0.09/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.09/0.16 % Command : eprover-ho %s --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --free-numbers -auto-schedule -p --cpu-limit=%d --neg-ext=all --pos-ext=all --ext-sup-max-depth=2 --schedule-kind=CASC 0.16/0.37 % Computer : n029.cluster.edu 0.16/0.37 % Model : x86_64 x86_64 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.16/0.37 % Memory : 8042.1875MB 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64 0.16/0.37 % CPULimit : 1200 0.16/0.37 % WCLimit : 120 0.16/0.37 % DateTime : Tue Jul 13 15:15:25 EDT 2021 0.16/0.37 % CPUTime : 0.16/0.38 % Number of cores: 8 0.16/0.38 % Python version: Python 3.6.8 0.16/0.38 # Version: 2.6rc1-ho 0.16/0.39 # No SInE strategy applied 0.16/0.39 # Trying AutoSched0 for 59 seconds 32.44/32.63 # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_S4d 32.44/32.63 # and selection function SelectCQIPrecWNTNp. 32.44/32.63 # 32.44/32.63 # Preprocessing time : 0.051 s 32.44/32.63 # Presaturation interreduction done 32.44/32.63 32.44/32.63 # Proof found! 32.44/32.63 # SZS status Theorem 32.44/32.63 # SZS output start CNFRefutation 32.44/32.63 thf(fact_107_local_Osup_Oorder__iff, axiom, ![X1:a, X3:a]:(less_eq @ X1 @ X3<=>(X3)=(sup @ X3 @ X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_107_local_Osup_Oorder__iff)). 32.44/32.63 thf(fact_7_local_Osup_Ocommute, axiom, ![X3:a, X1:a]:(sup @ X3 @ X1)=(sup @ X1 @ X3), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_7_local_Osup_Ocommute)). 32.44/32.63 thf(fact_40_local_Oinf__sup__absorb, axiom, ![X2:a, X13:a]:(inf @ X2 @ (sup @ X2 @ X13))=(X2), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_40_local_Oinf__sup__absorb)). 32.44/32.63 thf(fact_50_d__less__e, axiom, less_eq @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_50_d__less__e)). 32.44/32.63 thf(fact_0_local_Oinf_Oassoc, axiom, ![X3:a, X1:a, X4:a]:(inf @ (inf @ X3 @ X1) @ X4)=(inf @ X3 @ (inf @ X1 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_0_local_Oinf_Oassoc)). 32.44/32.63 thf(fact_1_local_Oinf_Ocommute, axiom, ![X3:a, X1:a]:(inf @ X3 @ X1)=(inf @ X1 @ X3), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_1_local_Oinf_Ocommute)). 32.44/32.63 thf(fact_33_local_Oinf__right__idem, axiom, ![X2:a, X13:a]:(inf @ (inf @ X2 @ X13) @ X13)=(inf @ X2 @ X13), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_33_local_Oinf__right__idem)). 32.44/32.63 thf(fact_23_local_Ob__meet__e, axiom, ![X1:a, X3:a, X4:a]:(inf @ X1 @ (modula1144073633_aux_a @ inf @ sup @ X3 @ X1 @ X4))=(inf @ X1 @ (sup @ X4 @ X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_23_local_Ob__meet__e)). 32.44/32.63 thf(fact_41_local_Osup__inf__absorb, axiom, ![X2:a, X13:a]:(sup @ X2 @ (inf @ X2 @ X13))=(X2), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_41_local_Osup__inf__absorb)). 32.44/32.63 thf(fact_6_local_Osup_Oassoc, axiom, ![X3:a, X1:a, X4:a]:(sup @ (sup @ X3 @ X1) @ X4)=(sup @ X3 @ (sup @ X1 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_6_local_Osup_Oassoc)). 32.44/32.63 thf(fact_36_local_Osup_Oright__idem, axiom, ![X3:a, X1:a]:(sup @ (sup @ X3 @ X1) @ X1)=(sup @ X3 @ X1), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_36_local_Osup_Oright__idem)). 32.44/32.63 thf(fact_17_b__meet__d, axiom, ![X1:a, X3:a, X4:a]:(inf @ X1 @ (modula1936294176_aux_a @ inf @ sup @ X3 @ X1 @ X4))=(sup @ (inf @ X1 @ X4) @ (inf @ X3 @ X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_17_b__meet__d)). 32.44/32.63 thf(fact_38_local_Osup__left__idem, axiom, ![X2:a, X13:a]:(sup @ X2 @ (sup @ X2 @ X13))=(sup @ X2 @ X13), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_38_local_Osup__left__idem)). 32.44/32.63 thf(fact_11_local_Osup__left__commute, axiom, ![X2:a, X13:a, X16:a]:(sup @ X2 @ (sup @ X13 @ X16))=(sup @ X13 @ (sup @ X2 @ X16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_11_local_Osup__left__commute)). 32.44/32.63 thf(fact_25_local_Oe__aux__def, axiom, ![X3:a, X1:a, X4:a]:(modula1144073633_aux_a @ inf @ sup @ X3 @ X1 @ X4)=(inf @ (inf @ (sup @ X3 @ X1) @ (sup @ X1 @ X4)) @ (sup @ X4 @ X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_25_local_Oe__aux__def)). 32.44/32.63 thf(fact_26_local_Oe__b__c__a, axiom, ![X1:a, X4:a, X3:a]:(modula1144073633_aux_a @ inf @ sup @ X1 @ X4 @ X3)=(modula1144073633_aux_a @ inf @ sup @ X3 @ X1 @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_26_local_Oe__b__c__a)). 32.44/32.63 thf(fact_24_local_Oc__meet__e, axiom, ![X4:a, X3:a, X1:a]:(inf @ X4 @ (modula1144073633_aux_a @ inf @ sup @ X3 @ X1 @ X4))=(inf @ X4 @ (sup @ X3 @ X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_24_local_Oc__meet__e)). 32.44/32.63 thf(fact_5_local_Oinf__left__commute, axiom, ![X2:a, X13:a, X16:a]:(inf @ X2 @ (inf @ X13 @ X16))=(inf @ X13 @ (inf @ X2 @ X16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_5_local_Oinf__left__commute)). 32.44/32.63 thf(fact_32_local_Oinf__left__idem, axiom, ![X2:a, X13:a]:(inf @ X2 @ (inf @ X2 @ X13))=(inf @ X2 @ X13), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_32_local_Oinf__left__idem)). 32.44/32.63 thf(fact_19_local_Od__aux__def, axiom, ![X3:a, X1:a, X4:a]:(modula1936294176_aux_a @ inf @ sup @ X3 @ X1 @ X4)=(sup @ (sup @ (inf @ X3 @ X1) @ (inf @ X1 @ X4)) @ (inf @ X4 @ X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_19_local_Od__aux__def)). 32.44/32.63 thf(fact_20_local_Od__b__c__a, axiom, ![X1:a, X4:a, X3:a]:(modula1936294176_aux_a @ inf @ sup @ X1 @ X4 @ X3)=(modula1936294176_aux_a @ inf @ sup @ X3 @ X1 @ X4), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_20_local_Od__b__c__a)). 32.44/32.63 thf(fact_18_c__meet__d, axiom, ![X4:a, X3:a, X1:a]:(inf @ X4 @ (modula1936294176_aux_a @ inf @ sup @ X3 @ X1 @ X4))=(sup @ (inf @ X4 @ X3) @ (inf @ X1 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_18_c__meet__d)). 32.44/32.63 thf(fact_15_a__meet__d, axiom, ![X3:a, X1:a, X4:a]:(inf @ X3 @ (modula1936294176_aux_a @ inf @ sup @ X3 @ X1 @ X4))=(sup @ (inf @ X3 @ X1) @ (inf @ X4 @ X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_15_a__meet__d)). 32.44/32.63 thf(fact_14_local_Oa__join__d, axiom, ![X3:a, X1:a, X4:a]:(sup @ X3 @ (modula1936294176_aux_a @ inf @ sup @ X3 @ X1 @ X4))=(sup @ X3 @ (inf @ X1 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_14_local_Oa__join__d)). 32.44/32.63 thf(fact_16_local_Ob__join__d, axiom, ![X1:a, X3:a, X4:a]:(sup @ X1 @ (modula1936294176_aux_a @ inf @ sup @ X3 @ X1 @ X4))=(sup @ X1 @ (inf @ X4 @ X3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_16_local_Ob__join__d)). 32.44/32.63 thf(fact_31_local_Oinf__idem, axiom, ![X2:a]:(inf @ X2 @ X2)=(X2), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_31_local_Oinf__idem)). 32.44/32.63 thf(fact_167_abel__semigroup_Ocommute, axiom, ![X10:a > a > a, X3:a, X1:a]:((X10 @ X3 @ X1)=(X10 @ X1 @ X3)<=abel_semigroup_a @ X10), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_167_abel__semigroup_Ocommute)). 32.44/32.63 thf(fact_58_local_Oinf_Oabel__semigroup__axioms, axiom, abel_semigroup_a @ inf, file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_58_local_Oinf_Oabel__semigroup__axioms)). 32.44/32.63 thf(fact_22_local_Oa__meet__e, axiom, ![X3:a, X1:a, X4:a]:(inf @ X3 @ (modula1144073633_aux_a @ inf @ sup @ X3 @ X1 @ X4))=(inf @ X3 @ (sup @ X1 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_22_local_Oa__meet__e)). 32.44/32.63 thf(fact_146_local_Ole__sup__iff, axiom, ![X2:a, X13:a, X16:a]:(less_eq @ (sup @ X2 @ X13) @ X16<=>(less_eq @ X2 @ X16&less_eq @ X13 @ X16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_146_local_Ole__sup__iff)). 32.44/32.63 thf(fact_104_local_Osup__ge1, axiom, ![X2:a, X13:a]:less_eq @ X2 @ (sup @ X2 @ X13), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_104_local_Osup__ge1)). 32.44/32.63 thf(fact_166_semilattice_Oleft__idem, axiom, ![X10:a > a > a, X3:a, X1:a]:((X10 @ X3 @ (X10 @ X3 @ X1))=(X10 @ X3 @ X1)<=semilattice_a @ X10), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_166_semilattice_Oleft__idem)). 32.44/32.63 thf(fact_137_a__def__equiv, axiom, ![X3:a, X1:a, X4:a]:(less_eq @ (modula1936294176_aux_a @ inf @ sup @ X3 @ X1 @ X4) @ (modula1144073633_aux_a @ inf @ sup @ X3 @ X1 @ X4)=>(modula17988509_aux_a @ inf @ sup @ X3 @ X1 @ X4)=(inf @ (sup @ X3 @ (modula1936294176_aux_a @ inf @ sup @ X3 @ X1 @ X4)) @ (modula1144073633_aux_a @ inf @ sup @ X3 @ X1 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_137_a__def__equiv)). 32.44/32.63 thf(fact_44_local_Oa__aux__def, axiom, ![X3:a, X1:a, X4:a]:(modula17988509_aux_a @ inf @ sup @ X3 @ X1 @ X4)=(sup @ (inf @ X3 @ (modula1144073633_aux_a @ inf @ sup @ X3 @ X1 @ X4)) @ (modula1936294176_aux_a @ inf @ sup @ X3 @ X1 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_44_local_Oa__aux__def)). 32.44/32.63 thf(fact_96_local_Oinf_Oabsorb__iff2, axiom, ![X1:a, X3:a]:(less_eq @ X1 @ X3<=>(inf @ X3 @ X1)=(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_96_local_Oinf_Oabsorb__iff2)). 32.44/32.63 thf(fact_55_local_Osup_Osemilattice__axioms, axiom, semilattice_a @ sup, file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_55_local_Osup_Osemilattice__axioms)). 32.44/32.63 thf(fact_87_local_Oinf_Oorder__iff, axiom, ![X3:a, X1:a]:(less_eq @ X3 @ X1<=>(X3)=(inf @ X3 @ X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_87_local_Oinf_Oorder__iff)). 32.44/32.63 thf(fact_165_semilattice_Oright__idem, axiom, ![X10:a > a > a, X3:a, X1:a]:((X10 @ (X10 @ X3 @ X1) @ X1)=(X10 @ X3 @ X1)<=semilattice_a @ X10), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_165_semilattice_Oright__idem)). 32.44/32.63 thf(fact_117_local_Osup_Oabsorb__iff2, axiom, ![X3:a, X1:a]:(less_eq @ X3 @ X1<=>(sup @ X3 @ X1)=(X1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_117_local_Osup_Oabsorb__iff2)). 32.44/32.63 thf(fact_57_local_Osup_Oabel__semigroup__axioms, axiom, abel_semigroup_a @ sup, file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_57_local_Osup_Oabel__semigroup__axioms)). 32.44/32.63 thf(fact_113_local_Osup_Ocobounded2, axiom, ![X1:a, X3:a]:less_eq @ X1 @ (sup @ X3 @ X1), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_113_local_Osup_Ocobounded2)). 32.44/32.63 thf(fact_126_local_Omodular, axiom, ![X2:a, X13:a, X16:a]:((sup @ X2 @ (inf @ X13 @ X16))=(inf @ X13 @ (sup @ X2 @ X16))<=less_eq @ X2 @ X13), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_126_local_Omodular)). 32.44/32.63 thf(fact_56_local_Oinf_Osemilattice__axioms, axiom, semilattice_a @ inf, file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_56_local_Oinf_Osemilattice__axioms)). 32.44/32.63 thf(fact_128_local_Odistrib__inf__le, axiom, ![X2:a, X13:a, X16:a]:less_eq @ (sup @ (inf @ X2 @ X13) @ (inf @ X2 @ X16)) @ (inf @ X2 @ (sup @ X13 @ X16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_128_local_Odistrib__inf__le)). 32.44/32.63 thf(fact_42_local_Ob__aux__def, axiom, ![X3:a, X1:a, X4:a]:(modula1373251614_aux_a @ inf @ sup @ X3 @ X1 @ X4)=(sup @ (inf @ X1 @ (modula1144073633_aux_a @ inf @ sup @ X3 @ X1 @ X4)) @ (modula1936294176_aux_a @ inf @ sup @ X3 @ X1 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_42_local_Ob__aux__def)). 32.44/32.63 thf(fact_61_local_Ob__a, axiom, ![X3:a, X1:a, X4:a]:(modula1373251614_aux_a @ inf @ sup @ X3 @ X1 @ X4)=(modula17988509_aux_a @ inf @ sup @ X1 @ X4 @ X3), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_61_local_Ob__a)). 32.44/32.63 thf(fact_141_a__meet__b__eq__d, axiom, ![X3:a, X1:a, X4:a]:((inf @ (modula17988509_aux_a @ inf @ sup @ X3 @ X1 @ X4) @ (modula1373251614_aux_a @ inf @ sup @ X3 @ X1 @ X4))=(modula1936294176_aux_a @ inf @ sup @ X3 @ X1 @ X4)<=less_eq @ (modula1936294176_aux_a @ inf @ sup @ X3 @ X1 @ X4) @ (modula1144073633_aux_a @ inf @ sup @ X3 @ X1 @ X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_141_a__meet__b__eq__d)). 32.44/32.63 thf(fact_139_b__def__equiv, axiom, ![X3:a, X1:a, X4:a]:(less_eq @ (modula1936294176_aux_a @ inf @ sup @ X3 @ X1 @ X4) @ (modula1144073633_aux_a @ inf @ sup @ X3 @ X1 @ X4)=>(modula1373251614_aux_a @ inf @ sup @ X3 @ X1 @ X4)=(inf @ (sup @ X1 @ (modula1936294176_aux_a @ inf @ sup @ X3 @ X1 @ X4)) @ (modula1144073633_aux_a @ inf @ sup @ X3 @ X1 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_139_b__def__equiv)). 32.44/32.63 thf(fact_37_local_Osup__idem, axiom, ![X2:a]:(sup @ X2 @ X2)=(X2), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_37_local_Osup__idem)). 32.44/32.63 thf(conj_0, conjecture, (sup @ (inf @ (sup @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) @ (inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))))=(inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ (inf @ (sup @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) @ (sup @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', conj_0)). 32.44/32.63 thf(fact_83_local_Oinf__le1, axiom, ![X2:a, X13:a]:less_eq @ (inf @ X2 @ X13) @ X2, file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_83_local_Oinf__le1)). 32.44/32.63 thf(fact_158_semilattice_Oaxioms_I1_J, axiom, ![X10:a > a > a]:(semilattice_a @ X10=>abel_semigroup_a @ X10), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_158_semilattice_Oaxioms_I1_J)). 32.44/32.63 thf(fact_92_local_Oinf_Ocobounded2, axiom, ![X3:a, X1:a]:less_eq @ (inf @ X3 @ X1) @ X1, file('/export/starexec/sandbox/benchmark/theBenchmark.p', fact_92_local_Oinf_Ocobounded2)). 32.44/32.63 thf(c_0_53, plain, ![X830:a, X831:a]:((~less_eq @ X830 @ X831|(X831)=(sup @ X831 @ X830))&((X831)!=(sup @ X831 @ X830)|less_eq @ X830 @ X831)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_107_local_Osup_Oorder__iff])])). 32.44/32.63 thf(c_0_54, plain, ![X779:a, X780:a]:(sup @ X779 @ X780)=(sup @ X780 @ X779), inference(variable_rename,[status(thm)],[fact_7_local_Osup_Ocommute])). 32.44/32.63 thf(c_0_55, plain, ![X835:a, X836:a]:(inf @ X835 @ (sup @ X835 @ X836))=(X835), inference(variable_rename,[status(thm)],[fact_40_local_Oinf__sup__absorb])). 32.44/32.63 thf(c_0_56, plain, ![X1:a, X2:a]:((X2)=(sup @ X2 @ X1)|~less_eq @ X1 @ X2), inference(split_conjunct,[status(thm)],[c_0_53])). 32.44/32.63 thf(c_0_57, plain, less_eq @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c), inference(split_conjunct,[status(thm)],[fact_50_d__less__e])). 32.44/32.63 thf(c_0_58, plain, ![X2:a, X1:a]:(sup @ X1 @ X2)=(sup @ X2 @ X1), inference(split_conjunct,[status(thm)],[c_0_54])). 32.44/32.63 thf(c_0_59, plain, ![X887:a, X888:a, X889:a]:(inf @ (inf @ X887 @ X888) @ X889)=(inf @ X887 @ (inf @ X888 @ X889)), inference(variable_rename,[status(thm)],[fact_0_local_Oinf_Oassoc])). 32.44/32.63 thf(c_0_60, plain, ![X2:a, X1:a]:(inf @ X1 @ (sup @ X1 @ X2))=(X1), inference(split_conjunct,[status(thm)],[c_0_55])). 32.44/32.63 thf(c_0_61, plain, (sup @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))=(modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_57]), c_0_58])). 32.44/32.63 thf(c_0_62, plain, ![X1:a, X2:a, X3:a]:(inf @ (inf @ X1 @ X2) @ X3)=(inf @ X1 @ (inf @ X2 @ X3)), inference(split_conjunct,[status(thm)],[c_0_59])). 32.44/32.63 thf(c_0_63, plain, (inf @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))=(modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c), inference(spm,[status(thm)],[c_0_60, c_0_61])). 32.44/32.63 thf(c_0_64, plain, ![X872:a, X873:a]:(inf @ X872 @ X873)=(inf @ X873 @ X872), inference(variable_rename,[status(thm)],[fact_1_local_Oinf_Ocommute])). 32.44/32.63 thf(c_0_65, plain, ![X735:a, X736:a]:(inf @ (inf @ X735 @ X736) @ X736)=(inf @ X735 @ X736), inference(variable_rename,[status(thm)],[fact_33_local_Oinf__right__idem])). 32.44/32.63 thf(c_0_66, plain, ![X1:a]:(inf @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ (inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ X1))=(inf @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ X1), inference(spm,[status(thm)],[c_0_62, c_0_63])). 32.44/32.63 thf(c_0_67, plain, ![X2:a, X1:a]:(inf @ X1 @ X2)=(inf @ X2 @ X1), inference(split_conjunct,[status(thm)],[c_0_64])). 32.44/32.63 thf(c_0_68, plain, ![X651:a, X652:a, X653:a]:(inf @ X651 @ (modula1144073633_aux_a @ inf @ sup @ X652 @ X651 @ X653))=(inf @ X651 @ (sup @ X653 @ X652)), inference(variable_rename,[status(thm)],[fact_23_local_Ob__meet__e])). 32.44/32.63 thf(c_0_69, plain, ![X1:a, X2:a]:(inf @ (inf @ X1 @ X2) @ X2)=(inf @ X1 @ X2), inference(split_conjunct,[status(thm)],[c_0_65])). 32.44/32.63 thf(c_0_70, plain, ![X1:a]:(inf @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ (inf @ X1 @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)))=(inf @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ X1), inference(spm,[status(thm)],[c_0_66, c_0_67])). 32.44/32.63 thf(c_0_71, plain, ![X1:a, X3:a, X2:a]:(inf @ X1 @ (modula1144073633_aux_a @ inf @ sup @ X2 @ X1 @ X3))=(inf @ X1 @ (sup @ X3 @ X2)), inference(split_conjunct,[status(thm)],[c_0_68])). 32.44/32.63 thf(c_0_72, plain, ![X814:a, X815:a]:(sup @ X814 @ (inf @ X814 @ X815))=(X814), inference(variable_rename,[status(thm)],[fact_41_local_Osup__inf__absorb])). 32.44/32.63 thf(c_0_73, plain, ![X2:a, X1:a]:(inf @ X1 @ (inf @ X2 @ X1))=(inf @ X2 @ X1), inference(rw,[status(thm)],[c_0_69, c_0_67])). 32.44/32.63 thf(c_0_74, plain, (inf @ b @ (inf @ (sup @ a2 @ c) @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))=(inf @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_71]), c_0_58]), c_0_67]), c_0_62]), c_0_67])). 32.44/32.63 thf(c_0_75, plain, ![X1166:a, X1167:a, X1168:a]:(sup @ (sup @ X1166 @ X1167) @ X1168)=(sup @ X1166 @ (sup @ X1167 @ X1168)), inference(variable_rename,[status(thm)],[fact_6_local_Osup_Oassoc])). 32.44/32.63 thf(c_0_76, plain, ![X1238:a, X1239:a]:(sup @ (sup @ X1238 @ X1239) @ X1239)=(sup @ X1238 @ X1239), inference(variable_rename,[status(thm)],[fact_36_local_Osup_Oright__idem])). 32.44/32.63 thf(c_0_77, plain, ![X2:a, X1:a]:(sup @ X1 @ (inf @ X1 @ X2))=(X1), inference(split_conjunct,[status(thm)],[c_0_72])). 32.44/32.63 thf(c_0_78, plain, (inf @ (sup @ a2 @ c) @ (inf @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))=(inf @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73, c_0_74]), c_0_62]), c_0_73])). 32.44/32.63 thf(c_0_79, plain, ![X1:a, X2:a, X3:a]:(sup @ (sup @ X1 @ X2) @ X3)=(sup @ X1 @ (sup @ X2 @ X3)), inference(split_conjunct,[status(thm)],[c_0_75])). 32.44/32.63 thf(c_0_80, plain, ![X1172:a, X1173:a, X1174:a]:(inf @ X1172 @ (modula1936294176_aux_a @ inf @ sup @ X1173 @ X1172 @ X1174))=(sup @ (inf @ X1172 @ X1174) @ (inf @ X1173 @ X1172)), inference(variable_rename,[status(thm)],[fact_17_b__meet__d])). 32.44/32.63 thf(c_0_81, plain, ![X1:a, X2:a]:(sup @ (sup @ X1 @ X2) @ X2)=(sup @ X1 @ X2), inference(split_conjunct,[status(thm)],[c_0_76])). 32.44/32.63 thf(c_0_82, plain, (sup @ a2 @ (sup @ c @ (inf @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))))=(sup @ a2 @ c), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_78]), c_0_79])). 32.44/32.63 thf(c_0_83, plain, ![X3:a, X2:a, X1:a]:(inf @ X1 @ (modula1936294176_aux_a @ inf @ sup @ X2 @ X1 @ X3))=(sup @ (inf @ X1 @ X3) @ (inf @ X2 @ X1)), inference(split_conjunct,[status(thm)],[c_0_80])). 32.44/32.63 thf(c_0_84, plain, ![X2:a, X1:a]:(sup @ X1 @ (sup @ X2 @ X1))=(sup @ X2 @ X1), inference(rw,[status(thm)],[c_0_81, c_0_58])). 32.44/32.63 thf(c_0_85, plain, (sup @ a2 @ (sup @ c @ (sup @ (inf @ a2 @ b) @ (inf @ b @ c))))=(sup @ a2 @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82, c_0_83]), c_0_58])). 32.44/32.63 thf(c_0_86, plain, ![X998:a, X999:a]:(sup @ X998 @ (sup @ X998 @ X999))=(sup @ X998 @ X999), inference(variable_rename,[status(thm)],[fact_38_local_Osup__left__idem])). 32.44/32.63 thf(c_0_87, plain, (sup @ c @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (sup @ a2 @ c))))=(sup @ a2 @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_85]), c_0_79]), c_0_79])). 32.44/32.63 thf(c_0_88, plain, ![X1:a, X2:a]:(sup @ X1 @ (sup @ X1 @ X2))=(sup @ X1 @ X2), inference(split_conjunct,[status(thm)],[c_0_86])). 32.44/32.63 thf(c_0_89, plain, (sup @ (inf @ a2 @ b) @ (sup @ (inf @ b @ c) @ (sup @ a2 @ c)))=(sup @ a2 @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_87]), c_0_79]), c_0_79]), c_0_79]), c_0_84]), c_0_88])). 32.44/32.63 thf(c_0_90, plain, ![X774:a, X775:a, X776:a]:(sup @ X774 @ (sup @ X775 @ X776))=(sup @ X775 @ (sup @ X774 @ X776)), inference(variable_rename,[status(thm)],[fact_11_local_Osup__left__commute])). 32.44/32.63 thf(c_0_91, plain, ![X1063:a, X1064:a, X1065:a]:(modula1144073633_aux_a @ inf @ sup @ X1063 @ X1064 @ X1065)=(inf @ (inf @ (sup @ X1063 @ X1064) @ (sup @ X1064 @ X1065)) @ (sup @ X1065 @ X1063)), inference(variable_rename,[status(thm)],[fact_25_local_Oe__aux__def])). 32.44/32.63 thf(c_0_92, plain, (sup @ (inf @ a2 @ b) @ (sup @ a2 @ c))=(sup @ a2 @ c), inference(spm,[status(thm)],[c_0_88, c_0_89])). 32.44/32.63 thf(c_0_93, plain, ![X1:a, X2:a, X3:a]:(sup @ X1 @ (sup @ X2 @ X3))=(sup @ X2 @ (sup @ X1 @ X3)), inference(split_conjunct,[status(thm)],[c_0_90])). 32.44/32.63 thf(c_0_94, plain, ![X3:a, X2:a, X1:a]:(modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X3)=(inf @ (inf @ (sup @ X1 @ X2) @ (sup @ X2 @ X3)) @ (sup @ X3 @ X1)), inference(split_conjunct,[status(thm)],[c_0_91])). 32.44/32.63 thf(c_0_95, plain, ![X2:a, X1:a]:(inf @ X1 @ (sup @ X2 @ X1))=(X1), inference(spm,[status(thm)],[c_0_60, c_0_58])). 32.44/32.63 thf(c_0_96, plain, (sup @ a2 @ (sup @ c @ (inf @ a2 @ b)))=(sup @ a2 @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_92, c_0_93]), c_0_58])). 32.44/32.63 thf(c_0_97, plain, ![X911:a, X912:a, X913:a]:(modula1144073633_aux_a @ inf @ sup @ X911 @ X912 @ X913)=(modula1144073633_aux_a @ inf @ sup @ X913 @ X911 @ X912), inference(variable_rename,[status(thm)],[fact_26_local_Oe__b__c__a])). 32.44/32.63 thf(c_0_98, plain, ![X811:a, X812:a, X813:a]:(inf @ X811 @ (modula1144073633_aux_a @ inf @ sup @ X812 @ X813 @ X811))=(inf @ X811 @ (sup @ X812 @ X813)), inference(variable_rename,[status(thm)],[fact_24_local_Oc__meet__e])). 32.44/32.63 thf(c_0_99, plain, ![X1:a, X2:a, X3:a]:(inf @ (sup @ X1 @ X2) @ (inf @ (sup @ X2 @ X3) @ (sup @ X3 @ X1)))=(modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X3), inference(rw,[status(thm)],[c_0_94, c_0_62])). 32.44/32.63 thf(c_0_100, plain, (inf @ (sup @ a2 @ c) @ (sup @ c @ (inf @ a2 @ b)))=(sup @ c @ (inf @ a2 @ b)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_96]), c_0_67])). 32.44/32.63 thf(c_0_101, plain, ![X1:a, X3:a, X2:a]:(modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X3)=(modula1144073633_aux_a @ inf @ sup @ X3 @ X1 @ X2), inference(split_conjunct,[status(thm)],[c_0_97])). 32.44/32.63 thf(c_0_102, plain, ![X884:a, X885:a, X886:a]:(inf @ X884 @ (inf @ X885 @ X886))=(inf @ X885 @ (inf @ X884 @ X886)), inference(variable_rename,[status(thm)],[fact_5_local_Oinf__left__commute])). 32.44/32.63 thf(c_0_103, plain, ![X826:a, X827:a]:(inf @ X826 @ (inf @ X826 @ X827))=(inf @ X826 @ X827), inference(variable_rename,[status(thm)],[fact_32_local_Oinf__left__idem])). 32.44/32.63 thf(c_0_104, plain, ![X1021:a, X1022:a, X1023:a]:(modula1936294176_aux_a @ inf @ sup @ X1021 @ X1022 @ X1023)=(sup @ (sup @ (inf @ X1021 @ X1022) @ (inf @ X1022 @ X1023)) @ (inf @ X1023 @ X1021)), inference(variable_rename,[status(thm)],[fact_19_local_Od__aux__def])). 32.44/32.63 thf(c_0_105, plain, ![X1:a, X2:a, X3:a]:(inf @ X1 @ (modula1144073633_aux_a @ inf @ sup @ X2 @ X3 @ X1))=(inf @ X1 @ (sup @ X2 @ X3)), inference(split_conjunct,[status(thm)],[c_0_98])). 32.44/32.63 thf(c_0_106, plain, (modula1144073633_aux_a @ inf @ sup @ a2 @ c @ (inf @ a2 @ b))=(inf @ a2 @ (sup @ c @ (inf @ a2 @ b))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99, c_0_100]), c_0_101]), c_0_101]), c_0_58]), c_0_77])). 32.44/32.63 thf(c_0_107, plain, (inf @ a2 @ (inf @ b @ (sup @ a2 @ c)))=(inf @ a2 @ b), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_89]), c_0_62])). 32.44/32.63 thf(c_0_108, plain, ![X1:a, X2:a, X3:a]:(inf @ X1 @ (inf @ X2 @ X3))=(inf @ X2 @ (inf @ X1 @ X3)), inference(split_conjunct,[status(thm)],[c_0_102])). 32.44/32.63 thf(c_0_109, plain, ![X1:a, X2:a]:(inf @ X1 @ (inf @ X1 @ X2))=(inf @ X1 @ X2), inference(split_conjunct,[status(thm)],[c_0_103])). 32.44/32.63 thf(c_0_110, plain, ![X3:a, X2:a, X1:a]:(modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3)=(sup @ (sup @ (inf @ X1 @ X2) @ (inf @ X2 @ X3)) @ (inf @ X3 @ X1)), inference(split_conjunct,[status(thm)],[c_0_104])). 32.44/32.63 thf(c_0_111, plain, ![X2:a, X1:a]:(sup @ X1 @ (inf @ X2 @ X1))=(X1), inference(spm,[status(thm)],[c_0_77, c_0_67])). 32.44/32.63 thf(c_0_112, plain, (inf @ a2 @ (inf @ b @ (sup @ c @ (inf @ a2 @ b))))=(inf @ a2 @ b), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105, c_0_106]), c_0_62]), c_0_62]), c_0_107]), c_0_108]), c_0_109])). 32.44/32.63 thf(c_0_113, plain, ![X747:a, X748:a, X749:a]:(modula1936294176_aux_a @ inf @ sup @ X747 @ X748 @ X749)=(modula1936294176_aux_a @ inf @ sup @ X749 @ X747 @ X748), inference(variable_rename,[status(thm)],[fact_20_local_Od__b__c__a])). 32.44/32.63 thf(c_0_114, plain, ![X1:a, X2:a, X3:a]:(sup @ (inf @ X1 @ X2) @ (sup @ (inf @ X2 @ X3) @ (inf @ X3 @ X1)))=(modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3), inference(rw,[status(thm)],[c_0_110, c_0_79])). 32.44/32.63 thf(c_0_115, plain, (sup @ (inf @ a2 @ b) @ (inf @ b @ (sup @ c @ (inf @ a2 @ b))))=(inf @ b @ (sup @ c @ (inf @ a2 @ b))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111, c_0_112]), c_0_58])). 32.44/32.63 thf(c_0_116, plain, ![X1:a, X3:a, X2:a]:(modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3)=(modula1936294176_aux_a @ inf @ sup @ X3 @ X1 @ X2), inference(split_conjunct,[status(thm)],[c_0_113])). 32.44/32.63 thf(c_0_117, plain, ![X1177:a, X1178:a, X1179:a]:(inf @ X1177 @ (modula1936294176_aux_a @ inf @ sup @ X1178 @ X1179 @ X1177))=(sup @ (inf @ X1177 @ X1178) @ (inf @ X1179 @ X1177)), inference(variable_rename,[status(thm)],[fact_18_c__meet__d])). 32.44/32.63 thf(c_0_118, plain, ![X654:a, X655:a, X656:a]:(inf @ X654 @ (modula1936294176_aux_a @ inf @ sup @ X654 @ X655 @ X656))=(sup @ (inf @ X654 @ X655) @ (inf @ X656 @ X654)), inference(variable_rename,[status(thm)],[fact_15_a__meet__d])). 32.44/32.63 thf(c_0_119, plain, ![X914:a, X915:a, X916:a]:(sup @ X914 @ (modula1936294176_aux_a @ inf @ sup @ X914 @ X915 @ X916))=(sup @ X914 @ (inf @ X915 @ X916)), inference(variable_rename,[status(thm)],[fact_14_local_Oa__join__d])). 32.44/32.63 thf(c_0_120, plain, (sup @ (inf @ a2 @ (sup @ c @ (inf @ a2 @ b))) @ (inf @ b @ (sup @ c @ (inf @ a2 @ b))))=(modula1936294176_aux_a @ inf @ sup @ a2 @ b @ (sup @ c @ (inf @ a2 @ b))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_115]), c_0_67]), c_0_116]), c_0_116])). 32.44/32.63 thf(c_0_121, plain, ![X3:a, X2:a, X1:a]:(inf @ X1 @ (modula1936294176_aux_a @ inf @ sup @ X2 @ X3 @ X1))=(sup @ (inf @ X1 @ X2) @ (inf @ X3 @ X1)), inference(split_conjunct,[status(thm)],[c_0_117])). 32.44/32.63 thf(c_0_122, plain, ![X3:a, X2:a, X1:a]:(inf @ X1 @ (modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3))=(sup @ (inf @ X1 @ X2) @ (inf @ X3 @ X1)), inference(split_conjunct,[status(thm)],[c_0_118])). 32.44/32.63 thf(c_0_123, plain, ![X1:a, X2:a, X3:a]:(sup @ X1 @ (modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3))=(sup @ X1 @ (inf @ X2 @ X3)), inference(split_conjunct,[status(thm)],[c_0_119])). 32.44/32.63 thf(c_0_124, plain, ![X1:a, X3:a, X2:a]:(sup @ X1 @ (sup @ X2 @ (inf @ X3 @ (sup @ X1 @ X2))))=(sup @ X1 @ X2), inference(spm,[status(thm)],[c_0_111, c_0_79])). 32.44/32.63 thf(c_0_125, plain, (sup @ (inf @ a2 @ b) @ (inf @ a2 @ (sup @ c @ (inf @ a2 @ b))))=(inf @ a2 @ (sup @ c @ (inf @ a2 @ b))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_120]), c_0_62]), c_0_121]), c_0_67]), c_0_120]), c_0_122]), c_0_67])). 32.44/32.63 thf(c_0_126, plain, ![X819:a, X820:a, X821:a]:(sup @ X819 @ (modula1936294176_aux_a @ inf @ sup @ X820 @ X819 @ X821))=(sup @ X819 @ (inf @ X821 @ X820)), inference(variable_rename,[status(thm)],[fact_16_local_Ob__join__d])). 32.44/32.63 thf(c_0_127, plain, ![X1:a, X2:a, X3:a]:(inf @ (sup @ X1 @ (inf @ X2 @ X3)) @ (modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3))=(modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_123]), c_0_67])). 32.44/32.63 thf(c_0_128, plain, (sup @ c @ (inf @ a2 @ (sup @ c @ (inf @ a2 @ b))))=(sup @ c @ (inf @ a2 @ b)), inference(spm,[status(thm)],[c_0_124, c_0_125])). 32.44/32.63 thf(c_0_129, plain, ![X1:a, X3:a, X2:a]:(sup @ X1 @ (modula1936294176_aux_a @ inf @ sup @ X2 @ X1 @ X3))=(sup @ X1 @ (inf @ X3 @ X2)), inference(split_conjunct,[status(thm)],[c_0_126])). 32.44/32.63 thf(c_0_130, plain, (modula1936294176_aux_a @ inf @ sup @ a2 @ (sup @ c @ (inf @ a2 @ b)) @ c)=(sup @ c @ (inf @ a2 @ b)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127, c_0_128]), c_0_121]), c_0_67]), c_0_60]), c_0_128]), c_0_116])). 32.44/32.63 thf(c_0_131, plain, (sup @ c @ (sup @ (inf @ a2 @ b) @ (inf @ a2 @ c)))=(sup @ c @ (inf @ a2 @ b)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129, c_0_130]), c_0_79]), c_0_84]), c_0_88]), c_0_67]), c_0_79])). 32.44/32.63 thf(c_0_132, plain, (inf @ (sup @ c @ (inf @ a2 @ b)) @ (sup @ (inf @ a2 @ b) @ (inf @ a2 @ c)))=(sup @ (inf @ a2 @ b) @ (inf @ a2 @ c)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_131]), c_0_67])). 32.44/32.63 thf(c_0_133, plain, (inf @ c @ (inf @ (sup @ a2 @ b) @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))=(inf @ c @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_105]), c_0_67]), c_0_62]), c_0_67])). 32.44/32.63 thf(c_0_134, plain, ![X1:a, X3:a, X2:a]:(sup @ (inf @ X1 @ (sup @ X2 @ X3)) @ (modula1144073633_aux_a @ inf @ sup @ X3 @ X1 @ X2))=(modula1144073633_aux_a @ inf @ sup @ X3 @ X1 @ X2), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111, c_0_71]), c_0_58])). 32.44/32.63 thf(c_0_135, plain, (modula1144073633_aux_a @ inf @ sup @ c @ (inf @ a2 @ b) @ (inf @ a2 @ c))=(inf @ c @ (sup @ (inf @ a2 @ b) @ (inf @ a2 @ c))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99, c_0_132]), c_0_58]), c_0_111]), c_0_101]), c_0_101])). 32.44/32.63 thf(c_0_136, plain, ![X1:a, X2:a, X3:a]:(inf @ X1 @ (inf @ (sup @ X2 @ X3) @ (modula1144073633_aux_a @ inf @ sup @ X3 @ X1 @ X2)))=(inf @ X1 @ (sup @ X2 @ X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73, c_0_71]), c_0_108]), c_0_67])). 32.44/32.63 thf(c_0_137, plain, ![X3:a, X2:a, X1:a]:(sup @ (inf @ X1 @ (sup @ X2 @ X3)) @ (modula1144073633_aux_a @ inf @ sup @ X2 @ X3 @ X1))=(modula1144073633_aux_a @ inf @ sup @ X2 @ X3 @ X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111, c_0_105]), c_0_58])). 32.44/32.63 thf(c_0_138, plain, (inf @ (sup @ a2 @ b) @ (inf @ c @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))=(inf @ c @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73, c_0_133]), c_0_62]), c_0_73])). 32.44/32.63 thf(c_0_139, plain, ![X1:a, X3:a, X2:a]:(inf @ (sup @ X1 @ (inf @ X2 @ X3)) @ (modula1936294176_aux_a @ inf @ sup @ X3 @ X1 @ X2))=(modula1936294176_aux_a @ inf @ sup @ X3 @ X1 @ X2), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_129]), c_0_67])). 32.44/32.63 thf(c_0_140, plain, (sup @ (inf @ a2 @ (inf @ b @ c)) @ (inf @ c @ (sup @ (inf @ a2 @ b) @ (inf @ a2 @ c))))=(inf @ c @ (sup @ (inf @ a2 @ b) @ (inf @ a2 @ c))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134, c_0_135]), c_0_58]), c_0_111]), c_0_62])). 32.44/32.63 thf(c_0_141, plain, (inf @ a2 @ (inf @ b @ (inf @ c @ (sup @ (inf @ a2 @ b) @ (inf @ a2 @ c)))))=(inf @ a2 @ (inf @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136, c_0_135]), c_0_58]), c_0_111]), c_0_109]), c_0_62]), c_0_58]), c_0_111]), c_0_62])). 32.44/32.63 thf(c_0_142, plain, (sup @ (inf @ a2 @ c) @ (inf @ c @ (sup @ (inf @ a2 @ b) @ (inf @ a2 @ c))))=(inf @ c @ (sup @ (inf @ a2 @ b) @ (inf @ a2 @ c))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137, c_0_135]), c_0_62]), c_0_60])). 32.44/32.63 thf(c_0_143, plain, ![X728:a]:(inf @ X728 @ X728)=(X728), inference(variable_rename,[status(thm)],[fact_31_local_Oinf__idem])). 32.44/32.63 thf(c_0_144, plain, ![X10:a > a > a, X3:a, X1:a]:(abel_semigroup_a @ X10=>(X10 @ X3 @ X1)=(X10 @ X1 @ X3)), inference(fof_simplification,[status(thm)],[fact_167_abel__semigroup_Ocommute])). 32.44/32.63 thf(c_0_145, plain, (sup @ a2 @ (sup @ b @ (inf @ c @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))))=(sup @ a2 @ b), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_138]), c_0_79])). 32.44/32.63 thf(c_0_146, plain, (modula1936294176_aux_a @ inf @ sup @ c @ (sup @ (inf @ a2 @ b) @ (inf @ a2 @ c)) @ (inf @ a2 @ (inf @ b @ c)))=(inf @ c @ (sup @ (inf @ a2 @ b) @ (inf @ a2 @ c))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139, c_0_140]), c_0_62]), c_0_122]), c_0_108]), c_0_108]), c_0_67]), c_0_141]), c_0_140]), c_0_109]), c_0_116])). 32.44/32.64 thf(c_0_147, plain, (sup @ (inf @ a2 @ b) @ (inf @ c @ (sup @ (inf @ a2 @ b) @ (inf @ a2 @ c))))=(sup @ (inf @ a2 @ b) @ (inf @ a2 @ c)), inference(spm,[status(thm)],[c_0_124, c_0_142])). 32.44/32.64 thf(c_0_148, plain, ![X1:a]:(inf @ X1 @ X1)=(X1), inference(split_conjunct,[status(thm)],[c_0_143])). 32.44/32.64 thf(c_0_149, plain, ![X3:a, X2:a, X1:a]:(sup @ X1 @ (inf @ X2 @ (inf @ X3 @ X1)))=(X1), inference(spm,[status(thm)],[c_0_111, c_0_62])). 32.44/32.64 thf(c_0_150, plain, ![X816:a > a > a, X817:a, X818:a]:(~abel_semigroup_a @ X816|(X816 @ X817 @ X818)=(X816 @ X818 @ X817)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_144])])). 32.44/32.64 thf(c_0_151, plain, (sup @ a2 @ (sup @ b @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c))))=(sup @ a2 @ b), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_145, c_0_121]), c_0_67])). 32.44/32.64 thf(c_0_152, plain, ![X1:a, X2:a, X3:a]:(sup @ X1 @ (sup @ (inf @ X2 @ X1) @ X3))=(sup @ X1 @ X3), inference(spm,[status(thm)],[c_0_79, c_0_111])). 32.44/32.64 thf(c_0_153, plain, (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (inf @ a2 @ (inf @ b @ c))))=(sup @ (inf @ a2 @ b) @ (inf @ a2 @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129, c_0_146]), c_0_79]), c_0_142]), c_0_147]), c_0_62]), c_0_62]), c_0_148]), c_0_79])). 32.44/32.64 thf(c_0_154, plain, ![X1:a]:(sup @ (inf @ b @ (sup @ a2 @ c)) @ (inf @ X1 @ (inf @ a2 @ b)))=(inf @ b @ (sup @ a2 @ c)), inference(spm,[status(thm)],[c_0_149, c_0_107])). 32.44/32.64 thf(c_0_155, plain, ![X2:a, X1:a, X10:a > a > a]:((X10 @ X1 @ X2)=(X10 @ X2 @ X1)|~abel_semigroup_a @ X10), inference(split_conjunct,[status(thm)],[c_0_150])). 32.44/32.64 thf(c_0_156, plain, abel_semigroup_a @ inf, inference(split_conjunct,[status(thm)],[fact_58_local_Oinf_Oabel__semigroup__axioms])). 32.44/32.64 thf(c_0_157, plain, ![X954:a, X955:a, X956:a]:(inf @ X954 @ (modula1144073633_aux_a @ inf @ sup @ X954 @ X955 @ X956))=(inf @ X954 @ (sup @ X955 @ X956)), inference(variable_rename,[status(thm)],[fact_22_local_Oa__meet__e])). 32.44/32.64 thf(c_0_158, plain, (sup @ b @ (sup @ (inf @ a2 @ c) @ (sup @ (inf @ b @ c) @ (sup @ a2 @ b))))=(sup @ a2 @ b), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_151]), c_0_79]), c_0_79])). 32.44/32.64 thf(c_0_159, plain, (sup @ b @ (sup @ (inf @ a2 @ c) @ (inf @ a2 @ (inf @ b @ c))))=(sup @ b @ (inf @ a2 @ c)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152, c_0_153]), c_0_152])). 32.44/32.64 thf(c_0_160, plain, ![X1:a, X2:a, X3:a]:(sup @ X1 @ (sup @ (inf @ X1 @ X2) @ X3))=(sup @ X1 @ X3), inference(spm,[status(thm)],[c_0_79, c_0_77])). 32.44/32.64 thf(c_0_161, plain, ![X1:a]:(sup @ (inf @ b @ (sup @ a2 @ c)) @ (inf @ a2 @ (inf @ b @ X1)))=(inf @ b @ (sup @ a2 @ c)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154, c_0_155]), c_0_62]), c_0_156])])). 32.44/32.64 thf(c_0_162, plain, ![X1:a, X2:a, X3:a]:(inf @ X1 @ (modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X3))=(inf @ X1 @ (sup @ X2 @ X3)), inference(split_conjunct,[status(thm)],[c_0_157])). 32.44/32.64 thf(c_0_163, plain, (sup @ (inf @ a2 @ c) @ (sup @ (inf @ b @ c) @ (sup @ a2 @ b)))=(sup @ a2 @ b), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_158]), c_0_79]), c_0_79]), c_0_79]), c_0_84]), c_0_88])). 32.44/32.64 thf(c_0_164, plain, (inf @ (sup @ b @ (inf @ a2 @ c)) @ (sup @ (inf @ a2 @ c) @ (inf @ a2 @ (inf @ b @ c))))=(sup @ (inf @ a2 @ c) @ (inf @ a2 @ (inf @ b @ c))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_159]), c_0_67])). 32.44/32.64 thf(c_0_165, plain, ![X1:a]:(sup @ b @ (inf @ a2 @ (inf @ b @ X1)))=(b), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160, c_0_161]), c_0_77])). 32.44/32.64 thf(c_0_166, plain, (inf @ a2 @ (inf @ (sup @ b @ c) @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))=(inf @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_162]), c_0_67]), c_0_62]), c_0_67])). 32.44/32.64 thf(c_0_167, plain, (inf @ a2 @ (inf @ c @ (sup @ a2 @ b)))=(inf @ a2 @ c), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_163]), c_0_62])). 32.44/32.64 thf(c_0_168, plain, (modula1144073633_aux_a @ inf @ sup @ b @ (inf @ a2 @ c) @ (inf @ a2 @ (inf @ b @ c)))=(inf @ b @ (sup @ (inf @ a2 @ c) @ (inf @ a2 @ (inf @ b @ c)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99, c_0_164]), c_0_58]), c_0_165]), c_0_101]), c_0_101])). 32.44/32.64 thf(c_0_169, plain, ![X844:a, X845:a, X846:a]:(((less_eq @ X844 @ X846|~less_eq @ (sup @ X844 @ X845) @ X846)&(less_eq @ X845 @ X846|~less_eq @ (sup @ X844 @ X845) @ X846))&(~less_eq @ X844 @ X846|~less_eq @ X845 @ X846|less_eq @ (sup @ X844 @ X845) @ X846)), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_146_local_Ole__sup__iff])])])). 32.44/32.64 thf(c_0_170, plain, (inf @ (sup @ b @ c) @ (inf @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))=(inf @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73, c_0_166]), c_0_62]), c_0_73])). 32.44/32.64 thf(c_0_171, plain, (sup @ (inf @ a2 @ c) @ (inf @ c @ (sup @ a2 @ b)))=(inf @ c @ (sup @ a2 @ b)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111, c_0_167]), c_0_58])). 32.44/32.64 thf(c_0_172, plain, (sup @ (inf @ a2 @ (inf @ b @ c)) @ (inf @ b @ (sup @ (inf @ a2 @ c) @ (inf @ a2 @ (inf @ b @ c)))))=(inf @ b @ (sup @ (inf @ a2 @ c) @ (inf @ a2 @ (inf @ b @ c)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134, c_0_168]), c_0_58]), c_0_165]), c_0_62]), c_0_67])). 32.44/32.64 thf(c_0_173, plain, ![X1:a, X3:a, X2:a]:(less_eq @ X1 @ X2|~less_eq @ (sup @ X1 @ X3) @ X2), inference(split_conjunct,[status(thm)],[c_0_169])). 32.44/32.64 thf(c_0_174, plain, ![X1017:a, X1018:a]:less_eq @ X1017 @ (sup @ X1017 @ X1018), inference(variable_rename,[status(thm)],[fact_104_local_Osup__ge1])). 32.44/32.64 thf(c_0_175, plain, (sup @ b @ (sup @ c @ (inf @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))))=(sup @ b @ c), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_170]), c_0_79])). 32.44/32.64 thf(c_0_176, plain, (sup @ (inf @ a2 @ b) @ (inf @ b @ (sup @ a2 @ c)))=(inf @ b @ (sup @ a2 @ c)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111, c_0_107]), c_0_58])). 32.44/32.64 thf(c_0_177, plain, (modula1936294176_aux_a @ inf @ sup @ (sup @ a2 @ b) @ a2 @ c)=(sup @ a2 @ (inf @ c @ (sup @ a2 @ b))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_171]), c_0_67]), c_0_60])). 32.44/32.64 thf(c_0_178, plain, (sup @ (inf @ a2 @ c) @ (inf @ b @ (sup @ (inf @ a2 @ c) @ (inf @ a2 @ (inf @ b @ c)))))=(sup @ (inf @ a2 @ c) @ (inf @ a2 @ (inf @ b @ c))), inference(spm,[status(thm)],[c_0_124, c_0_172])). 32.44/32.64 thf(c_0_179, plain, ![X1:a]:(less_eq @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ X1|~less_eq @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ X1), inference(spm,[status(thm)],[c_0_173, c_0_61])). 32.44/32.64 thf(c_0_180, plain, ![X1:a, X2:a]:less_eq @ X1 @ (sup @ X1 @ X2), inference(split_conjunct,[status(thm)],[c_0_174])). 32.44/32.64 thf(c_0_181, plain, ![X10:a > a > a, X3:a, X1:a]:(semilattice_a @ X10=>(X10 @ X3 @ (X10 @ X3 @ X1))=(X10 @ X3 @ X1)), inference(fof_simplification,[status(thm)],[fact_166_semilattice_Oleft__idem])). 32.44/32.64 thf(c_0_182, plain, (sup @ b @ (sup @ c @ (sup @ (inf @ a2 @ b) @ (inf @ a2 @ c))))=(sup @ b @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_175, c_0_122]), c_0_67])). 32.44/32.64 thf(c_0_183, plain, (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ (sup @ a2 @ c))=(sup @ a2 @ (inf @ b @ (sup @ a2 @ c))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_176]), c_0_116]), c_0_116]), c_0_67]), c_0_60])). 32.44/32.64 thf(c_0_184, plain, (inf @ c @ (sup @ a2 @ (inf @ c @ (sup @ a2 @ b))))=(inf @ c @ (sup @ a2 @ b)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121, c_0_177]), c_0_58]), c_0_171])). 32.44/32.64 thf(c_0_185, plain, (sup @ c @ (inf @ b @ (sup @ (inf @ a2 @ c) @ (inf @ a2 @ (inf @ b @ c)))))=(c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152, c_0_178]), c_0_152]), c_0_149])). 32.44/32.64 thf(c_0_186, plain, (sup @ a2 @ (inf @ b @ (sup @ (inf @ a2 @ c) @ (inf @ a2 @ (inf @ b @ c)))))=(a2), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160, c_0_178]), c_0_160]), c_0_77])). 32.44/32.64 thf(c_0_187, plain, ![X1:a]:less_eq @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ X1), inference(spm,[status(thm)],[c_0_179, c_0_180])). 32.44/32.64 thf(c_0_188, plain, ![X716:a > a > a, X717:a, X718:a]:(~semilattice_a @ X716|(X716 @ X717 @ (X716 @ X717 @ X718))=(X716 @ X717 @ X718)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_181])])). 32.44/32.64 thf(c_0_189, plain, (sup @ c @ (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (sup @ b @ c))))=(sup @ b @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_182]), c_0_79]), c_0_79])). 32.44/32.64 thf(c_0_190, plain, (inf @ (sup @ a2 @ c) @ (sup @ a2 @ (inf @ b @ (sup @ a2 @ c))))=(sup @ a2 @ (inf @ b @ (sup @ a2 @ c))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121, c_0_183]), c_0_67]), c_0_60])). 32.44/32.64 thf(c_0_191, plain, ![X1249:a, X1250:a, X1251:a]:(~less_eq @ (modula1936294176_aux_a @ inf @ sup @ X1249 @ X1250 @ X1251) @ (modula1144073633_aux_a @ inf @ sup @ X1249 @ X1250 @ X1251)|(modula17988509_aux_a @ inf @ sup @ X1249 @ X1250 @ X1251)=(inf @ (sup @ X1249 @ (modula1936294176_aux_a @ inf @ sup @ X1249 @ X1250 @ X1251)) @ (modula1144073633_aux_a @ inf @ sup @ X1249 @ X1250 @ X1251))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_137_a__def__equiv])])). 32.44/32.64 thf(c_0_192, plain, ![X781:a, X782:a, X783:a]:(modula17988509_aux_a @ inf @ sup @ X781 @ X782 @ X783)=(sup @ (inf @ X781 @ (modula1144073633_aux_a @ inf @ sup @ X781 @ X782 @ X783)) @ (modula1936294176_aux_a @ inf @ sup @ X781 @ X782 @ X783)), inference(variable_rename,[status(thm)],[fact_44_local_Oa__aux__def])). 32.44/32.64 thf(c_0_193, plain, (sup @ (inf @ c @ (sup @ a2 @ b)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ (inf @ c @ (sup @ a2 @ b)) @ c))=(modula1144073633_aux_a @ inf @ sup @ a2 @ (inf @ c @ (sup @ a2 @ b)) @ c), inference(spm,[status(thm)],[c_0_137, c_0_184])). 32.44/32.64 thf(c_0_194, plain, ![X1096:a, X1097:a]:((~less_eq @ X1096 @ X1097|(inf @ X1097 @ X1096)=(X1096))&((inf @ X1097 @ X1096)!=(X1096)|less_eq @ X1096 @ X1097)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_96_local_Oinf_Oabsorb__iff2])])). 32.44/32.64 thf(c_0_195, plain, (inf @ a2 @ (inf @ b @ (inf @ c @ (sup @ (inf @ a2 @ c) @ (inf @ a2 @ (inf @ b @ c))))))=(inf @ a2 @ (inf @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136, c_0_168]), c_0_58]), c_0_165]), c_0_109]), c_0_62]), c_0_58]), c_0_165]), c_0_62]), c_0_67]), c_0_108])). 32.44/32.64 thf(c_0_196, plain, (inf @ b @ (inf @ c @ (sup @ (inf @ a2 @ c) @ (inf @ a2 @ (inf @ b @ c)))))=(inf @ b @ (sup @ (inf @ a2 @ c) @ (inf @ a2 @ (inf @ b @ c)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_185]), c_0_62]), c_0_67])). 32.44/32.64 thf(c_0_197, plain, (inf @ a2 @ (inf @ b @ (sup @ (inf @ a2 @ c) @ (inf @ a2 @ (inf @ b @ c)))))=(inf @ b @ (sup @ (inf @ a2 @ c) @ (inf @ a2 @ (inf @ b @ c)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_186]), c_0_62]), c_0_67]), c_0_108])). 32.44/32.64 thf(c_0_198, plain, (sup @ (inf @ a2 @ c) @ (sup @ a2 @ b))=(sup @ a2 @ b), inference(spm,[status(thm)],[c_0_88, c_0_163])). 32.44/32.64 thf(c_0_199, plain, ![X1:a]:(sup @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ X1 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))=(sup @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_187]), c_0_79])). 32.44/32.64 thf(c_0_200, plain, ![X2:a, X1:a, X10:a > a > a]:((X10 @ X1 @ (X10 @ X1 @ X2))=(X10 @ X1 @ X2)|~semilattice_a @ X10), inference(split_conjunct,[status(thm)],[c_0_188])). 32.44/32.64 thf(c_0_201, plain, (sup @ (inf @ a2 @ b) @ (sup @ (inf @ a2 @ c) @ (sup @ b @ c)))=(sup @ b @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_189]), c_0_79]), c_0_79]), c_0_79]), c_0_84]), c_0_88])). 32.44/32.64 thf(c_0_202, plain, semilattice_a @ sup, inference(split_conjunct,[status(thm)],[fact_55_local_Osup_Osemilattice__axioms])). 32.44/32.64 thf(c_0_203, plain, (sup @ a2 @ (sup @ c @ (inf @ b @ (sup @ a2 @ c))))=(sup @ a2 @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_190]), c_0_79]), c_0_93]), c_0_88])). 32.44/32.64 thf(c_0_204, plain, ![X1:a, X2:a, X3:a]:((modula17988509_aux_a @ inf @ sup @ X1 @ X2 @ X3)=(inf @ (sup @ X1 @ (modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3)) @ (modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X3))|~less_eq @ (modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3) @ (modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X3)), inference(split_conjunct,[status(thm)],[c_0_191])). 32.44/32.64 thf(c_0_205, plain, ![X1:a, X2:a, X3:a]:(modula17988509_aux_a @ inf @ sup @ X1 @ X2 @ X3)=(sup @ (inf @ X1 @ (modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X3)) @ (modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3)), inference(split_conjunct,[status(thm)],[c_0_192])). 32.44/32.64 thf(c_0_206, plain, (inf @ c @ (inf @ (sup @ a2 @ b) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ (inf @ c @ (sup @ a2 @ b)) @ c)))=(inf @ c @ (sup @ a2 @ b)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_193]), c_0_62])). 32.44/32.64 thf(c_0_207, plain, ![X1:a, X2:a, X4:a, X3:a]:(inf @ X1 @ (inf @ X2 @ (modula1144073633_aux_a @ inf @ sup @ X3 @ (inf @ X1 @ X2) @ X4)))=(inf @ X1 @ (inf @ X2 @ (sup @ X4 @ X3))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_71]), c_0_62])). 32.44/32.64 thf(c_0_208, plain, ![X1:a, X2:a]:(less_eq @ X2 @ X1|(inf @ X1 @ X2)!=(X2)), inference(split_conjunct,[status(thm)],[c_0_194])). 32.44/32.64 thf(c_0_209, plain, (inf @ b @ (sup @ (inf @ a2 @ c) @ (inf @ a2 @ (inf @ b @ c))))=(inf @ a2 @ (inf @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_195, c_0_196]), c_0_197])). 32.44/32.64 thf(c_0_210, plain, ![X833:a, X834:a]:((~less_eq @ X833 @ X834|(X833)=(inf @ X833 @ X834))&((X833)!=(inf @ X833 @ X834)|less_eq @ X833 @ X834)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_87_local_Oinf_Oorder__iff])])). 32.44/32.64 thf(c_0_211, plain, less_eq @ (inf @ a2 @ c) @ (sup @ a2 @ b), inference(spm,[status(thm)],[c_0_180, c_0_198])). 32.44/32.64 thf(c_0_212, plain, ![X1:a]:(sup @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ X1))=(sup @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ X1), inference(spm,[status(thm)],[c_0_199, c_0_58])). 32.44/32.64 thf(c_0_213, plain, (sup @ (inf @ a2 @ b) @ (sup @ b @ c))=(sup @ b @ c), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200, c_0_201]), c_0_202])])). 32.44/32.64 thf(c_0_214, plain, ![X10:a > a > a, X3:a, X1:a]:(semilattice_a @ X10=>(X10 @ (X10 @ X3 @ X1) @ X1)=(X10 @ X3 @ X1)), inference(fof_simplification,[status(thm)],[fact_165_semilattice_Oright__idem])). 32.44/32.64 thf(c_0_215, plain, ![X1:a, X3:a, X2:a]:(inf @ X1 @ (inf @ X2 @ (sup @ X3 @ (inf @ X1 @ X2))))=(inf @ X1 @ X2), inference(spm,[status(thm)],[c_0_95, c_0_62])). 32.44/32.64 thf(c_0_216, plain, (inf @ (sup @ a2 @ c) @ (sup @ c @ (inf @ b @ (sup @ a2 @ c))))=(sup @ c @ (inf @ b @ (sup @ a2 @ c))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_203]), c_0_67])). 32.44/32.64 thf(c_0_217, plain, ![X1:a, X2:a, X3:a]:((inf @ (sup @ X1 @ (inf @ X2 @ X3)) @ (modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X3))=(modula17988509_aux_a @ inf @ sup @ X1 @ X2 @ X3)|~less_eq @ (modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3) @ (modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X3)), inference(rw,[status(thm)],[c_0_204, c_0_123])). 32.44/32.64 thf(c_0_218, plain, ![X1:a, X2:a, X3:a]:(sup @ (inf @ X1 @ (sup @ X2 @ X3)) @ (modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3))=(modula17988509_aux_a @ inf @ sup @ X1 @ X2 @ X3), inference(rw,[status(thm)],[c_0_205, c_0_162])). 32.44/32.64 thf(c_0_219, plain, (inf @ c @ (inf @ (sup @ a2 @ b) @ (sup @ a2 @ c)))=(inf @ c @ (sup @ a2 @ b)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_206, c_0_207]), c_0_58])). 32.44/32.64 thf(c_0_220, plain, ![X726:a, X727:a]:((~less_eq @ X726 @ X727|(sup @ X726 @ X727)=(X727))&((sup @ X726 @ X727)!=(X727)|less_eq @ X726 @ X727)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_117_local_Osup_Oabsorb__iff2])])). 32.44/32.64 thf(c_0_221, plain, ![X3:a, X2:a, X1:a]:(less_eq @ (modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X3) @ X2|(modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X3)!=(inf @ X2 @ (sup @ X3 @ X1))), inference(spm,[status(thm)],[c_0_208, c_0_71])). 32.44/32.64 thf(c_0_222, plain, (modula1144073633_aux_a @ inf @ sup @ b @ (inf @ a2 @ c) @ (inf @ a2 @ (inf @ b @ c)))=(inf @ a2 @ (inf @ b @ c)), inference(rw,[status(thm)],[c_0_168, c_0_209])). 32.44/32.64 thf(c_0_223, plain, ![X1:a, X2:a]:((X1)=(inf @ X1 @ X2)|~less_eq @ X1 @ X2), inference(split_conjunct,[status(thm)],[c_0_210])). 32.44/32.64 thf(c_0_224, plain, ![X1:a, X3:a, X2:a]:(sup @ X1 @ (sup @ X2 @ (inf @ (sup @ X1 @ X2) @ X3)))=(sup @ X1 @ X2), inference(spm,[status(thm)],[c_0_77, c_0_79])). 32.44/32.64 thf(c_0_225, plain, (sup @ a2 @ (sup @ b @ (inf @ a2 @ c)))=(sup @ a2 @ b), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_211]), c_0_79])). 32.44/32.64 thf(c_0_226, plain, ![X1:a]:(sup @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (inf @ X1 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))=(modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212, c_0_111]), c_0_58]), c_0_61])). 32.44/32.64 thf(c_0_227, plain, (sup @ b @ (sup @ c @ (inf @ a2 @ b)))=(sup @ b @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_213, c_0_93]), c_0_58])). 32.44/32.64 thf(c_0_228, plain, ![X984:a > a > a, X985:a, X986:a]:(~semilattice_a @ X984|(X984 @ (X984 @ X985 @ X986) @ X986)=(X984 @ X985 @ X986)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_214])])). 32.44/32.64 thf(c_0_229, plain, (inf @ b @ (sup @ c @ (inf @ b @ (sup @ a2 @ c))))=(inf @ b @ (sup @ a2 @ c)), inference(spm,[status(thm)],[c_0_215, c_0_216])). 32.44/32.64 thf(c_0_230, plain, (sup @ (inf @ a2 @ (sup @ b @ c)) @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))=(inf @ (sup @ a2 @ (inf @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217, c_0_57]), c_0_218])). 32.44/32.64 thf(c_0_231, plain, (sup @ (inf @ c @ (sup @ a2 @ b)) @ (inf @ (sup @ a2 @ b) @ (sup @ a2 @ c)))=(inf @ (sup @ a2 @ b) @ (sup @ a2 @ c)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111, c_0_219]), c_0_58])). 32.44/32.64 thf(c_0_232, plain, ![X1:a, X2:a]:((sup @ X1 @ X2)=(X2)|~less_eq @ X1 @ X2), inference(split_conjunct,[status(thm)],[c_0_220])). 32.44/32.64 thf(c_0_233, plain, less_eq @ (inf @ a2 @ (inf @ b @ c)) @ (inf @ a2 @ c), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221, c_0_222]), c_0_58]), c_0_165]), c_0_62]), c_0_67])])). 32.44/32.64 thf(c_0_234, plain, (sup @ b @ (sup @ (inf @ a2 @ c) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)))=(sup @ b @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199, c_0_129]), c_0_67]), c_0_58]), c_0_79]), c_0_58])). 32.44/32.64 thf(c_0_235, plain, ![X1:a]:(inf @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ X1))=(modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c), inference(spm,[status(thm)],[c_0_223, c_0_187])). 32.44/32.64 thf(c_0_236, plain, ![X1:a]:(sup @ a2 @ (sup @ b @ (sup @ (inf @ a2 @ c) @ (inf @ (sup @ a2 @ b) @ X1))))=(sup @ a2 @ b), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224, c_0_225]), c_0_79])). 32.44/32.64 thf(c_0_237, plain, (sup @ (inf @ a2 @ c) @ (sup @ (inf @ b @ c) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)))=(modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_226, c_0_121]), c_0_67]), c_0_93]), c_0_58])). 32.44/32.64 thf(c_0_238, plain, ![X1:a]:(sup @ b @ (sup @ c @ (sup @ (inf @ a2 @ b) @ (inf @ (sup @ b @ c) @ X1))))=(sup @ b @ c), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224, c_0_227]), c_0_79])). 32.44/32.64 thf(c_0_239, plain, ![X2:a, X1:a, X10:a > a > a]:((X10 @ (X10 @ X1 @ X2) @ X2)=(X10 @ X1 @ X2)|~semilattice_a @ X10), inference(split_conjunct,[status(thm)],[c_0_228])). 32.44/32.64 thf(c_0_240, plain, (sup @ (inf @ b @ (sup @ a2 @ c)) @ (modula1144073633_aux_a @ inf @ sup @ b @ c @ (inf @ b @ (sup @ a2 @ c))))=(modula1144073633_aux_a @ inf @ sup @ b @ c @ (inf @ b @ (sup @ a2 @ c))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137, c_0_229]), c_0_101]), c_0_101])). 32.44/32.64 thf(c_0_241, plain, ![X1:a, X2:a, X3:a, X4:a]:(inf @ X1 @ (inf @ X2 @ (modula1144073633_aux_a @ inf @ sup @ X3 @ X4 @ (inf @ X1 @ X2))))=(inf @ X1 @ (inf @ X2 @ (sup @ X3 @ X4))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_105]), c_0_62])). 32.44/32.64 thf(c_0_242, plain, (sup @ (inf @ a2 @ (sup @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))=(modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199, c_0_230]), c_0_111]), c_0_58])). 32.44/32.64 thf(c_0_243, plain, (modula1936294176_aux_a @ inf @ sup @ c @ (sup @ a2 @ b) @ (sup @ a2 @ c))=(sup @ c @ (inf @ (sup @ a2 @ b) @ (sup @ a2 @ c))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_231]), c_0_67]), c_0_95]), c_0_116]), c_0_116])). 32.44/32.64 thf(c_0_244, plain, ![X3:a, X2:a, X1:a]:(inf @ X1 @ (sup @ X2 @ (sup @ X3 @ X1)))=(X1), inference(spm,[status(thm)],[c_0_95, c_0_79])). 32.44/32.64 thf(c_0_245, plain, (sup @ (inf @ a2 @ c) @ (inf @ a2 @ (inf @ b @ c)))=(inf @ a2 @ c), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_232, c_0_233]), c_0_58])). 32.44/32.64 thf(c_0_246, plain, (sup @ (inf @ a2 @ c) @ (sup @ b @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)))=(sup @ b @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_234]), c_0_79]), c_0_84])). 32.44/32.64 thf(c_0_247, plain, ![X1:a]:(inf @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ X1 @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)))=(modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c), inference(spm,[status(thm)],[c_0_235, c_0_58])). 32.44/32.64 thf(c_0_248, plain, ![X1:a]:(sup @ a2 @ (sup @ b @ (sup @ (inf @ a2 @ c) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ X1))))=(sup @ a2 @ b), inference(spm,[status(thm)],[c_0_236, c_0_99])). 32.44/32.64 thf(c_0_249, plain, (sup @ (inf @ a2 @ c) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))=(modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200, c_0_237]), c_0_202])])). 32.44/32.64 thf(c_0_250, plain, ![X1:a]:(sup @ b @ (sup @ c @ (sup @ (inf @ a2 @ b) @ (modula1144073633_aux_a @ inf @ sup @ b @ c @ X1))))=(sup @ b @ c), inference(spm,[status(thm)],[c_0_238, c_0_99])). 32.44/32.64 thf(c_0_251, plain, (sup @ (inf @ b @ c) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))=(modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_239, c_0_237]), c_0_84]), c_0_202])])). 32.44/32.64 thf(c_0_252, plain, (inf @ b @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)))=(inf @ b @ (sup @ a2 @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_240]), c_0_62]), c_0_241])). 32.44/32.64 thf(c_0_253, plain, (inf @ a2 @ (inf @ (sup @ b @ c) @ (inf @ (sup @ a2 @ (inf @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))))=(inf @ a2 @ (sup @ b @ c)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_230]), c_0_62])). 32.44/32.64 thf(c_0_254, plain, (inf @ a2 @ (inf @ (sup @ b @ c) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)))=(inf @ a2 @ (sup @ b @ c)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_242]), c_0_62])). 32.44/32.64 thf(c_0_255, plain, (sup @ a2 @ (sup @ (inf @ b @ c) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)))=(sup @ a2 @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199, c_0_123]), c_0_58]), c_0_79]), c_0_58])). 32.44/32.64 thf(c_0_256, plain, ![X1:a, X2:a, X3:a]:(inf @ X1 @ (inf @ (sup @ X1 @ X2) @ X3))=(inf @ X1 @ X3), inference(spm,[status(thm)],[c_0_62, c_0_60])). 32.44/32.64 thf(c_0_257, plain, (inf @ (sup @ a2 @ b) @ (sup @ c @ (inf @ (sup @ a2 @ b) @ (sup @ a2 @ c))))=(inf @ (sup @ a2 @ b) @ (sup @ a2 @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_243]), c_0_58]), c_0_231])). 32.44/32.64 thf(c_0_258, plain, ![X1:a]:(inf @ a2 @ (inf @ b @ (inf @ c @ (sup @ X1 @ (inf @ a2 @ c)))))=(inf @ a2 @ (inf @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_244, c_0_245]), c_0_62]), c_0_62])). 32.44/32.64 thf(c_0_259, plain, abel_semigroup_a @ sup, inference(split_conjunct,[status(thm)],[fact_57_local_Osup_Oabel__semigroup__axioms])). 32.44/32.64 thf(c_0_260, plain, (inf @ a2 @ (inf @ c @ (sup @ b @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))))=(inf @ a2 @ c), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_246]), c_0_62])). 32.44/32.64 thf(c_0_261, plain, ![X1:a, X2:a]:(inf @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ X1 @ (sup @ X2 @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))))=(modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c), inference(spm,[status(thm)],[c_0_247, c_0_79])). 32.44/32.64 thf(c_0_262, plain, (sup @ a2 @ (sup @ b @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)))=(sup @ a2 @ b), inference(spm,[status(thm)],[c_0_248, c_0_249])). 32.44/32.64 thf(c_0_263, plain, ![X1:a]:(sup @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ X1))=(sup @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ X1), inference(spm,[status(thm)],[c_0_232, c_0_187])). 32.44/32.64 thf(c_0_264, plain, ![X1:a]:(sup @ b @ (sup @ c @ (sup @ (inf @ a2 @ b) @ (modula1144073633_aux_a @ inf @ sup @ X1 @ b @ c))))=(sup @ b @ c), inference(spm,[status(thm)],[c_0_250, c_0_101])). 32.44/32.64 thf(c_0_265, plain, (sup @ (inf @ a2 @ b) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))=(modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_226, c_0_83]), c_0_58]), c_0_93]), c_0_58]), c_0_251])). 32.44/32.64 thf(c_0_266, plain, (sup @ (inf @ b @ (sup @ a2 @ c)) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)))=(inf @ (sup @ a2 @ c) @ (sup @ b @ c)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111, c_0_252]), c_0_58])). 32.44/32.64 thf(c_0_267, plain, (inf @ a2 @ (inf @ (sup @ b @ c) @ (sup @ a2 @ (inf @ b @ c))))=(inf @ a2 @ (sup @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73, c_0_253]), c_0_62]), c_0_62]), c_0_108]), c_0_67]), c_0_254]), c_0_108]), c_0_67]), c_0_108]), c_0_109])). 32.44/32.64 thf(c_0_268, plain, (sup @ (inf @ b @ c) @ (sup @ a2 @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)))=(sup @ a2 @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_255]), c_0_79]), c_0_84])). 32.44/32.64 thf(c_0_269, plain, ![X745:a, X746:a]:less_eq @ X745 @ (sup @ X746 @ X745), inference(variable_rename,[status(thm)],[fact_113_local_Osup_Ocobounded2])). 32.44/32.64 thf(c_0_270, plain, (inf @ a2 @ (sup @ c @ (inf @ (sup @ a2 @ b) @ (sup @ a2 @ c))))=(a2), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_256, c_0_257]), c_0_256]), c_0_60])). 32.44/32.64 thf(c_0_271, plain, ![X1:a]:(inf @ a2 @ (inf @ b @ (inf @ c @ (sup @ (inf @ a2 @ c) @ X1))))=(inf @ a2 @ (inf @ b @ c)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_258, c_0_155]), c_0_259])])). 32.44/32.64 thf(c_0_272, plain, (sup @ (inf @ a2 @ c) @ (inf @ c @ (sup @ b @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))))=(inf @ c @ (sup @ b @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111, c_0_260]), c_0_58])). 32.44/32.64 thf(c_0_273, plain, ![X2:a, X13:a, X16:a]:(less_eq @ X2 @ X13=>(sup @ X2 @ (inf @ X13 @ X16))=(inf @ X13 @ (sup @ X2 @ X16))), inference(fof_simplification,[status(thm)],[fact_126_local_Omodular])). 32.44/32.64 thf(c_0_274, plain, ![X1:a, X4:a, X3:a, X2:a]:(sup @ (inf @ X1 @ (sup @ X2 @ X3)) @ (sup @ (modula1144073633_aux_a @ inf @ sup @ X2 @ X3 @ X4) @ (inf @ (sup @ X3 @ X4) @ (inf @ (sup @ X4 @ X2) @ X1))))=(modula1936294176_aux_a @ inf @ sup @ X1 @ (sup @ X2 @ X3) @ (inf @ (sup @ X3 @ X4) @ (sup @ X4 @ X2))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_99]), c_0_62])). 32.44/32.64 thf(c_0_275, plain, ![X1:a, X2:a]:(sup @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (inf @ X1 @ (inf @ X2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))))=(modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c), inference(spm,[status(thm)],[c_0_226, c_0_62])). 32.44/32.64 thf(c_0_276, plain, (inf @ (sup @ a2 @ b) @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))=(modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_261, c_0_262]), c_0_67])). 32.44/32.64 thf(c_0_277, plain, ![X1:a]:(sup @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ X1 @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)))=(sup @ X1 @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)), inference(spm,[status(thm)],[c_0_263, c_0_84])). 32.44/32.64 thf(c_0_278, plain, ![X1:a, X2:a, X3:a]:(sup @ (inf @ (sup @ X1 @ X2) @ (sup @ X2 @ X3)) @ (modula1144073633_aux_a @ inf @ sup @ X3 @ X1 @ X2))=(inf @ (sup @ X1 @ X2) @ (sup @ X2 @ X3)), inference(spm,[status(thm)],[c_0_111, c_0_99])). 32.44/32.64 thf(c_0_279, plain, (sup @ b @ (sup @ c @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)))=(sup @ b @ c), inference(spm,[status(thm)],[c_0_264, c_0_265])). 32.44/32.64 thf(c_0_280, plain, (modula1936294176_aux_a @ inf @ sup @ b @ (sup @ a2 @ c) @ (sup @ b @ c))=(sup @ b @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_266]), c_0_67]), c_0_60]), c_0_116]), c_0_116])). 32.44/32.64 thf(c_0_281, plain, (sup @ a2 @ (sup @ (inf @ b @ c) @ (inf @ a2 @ (sup @ b @ c))))=(sup @ a2 @ (inf @ b @ c)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149, c_0_267]), c_0_79])). 32.44/32.64 thf(c_0_282, plain, ![X3:a, X2:a, X1:a]:(sup @ X1 @ (inf @ X2 @ (inf @ X1 @ X3)))=(X1), inference(spm,[status(thm)],[c_0_77, c_0_108])). 32.44/32.64 thf(c_0_283, plain, (inf @ b @ (inf @ c @ (sup @ a2 @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))))=(inf @ b @ c), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_268]), c_0_62])). 32.44/32.64 thf(c_0_284, plain, ![X2:a, X1:a]:less_eq @ X1 @ (sup @ X2 @ X1), inference(split_conjunct,[status(thm)],[c_0_269])). 32.44/32.64 thf(c_0_285, plain, (sup @ c @ (inf @ (sup @ a2 @ b) @ (sup @ a2 @ c)))=(sup @ a2 @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111, c_0_270]), c_0_79]), c_0_58]), c_0_93]), c_0_124])). 32.44/32.64 thf(c_0_286, plain, (inf @ c @ (inf @ (sup @ a2 @ b) @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))=(sup @ (inf @ a2 @ c) @ (inf @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_133, c_0_121]), c_0_67])). 32.44/32.64 thf(c_0_287, plain, semilattice_a @ inf, inference(split_conjunct,[status(thm)],[fact_56_local_Oinf_Osemilattice__axioms])). 32.44/32.64 thf(c_0_288, plain, (inf @ a2 @ (inf @ b @ (inf @ c @ (sup @ b @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)))))=(inf @ a2 @ (inf @ b @ c)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_271, c_0_272]), c_0_109])). 32.44/32.64 thf(c_0_289, plain, ![X863:a, X864:a, X865:a]:(~less_eq @ X863 @ X864|(sup @ X863 @ (inf @ X864 @ X865))=(inf @ X864 @ (sup @ X863 @ X865))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_273])])). 32.44/32.64 thf(c_0_290, plain, (modula1936294176_aux_a @ inf @ sup @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)) @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))=(modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_274, c_0_275]), c_0_67]), c_0_276]), c_0_61]), c_0_58]), c_0_67]), c_0_116]), c_0_116])). 32.44/32.64 thf(c_0_291, plain, ![X1:a, X2:a, X3:a]:(inf @ (sup @ X1 @ X2) @ (modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X3))=(modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X3), inference(spm,[status(thm)],[c_0_109, c_0_99])). 32.44/32.64 thf(c_0_292, plain, (sup @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)) @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))=(inf @ (sup @ a2 @ c) @ (sup @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_277, c_0_278]), c_0_58]), c_0_67]), c_0_58]), c_0_67]), c_0_58])). 32.44/32.64 thf(c_0_293, plain, (inf @ (sup @ b @ c) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))=(modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_244, c_0_279]), c_0_67])). 32.44/32.64 thf(c_0_294, plain, ![X1:a, X2:a, X3:a]:(inf @ X1 @ (inf @ (sup @ X2 @ X1) @ X3))=(inf @ X1 @ X3), inference(spm,[status(thm)],[c_0_62, c_0_95])). 32.44/32.64 thf(c_0_295, plain, (inf @ (sup @ a2 @ c) @ (sup @ b @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))))=(inf @ (sup @ a2 @ c) @ (sup @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_280]), c_0_58]), c_0_266])). 32.44/32.64 thf(c_0_296, plain, ![X702:a, X703:a, X704:a]:less_eq @ (sup @ (inf @ X702 @ X703) @ (inf @ X702 @ X704)) @ (inf @ X702 @ (sup @ X703 @ X704)), inference(variable_rename,[status(thm)],[fact_128_local_Odistrib__inf__le])). 32.44/32.64 thf(c_0_297, plain, (inf @ (sup @ a2 @ (inf @ b @ c)) @ (sup @ (inf @ b @ c) @ (inf @ a2 @ (sup @ b @ c))))=(sup @ (inf @ b @ c) @ (inf @ a2 @ (sup @ b @ c))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_281]), c_0_67])). 32.44/32.64 thf(c_0_298, plain, ![X1:a]:(sup @ a2 @ (sup @ c @ (inf @ X1 @ (sup @ c @ (inf @ a2 @ b)))))=(sup @ a2 @ c), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_282, c_0_100]), c_0_79])). 32.44/32.64 thf(c_0_299, plain, ![X1:a]:(inf @ b @ (inf @ c @ (inf @ (sup @ a2 @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) @ X1)))=(inf @ b @ (inf @ c @ X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_283]), c_0_62]), c_0_62])). 32.44/32.64 thf(c_0_300, plain, ![X3:a, X2:a, X1:a]:less_eq @ (modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3) @ (sup @ X2 @ (inf @ X3 @ X1)), inference(spm,[status(thm)],[c_0_284, c_0_129])). 32.44/32.64 thf(c_0_301, plain, (modula1936294176_aux_a @ inf @ sup @ c @ (sup @ a2 @ b) @ (sup @ a2 @ c))=(sup @ a2 @ c), inference(rw,[status(thm)],[c_0_243, c_0_285])). 32.44/32.64 thf(c_0_302, plain, (inf @ (sup @ a2 @ b) @ (inf @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c)) @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))=(sup @ (inf @ a2 @ c) @ (inf @ b @ c)), inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_239, c_0_286]), c_0_287])]), c_0_108])). 32.44/32.64 thf(c_0_303, plain, ![X1138:a, X1139:a, X1140:a]:(modula1373251614_aux_a @ inf @ sup @ X1138 @ X1139 @ X1140)=(sup @ (inf @ X1139 @ (modula1144073633_aux_a @ inf @ sup @ X1138 @ X1139 @ X1140)) @ (modula1936294176_aux_a @ inf @ sup @ X1138 @ X1139 @ X1140)), inference(variable_rename,[status(thm)],[fact_42_local_Ob__aux__def])). 32.44/32.64 thf(c_0_304, plain, ![X785:a, X786:a, X787:a]:(modula1373251614_aux_a @ inf @ sup @ X785 @ X786 @ X787)=(modula17988509_aux_a @ inf @ sup @ X786 @ X787 @ X785), inference(variable_rename,[status(thm)],[fact_61_local_Ob__a])). 32.44/32.64 thf(c_0_305, plain, ![X1:a, X3:a, X2:a]:(sup @ X1 @ (sup @ X2 @ X3))=(sup @ X3 @ (sup @ X1 @ X2)), inference(spm,[status(thm)],[c_0_58, c_0_79])). 32.44/32.64 thf(c_0_306, plain, ![X1:a, X3:a, X2:a]:(sup @ (inf @ X1 @ X2) @ (inf @ X1 @ (inf @ X2 @ X3)))=(inf @ X1 @ X2), inference(spm,[status(thm)],[c_0_77, c_0_62])). 32.44/32.64 thf(c_0_307, plain, (sup @ (inf @ a2 @ (inf @ b @ c)) @ (inf @ c @ (sup @ b @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))))=(inf @ c @ (sup @ b @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149, c_0_288]), c_0_58])). 32.44/32.64 thf(c_0_308, plain, ![X1:a, X3:a, X2:a]:((sup @ X1 @ (inf @ X2 @ X3))=(inf @ X2 @ (sup @ X1 @ X3))|~less_eq @ X1 @ X2), inference(split_conjunct,[status(thm)],[c_0_289])). 32.44/32.64 thf(c_0_309, plain, (sup @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))))=(modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122, c_0_290]), c_0_291]), c_0_67]), c_0_276]), c_0_58])). 32.44/32.64 thf(c_0_310, plain, (inf @ (sup @ a2 @ c) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))=(modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139, c_0_290]), c_0_67]), c_0_276]), c_0_292]), c_0_62]), c_0_293])). 32.44/32.64 thf(c_0_311, plain, (inf @ c @ (sup @ b @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))))=(c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_294, c_0_295]), c_0_294]), c_0_95])). 32.44/32.64 thf(c_0_312, plain, ![X1:a, X2:a, X3:a]:less_eq @ (sup @ (inf @ X1 @ X2) @ (inf @ X1 @ X3)) @ (inf @ X1 @ (sup @ X2 @ X3)), inference(split_conjunct,[status(thm)],[c_0_296])). 32.44/32.64 thf(c_0_313, plain, (modula1144073633_aux_a @ inf @ sup @ a2 @ (inf @ b @ c) @ (inf @ a2 @ (sup @ b @ c)))=(inf @ a2 @ (sup @ (inf @ b @ c) @ (inf @ a2 @ (sup @ b @ c)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99, c_0_297]), c_0_58]), c_0_77]), c_0_101]), c_0_101])). 32.44/32.64 thf(c_0_314, plain, ![X3:a, X1:a, X4:a]:(less_eq @ (modula1936294176_aux_a @ inf @ sup @ X3 @ X1 @ X4) @ (modula1144073633_aux_a @ inf @ sup @ X3 @ X1 @ X4)=>(inf @ (modula17988509_aux_a @ inf @ sup @ X3 @ X1 @ X4) @ (modula1373251614_aux_a @ inf @ sup @ X3 @ X1 @ X4))=(modula1936294176_aux_a @ inf @ sup @ X3 @ X1 @ X4)), inference(fof_simplification,[status(thm)],[fact_141_a__meet__b__eq__d])). 32.44/32.64 thf(c_0_315, plain, ![X921:a, X922:a, X923:a]:(~less_eq @ (modula1936294176_aux_a @ inf @ sup @ X921 @ X922 @ X923) @ (modula1144073633_aux_a @ inf @ sup @ X921 @ X922 @ X923)|(modula1373251614_aux_a @ inf @ sup @ X921 @ X922 @ X923)=(inf @ (sup @ X922 @ (modula1936294176_aux_a @ inf @ sup @ X921 @ X922 @ X923)) @ (modula1144073633_aux_a @ inf @ sup @ X921 @ X922 @ X923))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_139_b__def__equiv])])). 32.44/32.64 thf(c_0_316, plain, ![X1:a]:(sup @ a2 @ (sup @ c @ (inf @ (sup @ c @ (inf @ a2 @ b)) @ X1)))=(sup @ a2 @ c), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_298, c_0_155]), c_0_156])])). 32.44/32.64 thf(c_0_317, plain, ![X1:a]:(inf @ b @ (inf @ c @ (sup @ a2 @ (sup @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ X1))))=(inf @ b @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_299, c_0_60]), c_0_283]), c_0_79])). 32.44/32.64 thf(c_0_318, plain, less_eq @ (sup @ a2 @ c) @ (sup @ a2 @ (sup @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_300, c_0_301]), c_0_67]), c_0_95]), c_0_79])). 32.44/32.64 thf(c_0_319, plain, ![X840:a]:(sup @ X840 @ X840)=(X840), inference(variable_rename,[status(thm)],[fact_37_local_Osup__idem])). 32.44/32.64 thf(c_0_320, plain, (inf @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c)) @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))=(sup @ (inf @ a2 @ c) @ (inf @ b @ c)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_239, c_0_302]), c_0_109]), c_0_287])])). 32.44/32.64 thf(c_0_321, negated_conjecture, (sup @ (inf @ (sup @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) @ (inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))))!=(inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ (inf @ (sup @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) @ (sup @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))), inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])])). 32.44/32.64 thf(c_0_322, plain, ![X1:a, X2:a, X3:a]:(modula1373251614_aux_a @ inf @ sup @ X1 @ X2 @ X3)=(sup @ (inf @ X2 @ (modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X3)) @ (modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3)), inference(split_conjunct,[status(thm)],[c_0_303])). 32.44/32.64 thf(c_0_323, plain, ![X3:a, X2:a, X1:a]:(modula1373251614_aux_a @ inf @ sup @ X1 @ X2 @ X3)=(modula17988509_aux_a @ inf @ sup @ X2 @ X3 @ X1), inference(split_conjunct,[status(thm)],[c_0_304])). 32.44/32.64 thf(c_0_324, plain, ![X3:a, X2:a, X1:a]:(sup @ (inf @ X1 @ X2) @ (sup @ (inf @ X2 @ X3) @ (modula1936294176_aux_a @ inf @ sup @ X2 @ X3 @ X1)))=(modula1936294176_aux_a @ inf @ sup @ X2 @ X3 @ X1), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111, c_0_122]), c_0_305]), c_0_58])). 32.44/32.64 thf(c_0_325, plain, ![X1:a, X2:a, X3:a]:(sup @ (inf @ X1 @ X2) @ (modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3))=(modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3), inference(spm,[status(thm)],[c_0_88, c_0_114])). 32.44/32.64 thf(c_0_326, plain, ![X1:a, X2:a, X3:a]:(modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ (inf @ X2 @ X3))=(sup @ (inf @ X1 @ X2) @ (inf @ X2 @ X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_109]), c_0_62]), c_0_306])). 32.44/32.64 thf(c_0_327, plain, ![X1027:a, X1028:a]:less_eq @ (inf @ X1027 @ X1028) @ X1027, inference(variable_rename,[status(thm)],[fact_83_local_Oinf__le1])). 32.44/32.64 thf(c_0_328, plain, ![X832:a > a > a]:(~semilattice_a @ X832|abel_semigroup_a @ X832), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_158_semilattice_Oaxioms_I1_J])])). 32.44/32.64 thf(c_0_329, plain, (modula1936294176_aux_a @ inf @ sup @ c @ (sup @ b @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) @ (inf @ a2 @ (inf @ b @ c)))=(inf @ c @ (sup @ b @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139, c_0_307]), c_0_62]), c_0_122]), c_0_108]), c_0_108]), c_0_67]), c_0_288]), c_0_307]), c_0_109]), c_0_116])). 32.44/32.64 thf(c_0_330, plain, ![X1:a, X2:a, X3:a]:(sup @ X1 @ (inf @ (sup @ X2 @ X1) @ X3))=(inf @ (sup @ X2 @ X1) @ (sup @ X1 @ X3)), inference(spm,[status(thm)],[c_0_308, c_0_284])). 32.44/32.64 thf(c_0_331, plain, (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)))=(modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_309]), c_0_62]), c_0_62]), c_0_293]), c_0_310]), c_0_291])). 32.44/32.64 thf(c_0_332, plain, (sup @ b @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)))=(sup @ b @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111, c_0_311]), c_0_79]), c_0_58]), c_0_124])). 32.44/32.64 thf(c_0_333, plain, ![X1:a, X2:a, X3:a]:(inf @ X1 @ (inf @ (sup @ X2 @ X3) @ (sup @ (inf @ X1 @ X2) @ (inf @ X1 @ X3))))=(sup @ (inf @ X1 @ X2) @ (inf @ X1 @ X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_223, c_0_312]), c_0_108]), c_0_67])). 32.44/32.64 thf(c_0_334, plain, (sup @ (inf @ a2 @ (sup @ b @ c)) @ (inf @ a2 @ (sup @ (inf @ b @ c) @ (inf @ a2 @ (sup @ b @ c)))))=(inf @ a2 @ (sup @ (inf @ b @ c) @ (inf @ a2 @ (sup @ b @ c)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137, c_0_313]), c_0_62]), c_0_267])). 32.44/32.64 thf(c_0_335, plain, ![X1125:a, X1126:a, X1127:a]:(~less_eq @ (modula1936294176_aux_a @ inf @ sup @ X1125 @ X1126 @ X1127) @ (modula1144073633_aux_a @ inf @ sup @ X1125 @ X1126 @ X1127)|(inf @ (modula17988509_aux_a @ inf @ sup @ X1125 @ X1126 @ X1127) @ (modula1373251614_aux_a @ inf @ sup @ X1125 @ X1126 @ X1127))=(modula1936294176_aux_a @ inf @ sup @ X1125 @ X1126 @ X1127)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_314])])). 32.44/32.64 thf(c_0_336, plain, ![X1:a, X2:a, X3:a]:((modula1373251614_aux_a @ inf @ sup @ X1 @ X2 @ X3)=(inf @ (sup @ X2 @ (modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3)) @ (modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X3))|~less_eq @ (modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3) @ (modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X3)), inference(split_conjunct,[status(thm)],[c_0_315])). 32.44/32.64 thf(c_0_337, plain, (sup @ a2 @ (sup @ c @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))=(sup @ a2 @ c), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_316, c_0_139]), c_0_116])). 32.44/32.64 thf(c_0_338, plain, ![X1:a, X3:a, X2:a]:(sup @ X1 @ (sup @ X2 @ (sup @ X3 @ (sup @ X1 @ X2))))=(sup @ X3 @ (sup @ X1 @ X2)), inference(spm,[status(thm)],[c_0_84, c_0_79])). 32.44/32.64 thf(c_0_339, plain, ![X3:a, X2:a, X1:a]:(sup @ X1 @ (sup @ X2 @ (sup @ X3 @ X1)))=(sup @ X2 @ (sup @ X3 @ X1)), inference(spm,[status(thm)],[c_0_84, c_0_79])). 32.44/32.64 thf(c_0_340, plain, ![X1:a]:(inf @ b @ (inf @ c @ (sup @ a2 @ (sup @ X1 @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)))))=(inf @ b @ c), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_317, c_0_155]), c_0_259])])). 32.44/32.64 thf(c_0_341, plain, ![X1:a, X2:a, X3:a]:(inf @ (sup @ X1 @ X2) @ (inf @ (sup @ X3 @ X2) @ (sup @ X3 @ X1)))=(modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X3), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99, c_0_155]), c_0_259])])). 32.44/32.64 thf(c_0_342, plain, (inf @ (sup @ a2 @ c) @ (sup @ a2 @ (sup @ b @ c)))=(sup @ a2 @ c), inference(spm,[status(thm)],[c_0_223, c_0_318])). 32.44/32.64 thf(c_0_343, plain, ![X1:a]:(sup @ X1 @ X1)=(X1), inference(split_conjunct,[status(thm)],[c_0_319])). 32.44/32.64 thf(c_0_344, plain, (sup @ (inf @ a2 @ c) @ (sup @ (inf @ b @ c) @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))=(modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111, c_0_320]), c_0_93]), c_0_58])). 32.44/32.64 thf(c_0_345, negated_conjecture, (sup @ (inf @ (sup @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) @ (inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))))!=(inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ (inf @ (sup @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) @ (sup @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))), inference(split_conjunct,[status(thm)],[c_0_321])). 32.44/32.64 thf(c_0_346, plain, ![X1:a, X2:a, X3:a]:(sup @ (inf @ X1 @ (sup @ X2 @ X3)) @ (modula1936294176_aux_a @ inf @ sup @ X3 @ X1 @ X2))=(modula17988509_aux_a @ inf @ sup @ X1 @ X2 @ X3), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_322, c_0_71]), c_0_323])). 32.44/32.64 thf(c_0_347, plain, ![X3:a, X2:a, X1:a]:(sup @ (inf @ X1 @ X2) @ (modula1936294176_aux_a @ inf @ sup @ X2 @ X3 @ X1))=(modula1936294176_aux_a @ inf @ sup @ X2 @ X3 @ X1), inference(rw,[status(thm)],[c_0_324, c_0_325])). 32.44/32.64 thf(c_0_348, plain, ![X1:a, X2:a, X3:a]:(modula17988509_aux_a @ inf @ sup @ X1 @ X2 @ (inf @ X2 @ X3))=(sup @ (inf @ X1 @ X2) @ (inf @ X2 @ X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218, c_0_77]), c_0_326]), c_0_88])). 32.44/32.64 thf(c_0_349, plain, ![X698:a, X699:a]:less_eq @ (inf @ X698 @ X699) @ X699, inference(variable_rename,[status(thm)],[fact_92_local_Oinf_Ocobounded2])). 32.44/32.64 thf(c_0_350, plain, ![X2:a, X1:a]:less_eq @ (inf @ X1 @ X2) @ X1, inference(split_conjunct,[status(thm)],[c_0_327])). 32.44/32.64 thf(c_0_351, plain, ![X10:a > a > a]:(abel_semigroup_a @ X10|~semilattice_a @ X10), inference(split_conjunct,[status(thm)],[c_0_328])). 32.44/32.64 thf(c_0_352, plain, (sup @ b @ (sup @ (inf @ a2 @ (inf @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)))=(sup @ b @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129, c_0_329]), c_0_79]), c_0_124]), c_0_62]), c_0_62]), c_0_148]), c_0_79]), c_0_58])). 32.44/32.64 thf(c_0_353, plain, (sup @ b @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))=(inf @ (sup @ a2 @ b) @ (sup @ b @ c)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_330, c_0_331]), c_0_332])). 32.44/32.64 thf(c_0_354, plain, ![X1:a, X3:a, X2:a]:(sup @ (inf @ X1 @ X2) @ (inf @ X1 @ (inf @ X3 @ X2)))=(inf @ X1 @ X2), inference(spm,[status(thm)],[c_0_111, c_0_108])). 32.44/32.64 thf(c_0_355, plain, (sup @ (inf @ a2 @ (inf @ b @ c)) @ (inf @ a2 @ (sup @ (inf @ b @ c) @ (inf @ a2 @ (sup @ b @ c)))))=(inf @ a2 @ (sup @ (inf @ b @ c) @ (inf @ a2 @ (sup @ b @ c)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134, c_0_313]), c_0_58]), c_0_77]), c_0_62]), c_0_67]), c_0_108])). 32.44/32.64 thf(c_0_356, plain, (inf @ a2 @ (sup @ (inf @ b @ c) @ (inf @ a2 @ (sup @ b @ c))))=(inf @ a2 @ (sup @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_333, c_0_334]), c_0_79]), c_0_152]), c_0_124]), c_0_108]), c_0_215]), c_0_109])). 32.44/32.64 thf(c_0_357, plain, ![X1:a, X2:a, X3:a]:((inf @ (modula17988509_aux_a @ inf @ sup @ X1 @ X2 @ X3) @ (modula1373251614_aux_a @ inf @ sup @ X1 @ X2 @ X3))=(modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3)|~less_eq @ (modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3) @ (modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X3)), inference(split_conjunct,[status(thm)],[c_0_335])). 32.44/32.64 thf(c_0_358, plain, ![X1:a, X3:a, X2:a]:((inf @ (sup @ X1 @ (inf @ X2 @ X3)) @ (modula1144073633_aux_a @ inf @ sup @ X3 @ X1 @ X2))=(modula17988509_aux_a @ inf @ sup @ X1 @ X2 @ X3)|~less_eq @ (modula1936294176_aux_a @ inf @ sup @ X3 @ X1 @ X2) @ (modula1144073633_aux_a @ inf @ sup @ X3 @ X1 @ X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_336, c_0_129]), c_0_323])). 32.44/32.64 thf(c_0_359, plain, ![X1:a]:(sup @ (inf @ a2 @ b) @ (sup @ (inf @ X1 @ a2) @ (inf @ b @ (inf @ (sup @ a2 @ c) @ X1))))=(modula1936294176_aux_a @ inf @ sup @ a2 @ (inf @ b @ (sup @ a2 @ c)) @ X1), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_107]), c_0_62]), c_0_305]), c_0_58]), c_0_116])). 32.44/32.64 thf(c_0_360, plain, (inf @ (sup @ a2 @ c) @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))=(modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_244, c_0_337]), c_0_67])). 32.44/32.64 thf(c_0_361, plain, ![X1:a, X2:a, X3:a]:(sup @ X1 @ (sup @ X2 @ (sup @ X1 @ X3)))=(sup @ X2 @ (sup @ X1 @ X3)), inference(rw,[status(thm)],[c_0_338, c_0_339])). 32.44/32.64 thf(c_0_362, plain, ![X1:a, X2:a, X3:a]:(sup @ (inf @ X1 @ X2) @ (sup @ (inf @ X1 @ X3) @ (inf @ X3 @ X2)))=(modula1936294176_aux_a @ inf @ sup @ X2 @ X1 @ X3), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_155]), c_0_156])])). 32.44/32.64 thf(c_0_363, plain, (inf @ b @ (inf @ c @ (sup @ a2 @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)))))=(inf @ b @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_340, c_0_278]), c_0_58]), c_0_67])). 32.44/32.64 thf(c_0_364, plain, (modula1144073633_aux_a @ inf @ sup @ a2 @ (sup @ b @ c) @ c)=(inf @ (sup @ a2 @ c) @ (sup @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_341, c_0_342]), c_0_79]), c_0_343]), c_0_67]), c_0_101])). 32.44/32.64 thf(c_0_365, plain, (inf @ a2 @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c)))=(inf @ a2 @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_344]), c_0_62]), c_0_121]), c_0_67])). 32.44/32.64 thf(c_0_366, negated_conjecture, (sup @ (inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))) @ (inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))))!=(inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ (inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))) @ (sup @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_345, c_0_67]), c_0_67])). 32.44/32.64 thf(c_0_367, plain, (inf @ (sup @ a2 @ b) @ (sup @ b @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)))=(sup @ b @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_262]), c_0_67])). 32.44/32.64 thf(c_0_368, plain, ![X1:a, X2:a, X3:a]:(sup @ X1 @ (inf @ (sup @ X1 @ X2) @ X3))=(inf @ (sup @ X1 @ X2) @ (sup @ X1 @ X3)), inference(spm,[status(thm)],[c_0_308, c_0_180])). 32.44/32.64 thf(c_0_369, plain, ![X1:a, X3:a, X2:a]:(inf @ (sup @ X1 @ X2) @ (sup @ X1 @ (sup @ X3 @ X2)))=(sup @ X1 @ X2), inference(spm,[status(thm)],[c_0_95, c_0_93])). 32.44/32.64 thf(c_0_370, plain, ![X1:a, X2:a, X3:a]:(sup @ (inf @ X1 @ X2) @ (sup @ (inf @ X3 @ X1) @ (inf @ X1 @ (inf @ X2 @ X3))))=(modula1936294176_aux_a @ inf @ sup @ X1 @ (inf @ X1 @ X2) @ X3), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_109]), c_0_62]), c_0_305]), c_0_58]), c_0_116])). 32.44/32.64 thf(c_0_371, plain, ![X1:a, X3:a, X2:a]:(modula1936294176_aux_a @ inf @ sup @ X1 @ (inf @ X1 @ X2) @ X3)=(sup @ (inf @ X3 @ X1) @ (inf @ X1 @ X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_346, c_0_77]), c_0_116]), c_0_347]), c_0_348])). 32.44/32.64 thf(c_0_372, plain, ![X1:a, X2:a]:less_eq @ (inf @ X1 @ X2) @ X2, inference(split_conjunct,[status(thm)],[c_0_349])). 32.44/32.64 thf(c_0_373, plain, ![X1:a, X2:a, X3:a]:(sup @ (inf @ X1 @ X2) @ (sup @ (inf @ X3 @ X2) @ (inf @ X3 @ X1)))=(modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_155]), c_0_156])])). 32.44/32.64 thf(c_0_374, plain, ![X1:a, X2:a, X3:a]:(sup @ (inf @ X1 @ X2) @ (inf @ X1 @ X3))=(inf @ X1 @ (sup @ (inf @ X1 @ X2) @ X3)), inference(spm,[status(thm)],[c_0_308, c_0_350])). 32.44/32.64 thf(c_0_375, plain, ![X2:a, X1:a, X10:a > a > a]:((X10 @ X1 @ (X10 @ X2 @ X1))=(X10 @ X2 @ X1)|~semilattice_a @ X10), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_200, c_0_155]), c_0_351])). 32.44/32.64 thf(c_0_376, plain, (sup @ b @ (sup @ (inf @ a2 @ (inf @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)))=(inf @ (sup @ a2 @ b) @ (sup @ b @ c)), inference(rw,[status(thm)],[c_0_352, c_0_353])). 32.44/32.64 thf(c_0_377, plain, (sup @ (inf @ (sup @ a2 @ b) @ (sup @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))=(inf @ (sup @ a2 @ b) @ (sup @ b @ c)), inference(spm,[status(thm)],[c_0_354, c_0_331])). 32.44/32.64 thf(c_0_378, plain, (sup @ (inf @ a2 @ (inf @ b @ c)) @ (inf @ a2 @ (sup @ b @ c)))=(inf @ a2 @ (sup @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_355, c_0_356]), c_0_356])). 32.44/32.64 thf(c_0_379, plain, ![X1:a, X2:a, X3:a]:((inf @ (modula17988509_aux_a @ inf @ sup @ X1 @ X2 @ X3) @ (modula17988509_aux_a @ inf @ sup @ X2 @ X3 @ X1))=(modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3)|~less_eq @ (modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3) @ (modula1144073633_aux_a @ inf @ sup @ X1 @ X2 @ X3)), inference(rw,[status(thm)],[c_0_357, c_0_323])). 32.44/32.64 thf(c_0_380, plain, (sup @ (inf @ b @ (sup @ a2 @ c)) @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))=(inf @ (sup @ b @ (inf @ a2 @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_358, c_0_57]), c_0_67]), c_0_218]), c_0_58]), c_0_116])). 32.44/32.64 thf(c_0_381, plain, (modula1936294176_aux_a @ inf @ sup @ a2 @ (inf @ b @ (sup @ a2 @ c)) @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))=(modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_359, c_0_360]), c_0_67]), c_0_122]), c_0_67]), c_0_83]), c_0_58]), c_0_79]), c_0_361]), c_0_362]), c_0_116]), c_0_116]), c_0_325])). 32.44/32.64 thf(c_0_382, plain, ![X1:a, X3:a, X2:a]:(inf @ (sup @ X1 @ X2) @ (sup @ X1 @ (sup @ X2 @ X3)))=(sup @ X1 @ X2), inference(spm,[status(thm)],[c_0_60, c_0_79])). 32.44/32.64 thf(c_0_383, plain, (sup @ a2 @ (sup @ (inf @ b @ c) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))))=(sup @ a2 @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149, c_0_363]), c_0_79]), c_0_58])). 32.44/32.64 thf(c_0_384, plain, (sup @ c @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)))=(inf @ (sup @ a2 @ c) @ (sup @ b @ c)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137, c_0_364]), c_0_244])). 32.44/32.64 thf(c_0_385, plain, (sup @ (inf @ a2 @ c) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ (inf @ a2 @ c) @ (inf @ b @ c)))=(modula1144073633_aux_a @ inf @ sup @ a2 @ (inf @ a2 @ c) @ (inf @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137, c_0_365]), c_0_101]), c_0_101])). 32.44/32.64 thf(c_0_386, negated_conjecture, (sup @ (inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))) @ (inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))))!=(inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ (sup @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)) @ (inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_366, c_0_58]), c_0_58])). 32.44/32.64 thf(c_0_387, plain, (sup @ (inf @ b @ c) @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))=(modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_239, c_0_344]), c_0_84]), c_0_202])])). 32.44/32.64 thf(c_0_388, plain, (inf @ (sup @ a2 @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) @ (sup @ b @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)))=(modula1144073633_aux_a @ inf @ sup @ a2 @ b @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99, c_0_367]), c_0_58]), c_0_101]), c_0_101])). 32.44/32.64 thf(c_0_389, plain, (sup @ a2 @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))=(inf @ (sup @ a2 @ b) @ (sup @ a2 @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_368, c_0_331]), c_0_368]), c_0_369])). 32.44/32.64 thf(c_0_390, plain, ![X1:a, X3:a, X2:a]:(sup @ (inf @ X1 @ X2) @ (sup @ (inf @ X3 @ X1) @ (inf @ X1 @ (inf @ X2 @ X3))))=(sup @ (inf @ X3 @ X1) @ (inf @ X1 @ X2)), inference(rw,[status(thm)],[c_0_370, c_0_371])). 32.44/32.64 thf(c_0_391, plain, ![X1:a, X2:a, X3:a]:(sup @ (inf @ X1 @ X2) @ (inf @ X2 @ X3))=(inf @ X2 @ (sup @ (inf @ X1 @ X2) @ X3)), inference(spm,[status(thm)],[c_0_308, c_0_372])). 32.44/32.64 thf(c_0_392, plain, ![X1:a, X2:a, X3:a]:(sup @ (inf @ X1 @ X2) @ (sup @ (inf @ X3 @ X1) @ (inf @ X2 @ X3)))=(modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_155]), c_0_259])])). 32.44/32.64 thf(c_0_393, plain, ![X1:a, X2:a, X3:a]:(sup @ (inf @ X1 @ X2) @ (inf @ X3 @ (sup @ (inf @ X3 @ X2) @ X1)))=(modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3), inference(rw,[status(thm)],[c_0_373, c_0_374])). 32.44/32.64 thf(c_0_394, plain, (sup @ (inf @ a2 @ (inf @ b @ c)) @ (inf @ (sup @ a2 @ b) @ (sup @ b @ c)))=(inf @ (sup @ a2 @ b) @ (sup @ b @ c)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_375, c_0_376]), c_0_79]), c_0_58]), c_0_377]), c_0_202])])). 32.44/32.64 thf(c_0_395, plain, ![X3:a, X2:a, X1:a]:(inf @ X1 @ (inf @ X2 @ (sup @ X3 @ X1)))=(inf @ X2 @ X1), inference(spm,[status(thm)],[c_0_108, c_0_95])). 32.44/32.64 thf(c_0_396, plain, (modula1936294176_aux_a @ inf @ sup @ a2 @ (sup @ b @ c) @ (inf @ b @ c))=(sup @ (inf @ b @ c) @ (inf @ a2 @ (sup @ b @ c))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_373, c_0_378]), c_0_108]), c_0_67]), c_0_95]), c_0_116])). 32.44/32.64 thf(c_0_397, plain, (inf @ (sup @ a2 @ (inf @ b @ c)) @ (inf @ (sup @ b @ (inf @ a2 @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)))=(modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_379, c_0_57]), c_0_218]), c_0_230]), c_0_218]), c_0_58]), c_0_116]), c_0_380]), c_0_62]), c_0_73])). 32.44/32.64 thf(c_0_398, plain, (inf @ (sup @ b @ (inf @ a2 @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))=(sup @ (inf @ a2 @ c) @ (inf @ b @ (sup @ a2 @ c))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129, c_0_381]), c_0_380]), c_0_67]), c_0_122]), c_0_67]), c_0_305]), c_0_58]), c_0_176])). 32.44/32.64 thf(c_0_399, plain, (inf @ (sup @ a2 @ (inf @ b @ c)) @ (sup @ a2 @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c))))=(sup @ a2 @ (inf @ b @ c)), inference(spm,[status(thm)],[c_0_382, c_0_383])). 32.44/32.64 thf(c_0_400, plain, (sup @ a2 @ (inf @ (sup @ a2 @ c) @ (sup @ b @ c)))=(sup @ a2 @ c), inference(spm,[status(thm)],[c_0_224, c_0_384])). 32.44/32.64 thf(c_0_401, plain, (inf @ a2 @ (inf @ c @ (modula1144073633_aux_a @ inf @ sup @ a2 @ (inf @ a2 @ c) @ (inf @ b @ c))))=(inf @ a2 @ c), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_385]), c_0_62])). 32.44/32.64 thf(c_0_402, negated_conjecture, (sup @ (inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))) @ (inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))))!=(inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ a2 @ (sup @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ (inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ b @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c)))))), inference(rw,[status(thm)],[c_0_386, c_0_79])). 32.44/32.64 thf(c_0_403, plain, (inf @ b @ (sup @ (inf @ a2 @ c) @ (inf @ b @ c)))=(inf @ b @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_387]), c_0_62]), c_0_121]), c_0_67])). 32.44/32.64 thf(c_0_404, plain, ![X1:a]:(inf @ (sup @ X1 @ a2) @ (inf @ (sup @ a2 @ b) @ (sup @ b @ (sup @ (inf @ a2 @ c) @ X1))))=(modula1144073633_aux_a @ inf @ sup @ a2 @ (sup @ b @ (inf @ a2 @ c)) @ X1), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99, c_0_225]), c_0_79]), c_0_108]), c_0_67]), c_0_101])). 32.44/32.64 thf(c_0_405, plain, (inf @ (sup @ a2 @ b) @ (inf @ (sup @ a2 @ c) @ (sup @ b @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))))=(modula1144073633_aux_a @ inf @ sup @ a2 @ b @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_388, c_0_389]), c_0_62])). 32.44/32.64 thf(c_0_406, plain, ![X1:a, X2:a, X3:a]:(inf @ (sup @ X1 @ X2) @ (inf @ (sup @ X1 @ X3) @ (sup @ X3 @ X2)))=(modula1144073633_aux_a @ inf @ sup @ X2 @ X1 @ X3), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99, c_0_155]), c_0_259])])). 32.44/32.64 thf(c_0_407, plain, ![X1:a, X3:a, X2:a]:(sup @ (inf @ X1 @ X2) @ (inf @ X3 @ X1))=(inf @ X1 @ (sup @ (inf @ X3 @ X1) @ X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_390, c_0_391]), c_0_374]), c_0_392]), c_0_122]), c_0_391])). 32.44/32.64 thf(c_0_408, plain, ![X1:a, X2:a, X3:a]:(sup @ (inf @ X1 @ X2) @ (inf @ X3 @ (sup @ (inf @ X1 @ X3) @ X2)))=(modula1936294176_aux_a @ inf @ sup @ X2 @ X1 @ X3), inference(rw,[status(thm)],[c_0_362, c_0_391])). 32.44/32.64 thf(c_0_409, plain, (modula1936294176_aux_a @ inf @ sup @ a2 @ (inf @ (sup @ a2 @ b) @ (sup @ b @ c)) @ (inf @ b @ c))=(sup @ (inf @ b @ c) @ (inf @ a2 @ (sup @ b @ c))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_393, c_0_394]), c_0_62]), c_0_108]), c_0_67]), c_0_95]), c_0_67]), c_0_62]), c_0_395]), c_0_67]), c_0_256]), c_0_116])). 32.44/32.64 thf(c_0_410, plain, (inf @ (sup @ b @ c) @ (sup @ (inf @ b @ c) @ (inf @ a2 @ (sup @ b @ c))))=(sup @ (inf @ b @ c) @ (inf @ a2 @ (sup @ b @ c))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139, c_0_396]), c_0_62]), c_0_67]), c_0_108]), c_0_79]), c_0_149])). 32.44/32.64 thf(c_0_411, plain, ![X1:a, X3:a, X2:a]:(sup @ (inf @ X1 @ X2) @ (sup @ (inf @ X1 @ X3) @ (inf @ X1 @ (sup @ X3 @ X2))))=(inf @ X1 @ (sup @ X3 @ X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_312]), c_0_305]), c_0_58])). 32.44/32.64 thf(c_0_412, plain, (inf @ (sup @ a2 @ (inf @ b @ c)) @ (sup @ (inf @ a2 @ c) @ (inf @ b @ (sup @ a2 @ c))))=(modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c), inference(rw,[status(thm)],[c_0_397, c_0_398])). 32.44/32.64 thf(c_0_413, plain, (inf @ (sup @ a2 @ c) @ (sup @ a2 @ (inf @ b @ c)))=(sup @ a2 @ (inf @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_399, c_0_400]), c_0_67])). 32.44/32.64 thf(c_0_414, plain, (inf @ a2 @ (inf @ c @ (sup @ a2 @ (inf @ b @ c))))=(inf @ a2 @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_401, c_0_207]), c_0_58])). 32.44/32.64 thf(c_0_415, plain, (sup @ (inf @ a2 @ c) @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))=(modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200, c_0_344]), c_0_202])])). 32.44/32.64 thf(c_0_416, negated_conjecture, (sup @ (inf @ (sup @ b @ (inf @ a2 @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) @ (inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ a2 @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))))!=(inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ a2 @ (sup @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ (inf @ (sup @ b @ (inf @ a2 @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_402, c_0_129]), c_0_67]), c_0_67]), c_0_58]), c_0_129]), c_0_67]), c_0_67])). 32.44/32.64 thf(c_0_417, plain, (inf @ b @ (inf @ c @ (inf @ (sup @ b @ (inf @ a2 @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))))=(inf @ b @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_294, c_0_397]), c_0_62]), c_0_121]), c_0_67]), c_0_403]), c_0_62])). 32.44/32.64 thf(c_0_418, plain, (modula1144073633_aux_a @ inf @ sup @ a2 @ (sup @ b @ (inf @ a2 @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))=(modula1144073633_aux_a @ inf @ sup @ a2 @ b @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_404, c_0_249]), c_0_58]), c_0_367]), c_0_388])). 32.44/32.64 thf(c_0_419, plain, (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))=(modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_405, c_0_353]), c_0_406]), c_0_101]), c_0_101]), c_0_291])). 32.44/32.64 thf(c_0_420, plain, (inf @ (sup @ a2 @ b) @ (sup @ b @ (inf @ a2 @ c)))=(sup @ b @ (inf @ a2 @ c)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_225]), c_0_67])). 32.44/32.64 thf(c_0_421, plain, ![X1:a, X3:a, X2:a]:(inf @ X1 @ (modula1936294176_aux_a @ inf @ sup @ X2 @ X3 @ X1))=(inf @ X1 @ (sup @ (inf @ X3 @ X1) @ X2)), inference(rw,[status(thm)],[c_0_121, c_0_407])). 32.44/32.64 thf(c_0_422, plain, (modula1936294176_aux_a @ inf @ sup @ a2 @ (inf @ b @ c) @ (inf @ (sup @ a2 @ b) @ (sup @ b @ c)))=(sup @ (inf @ b @ c) @ (inf @ a2 @ (sup @ b @ c))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_408, c_0_394]), c_0_256]), c_0_62]), c_0_395]), c_0_67]), c_0_395]), c_0_67]), c_0_58]), c_0_116]), c_0_116])). 32.44/32.64 thf(c_0_423, plain, (inf @ (sup @ a2 @ b) @ (sup @ (inf @ b @ c) @ (inf @ a2 @ (sup @ b @ c))))=(sup @ (inf @ b @ c) @ (inf @ a2 @ (sup @ b @ c))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139, c_0_409]), c_0_62]), c_0_67]), c_0_108]), c_0_58]), c_0_394]), c_0_62]), c_0_410])). 32.44/32.64 thf(c_0_424, plain, (sup @ (inf @ b @ (sup @ a2 @ (inf @ b @ c))) @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c))=(modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_411, c_0_412]), c_0_108]), c_0_67]), c_0_413]), c_0_108]), c_0_67]), c_0_414]), c_0_415])). 32.44/32.64 thf(c_0_425, negated_conjecture, (inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ a2 @ (sup @ (modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c) @ (inf @ (sup @ b @ (inf @ a2 @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)))))!=(sup @ (inf @ (sup @ a2 @ (inf @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) @ (inf @ (sup @ b @ (inf @ a2 @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_416, c_0_123]), c_0_67]), c_0_58])). 32.44/32.64 thf(c_0_426, plain, ![X1:a, X2:a, X3:a, X4:a]:(sup @ X1 @ (sup @ (modula1936294176_aux_a @ inf @ sup @ X1 @ X2 @ X3) @ X4))=(sup @ X1 @ (sup @ (inf @ X2 @ X3) @ X4)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_123]), c_0_79])). 32.44/32.64 thf(c_0_427, plain, (sup @ (inf @ b @ c) @ (inf @ (sup @ b @ (inf @ a2 @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)))=(inf @ (sup @ b @ (inf @ a2 @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149, c_0_417]), c_0_58])). 32.44/32.64 thf(c_0_428, plain, (modula1144073633_aux_a @ inf @ sup @ a2 @ (sup @ b @ (inf @ a2 @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))=(modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c), inference(rw,[status(thm)],[c_0_418, c_0_419])). 32.44/32.64 thf(c_0_429, plain, ![X1:a]:(inf @ (sup @ a2 @ b) @ (inf @ X1 @ (sup @ b @ (inf @ a2 @ c))))=(inf @ X1 @ (sup @ b @ (inf @ a2 @ c))), inference(spm,[status(thm)],[c_0_108, c_0_420])). 32.44/32.64 thf(c_0_430, plain, (inf @ (sup @ a2 @ b) @ (inf @ (sup @ b @ c) @ (sup @ a2 @ (inf @ b @ c))))=(sup @ (inf @ b @ c) @ (inf @ a2 @ (sup @ b @ c))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_421, c_0_422]), c_0_62]), c_0_410]), c_0_423]), c_0_62]), c_0_395]), c_0_67]), c_0_395]), c_0_67]), c_0_58]), c_0_62])). 32.44/32.64 thf(c_0_431, plain, (sup @ (inf @ a2 @ b) @ (inf @ b @ c))=(inf @ b @ (sup @ a2 @ (inf @ b @ c))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_424]), c_0_62]), c_0_127]), c_0_83]), c_0_58])). 32.44/32.64 thf(c_0_432, plain, ![X1:a]:(sup @ (inf @ X1 @ a2) @ (sup @ (inf @ a2 @ b) @ (inf @ b @ (inf @ (sup @ a2 @ c) @ X1))))=(modula1936294176_aux_a @ inf @ sup @ X1 @ a2 @ (inf @ b @ (sup @ a2 @ c))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_107]), c_0_62])). 32.44/32.64 thf(c_0_433, negated_conjecture, (sup @ (inf @ (sup @ a2 @ (inf @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)) @ (inf @ (sup @ b @ (inf @ a2 @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)))!=(inf @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c) @ (sup @ a2 @ (inf @ (sup @ b @ (inf @ a2 @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_425, c_0_426]), c_0_427])). 32.44/32.64 thf(c_0_434, plain, (sup @ (inf @ a2 @ c) @ (inf @ b @ (sup @ a2 @ c)))=(inf @ (sup @ a2 @ c) @ (sup @ b @ (inf @ a2 @ c))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71, c_0_428]), c_0_398]), c_0_58]), c_0_389]), c_0_108]), c_0_67]), c_0_429])). 32.44/32.64 thf(c_0_435, plain, ![X3:a, X2:a, X1:a]:(sup @ X1 @ (sup @ X2 @ (inf @ X1 @ X3)))=(sup @ X2 @ X1), inference(spm,[status(thm)],[c_0_93, c_0_77])). 32.44/32.64 thf(c_0_436, plain, (inf @ b @ (sup @ (inf @ b @ c) @ (inf @ a2 @ (sup @ b @ c))))=(inf @ b @ (sup @ a2 @ (inf @ b @ c))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_294, c_0_430]), c_0_256])). 32.44/32.64 thf(c_0_437, plain, (sup @ (inf @ a2 @ c) @ (inf @ b @ (sup @ a2 @ (inf @ b @ c))))=(modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_431]), c_0_67]), c_0_116]), c_0_116])). 32.44/32.64 thf(c_0_438, plain, (modula1936294176_aux_a @ inf @ sup @ a2 @ (inf @ b @ (sup @ a2 @ c)) @ (sup @ b @ c))=(sup @ (inf @ a2 @ (sup @ b @ c)) @ (inf @ b @ (sup @ a2 @ c))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_432, c_0_252]), c_0_67]), c_0_176]), c_0_116])). 32.44/32.64 thf(c_0_439, negated_conjecture, (sup @ (inf @ a2 @ c) @ (sup @ (inf @ b @ (sup @ a2 @ c)) @ (inf @ (sup @ a2 @ (inf @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))))!=(inf @ (sup @ a2 @ (inf @ b @ (sup @ a2 @ c))) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_433, c_0_398]), c_0_305]), c_0_58]), c_0_93]), c_0_398]), c_0_160]), c_0_67])). 32.44/32.64 thf(c_0_440, plain, (sup @ a2 @ (inf @ b @ (sup @ a2 @ c)))=(inf @ (sup @ a2 @ b) @ (sup @ a2 @ c)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160, c_0_434]), c_0_368]), c_0_435]), c_0_58]), c_0_67])). 32.44/32.64 thf(c_0_441, plain, (modula1936294176_aux_a @ inf @ sup @ b @ (inf @ a2 @ (sup @ b @ c)) @ c)=(modula1936294176_aux_a @ inf @ sup @ a2 @ b @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_393, c_0_436]), c_0_62]), c_0_67]), c_0_95]), c_0_437]), c_0_116])). 32.44/32.64 thf(c_0_442, plain, (inf @ (sup @ b @ c) @ (sup @ (inf @ a2 @ (sup @ b @ c)) @ (inf @ b @ (sup @ a2 @ c))))=(sup @ (inf @ a2 @ (sup @ b @ c)) @ (inf @ b @ (sup @ a2 @ c))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121, c_0_438]), c_0_67]), c_0_62]), c_0_252])). 32.44/32.64 thf(c_0_443, plain, ![X3:a, X2:a, X1:a]:(inf @ X1 @ (inf @ X2 @ (sup @ X1 @ X3)))=(inf @ X2 @ X1), inference(spm,[status(thm)],[c_0_108, c_0_60])). 32.44/32.64 thf(c_0_444, negated_conjecture, (sup @ (inf @ a2 @ c) @ (sup @ (inf @ b @ (sup @ a2 @ c)) @ (inf @ (sup @ a2 @ (inf @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))))!=(modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_439, c_0_440]), c_0_62]), c_0_310]), c_0_291])). 32.44/32.64 thf(c_0_445, plain, (inf @ (sup @ a2 @ (inf @ b @ c)) @ (modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c))=(sup @ (inf @ b @ c) @ (inf @ a2 @ (sup @ b @ c))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129, c_0_441]), c_0_230]), c_0_67]), c_0_58])). 32.44/32.64 thf(c_0_446, plain, (sup @ (inf @ a2 @ (sup @ b @ c)) @ (inf @ b @ (sup @ a2 @ c)))=(modula1144073633_aux_a @ inf @ sup @ a2 @ b @ c), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_421, c_0_438]), c_0_442]), c_0_62]), c_0_443]), c_0_67]), c_0_58]), c_0_440]), c_0_108]), c_0_67]), c_0_331])). 32.44/32.64 thf(c_0_447, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_444, c_0_445]), c_0_305]), c_0_58]), c_0_374]), c_0_93]), c_0_58]), c_0_111]), c_0_446]), c_0_249])]), ['proof']). 32.44/32.64 # SZS output end CNFRefutation 32.44/32.64 # Proof object total steps : 448 32.44/32.64 # Proof object clause steps : 342 32.44/32.64 # Proof object formula steps : 106 32.44/32.64 # Proof object conjectures : 12 32.44/32.64 # Proof object clause conjectures : 10 32.44/32.64 # Proof object formula conjectures : 2 32.44/32.64 # Proof object initial clauses used : 53 32.44/32.64 # Proof object initial formulas used : 53 32.44/32.64 # Proof object generating inferences : 246 32.44/32.64 # Proof object simplifying inferences : 638 32.44/32.64 # Training examples: 0 positive, 0 negative 32.44/32.64 # Parsed axioms : 293 32.44/32.64 # Removed by relevancy pruning/SinE : 0 32.44/32.64 # Initial clauses : 399 32.44/32.64 # Removed in clause preprocessing : 49 32.44/32.64 # Initial clauses in saturation : 350 32.44/32.64 # Processed clauses : 34698 32.44/32.64 # ...of these trivial : 9725 32.44/32.64 # ...subsumed : 17718 32.44/32.64 # ...remaining for further processing : 7255 32.44/32.64 # Other redundant clauses eliminated : 1997 32.44/32.64 # Clauses deleted for lack of memory : 860141 32.44/32.64 # Backward-subsumed : 62 32.44/32.64 # Backward-rewritten : 2763 32.44/32.64 # Generated clauses : 2039044 32.44/32.64 # ...of the previous two non-trivial : 1695223 32.44/32.64 # Contextual simplify-reflections : 19 32.44/32.64 # Paramodulations : 2026661 32.44/32.64 # Factorizations : 2 32.44/32.64 # NegExts : 48 32.44/32.64 # Equation resolutions : 1997 32.44/32.64 # Propositional unsat checks : 1 32.44/32.64 # Propositional check models : 0 32.44/32.64 # Propositional check unsatisfiable : 0 32.44/32.64 # Propositional clauses : 0 32.44/32.64 # Propositional clauses after purity: 0 32.44/32.64 # Propositional unsat core size : 0 32.44/32.64 # Propositional preprocessing time : 0.000 32.44/32.64 # Propositional encoding time : 2.524 32.44/32.64 # Propositional solver time : 1.001 32.44/32.64 # Success case prop preproc time : 0.000 32.44/32.64 # Success case prop encoding time : 0.000 32.44/32.64 # Success case prop solver time : 0.000 32.44/32.64 # Current number of processed clauses : 4153 32.44/32.64 # Positive orientable unit clauses : 2542 32.44/32.64 # Positive unorientable unit clauses: 23 32.44/32.64 # Negative unit clauses : 4 32.44/32.64 # Non-unit-clauses : 1584 32.44/32.64 # Current number of unprocessed clauses: 799026 32.44/32.64 # ...number of literals in the above : 1073098 32.44/32.64 # Current number of archived formulas : 0 32.44/32.64 # Current number of archived clauses : 3085 32.44/32.64 # Clause-clause subsumption calls (NU) : 988669 32.44/32.64 # Rec. Clause-clause subsumption calls : 911767 32.44/32.64 # Non-unit clause-clause subsumptions : 17291 32.44/32.64 # Unit Clause-clause subsumption calls : 68302 32.44/32.64 # Rewrite failures with RHS unbound : 0 32.44/32.64 # BW rewrite match attempts : 31164 32.44/32.64 # BW rewrite match successes : 2799 32.44/32.64 # Condensation attempts : 0 32.44/32.64 # Condensation successes : 0 32.44/32.64 # Termbank termtop insertions : 72056981 32.55/32.80 32.55/32.80 # ------------------------------------------------- 32.55/32.80 # User time : 31.196 s 32.55/32.80 # System time : 1.222 s 32.55/32.80 # Total time : 32.418 s 32.55/32.80 # Maximum resident set size: 1988 pages 32.55/32.80 EOF