead__list__stutters___24a1(Vvar__2___24Anonymous__783))))))) <=> (((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | ?[Vvar__1___24Anonymous__782: $i] : (cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__782) & ?[Vvar__2___24Anonymous__783: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vvar__2___24Anonymous__783) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783), cMaplists_2eMapLists_2ead__list__stutters___24a1(Vvar__2___24Anonymous__783))))))), ((cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l) => (((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | ?[Vvar__1___24Anonymous__782: $i] : (cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__782) & ?[Vvar__2___24Anonymous__783: $i] : ((cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vvar__2___24Anonymous__783) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783))) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783), cMaplists_2eMapLists_2ead__list__stutters___24a1(Vvar__2___24Anonymous__783))))))) <=> (((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | ?[Vvar__1___24Anonymous__782: $i] : (cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__782) & ?[Vvar__2___24Anonymous__783: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vvar__2___24Anonymous__783) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783), cMaplists_2eMapLists_2ead__list__stutters___24a1(Vvar__2___24Anonymous__783))))))))),
% 15.86/16.11 inference(bind,[status(th)],[])).
% 15.86/16.11 tff(24,plain,
% 15.86/16.11 (![V1__l: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l) => (((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | ?[Vvar__1___24Anonymous__782: $i] : (cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__782) & ?[Vvar__2___24Anonymous__783: $i] : ((cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vvar__2___24Anonymous__783) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783))) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783), cMaplists_2eMapLists_2ead__list__stutters___24a1(Vvar__2___24Anonymous__783))))))) <=> ![V1__l: $i] : (((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | ?[Vvar__1___24Anonymous__782: $i] : (cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__782) & ?[Vvar__2___24Anonymous__783: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vvar__2___24Anonymous__783) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783), cMaplists_2eMapLists_2ead__list__stutters___24a1(Vvar__2___24Anonymous__783))))))),
% 15.86/16.11 inference(quant_intro,[status(thm)],[23])).
% 15.86/16.11 tff(25,axiom,(![V1__l: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l) => (((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | ?[Vvar__1___24Anonymous__782: $i] : (cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__782) & ?[Vvar__2___24Anonymous__783: $i] : ((cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vvar__2___24Anonymous__783) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783))) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783), cMaplists_2eMapLists_2ead__list__stutters___24a1(Vvar__2___24Anonymous__783)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''$_def_Maplists.MapLists.ad_list_stutters'')).
% 15.86/16.11 tff(26,plain,
% 15.86/16.11 (![V1__l: $i] : (((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | ?[Vvar__1___24Anonymous__782: $i] : (cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__782) & ?[Vvar__2___24Anonymous__783: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vvar__2___24Anonymous__783) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783), cMaplists_2eMapLists_2ead__list__stutters___24a1(Vvar__2___24Anonymous__783))))))),
% 15.86/16.11 inference(modus_ponens,[status(thm)],[25, 24])).
% 15.86/16.11 tff(27,plain,
% 15.86/16.11 (![V1__l: $i] : (((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | ?[Vvar__1___24Anonymous__782: $i] : (cIntMap_2eMap_2ead___24t(Vvar__1___24Anonymous__782) & ?[Vvar__2___24Anonymous__783: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vvar__2___24Anonymous__783) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(Vvar__1___24Anonymous__782, Vvar__2___24Anonymous__783), cMaplists_2eMapLists_2ead__list__stutters___24a1(Vvar__2___24Anonymous__783))))))),
% 15.86/16.11 inference(modus_ponens,[status(thm)],[26, 22])).
% 15.86/16.11 tff(28,plain,(
% 15.86/16.11 ![V1__l: $i] : (((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l)) & (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))))))),
% 15.86/16.11 inference(skolemize,[status(sab)],[27])).
% 15.86/16.11 tff(29,plain,
% 15.86/16.11 (![V1__l: $i] : (((V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead)) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l)) & cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)) & (V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) & (cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))))))),
% 15.86/16.11 inference(modus_ponens,[status(thm)],[28, 21])).
% 15.86/16.11 tff(30,plain,
% 15.86/16.11 (![V1__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead))))) | (~((~cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) | (~(V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))))))))),
% 15.86/16.11 inference(modus_ponens,[status(thm)],[29, 19])).
% 15.86/16.11 tff(31,plain,
% 15.86/16.11 (![V1__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead))))) | (~((~cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) | (~(V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))))))))),
% 15.86/16.11 inference(modus_ponens,[status(thm)],[30, 17])).
% 15.86/16.11 tff(32,plain,
% 15.86/16.11 (((~![V1__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead))))) | (~((~cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) | (~(V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))))))))) | ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l!1722)) | (~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(V0__l!1722 = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead))))) | (~((~cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722))) | (~(V0__l!1722 = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)))) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722))))))))) <=> ((~![V1__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead))))) | (~((~cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) | (~(V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))))))))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l!1722)) | (~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(V0__l!1722 = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead))))) | (~((~cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722))) | (~(V0__l!1722 = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)))) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722))))))))),
% 15.86/16.11 inference(rewrite,[status(thm)],[])).
% 15.86/16.11 tff(33,plain,
% 15.86/16.11 ((~![V1__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead))))) | (~((~cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) | (~(V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))))))))) | ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l!1722)) | (~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(V0__l!1722 = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead))))) | (~((~cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722))) | (~(V0__l!1722 = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)))) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722))))))))),
% 15.86/16.11 inference(quant_inst,[status(thm)],[])).
% 15.86/16.11 tff(34,plain,
% 15.86/16.11 ((~![V1__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l)) | (~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead))))) | (~((~cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))) | (~(V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)))) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V1__l) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V1__l), tptp_fun_Vvar__2___24Anonymous__783_649(V1__l)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V1__l))))))))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l!1722)) | (~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(V0__l!1722 = cCoq_2eInit_2eDatatypes_2enil___24a1(cIntMap_2eMap_2ead))))) | (~((~cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722))) | (~(V0__l!1722 = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)))) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)))))))),
% 15.86/16.11 inference(modus_ponens,[status(thm)],[33, 32])).
% 15.86/16.11 tff(35,plain,
% 15.86/16.11 (~((~cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722))) | (~(V0__l!1722 = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)))) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722))))))),
% 15.86/16.11 inference(unit_resolution,[status(thm)],[34, 31, 15, 14])).
% 15.86/16.11 tff(36,plain,
% 15.86/16.11 (((~cIntMap_2eMap_2ead___24t(tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722))) | (~(V0__l!1722 = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)))) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2eorb___24a2(cMaplists_2eMapLists_2ead__in__list___24a2(tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)), cMaplists_2eMapLists_2ead__list__stutters___24a1(tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)))))) | (V0__l!1722 = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)))),
% 15.86/16.11 inference(tautology,[status(thm)],[])).
% 15.86/16.11 tff(37,plain,
% 15.86/16.11 (V0__l!1722 = cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722))),
% 15.86/16.11 inference(unit_resolution,[status(thm)],[36, 35])).
% 15.86/16.11 tff(38,plain,
% 15.86/16.11 (cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)) = V0__l!1722),
% 15.86/16.11 inference(symmetry,[status(thm)],[37])).
% 15.86/16.11 tff(39,plain,
% 15.86/16.11 (happ(cMaplists_2eMapLists_2ead__list__stutters, cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722))) = happ(cMaplists_2eMapLists_2ead__list__stutters, V0__l!1722)),
% 15.86/16.11 inference(monotonicity,[status(thm)],[38])).
% 15.86/16.11 tff(40,plain,
% 15.86/16.11 (happ(cMaplists_2eMapLists_2ead__list__stutters, V0__l!1722) = happ(cMaplists_2eMapLists_2ead__list__stutters, cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)))),
% 15.86/16.11 inference(symmetry,[status(thm)],[39])).
% 15.86/16.11 tff(41,plain,
% 15.86/16.11 (^[V_24X1: $i] : refl((happ(cMaplists_2eMapLists_2ead__list__stutters, V_24X1) = cMaplists_2eMapLists_2ead__list__stutters___24a1(V_24X1)) <=> (happ(cMaplists_2eMapLists_2ead__list__stutters, V_24X1) = cMaplists_2eMapLists_2ead__list__stutters___24a1(V_24X1)))),
% 15.86/16.11 inference(bind,[status(th)],[])).
% 15.86/16.11 tff(42,plain,
% 15.86/16.11 (![V_24X1: $i] : (happ(cMaplists_2eMapLists_2ead__list__stutters, V_24X1) = cMaplists_2eMapLists_2ead__list__stutters___24a1(V_24X1)) <=> ![V_24X1: $i] : (happ(cMaplists_2eMapLists_2ead__list__stutters, V_24X1) = cMaplists_2eMapLists_2ead__list__stutters___24a1(V_24X1))),
% 15.86/16.11 inference(quant_intro,[status(thm)],[41])).
% 15.86/16.11 tff(43,plain,
% 15.86/16.11 (![V_24X1: $i] : (happ(cMaplists_2eMapLists_2ead__list__stutters, V_24X1) = cMaplists_2eMapLists_2ead__list__stutters___24a1(V_24X1)) <=> ![V_24X1: $i] : (happ(cMaplists_2eMapLists_2ead__list__stutters, V_24X1) = cMaplists_2eMapLists_2ead__list__stutters___24a1(V_24X1))),
% 15.86/16.11 inference(rewrite,[status(thm)],[])).
% 15.86/16.11 tff(44,axiom,(![V_24X1: $i] : (happ(cMaplists_2eMapLists_2ead__list__stutters, V_24X1) = cMaplists_2eMapLists_2ead__list__stutters___24a1(V_24X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''$adef_Maplists.MapLists.ad_list_stutters_$a1'')).
% 15.86/16.11 tff(45,plain,
% 15.86/16.11 (![V_24X1: $i] : (happ(cMaplists_2eMapLists_2ead__list__stutters, V_24X1) = cMaplists_2eMapLists_2ead__list__stutters___24a1(V_24X1))),
% 15.86/16.11 inference(modus_ponens,[status(thm)],[44, 43])).
% 15.86/16.11 tff(46,plain,(
% 15.86/16.11 ![V_24X1: $i] : (happ(cMaplists_2eMapLists_2ead__list__stutters, V_24X1) = cMaplists_2eMapLists_2ead__list__stutters___24a1(V_24X1))),
% 15.86/16.11 inference(skolemize,[status(sab)],[45])).
% 15.86/16.11 tff(47,plain,
% 15.86/16.11 (![V_24X1: $i] : (happ(cMaplists_2eMapLists_2ead__list__stutters, V_24X1) = cMaplists_2eMapLists_2ead__list__stutters___24a1(V_24X1))),
% 15.86/16.11 inference(modus_ponens,[status(thm)],[46, 42])).
% 15.86/16.11 tff(48,plain,
% 15.86/16.11 ((~![V_24X1: $i] : (happ(cMaplists_2eMapLists_2ead__list__stutters, V_24X1) = cMaplists_2eMapLists_2ead__list__stutters___24a1(V_24X1))) | (happ(cMaplists_2eMapLists_2ead__list__stutters, V0__l!1722) = cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722))),
% 15.86/16.11 inference(quant_inst,[status(thm)],[])).
% 15.86/16.11 tff(49,plain,
% 15.86/16.11 (happ(cMaplists_2eMapLists_2ead__list__stutters, V0__l!1722) = cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722)),
% 15.86/16.11 inference(unit_resolution,[status(thm)],[48, 47])).
% 15.86/16.11 tff(50,plain,
% 15.86/16.11 (cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = happ(cMaplists_2eMapLists_2ead__list__stutters, V0__l!1722)),
% 15.86/16.11 inference(symmetry,[status(thm)],[49])).
% 15.86/16.11 tff(51,plain,
% 15.86/16.11 (cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = happ(cMaplists_2eMapLists_2ead__list__stutters, cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)))),
% 15.86/16.11 inference(transitivity,[status(thm)],[50, 40])).
% 15.86/16.11 tff(52,plain,
% 15.86/16.11 (cCoq_2eInit_2eDatatypes_2ebool___24t(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722)) <=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(cMaplists_2eMapLists_2ead__list__stutters, cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722))))),
% 15.86/16.11 inference(monotonicity,[status(thm)],[51])).
% 15.86/16.11 tff(53,plain,
% 15.86/16.11 (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(cMaplists_2eMapLists_2ead__list__stutters, cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)))) <=> cCoq_2eInit_2eDatatypes_2ebool___24t(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722))),
% 15.86/16.11 inference(symmetry,[status(thm)],[52])).
% 15.86/16.11 tff(54,plain,
% 15.86/16.11 (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722))) <=> cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l!1722)),
% 15.86/16.11 inference(monotonicity,[status(thm)],[38])).
% 15.86/16.11 tff(55,plain,
% 15.86/16.11 (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l!1722) <=> cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)))),
% 15.86/16.11 inference(symmetry,[status(thm)],[54])).
% 15.86/16.11 tff(56,plain,
% 15.86/16.11 (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)))),
% 15.86/16.11 inference(modus_ponens,[status(thm)],[15, 55])).
% 15.86/16.11 tff(57,plain,
% 15.86/16.11 (^[Vvar__786: $i] : refl((~((~((~c_24__type__785___24t(Vvar__786)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))) | (~(c_24__type__785___24t(Vvar__786) | (~(cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))))))))) <=> (~((~((~c_24__type__785___24t(Vvar__786)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))) | (~(c_24__type__785___24t(Vvar__786) | (~(cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))))))))))),
% 15.86/16.11 inference(bind,[status(th)],[])).
% 15.86/16.11 tff(58,plain,
% 15.86/16.11 (![Vvar__786: $i] : (~((~((~c_24__type__785___24t(Vvar__786)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))) | (~(c_24__type__785___24t(Vvar__786) | (~(cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))))))))) <=> ![Vvar__786: $i] : (~((~((~c_24__type__785___24t(Vvar__786)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))) | (~(c_24__type__785___24t(Vvar__786) | (~(cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786)))))))))),
% 15.86/16.11 inference(quant_intro,[status(thm)],[57])).
% 15.86/16.11 tff(59,plain,
% 15.86/16.11 (^[Vvar__786: $i] : rewrite((~((~((~c_24__type__785___24t(Vvar__786)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))) | (~(c_24__type__785___24t(Vvar__786) | (~(cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))))))))) <=> (~((~((~c_24__type__785___24t(Vvar__786)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))) | (~(c_24__type__785___24t(Vvar__786) | (~(cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))))))))))),
% 15.86/16.11 inference(bind,[status(th)],[])).
% 15.86/16.11 tff(60,plain,
% 15.86/16.11 (![Vvar__786: $i] : (~((~((~c_24__type__785___24t(Vvar__786)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))) | (~(c_24__type__785___24t(Vvar__786) | (~(cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))))))))) <=> ![Vvar__786: $i] : (~((~((~c_24__type__785___24t(Vvar__786)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))) | (~(c_24__type__785___24t(Vvar__786) | (~(cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786)))))))))),
% 15.86/16.11 inference(quant_intro,[status(thm)],[59])).
% 15.86/16.11 tff(61,plain,
% 15.86/16.11 (![Vvar__786: $i] : (~((~((~c_24__type__785___24t(Vvar__786)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))) | (~(c_24__type__785___24t(Vvar__786) | (~(cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))))))))) <=> ![Vvar__786: $i] : (~((~((~c_24__type__785___24t(Vvar__786)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))) | (~(c_24__type__785___24t(Vvar__786) | (~(cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786)))))))))),
% 15.86/16.11 inference(transitivity,[status(thm)],[60, 58])).
% 15.86/16.11 tff(62,plain,
% 15.86/16.11 (^[Vvar__786: $i] : trans(monotonicity(rewrite(((~c_24__type__785___24t(Vvar__786)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0)))) <=> ((~c_24__type__785___24t(Vvar__786)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))), ((((~c_24__type__785___24t(Vvar__786)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0)))) & (c_24__type__785___24t(Vvar__786) | (~(cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))))))) <=> (((~c_24__type__785___24t(Vvar__786)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0)))) & (c_24__type__785___24t(Vvar__786) | (~(cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))))))))), rewrite((((~c_24__type__785___24t(Vvar__786)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0)))) & (c_24__type__785___24t(Vvar__786) | (~(cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))))))) <=> (~((~((~c_24__type__785___24t(Vvar__786)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))) | (~(c_24__type__785___24t(Vvar__786) | (~(cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786)))))))))), ((((~c_24__type__785___24t(Vvar__786)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0)))) & (c_24__type__785___24t(Vvar__786) | (~(cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))))))) <=> (~((~((~c_24__type__785___24t(Vvar__786)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))) | (~(c_24__type__785___24t(Vvar__786) | (~(cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786)))))))))))),
% 15.86/16.12 inference(bind,[status(th)],[])).
% 15.86/16.12 tff(63,plain,
% 15.86/16.12 (![Vvar__786: $i] : (((~c_24__type__785___24t(Vvar__786)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0)))) & (c_24__type__785___24t(Vvar__786) | (~(cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))))))) <=> ![Vvar__786: $i] : (~((~((~c_24__type__785___24t(Vvar__786)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))) | (~(c_24__type__785___24t(Vvar__786) | (~(cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786)))))))))),
% 15.86/16.12 inference(quant_intro,[status(thm)],[62])).
% 15.86/16.12 tff(64,plain,
% 15.86/16.12 (![Vvar__786: $i] : (c_24__type__785___24t(Vvar__786) <=> ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0)))) <=> ![Vvar__786: $i] : (c_24__type__785___24t(Vvar__786) <=> ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))),
% 15.86/16.12 inference(rewrite,[status(thm)],[])).
% 15.86/16.12 tff(65,plain,
% 15.86/16.12 (^[Vvar__786: $i] : rewrite((c_24__type__785___24t(Vvar__786) <=> ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0) => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)))) <=> (c_24__type__785___24t(Vvar__786) <=> ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0)))))),
% 15.86/16.12 inference(bind,[status(th)],[])).
% 15.86/16.12 tff(66,plain,
% 15.86/16.12 (![Vvar__786: $i] : (c_24__type__785___24t(Vvar__786) <=> ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0) => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)))) <=> ![Vvar__786: $i] : (c_24__type__785___24t(Vvar__786) <=> ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))),
% 15.86/16.12 inference(quant_intro,[status(thm)],[65])).
% 15.86/16.12 tff(67,axiom,(![Vvar__786: $i] : (c_24__type__785___24t(Vvar__786) <=> ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0) => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''$_type_785'')).
% 15.86/16.12 tff(68,plain,
% 15.86/16.12 (![Vvar__786: $i] : (c_24__type__785___24t(Vvar__786) <=> ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))),
% 15.86/16.12 inference(modus_ponens,[status(thm)],[67, 66])).
% 15.86/16.12 tff(69,plain,
% 15.86/16.12 (![Vvar__786: $i] : (c_24__type__785___24t(Vvar__786) <=> ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))),
% 15.86/16.12 inference(modus_ponens,[status(thm)],[68, 64])).
% 15.86/16.12 tff(70,plain,(
% 15.86/16.12 ![Vvar__786: $i] : (((~c_24__type__785___24t(Vvar__786)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0)))) & (c_24__type__785___24t(Vvar__786) | (~(cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786)))))))),
% 15.86/16.12 inference(skolemize,[status(sab)],[69])).
% 15.86/16.12 tff(71,plain,
% 15.86/16.12 (![Vvar__786: $i] : (~((~((~c_24__type__785___24t(Vvar__786)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))) | (~(c_24__type__785___24t(Vvar__786) | (~(cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786)))))))))),
% 15.86/16.12 inference(modus_ponens,[status(thm)],[70, 63])).
% 15.86/16.12 tff(72,plain,
% 15.86/16.12 (![Vvar__786: $i] : (~((~((~c_24__type__785___24t(Vvar__786)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))) | (~(c_24__type__785___24t(Vvar__786) | (~(cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786)))))))))),
% 15.86/16.12 inference(modus_ponens,[status(thm)],[71, 61])).
% 15.86/16.12 tff(73,plain,
% 15.86/16.12 ((~![Vvar__786: $i] : (~((~((~c_24__type__785___24t(Vvar__786)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))) | (~(c_24__type__785___24t(Vvar__786) | (~(cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__786, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vv__CANONICAL__0_1581(Vvar__786)))))))))) | (~((~((~c_24__type__785___24t(cMaplists_2eMapLists_2ead__list__stutters)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(cMaplists_2eMapLists_2ead__list__stutters, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))) | (~(c_24__type__785___24t(cMaplists_2eMapLists_2ead__list__stutters) | (~(cCoq_2eInit_2eDatatypes_2ebool___24t(happ(cMaplists_2eMapLists_2ead__list__stutters, tptp_fun_Vv__CANONICAL__0_1581(cMaplists_2eMapLists_2ead__list__stutters))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vv__CANONICAL__0_1581(cMaplists_2eMapLists_2ead__list__stutters)))))))))),
% 15.86/16.12 inference(quant_inst,[status(thm)],[])).
% 15.86/16.12 tff(74,plain,
% 15.86/16.12 (~((~((~c_24__type__785___24t(cMaplists_2eMapLists_2ead__list__stutters)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(cMaplists_2eMapLists_2ead__list__stutters, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))) | (~(c_24__type__785___24t(cMaplists_2eMapLists_2ead__list__stutters) | (~(cCoq_2eInit_2eDatatypes_2ebool___24t(happ(cMaplists_2eMapLists_2ead__list__stutters, tptp_fun_Vv__CANONICAL__0_1581(cMaplists_2eMapLists_2ead__list__stutters))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vv__CANONICAL__0_1581(cMaplists_2eMapLists_2ead__list__stutters))))))))),
% 15.86/16.12 inference(unit_resolution,[status(thm)],[73, 72])).
% 15.86/16.12 tff(75,plain,
% 15.86/16.12 (((~((~c_24__type__785___24t(cMaplists_2eMapLists_2ead__list__stutters)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(cMaplists_2eMapLists_2ead__list__stutters, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))) | (~(c_24__type__785___24t(cMaplists_2eMapLists_2ead__list__stutters) | (~(cCoq_2eInit_2eDatatypes_2ebool___24t(happ(cMaplists_2eMapLists_2ead__list__stutters, tptp_fun_Vv__CANONICAL__0_1581(cMaplists_2eMapLists_2ead__list__stutters))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, tptp_fun_Vv__CANONICAL__0_1581(cMaplists_2eMapLists_2ead__list__stutters)))))))) | ((~c_24__type__785___24t(cMaplists_2eMapLists_2ead__list__stutters)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(cMaplists_2eMapLists_2ead__list__stutters, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))),
% 15.86/16.12 inference(tautology,[status(thm)],[])).
% 15.86/16.12 tff(76,plain,
% 15.86/16.12 ((~c_24__type__785___24t(cMaplists_2eMapLists_2ead__list__stutters)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(cMaplists_2eMapLists_2ead__list__stutters, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0)))),
% 15.86/16.12 inference(unit_resolution,[status(thm)],[75, 74])).
% 15.86/16.12 tff(77,plain,
% 15.86/16.12 (c_24__type__785___24t(cMaplists_2eMapLists_2ead__list__stutters) <=> c_24__type__785___24t(cMaplists_2eMapLists_2ead__list__stutters)),
% 15.86/16.12 inference(rewrite,[status(thm)],[])).
% 15.86/16.12 tff(78,axiom,(c_24__type__785___24t(cMaplists_2eMapLists_2ead__list__stutters)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''$_typeof_Maplists.MapLists.ad_list_stutters'')).
% 15.86/16.12 tff(79,plain,
% 15.86/16.12 (c_24__type__785___24t(cMaplists_2eMapLists_2ead__list__stutters)),
% 15.86/16.12 inference(modus_ponens,[status(thm)],[78, 77])).
% 15.86/16.12 tff(80,plain,
% 15.86/16.12 ((~((~c_24__type__785___24t(cMaplists_2eMapLists_2ead__list__stutters)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(cMaplists_2eMapLists_2ead__list__stutters, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))) | (~c_24__type__785___24t(cMaplists_2eMapLists_2ead__list__stutters)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(cMaplists_2eMapLists_2ead__list__stutters, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0)))),
% 15.86/16.12 inference(tautology,[status(thm)],[])).
% 15.86/16.12 tff(81,plain,
% 15.86/16.12 ((~((~c_24__type__785___24t(cMaplists_2eMapLists_2ead__list__stutters)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(cMaplists_2eMapLists_2ead__list__stutters, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0))))) | ![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(cMaplists_2eMapLists_2ead__list__stutters, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0)))),
% 15.86/16.12 inference(unit_resolution,[status(thm)],[80, 79])).
% 15.86/16.12 tff(82,plain,
% 15.86/16.12 (![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(cMaplists_2eMapLists_2ead__list__stutters, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0)))),
% 15.86/16.12 inference(unit_resolution,[status(thm)],[81, 76])).
% 15.86/16.12 tff(83,plain,
% 15.86/16.12 (((~![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(cMaplists_2eMapLists_2ead__list__stutters, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0)))) | (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(cMaplists_2eMapLists_2ead__list__stutters, cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)))))) <=> ((~![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(cMaplists_2eMapLists_2ead__list__stutters, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0)))) | cCoq_2eInit_2eDatatypes_2ebool___24t(happ(cMaplists_2eMapLists_2ead__list__stutters, cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)))))),
% 15.86/16.12 inference(rewrite,[status(thm)],[])).
% 15.86/16.12 tff(84,plain,
% 15.86/16.12 ((~![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(cMaplists_2eMapLists_2ead__list__stutters, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0)))) | (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(cMaplists_2eMapLists_2ead__list__stutters, cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)))))),
% 15.86/16.12 inference(quant_inst,[status(thm)],[])).
% 15.86/16.12 tff(85,plain,
% 15.86/16.12 ((~![Vv__CANONICAL__0: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(cMaplists_2eMapLists_2ead__list__stutters, Vv__CANONICAL__0)) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, Vv__CANONICAL__0)))) | cCoq_2eInit_2eDatatypes_2ebool___24t(happ(cMaplists_2eMapLists_2ead__list__stutters, cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722))))),
% 15.86/16.12 inference(modus_ponens,[status(thm)],[84, 83])).
% 15.86/16.12 tff(86,plain,
% 15.86/16.12 (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(cMaplists_2eMapLists_2ead__list__stutters, cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722)))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722))))),
% 15.86/16.12 inference(unit_resolution,[status(thm)],[85, 82])).
% 15.86/16.12 tff(87,plain,
% 15.86/16.12 (cCoq_2eInit_2eDatatypes_2ebool___24t(happ(cMaplists_2eMapLists_2ead__list__stutters, cCoq_2eInit_2eDatatypes_2econs___24a3(cIntMap_2eMap_2ead, tptp_fun_Vvar__1___24Anonymous__782_648(V0__l!1722), tptp_fun_Vvar__2___24Anonymous__783_649(V0__l!1722))))),
% 15.86/16.12 inference(unit_resolution,[status(thm)],[86, 56])).
% 15.86/16.12 tff(88,plain,
% 15.86/16.12 (cCoq_2eInit_2eDatatypes_2ebool___24t(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722))),
% 15.86/16.12 inference(modus_ponens,[status(thm)],[87, 53])).
% 15.86/16.12 tff(89,plain,
% 15.86/16.12 ((cCoq_2eInit_2eDatatypes_2efalse = cCoq_2eInit_2eDatatypes_2etrue) <=> (cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2efalse)),
% 15.86/16.12 inference(commutativity,[status(thm)],[])).
% 15.86/16.12 tff(90,plain,
% 15.86/16.12 (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27!1723)) = cCoq_2eInit_2eDatatypes_2efalse),
% 15.86/16.12 inference(or_elim,[status(thm)],[11])).
% 15.86/16.12 tff(91,plain,
% 15.86/16.12 ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27!1723)) = cCoq_2eInit_2eDatatypes_2etrue) <=> (cCoq_2eInit_2eDatatypes_2efalse = cCoq_2eInit_2eDatatypes_2etrue)),
% 15.86/16.12 inference(monotonicity,[status(thm)],[90])).
% 15.86/16.12 tff(92,plain,
% 15.86/16.12 ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27!1723)) = cCoq_2eInit_2eDatatypes_2etrue) <=> (cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2efalse)),
% 15.86/16.12 inference(transitivity,[status(thm)],[91, 89])).
% 15.86/16.12 tff(93,plain,
% 15.86/16.12 ((cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2efalse) <=> (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27!1723)) = cCoq_2eInit_2eDatatypes_2etrue)),
% 15.86/16.12 inference(symmetry,[status(thm)],[92])).
% 15.86/16.12 tff(94,plain,
% 15.86/16.12 ((~(cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2efalse)) <=> (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27!1723)) = cCoq_2eInit_2eDatatypes_2etrue))),
% 15.86/16.12 inference(monotonicity,[status(thm)],[93])).
% 15.86/16.12 tff(95,plain,
% 15.86/16.12 ((~(cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2efalse)) <=> (~(cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2efalse))),
% 15.86/16.12 inference(rewrite,[status(thm)],[])).
% 15.86/16.12 tff(96,axiom,(~(cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2efalse)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false'')).
% 15.86/16.12 tff(97,plain,
% 15.86/16.12 (~(cCoq_2eInit_2eDatatypes_2etrue = cCoq_2eInit_2eDatatypes_2efalse)),
% 15.86/16.12 inference(modus_ponens,[status(thm)],[96, 95])).
% 15.86/16.12 tff(98,plain,
% 15.86/16.12 (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27!1723)) = cCoq_2eInit_2eDatatypes_2etrue)),
% 15.86/16.12 inference(modus_ponens,[status(thm)],[97, 94])).
% 15.86/16.12 tff(99,plain,
% 15.86/16.12 (^[V0__l: $i] : refl(((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue)))) <=> ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue)))))),
% 15.86/16.12 inference(bind,[status(th)],[])).
% 15.86/16.12 tff(100,plain,
% 15.86/16.12 (![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue)))) <=> ![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue))))),
% 15.86/16.12 inference(quant_intro,[status(thm)],[99])).
% 15.86/16.12 tff(101,plain,
% 15.86/16.12 (^[V0__l: $i] : rewrite(((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue)))) <=> ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue)))))),
% 15.86/16.12 inference(bind,[status(th)],[])).
% 15.86/16.12 tff(102,plain,
% 15.86/16.12 (![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue)))) <=> ![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue))))),
% 15.86/16.12 inference(quant_intro,[status(thm)],[101])).
% 15.86/16.12 tff(103,plain,
% 15.86/16.12 (![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue)))) <=> ![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue))))),
% 15.86/16.12 inference(transitivity,[status(thm)],[102, 100])).
% 15.86/16.12 tff(104,plain,
% 15.86/16.12 (![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue)))) <=> ![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue))))),
% 15.86/16.12 inference(rewrite,[status(thm)],[])).
% 15.86/16.12 tff(105,plain,
% 15.86/16.12 (^[V0__l: $i] : trans(monotonicity(quant_intro(proof_bind(^[V1__l_27: $i] : trans(monotonicity(rewrite(((cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue) => (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue)) <=> ((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue)) | (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue))), ((cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27) => ((cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue) => (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue))) <=> (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27) => ((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue)) | (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue))))), rewrite((cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27) => ((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue)) | (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue))) <=> ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue)))), ((cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27) => ((cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue) => (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue))) <=> ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue)))))), (![V1__l_27: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27) => ((cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue) => (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue))) <=> ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue))))), ((cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l) => ![V1__l_27: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27) => ((cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue) => (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue)))) <=> (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l) => ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue)))))), rewrite((cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l) => ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue)))) <=> ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue))))), ((cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l) => ![V1__l_27: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27) => ((cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue) => (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue)))) <=> ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue))))))),
% 15.86/16.12 inference(bind,[status(th)],[])).
% 15.86/16.12 tff(106,plain,
% 15.86/16.12 (![V0__l: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l) => ![V1__l_27: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27) => ((cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue) => (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue)))) <=> ![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue))))),
% 15.86/16.12 inference(quant_intro,[status(thm)],[105])).
% 15.86/16.12 tff(107,axiom,(![V0__l: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l) => ![V1__l_27: $i] : (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27) => ((cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue) => (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''Maplists.MapLists.ad_list_stutters_app_l'')).
% 15.86/16.12 tff(108,plain,
% 15.86/16.12 (![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue))))),
% 15.86/16.12 inference(modus_ponens,[status(thm)],[107, 106])).
% 15.86/16.12 tff(109,plain,
% 15.86/16.12 (![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue))))),
% 15.86/16.12 inference(modus_ponens,[status(thm)],[108, 104])).
% 15.86/16.12 tff(110,plain,(
% 15.86/16.12 ![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue))))),
% 15.86/16.12 inference(skolemize,[status(sab)],[109])).
% 15.86/16.12 tff(111,plain,
% 15.86/16.12 (![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue))))),
% 15.86/16.12 inference(modus_ponens,[status(thm)],[110, 103])).
% 15.86/16.12 tff(112,plain,
% 15.86/16.12 (((~![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue))))) | ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l!1722)) | ![V1__l_27: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue)) | (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue)))) <=> ((~![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue))))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l!1722)) | ![V1__l_27: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue)) | (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue)))),
% 15.86/16.12 inference(rewrite,[status(thm)],[])).
% 15.86/16.12 tff(113,plain,
% 15.86/16.12 (((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l!1722)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue)))) <=> ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l!1722)) | ![V1__l_27: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue)) | (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue)))),
% 15.86/16.12 inference(rewrite,[status(thm)],[])).
% 15.86/16.12 tff(114,plain,
% 15.86/16.12 (((~![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue))))) | ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l!1722)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue))))) <=> ((~![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue))))) | ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l!1722)) | ![V1__l_27: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue)) | (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue))))),
% 15.86/16.12 inference(monotonicity,[status(thm)],[113])).
% 15.86/16.12 tff(115,plain,
% 15.86/16.12 (((~![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue))))) | ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l!1722)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue))))) <=> ((~![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue))))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l!1722)) | ![V1__l_27: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue)) | (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue)))),
% 15.86/16.12 inference(transitivity,[status(thm)],[114, 112])).
% 15.86/16.12 tff(116,plain,
% 15.86/16.12 ((~![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue))))) | ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l!1722)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue))))),
% 15.86/16.12 inference(quant_inst,[status(thm)],[])).
% 15.86/16.12 tff(117,plain,
% 15.86/16.12 ((~![V0__l: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l)) | ![V1__l_27: $i] : ((cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l) = cCoq_2eInit_2eDatatypes_2etrue))))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V0__l!1722)) | ![V1__l_27: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue)) | (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue))),
% 15.86/16.12 inference(modus_ponens,[status(thm)],[116, 115])).
% 15.86/16.12 tff(118,plain,
% 15.86/16.12 (![V1__l_27: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue)) | (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue))),
% 15.86/16.12 inference(unit_resolution,[status(thm)],[117, 111, 15])).
% 15.86/16.12 tff(119,plain,
% 15.86/16.12 (cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27!1723)),
% 15.86/16.12 inference(or_elim,[status(thm)],[11])).
% 15.86/16.12 tff(120,plain,
% 15.86/16.12 (((~![V1__l_27: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue)) | (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue))) | ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27!1723)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue)) | (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27!1723)) = cCoq_2eInit_2eDatatypes_2etrue))) <=> ((~![V1__l_27: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue)) | (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27!1723)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue)) | (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27!1723)) = cCoq_2eInit_2eDatatypes_2etrue))),
% 15.86/16.12 inference(rewrite,[status(thm)],[])).
% 15.86/16.12 tff(121,plain,
% 15.86/16.12 ((~![V1__l_27: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue)) | (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue))) | ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27!1723)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue)) | (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27!1723)) = cCoq_2eInit_2eDatatypes_2etrue))),
% 15.86/16.12 inference(quant_inst,[status(thm)],[])).
% 15.86/16.12 tff(122,plain,
% 15.86/16.12 ((~![V1__l_27: $i] : ((~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue)) | (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27)) = cCoq_2eInit_2eDatatypes_2etrue))) | (~cCoq_2eInit_2eDatatypes_2elist___24t(cIntMap_2eMap_2ead, V1__l_27!1723)) | (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue)) | (cMaplists_2eMapLists_2ead__list__stutters___24a1(cCoq_2eInit_2eDatatypes_2eapp___24a3(cIntMap_2eMap_2ead, V0__l!1722, V1__l_27!1723)) = cCoq_2eInit_2eDatatypes_2etrue)),
% 15.86/16.12 inference(modus_ponens,[status(thm)],[121, 120])).
% 15.86/16.12 tff(123,plain,
% 15.86/16.12 (~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue)),
% 15.86/16.12 inference(unit_resolution,[status(thm)],[122, 119, 118, 98])).
% 15.86/16.12 tff(124,plain,
% 15.86/16.12 (((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722)) = cCoq_2eInit_2eDatatypes_2efalse))) | (cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue)),
% 15.86/16.12 inference(tautology,[status(thm)],[])).
% 15.86/16.12 tff(125,plain,
% 15.86/16.12 ((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722)) = cCoq_2eInit_2eDatatypes_2efalse))),
% 15.86/16.12 inference(unit_resolution,[status(thm)],[124, 123])).
% 15.86/16.12 tff(126,plain,
% 15.86/16.12 (((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722)) = cCoq_2eInit_2eDatatypes_2etrue))) | (cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2efalse)),
% 15.86/16.12 inference(tautology,[status(thm)],[])).
% 15.86/16.12 tff(127,plain,
% 15.86/16.12 ((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722)) = cCoq_2eInit_2eDatatypes_2etrue))),
% 15.86/16.12 inference(unit_resolution,[status(thm)],[126, 12])).
% 15.86/16.12 tff(128,plain,
% 15.86/16.12 (^[V0__b: $i] : refl(((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2efalse)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)))) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2etrue)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse))))) <=> ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2efalse)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)))) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2etrue)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse))))))),
% 15.86/16.12 inference(bind,[status(th)],[])).
% 15.86/16.12 tff(129,plain,
% 15.86/16.12 (![V0__b: $i] : ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2efalse)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)))) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2etrue)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse))))) <=> ![V0__b: $i] : ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2efalse)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)))) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2etrue)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)))))),
% 15.86/16.12 inference(quant_intro,[status(thm)],[128])).
% 15.86/16.12 tff(130,plain,
% 15.86/16.12 (^[V0__b: $i] : trans(monotonicity(rewrite(((V0__b = cCoq_2eInit_2eDatatypes_2efalse) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)) <=> (~((~(V0__b = cCoq_2eInit_2eDatatypes_2efalse)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue))))), rewrite(((V0__b = cCoq_2eInit_2eDatatypes_2etrue) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)) <=> (~((~(V0__b = cCoq_2eInit_2eDatatypes_2etrue)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse))))), ((((V0__b = cCoq_2eInit_2eDatatypes_2efalse) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)) | ((V0__b = cCoq_2eInit_2eDatatypes_2etrue) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b))) <=> ((~((~(V0__b = cCoq_2eInit_2eDatatypes_2efalse)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)))) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2etrue)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)))) | (~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b))))), rewrite(((~((~(V0__b = cCoq_2eInit_2eDatatypes_2efalse)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)))) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2etrue)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)))) | (~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b))) <=> ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2efalse)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)))) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2etrue)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)))))), ((((V0__b = cCoq_2eInit_2eDatatypes_2efalse) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)) | ((V0__b = cCoq_2eInit_2eDatatypes_2etrue) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b))) <=> ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2efalse)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)))) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2etrue)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)))))))),
% 15.86/16.12 inference(bind,[status(th)],[])).
% 15.86/16.12 tff(131,plain,
% 15.86/16.12 (![V0__b: $i] : (((V0__b = cCoq_2eInit_2eDatatypes_2efalse) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)) | ((V0__b = cCoq_2eInit_2eDatatypes_2etrue) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b))) <=> ![V0__b: $i] : ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2efalse)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)))) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2etrue)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)))))),
% 15.86/16.12 inference(quant_intro,[status(thm)],[130])).
% 15.86/16.12 tff(132,plain,
% 15.86/16.12 (![V0__b: $i] : (((V0__b = cCoq_2eInit_2eDatatypes_2efalse) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)) | ((V0__b = cCoq_2eInit_2eDatatypes_2etrue) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b))) <=> ![V0__b: $i] : (((V0__b = cCoq_2eInit_2eDatatypes_2efalse) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)) | ((V0__b = cCoq_2eInit_2eDatatypes_2etrue) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)))),
% 15.86/16.12 inference(rewrite,[status(thm)],[])).
% 15.86/16.12 tff(133,plain,
% 15.86/16.12 (^[V0__b: $i] : trans(monotonicity(rewrite((((V0__b = cCoq_2eInit_2eDatatypes_2etrue) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)) | ((V0__b = cCoq_2eInit_2eDatatypes_2efalse) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue))) <=> (((V0__b = cCoq_2eInit_2eDatatypes_2efalse) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)) | ((V0__b = cCoq_2eInit_2eDatatypes_2etrue) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)))), ((cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b) => (((V0__b = cCoq_2eInit_2eDatatypes_2etrue) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)) | ((V0__b = cCoq_2eInit_2eDatatypes_2efalse) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)))) <=> (cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b) => (((V0__b = cCoq_2eInit_2eDatatypes_2efalse) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)) | ((V0__b = cCoq_2eInit_2eDatatypes_2etrue) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)))))), rewrite((cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b) => (((V0__b = cCoq_2eInit_2eDatatypes_2efalse) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)) | ((V0__b = cCoq_2eInit_2eDatatypes_2etrue) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)))) <=> (((V0__b = cCoq_2eInit_2eDatatypes_2efalse) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)) | ((V0__b = cCoq_2eInit_2eDatatypes_2etrue) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)))), ((cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b) => (((V0__b = cCoq_2eInit_2eDatatypes_2etrue) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)) | ((V0__b = cCoq_2eInit_2eDatatypes_2efalse) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)))) <=> (((V0__b = cCoq_2eInit_2eDatatypes_2efalse) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)) | ((V0__b = cCoq_2eInit_2eDatatypes_2etrue) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)))))),
% 15.86/16.12 inference(bind,[status(th)],[])).
% 15.86/16.12 tff(134,plain,
% 15.86/16.12 (![V0__b: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b) => (((V0__b = cCoq_2eInit_2eDatatypes_2etrue) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)) | ((V0__b = cCoq_2eInit_2eDatatypes_2efalse) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)))) <=> ![V0__b: $i] : (((V0__b = cCoq_2eInit_2eDatatypes_2efalse) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)) | ((V0__b = cCoq_2eInit_2eDatatypes_2etrue) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)))),
% 15.86/16.12 inference(quant_intro,[status(thm)],[133])).
% 15.86/16.12 tff(135,axiom,(![V0__b: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b) => (((V0__b = cCoq_2eInit_2eDatatypes_2etrue) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)) | ((V0__b = cCoq_2eInit_2eDatatypes_2efalse) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',''$_def_Coq.Init.Datatypes.negb'')).
% 15.86/16.12 tff(136,plain,
% 15.86/16.12 (![V0__b: $i] : (((V0__b = cCoq_2eInit_2eDatatypes_2efalse) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)) | ((V0__b = cCoq_2eInit_2eDatatypes_2etrue) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)))),
% 15.86/16.12 inference(modus_ponens,[status(thm)],[135, 134])).
% 15.86/16.12 tff(137,plain,
% 15.86/16.12 (![V0__b: $i] : (((V0__b = cCoq_2eInit_2eDatatypes_2efalse) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)) | ((V0__b = cCoq_2eInit_2eDatatypes_2etrue) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)))),
% 15.86/16.12 inference(modus_ponens,[status(thm)],[136, 132])).
% 15.86/16.12 tff(138,plain,(
% 15.86/16.12 ![V0__b: $i] : (((V0__b = cCoq_2eInit_2eDatatypes_2efalse) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)) | ((V0__b = cCoq_2eInit_2eDatatypes_2etrue) & (cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)) | (~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)))),
% 15.86/16.12 inference(skolemize,[status(sab)],[137])).
% 15.86/16.12 tff(139,plain,
% 15.86/16.12 (![V0__b: $i] : ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2efalse)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)))) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2etrue)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)))))),
% 15.86/16.12 inference(modus_ponens,[status(thm)],[138, 131])).
% 15.86/16.12 tff(140,plain,
% 15.86/16.12 (![V0__b: $i] : ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2efalse)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)))) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2etrue)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)))))),
% 15.86/16.12 inference(modus_ponens,[status(thm)],[139, 129])).
% 15.86/16.12 tff(141,plain,
% 15.86/16.12 (((~![V0__b: $i] : ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2efalse)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)))) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2etrue)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)))))) | ((~cCoq_2eInit_2eDatatypes_2ebool___24t(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722))) | (~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722)) = cCoq_2eInit_2eDatatypes_2etrue)))) | (~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722)) = cCoq_2eInit_2eDatatypes_2efalse)))))) <=> ((~![V0__b: $i] : ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2efalse)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)))) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2etrue)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)))))) | (~cCoq_2eInit_2eDatatypes_2ebool___24t(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722))) | (~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722)) = cCoq_2eInit_2eDatatypes_2etrue)))) | (~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722)) = cCoq_2eInit_2eDatatypes_2efalse)))))),
% 15.86/16.12 inference(rewrite,[status(thm)],[])).
% 15.86/16.12 tff(142,plain,
% 15.86/16.12 ((~![V0__b: $i] : ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2efalse)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)))) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2etrue)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)))))) | ((~cCoq_2eInit_2eDatatypes_2ebool___24t(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722))) | (~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722)) = cCoq_2eInit_2eDatatypes_2etrue)))) | (~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722)) = cCoq_2eInit_2eDatatypes_2efalse)))))),
% 15.86/16.12 inference(quant_inst,[status(thm)],[])).
% 15.86/16.12 tff(143,plain,
% 15.86/16.12 ((~![V0__b: $i] : ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2efalse)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue)))) | (~((~(V0__b = cCoq_2eInit_2eDatatypes_2etrue)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse)))))) | (~cCoq_2eInit_2eDatatypes_2ebool___24t(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722))) | (~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722)) = cCoq_2eInit_2eDatatypes_2etrue)))) | (~((~(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(cCoq_2eInit_2eDatatypes_2enegb___24a1(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722)) = cCoq_2eInit_2eDatatypes_2efalse))))),
% 16.14/16.32 inference(modus_ponens,[status(thm)],[142, 141])).
% 16.14/16.32 tff(144,plain,
% 16.14/16.32 (~cCoq_2eInit_2eDatatypes_2ebool___24t(cMaplists_2eMapLists_2ead__list__stutters___24a1(V0__l!1722))),
% 16.14/16.32 inference(unit_resolution,[status(thm)],[143, 140, 127, 125])).
% 16.14/16.32 tff(145,plain,
% 16.14/16.32 ($false),
% 16.14/16.32 inference(unit_resolution,[status(thm)],[144, 88])).
% 16.14/16.32 % SZS output end Proof
% 16.14/16.33 % E exiting
%------------------------------------------------------------------------------