%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEV607+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n018.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 06:56:00 PM UTC 2026
% Result : Theorem 10.96s 11.17s
% Output : Proof 11.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV607+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.13/0.32 % Computer : n018.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 05:26:03 EDT 2026
% 0.13/0.32 % CPUTime :
% 10.96/11.17 % SZS status Theorem
% 10.96/11.17 % SZS output start Proof
% 10.96/11.17 tff(cCoq_2eNumbers_2eBinNums_2eZ___24t_type, type, (
% 10.96/11.17 cCoq_2eNumbers_2eBinNums_2eZ___24t: $i > $o)).
% 10.96/11.17 tff(happ_type, type, (
% 10.96/11.17 happ: ( $i * $i ) > $i)).
% 10.96/11.17 tff(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2_type, type, (
% 10.96/11.17 cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2: ( $i * $i ) > $i)).
% 10.96/11.17 tff(cCoq_2eNumbers_2eBinNums_2eZpos___24a1_type, type, (
% 10.96/11.17 cCoq_2eNumbers_2eBinNums_2eZpos___24a1: $i > $i)).
% 10.96/11.17 tff(cCoq_2eNumbers_2eBinNums_2exH_type, type, (
% 10.96/11.17 cCoq_2eNumbers_2eBinNums_2exH: $i)).
% 10.96/11.17 tff(tptp_fun_V0__n_980_type, type, (
% 10.96/11.17 tptp_fun_V0__n_980: $i)).
% 10.96/11.17 tff(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare_type, type, (
% 10.96/11.17 cCoq_2eZArith_2eBinIntDef_2eZ_2esquare: $i)).
% 10.96/11.17 tff(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1_type, type, (
% 10.96/11.17 cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1: $i > $i)).
% 10.96/11.17 tff(p_type, type, (
% 10.96/11.17 p: $i > $o)).
% 10.96/11.17 tff(cCoq_2eZArith_2eZeven_2eZodd___24a1_type, type, (
% 10.96/11.17 cCoq_2eZArith_2eZeven_2eZodd___24a1: $i > $i)).
% 10.96/11.17 tff(cCoq_2eZArith_2eZeven_2eZeven___24a1_type, type, (
% 10.96/11.17 cCoq_2eZArith_2eZeven_2eZeven___24a1: $i > $i)).
% 10.96/11.17 tff(cCoq_2eInit_2eDatatypes_2etrue_type, type, (
% 10.96/11.17 cCoq_2eInit_2eDatatypes_2etrue: $i)).
% 10.96/11.17 tff(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1_type, type, (
% 10.96/11.17 cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1: $i > $i)).
% 10.96/11.17 tff(cCoq_2eInit_2eDatatypes_2enegb___24a1_type, type, (
% 10.96/11.17 cCoq_2eInit_2eDatatypes_2enegb___24a1: $i > $i)).
% 10.96/11.17 tff(cCoq_2eInit_2eDatatypes_2efalse_type, type, (
% 10.96/11.17 cCoq_2eInit_2eDatatypes_2efalse: $i)).
% 10.96/11.17 tff(cCoq_2eInit_2eDatatypes_2ebool___24t_type, type, (
% 10.96/11.17 cCoq_2eInit_2eDatatypes_2ebool___24t: $i > $o)).
% 10.96/11.17 tff(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1_type, type, (
% 10.96/11.17 cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1: $i > $i)).
% 10.96/11.17 tff(cCoq_2eNumbers_2eBinNums_2eZ0_type, type, (
% 10.96/11.17 cCoq_2eNumbers_2eBinNums_2eZ0: $i)).
% 10.96/11.17 tff(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1_type, type, (
% 10.96/11.17 c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1: $i > $i)).
% 10.96/11.17 tff(c_24__type__30___24t_type, type, (
% 10.96/11.17 c_24__type__30___24t: $i > $o)).
% 10.96/11.17 tff(tptp_fun_Vv__CANONICAL__0_802_type, type, (
% 10.96/11.17 tptp_fun_Vv__CANONICAL__0_802: $i > $i)).
% 10.96/11.17 tff(1,plain,
% 10.96/11.17 ((~(p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n!980)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | (~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980)))))) <=> (~(p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n!980)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | (~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980))))))),
% 10.96/11.17 inference(rewrite,[status(thm)],[])).
% 10.96/11.17 tff(2,plain,
% 10.96/11.17 ((~![V0__n: $i] : (p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n)))))) <=> (~![V0__n: $i] : (p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n))))))),
% 10.96/11.17 inference(rewrite,[status(thm)],[])).
% 10.96/11.17 tff(3,plain,
% 10.96/11.17 ((~![V0__n: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => (p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n))) => p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))))) <=> (~![V0__n: $i] : (p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n))))))),
% 10.96/11.17 inference(rewrite,[status(thm)],[])).
% 10.96/11.17 tff(4,axiom,(~![V0__n: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => (p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n))) => p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''_HAMMER_GOAL'')).
% 10.96/11.17 tff(5,plain,
% 10.96/11.17 (~![V0__n: $i] : (p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n)))))),
% 10.96/11.17 inference(modus_ponens,[status(thm)],[4, 3])).
% 10.96/11.17 tff(6,plain,
% 10.96/11.17 (~![V0__n: $i] : (p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n)))))),
% 10.96/11.17 inference(modus_ponens,[status(thm)],[5, 2])).
% 10.96/11.17 tff(7,plain,
% 10.96/11.17 (~![V0__n: $i] : (p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n)))))),
% 10.96/11.17 inference(modus_ponens,[status(thm)],[6, 2])).
% 10.96/11.17 tff(8,plain,
% 10.96/11.17 (~![V0__n: $i] : (p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n)))))),
% 10.96/11.17 inference(modus_ponens,[status(thm)],[7, 2])).
% 10.96/11.17 tff(9,plain,(
% 10.96/11.17 ~(p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n!980)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | (~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980)))))),
% 10.96/11.17 inference(skolemize,[status(sab)],[8])).
% 10.96/11.17 tff(10,plain,
% 10.96/11.17 (~(p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n!980)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | (~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980)))))),
% 10.96/11.17 inference(modus_ponens,[status(thm)],[9, 1])).
% 10.96/11.17 tff(11,plain,
% 10.96/11.17 (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)),
% 10.96/11.17 inference(or_elim,[status(thm)],[10])).
% 10.96/11.17 tff(12,plain,
% 10.96/11.17 (^[V0__n: $i] : refl(((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n))) <=> ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n))))),
% 10.96/11.17 inference(bind,[status(th)],[])).
% 10.96/11.17 tff(13,plain,
% 10.96/11.17 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n))) <=> ![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n)))),
% 10.96/11.17 inference(quant_intro,[status(thm)],[12])).
% 10.96/11.17 tff(14,plain,
% 10.96/11.17 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n))) <=> ![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n)))),
% 10.96/11.17 inference(rewrite,[status(thm)],[])).
% 10.96/11.17 tff(15,plain,
% 10.96/11.17 (^[V0__n: $i] : rewrite((cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => (cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n))) <=> ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n))))),
% 10.96/11.17 inference(bind,[status(th)],[])).
% 10.96/11.17 tff(16,plain,
% 10.96/11.17 (![V0__n: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => (cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n))) <=> ![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n)))),
% 10.96/11.17 inference(quant_intro,[status(thm)],[15])).
% 10.96/11.17 tff(17,axiom,(![V0__n: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => (cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''Coq.ZArith.BinInt.Z.square_spec'')).
% 10.96/11.17 tff(18,plain,
% 10.96/11.17 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n)))),
% 10.96/11.17 inference(modus_ponens,[status(thm)],[17, 16])).
% 10.96/11.17 tff(19,plain,
% 10.96/11.17 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n)))),
% 10.96/11.17 inference(modus_ponens,[status(thm)],[18, 14])).
% 10.96/11.17 tff(20,plain,(
% 10.96/11.17 ![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n)))),
% 10.96/11.17 inference(skolemize,[status(sab)],[19])).
% 10.96/11.17 tff(21,plain,
% 10.96/11.17 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n)))),
% 10.96/11.17 inference(modus_ponens,[status(thm)],[20, 13])).
% 10.96/11.17 tff(22,plain,
% 10.96/11.17 (((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n)))) | ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | (cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__n!980) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980)))) <=> ((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n)))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | (cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__n!980) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980)))),
% 10.96/11.17 inference(rewrite,[status(thm)],[])).
% 10.96/11.17 tff(23,plain,
% 10.96/11.17 ((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n)))) | ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | (cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__n!980) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980)))),
% 10.96/11.17 inference(quant_inst,[status(thm)],[])).
% 10.96/11.17 tff(24,plain,
% 10.96/11.17 ((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, V0__n)))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | (cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__n!980) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980))),
% 10.96/11.17 inference(modus_ponens,[status(thm)],[23, 22])).
% 10.96/11.17 tff(25,plain,
% 10.96/11.17 (cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__n!980) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980)),
% 10.96/11.17 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 10.96/11.17 tff(26,plain,
% 10.96/11.17 (^[V0__n: $i] : refl(((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) <=> ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))),
% 10.96/11.17 inference(bind,[status(th)],[])).
% 10.96/11.17 tff(27,plain,
% 10.96/11.17 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) <=> ![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))),
% 10.96/11.17 inference(quant_intro,[status(thm)],[26])).
% 10.96/11.17 tff(28,plain,
% 10.96/11.17 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) <=> ![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))),
% 10.96/11.17 inference(rewrite,[status(thm)],[])).
% 10.96/11.17 tff(29,plain,
% 10.96/11.17 (^[V0__n: $i] : rewrite((cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => (V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) <=> ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))),
% 10.96/11.17 inference(bind,[status(th)],[])).
% 10.96/11.17 tff(30,plain,
% 10.96/11.17 (![V0__n: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => (V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) <=> ![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))),
% 10.96/11.17 inference(quant_intro,[status(thm)],[29])).
% 10.96/11.17 tff(31,axiom,(![V0__n: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => (V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''Coq.omega.OmegaLemmas.Zred_factor0'')).
% 10.96/11.17 tff(32,plain,
% 10.96/11.17 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))),
% 10.96/11.17 inference(modus_ponens,[status(thm)],[31, 30])).
% 10.96/11.17 tff(33,plain,
% 10.96/11.17 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))),
% 10.96/11.17 inference(modus_ponens,[status(thm)],[32, 28])).
% 10.96/11.17 tff(34,plain,(
% 10.96/11.17 ![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))),
% 10.96/11.17 inference(skolemize,[status(sab)],[33])).
% 10.96/11.17 tff(35,plain,
% 10.96/11.17 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))),
% 10.96/11.17 inference(modus_ponens,[status(thm)],[34, 27])).
% 10.96/11.17 tff(36,plain,
% 10.96/11.17 (((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) | ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | (V0__n!980 = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) <=> ((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | (V0__n!980 = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))),
% 10.96/11.17 inference(rewrite,[status(thm)],[])).
% 10.96/11.17 tff(37,plain,
% 10.96/11.17 ((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) | ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | (V0__n!980 = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))),
% 10.96/11.17 inference(quant_inst,[status(thm)],[])).
% 10.96/11.17 tff(38,plain,
% 10.96/11.17 ((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | (V0__n!980 = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))),
% 10.96/11.17 inference(modus_ponens,[status(thm)],[37, 36])).
% 10.96/11.17 tff(39,plain,
% 10.96/11.17 (V0__n!980 = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))),
% 10.96/11.17 inference(unit_resolution,[status(thm)],[38, 35, 11])).
% 10.96/11.17 tff(40,plain,
% 10.96/11.17 (cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = V0__n!980),
% 10.96/11.17 inference(symmetry,[status(thm)],[39])).
% 10.96/11.17 tff(41,plain,
% 10.96/11.17 (cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) = cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V0__n!980)),
% 10.96/11.17 inference(monotonicity,[status(thm)],[40])).
% 10.96/11.17 tff(42,plain,
% 10.96/11.17 (^[V_24X1: $i] : refl((happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V_24X1)) <=> (happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V_24X1)))),
% 10.96/11.17 inference(bind,[status(th)],[])).
% 10.96/11.17 tff(43,plain,
% 10.96/11.17 (![V_24X1: $i] : (happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V_24X1)) <=> ![V_24X1: $i] : (happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V_24X1))),
% 10.96/11.17 inference(quant_intro,[status(thm)],[42])).
% 10.96/11.17 tff(44,plain,
% 10.96/11.17 (![V_24X1: $i] : (happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V_24X1)) <=> ![V_24X1: $i] : (happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V_24X1))),
% 10.96/11.17 inference(rewrite,[status(thm)],[])).
% 10.96/11.17 tff(45,axiom,(![V_24X1: $i] : (happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V_24X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''$adef_Coq.ZArith.BinIntDef.Z.square_$a1'')).
% 10.96/11.17 tff(46,plain,
% 10.96/11.17 (![V_24X1: $i] : (happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V_24X1))),
% 10.96/11.17 inference(modus_ponens,[status(thm)],[45, 44])).
% 10.96/11.17 tff(47,plain,(
% 10.96/11.17 ![V_24X1: $i] : (happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V_24X1))),
% 10.96/11.17 inference(skolemize,[status(sab)],[46])).
% 10.96/11.17 tff(48,plain,
% 10.96/11.17 (![V_24X1: $i] : (happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V_24X1))),
% 10.96/11.17 inference(modus_ponens,[status(thm)],[47, 43])).
% 10.96/11.17 tff(49,plain,
% 10.96/11.17 ((~![V_24X1: $i] : (happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(V_24X1))) | (happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) = cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))),
% 10.96/11.17 inference(quant_inst,[status(thm)],[])).
% 10.96/11.17 tff(50,plain,
% 10.96/11.17 (happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) = cCoq_2eZArith_2eBinIntDef_2eZ_2esquare___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))),
% 10.96/11.17 inference(unit_resolution,[status(thm)],[49, 48])).
% 10.96/11.17 tff(51,plain,
% 10.96/11.17 (happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980)),
% 10.96/11.17 inference(transitivity,[status(thm)],[50, 41, 25])).
% 10.96/11.17 tff(52,plain,
% 10.96/11.17 (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) <=> cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980))),
% 10.96/11.17 inference(monotonicity,[status(thm)],[51])).
% 10.96/11.17 tff(53,plain,
% 10.96/11.17 (cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980)) <=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))),
% 10.96/11.17 inference(symmetry,[status(thm)],[52])).
% 10.96/11.17 tff(54,plain,
% 10.96/11.17 ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980))) <=> (~cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))),
% 10.96/11.17 inference(monotonicity,[status(thm)],[53])).
% 10.96/11.17 tff(55,plain,
% 10.96/11.17 (^[V0__n: $i] : refl(((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n)))) <=> ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n)))))),
% 10.96/11.17 inference(bind,[status(th)],[])).
% 10.96/11.17 tff(56,plain,
% 10.96/11.17 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n)))) <=> ![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))))),
% 10.96/11.17 inference(quant_intro,[status(thm)],[55])).
% 10.96/11.17 tff(57,plain,
% 10.96/11.17 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n)))) <=> ![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))))),
% 10.96/11.17 inference(rewrite,[status(thm)],[])).
% 10.96/11.17 tff(58,plain,
% 10.96/11.17 (^[V0__n: $i] : rewrite((cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => ((cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n)))) <=> ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n)))))),
% 10.96/11.17 inference(bind,[status(th)],[])).
% 10.96/11.17 tff(59,plain,
% 10.96/11.17 (![V0__n: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => ((cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n)))) <=> ![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))))),
% 10.96/11.17 inference(quant_intro,[status(thm)],[58])).
% 10.96/11.17 tff(60,axiom,(![V0__n: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => ((cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''Coq.ZArith.Zeven.Zeven_bool_iff'')).
% 10.96/11.17 tff(61,plain,
% 10.96/11.17 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))))),
% 10.96/11.17 inference(modus_ponens,[status(thm)],[60, 59])).
% 10.96/11.17 tff(62,plain,
% 10.96/11.17 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))))),
% 10.96/11.17 inference(modus_ponens,[status(thm)],[61, 57])).
% 10.96/11.17 tff(63,plain,(
% 10.96/11.17 ![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))))),
% 10.96/11.17 inference(skolemize,[status(sab)],[62])).
% 10.96/11.17 tff(64,plain,
% 10.96/11.17 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))))),
% 10.96/11.17 inference(modus_ponens,[status(thm)],[63, 56])).
% 10.96/11.17 tff(65,plain,
% 10.96/11.17 (((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))))) | ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n!980))))) <=> ((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n!980))))),
% 10.96/11.17 inference(rewrite,[status(thm)],[])).
% 10.96/11.17 tff(66,plain,
% 10.96/11.17 ((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))))) | ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n!980))))),
% 10.96/11.17 inference(quant_inst,[status(thm)],[])).
% 10.96/11.17 tff(67,plain,
% 10.96/11.17 ((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n!980)))),
% 10.96/11.17 inference(modus_ponens,[status(thm)],[66, 65])).
% 10.96/11.17 tff(68,plain,
% 10.96/11.17 ((cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n!980))),
% 10.96/11.17 inference(unit_resolution,[status(thm)],[67, 64, 11])).
% 10.96/11.17 tff(69,plain,
% 10.96/11.17 (^[V0__b: $i] : refl(((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | ((cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue) <=> (V0__b = cCoq_2eInit_2eDatatypes_2efalse))) <=> ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | ((cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue) <=> (V0__b = cCoq_2eInit_2eDatatypes_2efalse))))),
% 10.96/11.17 inference(bind,[status(th)],[])).
% 10.96/11.17 tff(70,plain,
% 10.96/11.17 (![V0__b: $i] : ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | ((cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue) <=> (V0__b = cCoq_2eInit_2eDatatypes_2efalse))) <=> ![V0__b: $i] : ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | ((cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue) <=> (V0__b = cCoq_2eInit_2eDatatypes_2efalse)))),
% 10.96/11.17 inference(quant_intro,[status(thm)],[69])).
% 10.96/11.17 tff(71,plain,
% 10.96/11.17 (![V0__b: $i] : ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | ((cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue) <=> (V0__b = cCoq_2eInit_2eDatatypes_2efalse))) <=> ![V0__b: $i] : ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | ((cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue) <=> (V0__b = cCoq_2eInit_2eDatatypes_2efalse)))),
% 10.96/11.17 inference(rewrite,[status(thm)],[])).
% 10.96/11.17 tff(72,plain,
% 10.96/11.17 (^[V0__b: $i] : rewrite((cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b) => ((cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue) <=> (V0__b = cCoq_2eInit_2eDatatypes_2efalse))) <=> ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | ((cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue) <=> (V0__b = cCoq_2eInit_2eDatatypes_2efalse))))),
% 10.96/11.17 inference(bind,[status(th)],[])).
% 10.96/11.17 tff(73,plain,
% 10.96/11.17 (![V0__b: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b) => ((cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue) <=> (V0__b = cCoq_2eInit_2eDatatypes_2efalse))) <=> ![V0__b: $i] : ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | ((cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue) <=> (V0__b = cCoq_2eInit_2eDatatypes_2efalse)))),
% 10.96/11.17 inference(quant_intro,[status(thm)],[72])).
% 10.96/11.17 tff(74,axiom,(![V0__b: $i] : (cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b) => ((cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue) <=> (V0__b = cCoq_2eInit_2eDatatypes_2efalse)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''Coq.Bool.Bool.negb_true_iff'')).
% 10.96/11.17 tff(75,plain,
% 10.96/11.17 (![V0__b: $i] : ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | ((cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue) <=> (V0__b = cCoq_2eInit_2eDatatypes_2efalse)))),
% 10.96/11.17 inference(modus_ponens,[status(thm)],[74, 73])).
% 10.96/11.17 tff(76,plain,
% 10.96/11.17 (![V0__b: $i] : ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | ((cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue) <=> (V0__b = cCoq_2eInit_2eDatatypes_2efalse)))),
% 10.96/11.17 inference(modus_ponens,[status(thm)],[75, 71])).
% 10.96/11.17 tff(77,plain,(
% 10.96/11.17 ![V0__b: $i] : ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | ((cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue) <=> (V0__b = cCoq_2eInit_2eDatatypes_2efalse)))),
% 10.96/11.17 inference(skolemize,[status(sab)],[76])).
% 10.96/11.17 tff(78,plain,
% 10.96/11.17 (![V0__b: $i] : ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | ((cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue) <=> (V0__b = cCoq_2eInit_2eDatatypes_2efalse)))),
% 10.96/11.17 inference(modus_ponens,[status(thm)],[77, 70])).
% 10.96/11.17 tff(79,plain,
% 10.96/11.17 (cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse) <=> cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse)),
% 10.96/11.17 inference(rewrite,[status(thm)],[])).
% 10.96/11.17 tff(80,axiom,(cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''$_typeof_Coq.Init.Datatypes.false'')).
% 10.96/11.17 tff(81,plain,
% 10.96/11.17 (cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse)),
% 10.96/11.17 inference(modus_ponens,[status(thm)],[80, 79])).
% 10.96/11.17 tff(82,plain,
% 10.96/11.17 (((~![V0__b: $i] : ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | ((cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue) <=> (V0__b = cCoq_2eInit_2eDatatypes_2efalse)))) | ((~cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse)) | (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eInit_2eDatatypes_2efalse) = cCoq_2eInit_2eDatatypes_2etrue))) <=> ((~![V0__b: $i] : ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | ((cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue) <=> (V0__b = cCoq_2eInit_2eDatatypes_2efalse)))) | (~cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse)) | (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eInit_2eDatatypes_2efalse) = cCoq_2eInit_2eDatatypes_2etrue))),
% 10.96/11.17 inference(rewrite,[status(thm)],[])).
% 10.96/11.17 tff(83,plain,
% 10.96/11.17 (((~cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse)) | ((cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eInit_2eDatatypes_2efalse) = cCoq_2eInit_2eDatatypes_2etrue) <=> (cCoq_2eInit_2eDatatypes_2efalse = cCoq_2eInit_2eDatatypes_2efalse))) <=> ((~cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse)) | (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eInit_2eDatatypes_2efalse) = cCoq_2eInit_2eDatatypes_2etrue))),
% 10.96/11.17 inference(rewrite,[status(thm)],[])).
% 10.96/11.17 tff(84,plain,
% 10.96/11.17 (((~![V0__b: $i] : ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | ((cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue) <=> (V0__b = cCoq_2eInit_2eDatatypes_2efalse)))) | ((~cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse)) | ((cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eInit_2eDatatypes_2efalse) = cCoq_2eInit_2eDatatypes_2etrue) <=> (cCoq_2eInit_2eDatatypes_2efalse = cCoq_2eInit_2eDatatypes_2efalse)))) <=> ((~![V0__b: $i] : ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | ((cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue) <=> (V0__b = cCoq_2eInit_2eDatatypes_2efalse)))) | ((~cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse)) | (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eInit_2eDatatypes_2efalse) = cCoq_2eInit_2eDatatypes_2etrue)))),
% 10.96/11.17 inference(monotonicity,[status(thm)],[83])).
% 10.96/11.17 tff(85,plain,
% 10.96/11.17 (((~![V0__b: $i] : ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | ((cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue) <=> (V0__b = cCoq_2eInit_2eDatatypes_2efalse)))) | ((~cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse)) | ((cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eInit_2eDatatypes_2efalse) = cCoq_2eInit_2eDatatypes_2etrue) <=> (cCoq_2eInit_2eDatatypes_2efalse = cCoq_2eInit_2eDatatypes_2efalse)))) <=> ((~![V0__b: $i] : ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | ((cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue) <=> (V0__b = cCoq_2eInit_2eDatatypes_2efalse)))) | (~cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse)) | (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eInit_2eDatatypes_2efalse) = cCoq_2eInit_2eDatatypes_2etrue))),
% 10.96/11.17 inference(transitivity,[status(thm)],[84, 82])).
% 10.96/11.17 tff(86,plain,
% 10.96/11.17 ((~![V0__b: $i] : ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | ((cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue) <=> (V0__b = cCoq_2eInit_2eDatatypes_2efalse)))) | ((~cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse)) | ((cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eInit_2eDatatypes_2efalse) = cCoq_2eInit_2eDatatypes_2etrue) <=> (cCoq_2eInit_2eDatatypes_2efalse = cCoq_2eInit_2eDatatypes_2efalse)))),
% 10.96/11.17 inference(quant_inst,[status(thm)],[])).
% 10.96/11.17 tff(87,plain,
% 10.96/11.17 ((~![V0__b: $i] : ((~cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)) | ((cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue) <=> (V0__b = cCoq_2eInit_2eDatatypes_2efalse)))) | (~cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse)) | (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eInit_2eDatatypes_2efalse) = cCoq_2eInit_2eDatatypes_2etrue)),
% 10.96/11.17 inference(modus_ponens,[status(thm)],[86, 85])).
% 10.96/11.17 tff(88,plain,
% 10.96/11.17 (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eInit_2eDatatypes_2efalse) = cCoq_2eInit_2eDatatypes_2etrue),
% 10.96/11.17 inference(unit_resolution,[status(thm)],[87, 81, 78])).
% 10.96/11.17 tff(89,plain,
% 10.96/11.17 (^[V0__n: $i] : refl(((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n)))) <=> ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n)))))),
% 10.96/11.17 inference(bind,[status(th)],[])).
% 10.96/11.17 tff(90,plain,
% 10.96/11.17 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n)))) <=> ![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))))),
% 10.96/11.17 inference(quant_intro,[status(thm)],[89])).
% 10.96/11.17 tff(91,plain,
% 10.96/11.17 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n)))) <=> ![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))))),
% 10.96/11.18 inference(rewrite,[status(thm)],[])).
% 10.96/11.18 tff(92,plain,
% 10.96/11.18 (^[V0__n: $i] : rewrite((cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n)))) <=> ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n)))))),
% 10.96/11.18 inference(bind,[status(th)],[])).
% 10.96/11.18 tff(93,plain,
% 10.96/11.18 (![V0__n: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n)))) <=> ![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))))),
% 10.96/11.18 inference(quant_intro,[status(thm)],[92])).
% 10.96/11.18 tff(94,axiom,(![V0__n: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''Coq.ZArith.Zeven.Zodd_bool_iff'')).
% 10.96/11.18 tff(95,plain,
% 10.96/11.18 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[94, 93])).
% 10.96/11.18 tff(96,plain,
% 10.96/11.18 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[95, 91])).
% 10.96/11.18 tff(97,plain,(
% 10.96/11.18 ![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))))),
% 10.96/11.18 inference(skolemize,[status(sab)],[96])).
% 10.96/11.18 tff(98,plain,
% 10.96/11.18 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[97, 90])).
% 10.96/11.18 tff(99,plain,
% 10.96/11.18 (((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))))) | ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n!980))))) <=> ((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n!980))))),
% 10.96/11.18 inference(rewrite,[status(thm)],[])).
% 10.96/11.18 tff(100,plain,
% 10.96/11.18 ((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))))) | ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n!980))))),
% 10.96/11.18 inference(quant_inst,[status(thm)],[])).
% 10.96/11.18 tff(101,plain,
% 10.96/11.18 ((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n!980)))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[100, 99])).
% 10.96/11.18 tff(102,plain,
% 10.96/11.18 ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n!980))),
% 10.96/11.18 inference(unit_resolution,[status(thm)],[101, 98, 11])).
% 10.96/11.18 tff(103,plain,
% 10.96/11.18 (~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n!980))),
% 10.96/11.18 inference(or_elim,[status(thm)],[10])).
% 10.96/11.18 tff(104,plain,
% 10.96/11.18 ((~((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n!980)))) | (~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2etrue)) | p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n!980))),
% 10.96/11.18 inference(tautology,[status(thm)],[])).
% 10.96/11.18 tff(105,plain,
% 10.96/11.18 ((~((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n!980)))) | (~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2etrue))),
% 10.96/11.18 inference(unit_resolution,[status(thm)],[104, 103])).
% 10.96/11.18 tff(106,plain,
% 10.96/11.18 (~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2etrue)),
% 10.96/11.18 inference(unit_resolution,[status(thm)],[105, 102])).
% 10.96/11.18 tff(107,plain,
% 10.96/11.18 (((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(V0__n!980) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) | (cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2etrue)),
% 10.96/11.18 inference(tautology,[status(thm)],[])).
% 10.96/11.18 tff(108,plain,
% 10.96/11.18 ((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(V0__n!980) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))),
% 10.96/11.18 inference(unit_resolution,[status(thm)],[107, 106])).
% 10.96/11.18 tff(109,plain,
% 10.96/11.18 (^[Vv__CANONICAL__0: $i] : refl(((~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)))) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))) <=> ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)))) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))))),
% 10.96/11.18 inference(bind,[status(th)],[])).
% 10.96/11.18 tff(110,plain,
% 10.96/11.18 (![Vv__CANONICAL__0: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)))) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))) <=> ![Vv__CANONICAL__0: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)))) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))))),
% 10.96/11.18 inference(quant_intro,[status(thm)],[109])).
% 10.96/11.18 tff(111,plain,
% 10.96/11.18 (^[Vv__CANONICAL__0: $i] : trans(monotonicity(rewrite(((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)) <=> (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0))))), rewrite(((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) <=> (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))), ((((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))) <=> ((~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)))) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))), rewrite(((~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)))) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))) <=> ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)))) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))))), ((((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))) <=> ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)))) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))))))),
% 10.96/11.18 inference(bind,[status(th)],[])).
% 10.96/11.18 tff(112,plain,
% 10.96/11.18 (![Vv__CANONICAL__0: $i] : (((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))) <=> ![Vv__CANONICAL__0: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)))) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))))),
% 10.96/11.18 inference(quant_intro,[status(thm)],[111])).
% 10.96/11.18 tff(113,plain,
% 10.96/11.18 (![Vv__CANONICAL__0: $i] : (((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))) <=> ![Vv__CANONICAL__0: $i] : (((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)))),
% 10.96/11.18 inference(rewrite,[status(thm)],[])).
% 10.96/11.18 tff(114,plain,
% 10.96/11.18 (^[Vv__CANONICAL__0: $i] : trans(monotonicity(rewrite((((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0))) <=> (((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))), ((cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0) => (((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)))) <=> (cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0) => (((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))))), rewrite((cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0) => (((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))) <=> (((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)))), ((cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0) => (((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)))) <=> (((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)))))),
% 10.96/11.18 inference(bind,[status(th)],[])).
% 10.96/11.18 tff(115,plain,
% 10.96/11.18 (![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0) => (((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)))) <=> ![Vv__CANONICAL__0: $i] : (((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)))),
% 10.96/11.18 inference(quant_intro,[status(thm)],[114])).
% 10.96/11.18 tff(116,axiom,(![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0) => (((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''$_case_Coq.Init.Datatypes.bool$66339'')).
% 10.96/11.18 tff(117,plain,
% 10.96/11.18 (![Vv__CANONICAL__0: $i] : (((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[116, 115])).
% 10.96/11.18 tff(118,plain,
% 10.96/11.18 (![Vv__CANONICAL__0: $i] : (((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[117, 113])).
% 10.96/11.18 tff(119,plain,(
% 10.96/11.18 ![Vv__CANONICAL__0: $i] : (((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)) | ((cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue) & (c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)))),
% 10.96/11.18 inference(skolemize,[status(sab)],[118])).
% 10.96/11.18 tff(120,plain,
% 10.96/11.18 (![Vv__CANONICAL__0: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)))) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[119, 112])).
% 10.96/11.18 tff(121,plain,
% 10.96/11.18 (![Vv__CANONICAL__0: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)))) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[120, 110])).
% 10.96/11.18 tff(122,plain,
% 10.96/11.18 (((~![Vv__CANONICAL__0: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)))) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))))) | ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(V0__n!980) = cCoq_2eNumbers_2eBinNums_2eZ0)))) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(V0__n!980) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))))) <=> ((~![Vv__CANONICAL__0: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)))) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(V0__n!980) = cCoq_2eNumbers_2eBinNums_2eZ0)))) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(V0__n!980) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))))),
% 10.96/11.18 inference(rewrite,[status(thm)],[])).
% 10.96/11.18 tff(123,plain,
% 10.96/11.18 ((~![Vv__CANONICAL__0: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)))) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))))) | ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(V0__n!980) = cCoq_2eNumbers_2eBinNums_2eZ0)))) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(V0__n!980) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))))),
% 10.96/11.18 inference(quant_inst,[status(thm)],[])).
% 10.96/11.18 tff(124,plain,
% 10.96/11.18 ((~![Vv__CANONICAL__0: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0)))) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(V0__n!980) = cCoq_2eNumbers_2eBinNums_2eZ0)))) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(V0__n!980) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[123, 122])).
% 10.96/11.18 tff(125,plain,
% 10.96/11.18 ((~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(V0__n!980) = cCoq_2eNumbers_2eBinNums_2eZ0)))) | (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2etrue)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(V0__n!980) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))),
% 10.96/11.18 inference(unit_resolution,[status(thm)],[124, 121, 11])).
% 10.96/11.18 tff(126,plain,
% 10.96/11.18 (~((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(V0__n!980) = cCoq_2eNumbers_2eBinNums_2eZ0)))),
% 10.96/11.18 inference(unit_resolution,[status(thm)],[125, 108])).
% 10.96/11.18 tff(127,plain,
% 10.96/11.18 (((~(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2efalse)) | (~(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2466339___24a1(V0__n!980) = cCoq_2eNumbers_2eBinNums_2eZ0))) | (cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2efalse)),
% 10.96/11.18 inference(tautology,[status(thm)],[])).
% 10.96/11.18 tff(128,plain,
% 10.96/11.18 (cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2efalse),
% 10.96/11.18 inference(unit_resolution,[status(thm)],[127, 126])).
% 10.96/11.18 tff(129,plain,
% 10.96/11.18 (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980)) = cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eInit_2eDatatypes_2efalse)),
% 10.96/11.18 inference(monotonicity,[status(thm)],[128])).
% 10.96/11.18 tff(130,plain,
% 10.96/11.18 (^[V0__n: $i] : refl(((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n))) <=> ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n))))),
% 10.96/11.18 inference(bind,[status(th)],[])).
% 10.96/11.18 tff(131,plain,
% 10.96/11.18 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n))) <=> ![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n)))),
% 10.96/11.18 inference(quant_intro,[status(thm)],[130])).
% 10.96/11.18 tff(132,plain,
% 10.96/11.18 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n))) <=> ![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n)))),
% 10.96/11.18 inference(rewrite,[status(thm)],[])).
% 10.96/11.18 tff(133,plain,
% 10.96/11.18 (^[V0__n: $i] : rewrite((cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n))) <=> ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n))))),
% 10.96/11.18 inference(bind,[status(th)],[])).
% 10.96/11.18 tff(134,plain,
% 10.96/11.18 (![V0__n: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n))) <=> ![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n)))),
% 10.96/11.18 inference(quant_intro,[status(thm)],[133])).
% 10.96/11.18 tff(135,axiom,(![V0__n: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''Coq.ZArith.BinInt.Z.negb_odd'')).
% 10.96/11.18 tff(136,plain,
% 10.96/11.18 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n)))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[135, 134])).
% 10.96/11.18 tff(137,plain,
% 10.96/11.18 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n)))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[136, 132])).
% 10.96/11.18 tff(138,plain,(
% 10.96/11.18 ![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n)))),
% 10.96/11.18 inference(skolemize,[status(sab)],[137])).
% 10.96/11.18 tff(139,plain,
% 10.96/11.18 (![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n)))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[138, 131])).
% 10.96/11.18 tff(140,plain,
% 10.96/11.18 (((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n)))) | ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n!980)))) <=> ((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n)))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n!980)))),
% 10.96/11.18 inference(rewrite,[status(thm)],[])).
% 10.96/11.18 tff(141,plain,
% 10.96/11.18 ((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n)))) | ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n!980)))),
% 10.96/11.18 inference(quant_inst,[status(thm)],[])).
% 10.96/11.18 tff(142,plain,
% 10.96/11.18 ((~![V0__n: $i] : ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)) | (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n)))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n!980))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[141, 140])).
% 10.96/11.18 tff(143,plain,
% 10.96/11.18 (cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n!980)),
% 10.96/11.18 inference(unit_resolution,[status(thm)],[142, 139, 11])).
% 10.96/11.18 tff(144,plain,
% 10.96/11.18 (cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__n!980))),
% 10.96/11.18 inference(symmetry,[status(thm)],[143])).
% 10.96/11.18 tff(145,plain,
% 10.96/11.18 (cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2etrue),
% 10.96/11.18 inference(transitivity,[status(thm)],[144, 129, 88])).
% 10.96/11.18 tff(146,plain,
% 10.96/11.18 ((~((cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2etrue) <=> p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n!980)))) | (~(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__n!980) = cCoq_2eInit_2eDatatypes_2etrue)) | p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n!980))),
% 10.96/11.18 inference(tautology,[status(thm)],[])).
% 10.96/11.18 tff(147,plain,
% 10.96/11.18 (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n!980))),
% 10.96/11.18 inference(unit_resolution,[status(thm)],[146, 145, 68])).
% 10.96/11.18 tff(148,plain,
% 10.96/11.18 (^[V0__z: $i] : refl((p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z))) <=> (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z))))),
% 10.96/11.18 inference(bind,[status(th)],[])).
% 10.96/11.18 tff(149,plain,
% 10.96/11.18 (![V0__z: $i] : (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z))) <=> ![V0__z: $i] : (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)))),
% 10.96/11.18 inference(quant_intro,[status(thm)],[148])).
% 10.96/11.18 tff(150,plain,
% 10.96/11.18 (![V0__z: $i] : (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z))) <=> ![V0__z: $i] : (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)))),
% 10.96/11.18 inference(rewrite,[status(thm)],[])).
% 10.96/11.18 tff(151,plain,
% 10.96/11.18 (^[V0__z: $i] : trans(monotonicity(rewrite((p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)) => p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z)))) <=> ((~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))) | p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))))), ((cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z) => (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)) => p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))))) <=> (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z) => ((~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))) | p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))))))), rewrite((cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z) => ((~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))) | p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))))) <=> (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)))), ((cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z) => (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)) => p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))))) <=> (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)))))),
% 10.96/11.18 inference(bind,[status(th)],[])).
% 10.96/11.18 tff(152,plain,
% 10.96/11.18 (![V0__z: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z) => (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)) => p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))))) <=> ![V0__z: $i] : (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)))),
% 10.96/11.18 inference(quant_intro,[status(thm)],[151])).
% 10.96/11.18 tff(153,axiom,(![V0__z: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z) => (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)) => p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ArithCompl.Zeven_sqr1'')).
% 10.96/11.18 tff(154,plain,
% 10.96/11.18 (![V0__z: $i] : (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[153, 152])).
% 10.96/11.18 tff(155,plain,
% 10.96/11.18 (![V0__z: $i] : (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[154, 150])).
% 10.96/11.18 tff(156,plain,(
% 10.96/11.18 ![V0__z: $i] : (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)))),
% 10.96/11.18 inference(skolemize,[status(sab)],[155])).
% 10.96/11.18 tff(157,plain,
% 10.96/11.18 (![V0__z: $i] : (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[156, 149])).
% 10.96/11.18 tff(158,plain,
% 10.96/11.18 (((~![V0__z: $i] : (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)))) | ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n!980))) | p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980))))) <=> ((~![V0__z: $i] : (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n!980))) | p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980))))),
% 10.96/11.18 inference(rewrite,[status(thm)],[])).
% 10.96/11.18 tff(159,plain,
% 10.96/11.18 ((p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n!980))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980))) <=> ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n!980))) | p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980))))),
% 10.96/11.18 inference(rewrite,[status(thm)],[])).
% 10.96/11.18 tff(160,plain,
% 10.96/11.18 (((~![V0__z: $i] : (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)))) | (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n!980))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)))) <=> ((~![V0__z: $i] : (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)))) | ((~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n!980))) | p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980)))))),
% 10.96/11.18 inference(monotonicity,[status(thm)],[159])).
% 10.96/11.18 tff(161,plain,
% 10.96/11.18 (((~![V0__z: $i] : (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)))) | (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n!980))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)))) <=> ((~![V0__z: $i] : (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n!980))) | p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980))))),
% 10.96/11.18 inference(transitivity,[status(thm)],[160, 158])).
% 10.96/11.18 tff(162,plain,
% 10.96/11.18 ((~![V0__z: $i] : (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)))) | (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n!980))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)))),
% 10.96/11.18 inference(quant_inst,[status(thm)],[])).
% 10.96/11.18 tff(163,plain,
% 10.96/11.18 ((~![V0__z: $i] : (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__z, V0__z))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n!980))) | p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980)))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[162, 161])).
% 10.96/11.18 tff(164,plain,
% 10.96/11.18 ((~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n!980))) | p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980)))),
% 10.96/11.18 inference(unit_resolution,[status(thm)],[163, 157, 11])).
% 10.96/11.18 tff(165,plain,
% 10.96/11.18 (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980)))),
% 10.96/11.18 inference(unit_resolution,[status(thm)],[164, 147])).
% 10.96/11.18 tff(166,plain,
% 10.96/11.18 (p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980)))),
% 10.96/11.18 inference(or_elim,[status(thm)],[10])).
% 10.96/11.18 tff(167,plain,
% 10.96/11.18 (^[V0__n: $i] : refl(((~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n))) <=> ((~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n))))),
% 10.96/11.18 inference(bind,[status(th)],[])).
% 10.96/11.18 tff(168,plain,
% 10.96/11.18 (![V0__n: $i] : ((~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n))) <=> ![V0__n: $i] : ((~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)))),
% 10.96/11.18 inference(quant_intro,[status(thm)],[167])).
% 10.96/11.18 tff(169,plain,
% 10.96/11.18 (![V0__n: $i] : ((~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n))) <=> ![V0__n: $i] : ((~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)))),
% 10.96/11.18 inference(rewrite,[status(thm)],[])).
% 10.96/11.18 tff(170,plain,
% 10.96/11.18 (^[V0__n: $i] : trans(monotonicity(rewrite((p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n)) => (~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n)))) <=> ((~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))) | (~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))))), ((cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n)) => (~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))))) <=> (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => ((~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))) | (~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))))))), rewrite((cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => ((~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))) | (~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))))) <=> ((~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)))), ((cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n)) => (~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))))) <=> ((~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)))))),
% 10.96/11.18 inference(bind,[status(th)],[])).
% 10.96/11.18 tff(171,plain,
% 10.96/11.18 (![V0__n: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n)) => (~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))))) <=> ![V0__n: $i] : ((~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)))),
% 10.96/11.18 inference(quant_intro,[status(thm)],[170])).
% 10.96/11.18 tff(172,axiom,(![V0__n: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n) => (p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n)) => (~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''Coq.ZArith.Zeven.Zeven_not_Zodd'')).
% 10.96/11.18 tff(173,plain,
% 10.96/11.18 (![V0__n: $i] : ((~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[172, 171])).
% 10.96/11.18 tff(174,plain,
% 10.96/11.18 (![V0__n: $i] : ((~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[173, 169])).
% 10.96/11.18 tff(175,plain,(
% 10.96/11.18 ![V0__n: $i] : ((~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)))),
% 10.96/11.18 inference(skolemize,[status(sab)],[174])).
% 10.96/11.18 tff(176,plain,
% 10.96/11.18 (![V0__n: $i] : ((~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[175, 168])).
% 10.96/11.18 tff(177,plain,
% 10.96/11.18 (((~![V0__n: $i] : ((~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)))) | ((~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980)))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980)))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980))))) <=> ((~![V0__n: $i] : ((~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)))) | (~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980)))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980)))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980))))),
% 10.96/11.18 inference(rewrite,[status(thm)],[])).
% 10.96/11.18 tff(178,plain,
% 10.96/11.18 ((~![V0__n: $i] : ((~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)))) | ((~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980)))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980)))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980))))),
% 10.96/11.18 inference(quant_inst,[status(thm)],[])).
% 10.96/11.18 tff(179,plain,
% 10.96/11.18 ((~![V0__n: $i] : ((~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__n))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__n))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)))) | (~p(cCoq_2eZArith_2eZeven_2eZodd___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980)))) | (~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980)))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980)))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[178, 177])).
% 10.96/11.18 tff(180,plain,
% 10.96/11.18 ((~p(cCoq_2eZArith_2eZeven_2eZeven___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980)))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980)))),
% 10.96/11.18 inference(unit_resolution,[status(thm)],[179, 176, 166])).
% 10.96/11.18 tff(181,plain,
% 10.96/11.18 (~cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, V0__n!980))),
% 10.96/11.18 inference(unit_resolution,[status(thm)],[180, 165])).
% 10.96/11.18 tff(182,plain,
% 10.96/11.18 (~cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[181, 54])).
% 10.96/11.18 tff(183,plain,
% 10.96/11.18 (cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) <=> cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980)),
% 10.96/11.18 inference(monotonicity,[status(thm)],[40])).
% 10.96/11.18 tff(184,plain,
% 10.96/11.18 (cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n!980) <=> cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))),
% 10.96/11.18 inference(symmetry,[status(thm)],[183])).
% 10.96/11.18 tff(185,plain,
% 10.96/11.18 (cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[11, 184])).
% 10.96/11.18 tff(186,plain,
% 10.96/11.18 (^[Vvar__31: $i] : refl((~((~((~c_24__type__30___24t(Vvar__31)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))) | (~(c_24__type__30___24t(Vvar__31) | (~(cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, tptp_fun_Vv__CANONICAL__0_802(Vvar__31))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(tptp_fun_Vv__CANONICAL__0_802(Vvar__31))))))))) <=> (~((~((~c_24__type__30___24t(Vvar__31)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))) | (~(c_24__type__30___24t(Vvar__31) | (~(cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, tptp_fun_Vv__CANONICAL__0_802(Vvar__31))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(tptp_fun_Vv__CANONICAL__0_802(Vvar__31))))))))))),
% 10.96/11.18 inference(bind,[status(th)],[])).
% 10.96/11.18 tff(187,plain,
% 10.96/11.18 (![Vvar__31: $i] : (~((~((~c_24__type__30___24t(Vvar__31)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))) | (~(c_24__type__30___24t(Vvar__31) | (~(cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, tptp_fun_Vv__CANONICAL__0_802(Vvar__31))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(tptp_fun_Vv__CANONICAL__0_802(Vvar__31))))))))) <=> ![Vvar__31: $i] : (~((~((~c_24__type__30___24t(Vvar__31)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))) | (~(c_24__type__30___24t(Vvar__31) | (~(cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, tptp_fun_Vv__CANONICAL__0_802(Vvar__31))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(tptp_fun_Vv__CANONICAL__0_802(Vvar__31)))))))))),
% 10.96/11.18 inference(quant_intro,[status(thm)],[186])).
% 10.96/11.18 tff(188,plain,
% 10.96/11.18 (^[Vvar__31: $i] : rewrite((~((~((~c_24__type__30___24t(Vvar__31)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))) | (~(c_24__type__30___24t(Vvar__31) | (~(cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, tptp_fun_Vv__CANONICAL__0_802(Vvar__31))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(tptp_fun_Vv__CANONICAL__0_802(Vvar__31))))))))) <=> (~((~((~c_24__type__30___24t(Vvar__31)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))) | (~(c_24__type__30___24t(Vvar__31) | (~(cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, tptp_fun_Vv__CANONICAL__0_802(Vvar__31))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(tptp_fun_Vv__CANONICAL__0_802(Vvar__31))))))))))),
% 10.96/11.18 inference(bind,[status(th)],[])).
% 10.96/11.18 tff(189,plain,
% 10.96/11.18 (![Vvar__31: $i] : (~((~((~c_24__type__30___24t(Vvar__31)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))) | (~(c_24__type__30___24t(Vvar__31) | (~(cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, tptp_fun_Vv__CANONICAL__0_802(Vvar__31))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(tptp_fun_Vv__CANONICAL__0_802(Vvar__31))))))))) <=> ![Vvar__31: $i] : (~((~((~c_24__type__30___24t(Vvar__31)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))) | (~(c_24__type__30___24t(Vvar__31) | (~(cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, tptp_fun_Vv__CANONICAL__0_802(Vvar__31))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(tptp_fun_Vv__CANONICAL__0_802(Vvar__31)))))))))),
% 10.96/11.18 inference(quant_intro,[status(thm)],[188])).
% 10.96/11.18 tff(190,plain,
% 10.96/11.18 (![Vvar__31: $i] : (~((~((~c_24__type__30___24t(Vvar__31)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))) | (~(c_24__type__30___24t(Vvar__31) | (~(cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, tptp_fun_Vv__CANONICAL__0_802(Vvar__31))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(tptp_fun_Vv__CANONICAL__0_802(Vvar__31))))))))) <=> ![Vvar__31: $i] : (~((~((~c_24__type__30___24t(Vvar__31)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))) | (~(c_24__type__30___24t(Vvar__31) | (~(cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, tptp_fun_Vv__CANONICAL__0_802(Vvar__31))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(tptp_fun_Vv__CANONICAL__0_802(Vvar__31)))))))))),
% 10.96/11.18 inference(transitivity,[status(thm)],[189, 187])).
% 10.96/11.18 tff(191,plain,
% 10.96/11.18 (^[Vvar__31: $i] : trans(monotonicity(rewrite(((~c_24__type__30___24t(Vvar__31)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)))) <=> ((~c_24__type__30___24t(Vvar__31)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))), ((((~c_24__type__30___24t(Vvar__31)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)))) & (c_24__type__30___24t(Vvar__31) | (~(cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, tptp_fun_Vv__CANONICAL__0_802(Vvar__31))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(tptp_fun_Vv__CANONICAL__0_802(Vvar__31))))))) <=> (((~c_24__type__30___24t(Vvar__31)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)))) & (c_24__type__30___24t(Vvar__31) | (~(cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, tptp_fun_Vv__CANONICAL__0_802(Vvar__31))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(tptp_fun_Vv__CANONICAL__0_802(Vvar__31))))))))), rewrite((((~c_24__type__30___24t(Vvar__31)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)))) & (c_24__type__30___24t(Vvar__31) | (~(cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, tptp_fun_Vv__CANONICAL__0_802(Vvar__31))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(tptp_fun_Vv__CANONICAL__0_802(Vvar__31))))))) <=> (~((~((~c_24__type__30___24t(Vvar__31)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))) | (~(c_24__type__30___24t(Vvar__31) | (~(cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, tptp_fun_Vv__CANONICAL__0_802(Vvar__31))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(tptp_fun_Vv__CANONICAL__0_802(Vvar__31)))))))))), ((((~c_24__type__30___24t(Vvar__31)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)))) & (c_24__type__30___24t(Vvar__31) | (~(cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, tptp_fun_Vv__CANONICAL__0_802(Vvar__31))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(tptp_fun_Vv__CANONICAL__0_802(Vvar__31))))))) <=> (~((~((~c_24__type__30___24t(Vvar__31)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))) | (~(c_24__type__30___24t(Vvar__31) | (~(cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, tptp_fun_Vv__CANONICAL__0_802(Vvar__31))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(tptp_fun_Vv__CANONICAL__0_802(Vvar__31)))))))))))),
% 10.96/11.18 inference(bind,[status(th)],[])).
% 10.96/11.18 tff(192,plain,
% 10.96/11.18 (![Vvar__31: $i] : (((~c_24__type__30___24t(Vvar__31)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)))) & (c_24__type__30___24t(Vvar__31) | (~(cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, tptp_fun_Vv__CANONICAL__0_802(Vvar__31))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(tptp_fun_Vv__CANONICAL__0_802(Vvar__31))))))) <=> ![Vvar__31: $i] : (~((~((~c_24__type__30___24t(Vvar__31)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))) | (~(c_24__type__30___24t(Vvar__31) | (~(cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, tptp_fun_Vv__CANONICAL__0_802(Vvar__31))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(tptp_fun_Vv__CANONICAL__0_802(Vvar__31)))))))))),
% 10.96/11.18 inference(quant_intro,[status(thm)],[191])).
% 10.96/11.18 tff(193,plain,
% 10.96/11.18 (![Vvar__31: $i] : (c_24__type__30___24t(Vvar__31) <=> ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)))) <=> ![Vvar__31: $i] : (c_24__type__30___24t(Vvar__31) <=> ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))),
% 10.96/11.18 inference(rewrite,[status(thm)],[])).
% 10.96/11.18 tff(194,plain,
% 10.96/11.18 (^[Vvar__31: $i] : rewrite((c_24__type__30___24t(Vvar__31) <=> ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0) => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)))) <=> (c_24__type__30___24t(Vvar__31) <=> ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)))))),
% 10.96/11.18 inference(bind,[status(th)],[])).
% 10.96/11.18 tff(195,plain,
% 10.96/11.18 (![Vvar__31: $i] : (c_24__type__30___24t(Vvar__31) <=> ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0) => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)))) <=> ![Vvar__31: $i] : (c_24__type__30___24t(Vvar__31) <=> ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))),
% 10.96/11.18 inference(quant_intro,[status(thm)],[194])).
% 10.96/11.18 tff(196,axiom,(![Vvar__31: $i] : (c_24__type__30___24t(Vvar__31) <=> ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0) => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''$_type_30'')).
% 10.96/11.18 tff(197,plain,
% 10.96/11.18 (![Vvar__31: $i] : (c_24__type__30___24t(Vvar__31) <=> ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[196, 195])).
% 10.96/11.18 tff(198,plain,
% 10.96/11.18 (![Vvar__31: $i] : (c_24__type__30___24t(Vvar__31) <=> ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[197, 193])).
% 10.96/11.18 tff(199,plain,(
% 10.96/11.18 ![Vvar__31: $i] : (((~c_24__type__30___24t(Vvar__31)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)))) & (c_24__type__30___24t(Vvar__31) | (~(cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, tptp_fun_Vv__CANONICAL__0_802(Vvar__31))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(tptp_fun_Vv__CANONICAL__0_802(Vvar__31)))))))),
% 10.96/11.18 inference(skolemize,[status(sab)],[198])).
% 10.96/11.18 tff(200,plain,
% 10.96/11.18 (![Vvar__31: $i] : (~((~((~c_24__type__30___24t(Vvar__31)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))) | (~(c_24__type__30___24t(Vvar__31) | (~(cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, tptp_fun_Vv__CANONICAL__0_802(Vvar__31))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(tptp_fun_Vv__CANONICAL__0_802(Vvar__31)))))))))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[199, 192])).
% 10.96/11.18 tff(201,plain,
% 10.96/11.18 (![Vvar__31: $i] : (~((~((~c_24__type__30___24t(Vvar__31)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))) | (~(c_24__type__30___24t(Vvar__31) | (~(cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, tptp_fun_Vv__CANONICAL__0_802(Vvar__31))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(tptp_fun_Vv__CANONICAL__0_802(Vvar__31)))))))))),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[200, 190])).
% 10.96/11.18 tff(202,plain,
% 10.96/11.18 ((~![Vvar__31: $i] : (~((~((~c_24__type__30___24t(Vvar__31)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))) | (~(c_24__type__30___24t(Vvar__31) | (~(cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31, tptp_fun_Vv__CANONICAL__0_802(Vvar__31))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(tptp_fun_Vv__CANONICAL__0_802(Vvar__31)))))))))) | (~((~((~c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))) | (~(c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare) | (~(cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, tptp_fun_Vv__CANONICAL__0_802(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(tptp_fun_Vv__CANONICAL__0_802(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare)))))))))),
% 10.96/11.18 inference(quant_inst,[status(thm)],[])).
% 10.96/11.18 tff(203,plain,
% 10.96/11.18 (~((~((~c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))) | (~(c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare) | (~(cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, tptp_fun_Vv__CANONICAL__0_802(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(tptp_fun_Vv__CANONICAL__0_802(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare))))))))),
% 10.96/11.18 inference(unit_resolution,[status(thm)],[202, 201])).
% 10.96/11.18 tff(204,plain,
% 10.96/11.18 (((~((~c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))) | (~(c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare) | (~(cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, tptp_fun_Vv__CANONICAL__0_802(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(tptp_fun_Vv__CANONICAL__0_802(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare)))))))) | ((~c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))),
% 10.96/11.18 inference(tautology,[status(thm)],[])).
% 10.96/11.18 tff(205,plain,
% 10.96/11.18 ((~c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)))),
% 10.96/11.18 inference(unit_resolution,[status(thm)],[204, 203])).
% 10.96/11.18 tff(206,plain,
% 10.96/11.18 (c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare) <=> c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare)),
% 10.96/11.18 inference(rewrite,[status(thm)],[])).
% 10.96/11.18 tff(207,axiom,(c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''$_typeof_Coq.ZArith.BinIntDef.Z.square'')).
% 10.96/11.18 tff(208,plain,
% 10.96/11.18 (c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare)),
% 10.96/11.18 inference(modus_ponens,[status(thm)],[207, 206])).
% 10.96/11.18 tff(209,plain,
% 10.96/11.18 ((~((~c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))) | (~c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)))),
% 10.96/11.18 inference(tautology,[status(thm)],[])).
% 10.96/11.18 tff(210,plain,
% 10.96/11.18 ((~((~c_24__type__30___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare)) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0))))) | ![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)))),
% 10.96/11.18 inference(unit_resolution,[status(thm)],[209, 208])).
% 10.96/11.18 tff(211,plain,
% 10.96/11.18 (![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)))),
% 10.96/11.18 inference(unit_resolution,[status(thm)],[210, 205])).
% 10.96/11.18 tff(212,plain,
% 10.96/11.18 (((~![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)))) | (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))) <=> ((~![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)))) | cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))),
% 11.13/11.32 inference(rewrite,[status(thm)],[])).
% 11.13/11.32 tff(213,plain,
% 11.13/11.32 ((~![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)))) | (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))))),
% 11.13/11.32 inference(quant_inst,[status(thm)],[])).
% 11.13/11.32 tff(214,plain,
% 11.13/11.32 ((~![Vv__CANONICAL__0: $i] : (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, Vv__CANONICAL__0)) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)))) | cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) | (~cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))),
% 11.13/11.32 inference(modus_ponens,[status(thm)],[213, 212])).
% 11.13/11.32 tff(215,plain,
% 11.13/11.32 (cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esquare, cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n!980, cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))),
% 11.13/11.32 inference(unit_resolution,[status(thm)],[214, 211, 185])).
% 11.13/11.32 tff(216,plain,
% 11.13/11.32 ($false),
% 11.13/11.32 inference(unit_resolution,[status(thm)],[215, 182])).
% 11.13/11.32 % SZS output end Proof
% 11.13/11.33 % E exiting
%------------------------------------------------------------------------------