0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 180 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39 0.14/0.41 % Computer : n010.cluster.edu 0.14/0.41 % Model : x86_64 x86_64 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.41 % Memory : 8046.5625MB 0.14/0.41 % OS : Linux 6.8.0-71-generic 0.14/0.41 % CPULimit : 1440 0.14/0.41 % WCLimit : 180 0.14/0.41 % DateTime : Mon Jul 27 10:29:04 UTC 2026 0.14/0.41 % CPUTime : 0.14/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 180 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39 0.89/1.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 1.81/1.39 % [INFO] Parsing done (379ms). 2.30/1.41 % [INFO] Running in sequential loop mode. 3.08/1.80 % [INFO] eprover registered as external prover. 3.08/1.81 % [INFO] Scanning for conjecture ... 3.25/1.94 % [INFO] Found a conjecture (or negated_conjecture) and 253 axioms. Running axiom selection ... 3.53/2.07 % [INFO] Axiom selection finished. Selected 253 axioms (removed 0 axioms). 4.25/2.31 % [INFO] Problem is higher-order (TPTP THF). 4.25/2.34 % [INFO] Type checking passed. 4.25/2.35 % [CONFIG] Using configuration: timeout(180) with strategy. Searching for refutation ... 51.53/15.21 % External prover 'e' found a proof! 51.53/15.21 % [INFO] Killing All external provers ... 51.53/15.21 % Time passed: 14659ms (effective reasoning time: 13796ms) 51.53/15.21 % Solved by strategy 51.53/15.22 % Axioms used in derivation (253): fact_158_local_Ole__inf__iff, fact_139_local_Oorder__refl, fact_130_local_Osup_Ostrict__coboundedI1, fact_57_local_Ole__less, fact_95_local_Ole__iff__sup, fact_156_local_Ono__distrib__def, fact_206_abel__semigroup_Oaxioms_I1_J, fact_65_local_Oorder_Oorder__iff__strict, fact_93_local_Ole__infI1, fact_42_local_Osup__commute, fact_79_local_Oinf_OcoboundedI2, fact_127_local_Oless__supI1, fact_148_local_Osup_Oright__idem, fact_149_local_Osup__idem, fact_146_local_Osup_Oidem, fact_90_local_Ole__iff__inf, fact_34_local_Oinf_Oleft__commute, fact_246_local_Obdd__belowI, fact_131_local_Osup_Ostrict__coboundedI2, fact_195_local_Oc__a, fact_63_local_Oless__le__trans, fact_227_semilattice__order_OboundedI, fact_175_local_Oc__meet__e, fact_114_local_Osup__absorb1, fact_64_local_Oorder_Onot__eq__order__implies__strict, fact_13_local_Odual__order_Oasym, fact_141_local_Oinf_Oleft__idem, fact_165_local_OLeast1__le, fact_209_semigroup_Ointro, fact_140_local_Oinf_Oidem, fact_245_local_Obdd__above__def, fact_120_local_Osup__unique, fact_238_semilattice__order_Ostrict__coboundedI1, fact_48_local_Oantisym__conv2, fact_204_local_Oinf_Oabel__semigroup__axioms, fact_164_local_OLeast1I, fact_229_semilattice__order_Ocobounded1, fact_60_local_Oless__imp__le, fact_233_semilattice__order_Obounded__iff, fact_96_local_Ole__supE, fact_109_local_Osup_OcoboundedI2, fact_1_local_Oantisym__conv, conj_3, fact_66_local_Oorder_Ostrict__iff__order, fact_40_local_Osup_Oleft__commute, fact_224_semilattice__order_Oabsorb1, fact_28_local_Oorder_Oasym, fact_189_lattice_Od__aux_Ocong, fact_8_local_Oord__le__eq__trans, fact_75_local_Oinf_OboundedI, fact_170_local_Od__aux__def, fact_161_local_Oinf__sup__absorb, fact_191_local_Oorder_Oordering__axioms, fact_136_local_Odistrib__sup__le, fact_153_local_Omax__def, fact_3_local_Odual__order_Oeq__iff, fact_117_local_Osup__ge2, fact_241_semilattice_Oleft__idem, fact_30_local_Oorder_Ostrict__implies__not__eq, fact_134_local_Odistrib__imp2, fact_222_semilattice__order_OorderE, fact_21_local_Oless__imp__not__less, fact_205_semilattice__order__set_Oaxioms_I1_J, fact_218_semilattice__set_Oaxioms, fact_197_lattice_Ob__aux_Ocong, fact_188_lattice_Oe__aux_Ocong, fact_225_semilattice__order_Oabsorb2, fact_145_local_Oinf__right__idem, fact_163_local_OM5__lattice__def, fact_22_local_Oless__imp__triv, fact_247_local_Obdd__aboveI, fact_157_local_Oinf_Obounded__iff, fact_27_local_Oord__less__eq__trans, fact_176_local_Oe__aux__def, fact_97_local_Ole__supI, fact_92_local_Ole__infI, fact_135_local_Odistrib__inf__le, fact_178_local_Oe__c__a__b, fact_12_local_Oorder__trans, fact_107_local_Osup_Ocobounded2, fact_41_local_Osup__assoc, fact_108_local_Osup_OcoboundedI1, fact_124_local_Oinf_Ostrict__order__iff, fact_198_lattice_Oa__aux_Ocong, fact_196_lattice_Oc__aux_Ocong, fact_54_local_Odual__order_Ostrict__trans2, fact_213_local_OSup__fin_Osemilattice__set__axioms, fact_155_local_ON5__lattice__def, fact_46_Collect__mem__eq, fact_202_local_Oinf_Osemilattice__axioms, fact_73_local_Oinf_Oabsorb__iff2, fact_212_semilattice_Oaxioms_I1_J, fact_115_local_Osup__absorb2, fact_211_semigroup__def, fact_248_local_Obdd__below__Ioo, fact_230_semilattice__order_Ocobounded2, fact_62_local_Oless__le__not__le, fact_15_local_Odual__order_Ostrict__trans, fact_85_local_Oinf__greatest, fact_103_local_Osup_Oabsorb__iff2, fact_137_local_Oincomp__def, fact_58_local_Ole__less__trans, fact_32_local_Oinf_Oassoc, fact_81_local_Oinf_OorderI, fact_190_local_Oinf_Osemilattice__order__axioms, fact_232_semilattice__order_Oabsorb__iff2, conj_2, fact_154_local_Omin__def, fact_244_local_Obdd__below__def, fact_147_local_Osup_Oleft__idem, fact_84_local_Oinf__absorb2, fact_100_local_Osup_Oabsorb1, fact_102_local_Osup_Oabsorb__iff1, fact_129_local_Osup_Ostrict__boundedE, fact_180_local_OM5__lattice__incomp, fact_20_local_Oless__imp__not__eq2, fact_19_local_Oless__imp__not__eq, fact_94_local_Ole__infI2, fact_104_local_Osup_OboundedE, fact_44_local_Oantisym__conv1, fact_31_local_Oorder_Ostrict__trans, fact_138_local_Oorder_Orefl, fact_201_local_Osup_Osemilattice__axioms, fact_123_local_Oinf_Ostrict__coboundedI2, fact_77_local_Oinf_Ocobounded2, fact_239_semilattice__order_Ostrict__coboundedI2, fact_142_local_Oinf_Oright__idem, fact_69_local_Oorder_Ostrict__trans2, fact_228_semilattice__order_Oorder__iff, fact_61_local_Oless__le, fact_215_semilattice__order__set_Oaxioms_I2_J, fact_18_local_Oless__imp__neq, fact_174_local_Ob__meet__e, fact_25_local_Oless__trans, fact_194_local_Ob__a, fact_52_local_Odual__order_Ostrict__implies__order, fact_223_semilattice__order_OorderI, fact_70_local_Oinf_Oabsorb1, fact_80_local_Oinf_OorderE, fact_226_semilattice__order_OboundedE, fact_29_local_Oorder_Oirrefl, fact_37_local_Oinf__left__commute, fact_171_local_Od__b__c__a, fact_2_local_Odual__order_Oantisym, fact_221_semilattice__order_Omono, fact_231_semilattice__order_Oabsorb__iff1, fact_50_local_Odual__order_Oorder__iff__strict, fact_214_local_OInf__fin_Osemilattice__set__axioms, fact_45_mem__Collect__eq, fact_10_local_Oorder_Oeq__iff, fact_118_local_Osup__least, fact_38_local_Osup_Oassoc, fact_87_local_Oinf__le2, fact_7_local_Oord__eq__le__trans, fact_168_local_Oa__join__d, fact_76_local_Oinf_Ocobounded1, fact_210_semigroup_Oassoc, fact_24_local_Oless__not__sym, fact_83_local_Oinf__absorb1, fact_35_local_Oinf__assoc, fact_192_local_Ocomp__fun__idem__sup, fact_160_local_Osup_Obounded__iff, fact_106_local_Osup_Ocobounded1, fact_125_local_Oless__infI1, fact_162_local_Osup__inf__absorb, fact_242_semilattice_Oright__idem, fact_220_semilattice__order__set_Ointro, fact_5_local_Oeq__iff, fact_59_local_Ole__neq__trans, fact_88_local_Oinf__mono, fact_144_local_Oinf__left__idem, fact_186_lattice_OM5__lattice_Ocong, fact_167_local_OLeast__equality, fact_172_local_Od__c__a__b, fact_121_local_Oinf_Ostrict__boundedE, fact_72_local_Oinf_Oabsorb__iff1, fact_11_local_Oorder_Otrans, fact_47_Collect__cong, fact_216_semilattice__set__def, fact_203_local_Osup_Oabel__semigroup__axioms, fact_86_local_Oinf__le1, fact_119_local_Osup__mono, fact_23_local_Oless__irrefl, fact_39_local_Osup_Ocommute, fact_105_local_Osup_OboundedI, fact_132_local_Osup_Ostrict__order__iff, fact_183_local_Oa__aux__def, fact_51_local_Odual__order_Ostrict__iff__order, fact_199_local_Osup_Osemigroup__axioms, fact_98_local_Ole__supI1, fact_26_local_Oord__eq__less__trans, fact_82_local_Oinf_Oorder__iff, fact_143_local_Oinf__idem, fact_200_local_Oinf_Osemigroup__axioms, fact_207_abel__semigroup_Oleft__commute, fact_234_semilattice__order_OcoboundedI1, fact_111_local_Osup_OorderE, fact_126_local_Oless__infI2, conj_1, fact_159_local_Ole__sup__iff, fact_179_local_OInf__fin_Osemilattice__order__set__axioms, fact_16_local_Oless__asym, fact_55_local_OleD, fact_177_local_Oe__b__c__a, fact_243_semilattice__order_Oaxioms_I1_J, fact_184_lattice_Ono__distrib_Ocong, fact_236_semilattice__order_Ostrict__boundedE, fact_89_local_Oinf__unique, fact_91_local_Ole__infE, fact_173_local_Oa__meet__e, fact_110_local_Osup_Omono, fact_53_local_Odual__order_Ostrict__trans1, fact_182_local_Ob__aux__def, fact_33_local_Oinf_Ocommute, fact_152_local_OGreatest__equality, fact_217_semilattice__set_Ointro, fact_187_lattice_Oincomp_Ocong, fact_237_semilattice__order_Ostrict__order__iff, fact_113_local_Osup_Oorder__iff, fact_219_semilattice__order__set__def, fact_68_local_Oorder_Ostrict__trans1, fact_151_local_OGreatestI2__order, fact_133_local_Odistrib__imp1, fact_122_local_Oinf_Ostrict__coboundedI1, fact_71_local_Oinf_Oabsorb2, fact_17_local_Oless__asym_H, fact_6_local_Oeq__refl, fact_208_abel__semigroup_Ocommute, fact_43_local_Osup__left__commute, fact_128_local_Oless__supI2, fact_181_local_Oc__aux__def, fact_99_local_Ole__supI2, fact_166_local_OLeastI2__order, fact_78_local_Oinf_OcoboundedI1, fact_14_local_Odual__order_Ostrict__implies__not__eq, fact_56_local_Ole__imp__less__or__eq, fact_36_local_Oinf__commute, conj_0, fact_4_local_Odual__order_Otrans, fact_116_local_Osup__ge1, fact_193_local_Ocomp__fun__idem__inf, fact_0_local_Oantisym, fact_185_lattice_ON5__lattice_Ocong, fact_9_local_Oorder_Oantisym, fact_49_local_Odual__order_Onot__eq__order__implies__strict, fact_74_local_Oinf_OboundedE, fact_67_local_Oorder_Ostrict__implies__order, fact_112_local_Osup_OorderI, fact_150_local_Osup__left__idem, fact_101_local_Osup_Oabsorb2, fact_235_semilattice__order_OcoboundedI2, fact_169_local_Ob__join__d, fact_240_semilattice_Oidem 51.53/15.22 % No. of inferences in proof: 622 51.53/15.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 14659 ms resp. 13796 ms w/o parsing 52.41/15.44 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p 52.41/15.44 thf(set_a_type, type, set_a: $tType). 52.41/15.44 thf(a_type, type, a: $tType). 52.41/15.44 thf(condit1627435690bove_a_decl, type, condit1627435690bove_a: ((a > (a > $o)) > (set_a > $o))). 52.41/15.44 thf(condit1001553558elow_a_decl, type, condit1001553558elow_a: ((a > (a > $o)) > (set_a > $o))). 52.41/15.44 thf(finite40241356em_a_a_decl, type, finite40241356em_a_a: ((a > (a > a)) > $o)). 52.41/15.44 thf(abel_semigroup_a_decl, type, abel_semigroup_a: ((a > (a > a)) > $o)). 52.41/15.44 thf(semigroup_a_decl, type, semigroup_a: ((a > (a > a)) > $o)). 52.41/15.44 thf(lattice_a_decl, type, lattice_a: ((a > (a > a)) > ((a > (a > $o)) > ((a > (a > $o)) > ((a > (a > a)) > $o))))). 52.41/15.44 thf(semilattice_a_decl, type, semilattice_a: ((a > (a > a)) > $o)). 52.41/15.44 thf(semilattice_order_a_decl, type, semilattice_order_a: ((a > (a > a)) > ((a > (a > $o)) > ((a > (a > $o)) > $o)))). 52.41/15.44 thf(lattic655834328_set_a_decl, type, lattic655834328_set_a: ((a > (a > a)) > ((a > (a > $o)) > ((a > (a > $o)) > $o)))). 52.41/15.44 thf(lattic1885654924_set_a_decl, type, lattic1885654924_set_a: ((a > (a > a)) > $o)). 52.41/15.44 thf(modula1376131916tice_a_decl, type, modula1376131916tice_a: ((a > (a > a)) > ((a > (a > $o)) > ((a > (a > a)) > (a > (a > (a > $o))))))). 52.41/15.44 thf(modula397570059tice_a_decl, type, modula397570059tice_a: ((a > (a > a)) > ((a > (a > $o)) > ((a > (a > a)) > (a > (a > (a > $o))))))). 52.41/15.44 thf(modula17988509_aux_a_decl, type, modula17988509_aux_a: ((a > (a > a)) > ((a > (a > a)) > (a > (a > (a > a)))))). 52.41/15.44 thf(modula1373251614_aux_a_decl, type, modula1373251614_aux_a: ((a > (a > a)) > ((a > (a > a)) > (a > (a > (a > a)))))). 52.41/15.44 thf(modula581031071_aux_a_decl, type, modula581031071_aux_a: ((a > (a > a)) > ((a > (a > a)) > (a > (a > (a > a)))))). 52.41/15.44 thf(modula1936294176_aux_a_decl, type, modula1936294176_aux_a: ((a > (a > a)) > ((a > (a > a)) > (a > (a > (a > a)))))). 52.41/15.44 thf(modula1144073633_aux_a_decl, type, modula1144073633_aux_a: ((a > (a > a)) > ((a > (a > a)) > (a > (a > (a > a)))))). 52.41/15.44 thf(modula1727524044comp_a_decl, type, modula1727524044comp_a: ((a > (a > $o)) > (a > (a > $o)))). 52.41/15.44 thf(modula1962211574trib_a_decl, type, modula1962211574trib_a: ((a > (a > a)) > ((a > (a > $o)) > ((a > (a > a)) > (a > (a > (a > $o))))))). 52.41/15.44 thf(least_a_decl, type, least_a: ((a > (a > $o)) > ((a > $o) > a))). 52.41/15.44 thf(max_a_decl, type, max_a: ((a > (a > $o)) > (a > (a > a)))). 52.41/15.44 thf(min_a_decl, type, min_a: ((a > (a > $o)) > (a > (a > a)))). 52.41/15.44 thf(greatest_a_decl, type, greatest_a: ((a > (a > $o)) > ((a > $o) > a))). 52.41/15.44 thf(ordering_a_decl, type, ordering_a: ((a > (a > $o)) > ((a > (a > $o)) > $o))). 52.41/15.44 thf(collect_a_decl, type, collect_a: ((a > $o) > set_a)). 52.41/15.44 thf(set_gr1491433118Than_a_decl, type, set_gr1491433118Than_a: ((a > (a > $o)) > (a > (a > set_a)))). 52.41/15.44 thf(member_a_decl, type, member_a: (a > (set_a > $o))). 52.41/15.44 thf(inf_decl, type, inf: (a > (a > a))). 52.41/15.44 thf(less_decl, type, less: (a > (a > $o))). 52.41/15.44 thf(less_eq_decl, type, less_eq: (a > (a > $o))). 52.41/15.44 thf(sup_decl, type, sup: (a > (a > a))). 52.41/15.44 thf(x_decl, type, x: a). 52.41/15.44 thf(y_decl, type, y: a). 52.41/15.44 thf(z_decl, type, z: a). 52.41/15.44 thf(sk1_decl, type, sk1: ((a > $o) > ((a > $o) > a))). 52.41/15.44 thf(sk2_decl, type, sk2: ((a > (a > a)) > a)). 52.41/15.44 thf(sk3_decl, type, sk3: ((a > (a > a)) > a)). 52.41/15.44 thf(sk4_decl, type, sk4: ((a > (a > a)) > a)). 52.41/15.44 thf(sk41_decl, type, sk41: a). 52.41/15.44 thf(sk42_decl, type, sk42: a). 52.41/15.44 thf(sk43_decl, type, sk43: a). 52.41/15.44 thf(sk44_decl, type, sk44: a). 52.41/15.44 thf(sk45_decl, type, sk45: a). 52.41/15.44 thf(sk46_decl, type, sk46: a). 52.41/15.44 thf(sk47_decl, type, sk47: a). 52.41/15.44 thf(sk48_decl, type, sk48: a). 52.41/15.44 thf(sk49_decl, type, sk49: a). 52.41/15.44 thf(sk50_decl, type, sk50: a). 52.41/15.44 thf(sk1_def, definition, sk1 = (^ [A:(a > $o),B:(a > $o)]: (@+ [C:a]: ~ ((B @ C) = (A @ C)))) ). 52.41/15.44 thf(sk2_def, definition, sk2 = (^ [A:(a > (a > a))]: (@+ [B:a]: ~ (! [C:a,D:a]: ((A @ (A @ B @ C) @ D) = (A @ B @ (A @ C @ D)))))) ). 52.41/15.44 thf(sk3_def, definition, sk3 = (^ [A:(a > (a > a))]: (@+ [B:a]: ~ (! [C:a]: ((A @ (A @ (sk2 @ A) @ B) @ C) = (A @ (sk2 @ A) @ (A @ B @ C)))))) ). 52.41/15.44 thf(sk4_def, definition, sk4 = (^ [A:(a > (a > a))]: (@+ [B:a]: ~ ((A @ (A @ (sk2 @ A) @ (sk3 @ A)) @ B) = (A @ (sk2 @ A) @ (A @ (sk3 @ A) @ B))))) ). 52.41/15.44 thf(245,axiom,((! [A:a,B:a]: ((inf @ A @ B) = (inf @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_local_Oinf__commute)). 52.41/15.44 thf(1036,plain,((! [A:a,B:a]: ((inf @ A @ B) = (inf @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])). 52.41/15.44 thf(241,axiom,((! [A:a,B:a,C:a,D:a]: ((less_eq @ A @ B) => ((less_eq @ C @ D) => (less_eq @ (inf @ A @ C) @ (inf @ B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_local_Oinf__mono)). 52.41/15.44 thf(1024,plain,((! [A:a,B:a,C:a,D:a]: ((less_eq @ A @ B) => ((less_eq @ C @ D) => (less_eq @ (inf @ A @ C) @ (inf @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 52.41/15.44 thf(34,axiom,((! [A:a,B:a]: ((less @ A @ B) => (B != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_local_Oless__imp__not__eq2)). 52.41/15.44 thf(347,plain,((! [A:a,B:a]: ((less @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 52.41/15.44 thf(220,axiom,((! [A:a]: (less_eq @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_local_Oorder_Orefl)). 52.41/15.44 thf(962,plain,((! [A:a]: (less_eq @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])). 52.41/15.44 thf(214,axiom,((! [A:a,B:a,C:a]: ((modula1962211574trib_a @ inf @ less @ sup @ A @ B @ C) = (less @ (sup @ (inf @ A @ B) @ (inf @ C @ A)) @ (inf @ A @ (sup @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_local_Ono__distrib__def)). 52.41/15.44 thf(941,plain,((! [A:a,B:a,C:a]: ((modula1962211574trib_a @ (inf) @ (less) @ (sup) @ A @ B @ C) = (less @ (sup @ (inf @ A @ B) @ (inf @ C @ A)) @ (inf @ A @ (sup @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 52.41/15.44 thf(123,axiom,((! [A:a,B:a,C:a]: (((less @ C @ B) <= (less @ C @ A)) <= (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_local_Odual__order_Ostrict__trans1)). 52.41/15.44 thf(666,plain,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => ((less @ C @ A) => (less @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 52.41/15.44 thf(203,axiom,((! [A:a,B:a]: ((less_eq @ A @ B) = ((A = B) | (less @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_local_Oorder_Oorder__iff__strict)). 52.41/15.44 thf(909,plain,((! [A:a,B:a]: ((less_eq @ A @ B) = ((A = B) | (less @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 52.41/15.44 thf(30,axiom,((! [A:set_a]: ((collect_a @ (^ [B:a]: (member_a @ B @ A))) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__mem__eq)). 52.41/15.44 thf(333,plain,((! [A:set_a]: ((collect_a @ (^ [B:a]: (member_a @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 52.41/15.44 thf(111,axiom,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => ((less_eq @ (sup @ A @ C) @ B) <= (less_eq @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_local_Osup__least)). 52.41/15.44 thf(628,plain,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => ((less_eq @ C @ B) => (less_eq @ (sup @ A @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 52.41/15.44 thf(225,axiom,((! [A:a,B:a,C:a]: (less_eq @ (sup @ (inf @ A @ B) @ (inf @ A @ C)) @ (inf @ A @ (sup @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_local_Odistrib__inf__le)). 52.41/15.44 thf(977,plain,((! [A:a,B:a,C:a]: (less_eq @ (sup @ (inf @ A @ B) @ (inf @ A @ C)) @ (inf @ A @ (sup @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])). 52.41/15.44 thf(151,axiom,((! [A:a,B:a]: (less_eq @ A @ (sup @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_local_Osup_Ocobounded1)). 52.41/15.44 thf(762,plain,((! [A:a,B:a]: (less_eq @ A @ (sup @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 52.41/15.44 thf(78,axiom,((less_eq @ x @ y)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1)). 52.41/15.44 thf(498,plain,((less_eq @ x @ y)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 52.41/15.44 thf(1,conjecture,((less_eq @ x @ (sup @ (inf @ y @ (sup @ x @ z)) @ z))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4)). 52.41/15.44 thf(2,negated_conjecture,((~ (less_eq @ x @ (sup @ (inf @ y @ (sup @ x @ z)) @ z)))),inference(neg_conjecture,[status(cth)],[1])). 52.41/15.44 thf(256,plain,((~ (less_eq @ x @ (sup @ (inf @ y @ (sup @ x @ z)) @ z)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 52.41/15.44 thf(1070,plain,(~ (($true)) | ((less_eq @ x @ (sup @ (inf @ y @ (sup @ x @ z)) @ z)) != (less_eq @ x @ y))),inference(paramod_ordered,[status(thm)],[498,256])). 52.41/15.44 thf(1071,plain,(((less_eq @ x @ (sup @ (inf @ y @ (sup @ x @ z)) @ z)) != (less_eq @ x @ y))),inference(simp,[status(thm)],[1070])). 52.41/15.44 thf(1072,plain,((x != x) | ((sup @ (inf @ y @ (sup @ x @ z)) @ z) != y)),inference(simp,[status(thm)],[1071])). 52.41/15.44 thf(1073,plain,(((sup @ (inf @ y @ (sup @ x @ z)) @ z) != y)),inference(simp,[status(thm)],[1072])). 52.41/15.44 thf(189,axiom,((! [A:a,B:a]: ((less @ A @ B) = ((less_eq @ A @ B) & (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_local_Oless__le)). 52.41/15.44 thf(873,plain,((! [A:a,B:a]: ((less @ A @ B) = ((less_eq @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 52.41/15.44 thf(45,axiom,((! [A:(a > (a > a)),B:a,C:a]: (((A @ B @ (A @ B @ C)) = (A @ B @ C)) <= (semilattice_a @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_semilattice_Oleft__idem)). 52.41/15.44 thf(379,plain,((! [A:(a > (a > a)),B:a,C:a]: ((semilattice_a @ (A)) => ((A @ B @ (A @ B @ C)) = (A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 52.41/15.44 thf(83,axiom,((! [A:(a > $o),B:a]: ((? [C:a]: ((A @ C) & ! [D:a]: ((A @ D) => (less_eq @ C @ D)) & ! [D:a]: (((A @ D) & ! [E:a]: ((less_eq @ D @ E) <= (A @ E))) => (D = C)))) => ((less_eq @ (least_a @ less_eq @ A) @ B) <= (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_local_OLeast1__le)). 52.41/15.44 thf(511,plain,((! [A:(a > $o),B:a]: ((? [C:a]: ((A @ C) & ! [D:a]: ((A @ D) => (less_eq @ C @ D)) & ! [D:a]: (((A @ D) & ! [E:a]: ((A @ E) => (less_eq @ D @ E))) => (D = C)))) => ((A @ B) => (less_eq @ (least_a @ (less_eq) @ (A)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 52.41/15.44 thf(7,axiom,((! [A:(a > (a > a))]: ((semilattice_a @ A) => (abel_semigroup_a @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_semilattice_Oaxioms_I1_J)). 52.41/15.44 thf(268,plain,((! [A:(a > (a > a))]: ((semilattice_a @ (A)) => (abel_semigroup_a @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 52.41/15.44 thf(269,plain,(! [A:(a > (a > a))] : ((~ (semilattice_a @ (A))) | (abel_semigroup_a @ (A)))),inference(cnf,[status(esa)],[268])). 52.41/15.44 thf(103,axiom,((! [A:(a > $o),B:a]: ((A @ B) => (((greatest_a @ less_eq @ A) = B) <= (! [C:a]: ((A @ C) => (less_eq @ C @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_local_OGreatest__equality)). 52.41/15.44 thf(597,plain,((! [A:(a > $o),B:a]: ((A @ B) => ((! [C:a]: ((A @ C) => (less_eq @ C @ B))) => ((greatest_a @ (less_eq) @ (A)) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 52.41/15.44 thf(193,axiom,((semilattice_order_a @ inf @ less_eq @ less)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_local_Oinf_Osemilattice__order__axioms)). 52.41/15.44 thf(884,plain,((semilattice_order_a @ (inf) @ (less_eq) @ (less))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 52.41/15.44 thf(14,axiom,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a]: (((C @ D @ E) = ((D != E) & (D = (A @ D @ E)))) <= (semilattice_order_a @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_semilattice__order_Ostrict__order__iff)). 52.41/15.44 thf(286,plain,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a]: ((semilattice_order_a @ (A) @ (B) @ (C)) => ((C @ D @ E) = (~ (D = E) & (D = (A @ D @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 52.41/15.44 thf(287,plain,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o))]: ((semilattice_order_a @ (A) @ (B) @ (C)) => (! [D:a,E:a]: ((C @ D @ E) = (~ (D = E) & (D = (A @ D @ E)))))))),inference(miniscope,[status(thm)],[286])). 52.41/15.44 thf(288,plain,(! [E:a,D:a,C:(a > (a > $o)),B:(a > (a > $o)),A:(a > (a > a))] : ((~ (semilattice_order_a @ (A) @ (B) @ (C))) | ((C @ D @ E) = (~ (D = E) & (D = (A @ D @ E)))))),inference(cnf,[status(esa)],[287])). 52.41/15.44 thf(289,plain,(! [E:a,D:a,C:(a > (a > $o)),B:(a > (a > $o)),A:(a > (a > a))] : (((C @ D @ E) = (~ (D = E) & (D = (A @ D @ E)))) | (~ (semilattice_order_a @ (A) @ (B) @ (C))))),inference(lifteq,[status(thm)],[288])). 52.41/15.44 thf(2188,plain,(! [E:a,D:a,C:(a > (a > $o)),B:(a > (a > $o)),A:(a > (a > a))] : ((~ (semilattice_order_a @ (A) @ (B) @ (C))) | (~ (D = E) & (D = (A @ D @ E))) | ((C @ D @ E) != (less_eq @ x @ y)))),inference(paramod_ordered,[status(thm)],[289,498])). 52.41/15.44 thf(2214,plain,(! [C:a,B:(a > (a > $o)),A:(a > (a > a))] : ((~ (semilattice_order_a @ (A) @ (B) @ (^ [D:a,E:a]: (less_eq @ E @ y)))) | (~ (C = x) & (C = (A @ C @ x))))),inference(pre_uni,[status(thm)],[2188:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(^ [F:a,G:a]: (less_eq @ G @ y))),bind(D, $thf(D)),bind(E, $thf(x))]])). 52.41/15.44 thf(2321,plain,(! [C:a,B:(a > (a > $o)),A:(a > (a > a))] : (((~ (semilattice_order_a @ (A) @ (B) @ (^ [D:a,E:a]: (less_eq @ E @ y))) | ~ (C = x)) & (~ (semilattice_order_a @ (A) @ (B) @ (^ [D:a,E:a]: (less_eq @ E @ y))) | (C = (A @ C @ x)))))),inference(cnf,[status(esa)],[2214])). 52.41/15.44 thf(2322,plain,(! [C:a,B:(a > (a > $o)),A:(a > (a > a))] : ((~ (semilattice_order_a @ (A) @ (B) @ (^ [D:a,E:a]: (less_eq @ E @ y)))) | (~ (C = x)))),inference(cnfConj,[status(thm)],[2321])). 52.41/15.44 thf(2324,plain,(! [C:a,B:(a > (a > $o)),A:(a > (a > a))] : ((C != x) | (~ (semilattice_order_a @ (A) @ (B) @ (^ [D:a,E:a]: (less_eq @ E @ y)))))),inference(lifteq,[status(thm)],[2322])). 52.41/15.44 thf(2325,plain,(! [B:(a > (a > $o)),A:(a > (a > a))] : ((~ (semilattice_order_a @ (A) @ (B) @ (^ [C:a,D:a]: (less_eq @ D @ y)))))),inference(simp,[status(thm)],[2324])). 52.41/15.44 thf(3044,plain,(! [B:(a > (a > $o)),A:(a > (a > a))] : (~ (($true)) | ((semilattice_order_a @ (inf) @ (less_eq) @ (less)) != (semilattice_order_a @ (A) @ (B) @ (^ [C:a,D:a]: (less_eq @ D @ y)))))),inference(paramod_ordered,[status(thm)],[884,2325])). 52.41/15.44 thf(3045,plain,(! [B:(a > (a > $o)),A:(a > (a > a))] : (((semilattice_order_a @ (inf) @ (less_eq) @ (less)) != (semilattice_order_a @ (A) @ (B) @ (^ [C:a,D:a]: (less_eq @ D @ y)))))),inference(simp,[status(thm)],[3044])). 52.41/15.44 thf(3059,plain,(! [B:(a > (a > $o)),A:(a > (a > a))] : (((inf) != (A)) | ((less_eq) != (B)) | ((less) != (^ [C:a,D:a]: (less_eq @ D @ y))))),inference(simp,[status(thm)],[3045])). 52.41/15.44 thf(3079,plain,(((less) != (^ [A:a,B:a]: (less_eq @ B @ y)))),inference(simp,[status(thm)],[3059])). 52.41/15.44 thf(3382,plain,(((less_eq @ sk48 @ y) != (less @ sk47 @ sk48))),inference(func_ext,[status(esa)],[3079])). 52.41/15.44 thf(85,axiom,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => (less_eq @ (inf @ A @ C) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_local_Ole__infI1)). 52.41/15.44 thf(533,plain,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => (less_eq @ (inf @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 52.41/15.44 thf(164,axiom,((semigroup_a @ sup)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_local_Osup_Osemigroup__axioms)). 52.41/15.44 thf(797,plain,((semigroup_a @ (sup))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 52.41/15.44 thf(171,axiom,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => ((less @ A @ C) <= (less @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_local_Oorder_Ostrict__trans1)). 52.41/15.44 thf(814,plain,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => ((less @ B @ C) => (less @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 52.41/15.44 thf(176,axiom,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => (less_eq @ (inf @ C @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_local_Ole__infI2)). 52.41/15.44 thf(829,plain,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => (less_eq @ (inf @ C @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 52.41/15.44 thf(233,axiom,((! [A:a,B:a]: (((less @ A @ B) | (A = B)) <= (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_local_Ole__imp__less__or__eq)). 52.41/15.44 thf(1001,plain,((! [A:a,B:a]: ((less_eq @ A @ B) => ((less @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 52.41/15.44 thf(194,axiom,((! [A:a,B:a]: (((less_eq @ B @ A) => (A = B)) <= (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_local_Oorder_Oantisym)). 52.41/15.44 thf(885,plain,((! [A:a,B:a]: ((less_eq @ A @ B) => ((less_eq @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 52.41/15.44 thf(19,axiom,((! [A:(a > (a > a))]: ((semigroup_a @ A) <= (abel_semigroup_a @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_abel__semigroup_Oaxioms_I1_J)). 52.41/15.44 thf(301,plain,((! [A:(a > (a > a))]: ((abel_semigroup_a @ (A)) => (semigroup_a @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 52.41/15.44 thf(91,axiom,((! [A:a,B:a]: ((less_eq @ A @ B) = ((sup @ B @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_local_Osup_Oabsorb__iff1)). 52.41/15.44 thf(565,plain,((! [A:a,B:a]: ((less_eq @ A @ B) = ((sup @ B @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 52.41/15.44 thf(118,axiom,((! [A:a,B:a,C:a]: ((inf @ A @ (modula1144073633_aux_a @ inf @ sup @ B @ A @ C)) = (inf @ A @ (sup @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_local_Ob__meet__e)). 52.41/15.44 thf(651,plain,((! [A:a,B:a,C:a]: ((inf @ A @ (modula1144073633_aux_a @ (inf) @ (sup) @ B @ A @ C)) = (inf @ A @ (sup @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 52.41/15.44 thf(3,axiom,((! [A:(a > $o),B:(a > $o)]: (((collect_a @ A) = (collect_a @ B)) <= (! [C:a]: ((A @ C) = (B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Collect__cong)). 52.41/15.44 thf(257,plain,((! [A:(a > $o),B:(a > $o)]: ((! [C:a]: ((A @ C) = (B @ C))) => ((collect_a @ (A)) = (collect_a @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 52.41/15.44 thf(99,axiom,((lattic655834328_set_a @ inf @ less_eq @ less)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_local_OInf__fin_Osemilattice__order__set__axioms)). 52.41/15.44 thf(587,plain,((lattic655834328_set_a @ (inf) @ (less_eq) @ (less))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 52.41/15.44 thf(206,axiom,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => ((less_eq @ (sup @ A @ C) @ B) <= (less_eq @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_local_Ole__supI)). 52.41/15.44 thf(917,plain,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => ((less_eq @ C @ B) => (less_eq @ (sup @ A @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 52.41/15.44 thf(172,axiom,((! [A:a,B:a,C:a]: ((sup @ A @ (modula1936294176_aux_a @ inf @ sup @ A @ B @ C)) = (sup @ A @ (inf @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_local_Oa__join__d)). 52.41/15.44 thf(817,plain,((! [A:a,B:a,C:a]: ((sup @ A @ (modula1936294176_aux_a @ (inf) @ (sup) @ A @ B @ C)) = (sup @ A @ (inf @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 52.41/15.44 thf(115,axiom,((! [A:(a > (a > a)),B:a,C:a]: (((! [D:a,E:a]: (less_eq @ (A @ D @ E) @ E)) => (((inf @ B @ C) = (A @ B @ C)) <= (! [D:a,E:a,F:a]: ((less_eq @ D @ E) => ((less_eq @ D @ (A @ E @ F)) <= (less_eq @ D @ F)))))) <= (! [D:a,E:a]: (less_eq @ (A @ D @ E) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_local_Oinf__unique)). 52.41/15.44 thf(638,plain,((! [A:(a > (a > a)),B:a,C:a]: ((! [D:a,E:a]: (less_eq @ (A @ D @ E) @ D)) => ((! [D:a,E:a]: (less_eq @ (A @ D @ E) @ E)) => ((! [D:a,E:a,F:a]: ((less_eq @ D @ E) => ((less_eq @ D @ F) => (less_eq @ D @ (A @ E @ F))))) => ((inf @ B @ C) = (A @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 52.41/15.44 thf(2215,plain,(! [C:a,B:(a > (a > $o)),A:(a > (a > a))] : ((~ (semilattice_order_a @ (A) @ (B) @ (^ [D:a,E:a]: (less_eq @ x @ D)))) | (~ (y = C) & (y = (A @ y @ C))))),inference(pre_uni,[status(thm)],[2188:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(^ [F:a,G:a]: (less_eq @ x @ F))),bind(D, $thf(y)),bind(E, $thf(E))]])). 52.41/15.44 thf(2328,plain,(! [C:a,B:(a > (a > $o)),A:(a > (a > a))] : (((~ (semilattice_order_a @ (A) @ (B) @ (^ [D:a,E:a]: (less_eq @ x @ D))) | ~ (y = C)) & (~ (semilattice_order_a @ (A) @ (B) @ (^ [D:a,E:a]: (less_eq @ x @ D))) | (y = (A @ y @ C)))))),inference(cnf,[status(esa)],[2215])). 52.41/15.44 thf(2329,plain,(! [C:a,B:(a > (a > $o)),A:(a > (a > a))] : ((~ (semilattice_order_a @ (A) @ (B) @ (^ [D:a,E:a]: (less_eq @ x @ D)))) | (~ (y = C)))),inference(cnfConj,[status(thm)],[2328])). 52.41/15.44 thf(2331,plain,(! [C:a,B:(a > (a > $o)),A:(a > (a > a))] : ((y != C) | (~ (semilattice_order_a @ (A) @ (B) @ (^ [D:a,E:a]: (less_eq @ x @ D)))))),inference(lifteq,[status(thm)],[2329])). 52.41/15.44 thf(2332,plain,(! [B:(a > (a > $o)),A:(a > (a > a))] : ((~ (semilattice_order_a @ (A) @ (B) @ (^ [C:a,D:a]: (less_eq @ x @ C)))))),inference(simp,[status(thm)],[2331])). 52.41/15.44 thf(3443,plain,(! [B:(a > (a > $o)),A:(a > (a > a))] : (~ (($true)) | ((semilattice_order_a @ (inf) @ (less_eq) @ (less)) != (semilattice_order_a @ (A) @ (B) @ (^ [C:a,D:a]: (less_eq @ x @ C)))))),inference(paramod_ordered,[status(thm)],[884,2332])). 52.41/15.44 thf(3444,plain,(! [B:(a > (a > $o)),A:(a > (a > a))] : (((semilattice_order_a @ (inf) @ (less_eq) @ (less)) != (semilattice_order_a @ (A) @ (B) @ (^ [C:a,D:a]: (less_eq @ x @ C)))))),inference(simp,[status(thm)],[3443])). 52.41/15.44 thf(3456,plain,(! [B:(a > (a > $o)),A:(a > (a > a))] : (((inf) != (A)) | ((less_eq) != (B)) | ((less) != (^ [C:a,D:a]: (less_eq @ x @ C))))),inference(simp,[status(thm)],[3444])). 52.41/15.44 thf(3463,plain,(((less) != (^ [A:a,B:a]: (less_eq @ x @ A)))),inference(simp,[status(thm)],[3456])). 52.41/15.44 thf(60,axiom,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a,F:a]: (((B @ D @ (A @ E @ F)) = ((B @ D @ E) & (B @ D @ F))) <= (semilattice_order_a @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_semilattice__order_Obounded__iff)). 52.41/15.44 thf(421,plain,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a,F:a]: ((semilattice_order_a @ (A) @ (B) @ (C)) => ((B @ D @ (A @ E @ F)) = ((B @ D @ E) & (B @ D @ F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 52.41/15.44 thf(104,axiom,((! [A:a,B:a,C:a]: ((inf @ A @ (inf @ B @ C)) = (inf @ B @ (inf @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_local_Oinf_Oleft__commute)). 52.41/15.44 thf(606,plain,((! [A:a,B:a,C:a]: ((inf @ A @ (inf @ B @ C)) = (inf @ B @ (inf @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 52.41/15.44 thf(25,axiom,((! [A:a,B:a]: ((~ (less @ B @ A)) <= (less @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_local_Oorder_Oasym)). 52.41/15.44 thf(316,plain,((! [A:a,B:a]: ((less @ A @ B) => (~ (less @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 52.41/15.44 thf(237,axiom,((! [A:a,B:a]: (less_eq @ A @ (sup @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_local_Osup_Ocobounded2)). 52.41/15.44 thf(1013,plain,((! [A:a,B:a]: (less_eq @ A @ (sup @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 52.41/15.44 thf(13,axiom,((lattic1885654924_set_a = semilattice_a)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_semilattice__set__def)). 52.41/15.44 thf(284,plain,(((lattic1885654924_set_a) = (semilattice_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 52.41/15.44 thf(154,axiom,((! [A:a,B:a]: ((inf @ (inf @ A @ B) @ B) = (inf @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_local_Oinf__right__idem)). 52.41/15.44 thf(770,plain,((! [A:a,B:a]: ((inf @ (inf @ A @ B) @ B) = (inf @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 52.41/15.44 thf(73,axiom,((! [A:set_a,B:a]: ((! [C:a]: ((less_eq @ C @ B) <= (member_a @ C @ A))) => (condit1627435690bove_a @ less_eq @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_local_Obdd__aboveI)). 52.41/15.44 thf(475,plain,((! [A:set_a,B:a]: ((! [C:a]: ((member_a @ C @ A) => (less_eq @ C @ B))) => (condit1627435690bove_a @ (less_eq) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 52.41/15.44 thf(76,axiom,((! [A:a,B:a]: ((less_eq @ A @ B) = ((sup @ A @ B) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_local_Ole__iff__sup)). 52.41/15.44 thf(492,plain,((! [A:a,B:a]: ((less_eq @ A @ B) = ((sup @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 52.41/15.44 thf(101,axiom,((! [A:a,B:a,C:a]: ((less @ A @ (inf @ B @ C)) => (~ ((less @ A @ B) => (~ (less @ A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_local_Oinf_Ostrict__boundedE)). 52.41/15.44 thf(591,plain,((! [A:a,B:a,C:a]: ((less @ A @ (inf @ B @ C)) => (~ ((less @ A @ B) => (~ (less @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 52.41/15.44 thf(44,axiom,((! [A:a,B:(a > $o)]: ((member_a @ A @ (collect_a @ B)) = (B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mem__Collect__eq)). 52.41/15.44 thf(376,plain,((! [A:a,B:(a > $o)]: ((member_a @ A @ (collect_a @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 52.41/15.44 thf(50,axiom,((lattic655834328_set_a = (^ [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o))]: ((lattic1885654924_set_a @ A) & (semilattice_order_a @ A @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_semilattice__order__set__def)). 52.41/15.44 thf(393,plain,(((lattic655834328_set_a) = (^ [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o))]: ((lattic1885654924_set_a @ A) & (semilattice_order_a @ A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 52.41/15.44 thf(394,plain,(((lattic655834328_set_a) = (^ [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o))]: ((lattic1885654924_set_a @ A) & (semilattice_order_a @ A @ B @ C))))),inference(lifteq,[status(thm)],[393])). 52.41/15.44 thf(285,plain,(((lattic1885654924_set_a) = (semilattice_a))),inference(lifteq,[status(thm)],[284])). 52.41/15.44 thf(1066,plain,(! [A:(a > (a > a))] : (((lattic1885654924_set_a @ (A)) = (semilattice_a @ (A))))),inference(func_ext,[status(esa)],[285])). 52.41/15.44 thf(1136,plain,(((lattic655834328_set_a) = (^ [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o))]: ((semilattice_a @ A) & (semilattice_order_a @ A @ B @ C))))),inference(rewrite,[status(thm)],[394,1066])). 52.41/15.44 thf(251,axiom,((! [A:a,B:a]: ((A = (inf @ A @ B)) <= (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_local_Oinf_OorderE)). 52.41/15.44 thf(1051,plain,((! [A:a,B:a]: ((less_eq @ A @ B) => (A = (inf @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])). 52.41/15.44 thf(74,axiom,((! [A:a,B:a,C:a]: ((inf @ (inf @ A @ B) @ C) = (inf @ A @ (inf @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_local_Oinf__assoc)). 52.41/15.44 thf(480,plain,((! [A:a,B:a,C:a]: ((inf @ (inf @ A @ B) @ C) = (inf @ A @ (inf @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 52.41/15.44 thf(239,axiom,((! [A:a]: ((sup @ A @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_local_Osup__idem)). 52.41/15.44 thf(1018,plain,((! [A:a]: ((sup @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 52.41/15.44 thf(1019,plain,(! [A:a] : (((sup @ A @ A) = A))),inference(cnf,[status(esa)],[1018])). 52.41/15.44 thf(1020,plain,(! [A:a] : (((sup @ A @ A) = A))),inference(lifteq,[status(thm)],[1019])). 52.41/15.44 thf(94,axiom,((semilattice_a @ inf)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_local_Oinf_Osemilattice__axioms)). 52.41/15.44 thf(574,plain,((semilattice_a @ (inf))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 52.41/15.44 thf(52,axiom,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a]: ((semilattice_order_a @ A @ B @ C) => (B @ (A @ D @ E) @ E)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_semilattice__order_Ocobounded2)). 52.41/15.44 thf(397,plain,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a]: ((semilattice_order_a @ (A) @ (B) @ (C)) => (B @ (A @ D @ E) @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 52.41/15.44 thf(113,axiom,((finite40241356em_a_a @ inf)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_local_Ocomp__fun__idem__inf)). 52.41/15.44 thf(634,plain,((finite40241356em_a_a @ (inf))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 52.41/15.44 thf(147,axiom,((! [A:a,B:a,C:a]: (((less @ B @ C) => (less @ A @ C)) <= (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_local_Ole__less__trans)). 52.41/15.44 thf(734,plain,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => ((less @ B @ C) => (less @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 52.41/15.44 thf(15,axiom,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a,F:a]: ((semilattice_order_a @ A @ B @ C) => ((C @ D @ (A @ E @ F)) => (~ ((~ (C @ D @ F)) <= (C @ D @ E))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_semilattice__order_Ostrict__boundedE)). 52.41/15.44 thf(290,plain,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a,F:a]: ((semilattice_order_a @ (A) @ (B) @ (C)) => ((C @ D @ (A @ E @ F)) => (~ ((C @ D @ E) => (~ (C @ D @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 52.41/15.44 thf(291,plain,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o))]: ((semilattice_order_a @ (A) @ (B) @ (C)) => (! [D:a,E:a,F:a]: ((C @ D @ (A @ E @ F)) => (~ ((C @ D @ E) => (~ (C @ D @ F))))))))),inference(miniscope,[status(thm)],[290])). 52.41/15.44 thf(292,plain,(! [F:a,E:a,D:a,C:(a > (a > $o)),B:(a > (a > $o)),A:(a > (a > a))] : (((~ (semilattice_order_a @ (A) @ (B) @ (C)) | ~ (C @ D @ (A @ E @ F)) | (C @ D @ E)) & (~ (semilattice_order_a @ (A) @ (B) @ (C)) | ~ (C @ D @ (A @ E @ F)) | (C @ D @ F))))),inference(cnf,[status(esa)],[291])). 52.41/15.44 thf(293,plain,(! [F:a,E:a,D:a,C:(a > (a > $o)),B:(a > (a > $o)),A:(a > (a > a))] : ((~ (semilattice_order_a @ (A) @ (B) @ (C))) | (~ (C @ D @ (A @ E @ F))) | (C @ D @ E))),inference(cnfConj,[status(thm)],[292])). 52.41/15.44 thf(121,axiom,((! [A:a,B:a,C:a]: ((sup @ (sup @ A @ B) @ C) = (sup @ A @ (sup @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_local_Osup_Oassoc)). 52.41/15.44 thf(660,plain,((! [A:a,B:a,C:a]: ((sup @ (sup @ A @ B) @ C) = (sup @ A @ (sup @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 52.41/15.44 thf(232,axiom,((! [A:a,B:a,C:a]: ((less_eq @ (inf @ C @ A) @ B) <= (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_local_Oinf_OcoboundedI2)). 52.41/15.44 thf(998,plain,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => (less_eq @ (inf @ C @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 52.41/15.44 thf(56,axiom,((! [A:a,B:a,C:a]: ((less @ A @ B) => ((less @ C @ A) => (less @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_local_Odual__order_Ostrict__trans)). 52.41/15.44 thf(411,plain,((! [A:a,B:a,C:a]: ((less @ A @ B) => ((less @ C @ A) => (less @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 52.41/15.44 thf(6,axiom,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o))]: ((lattic1885654924_set_a @ A) <= (lattic655834328_set_a @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_semilattice__order__set_Oaxioms_I2_J)). 52.41/15.44 thf(265,plain,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o))]: ((lattic655834328_set_a @ (A) @ (B) @ (C)) => (lattic1885654924_set_a @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 52.41/15.44 thf(191,axiom,((! [A:a,B:a,C:a]: ((modula1376131916tice_a @ inf @ less @ sup @ A @ B @ C) => (modula1727524044comp_a @ less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_local_OM5__lattice__incomp)). 52.41/15.44 thf(877,plain,((! [A:a,B:a,C:a]: ((modula1376131916tice_a @ (inf) @ (less) @ (sup) @ A @ B @ C) => (modula1727524044comp_a @ (less_eq) @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 52.41/15.44 thf(131,axiom,((ordering_a @ less_eq @ less)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_local_Oorder_Oordering__axioms)). 52.41/15.44 thf(692,plain,((ordering_a @ (less_eq) @ (less))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 52.41/15.44 thf(22,axiom,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a]: ((semilattice_order_a @ A @ B @ C) => ((D = (A @ D @ E)) => (B @ D @ E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_semilattice__order_OorderI)). 52.41/15.44 thf(307,plain,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a]: ((semilattice_order_a @ (A) @ (B) @ (C)) => ((D = (A @ D @ E)) => (B @ D @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 52.41/15.44 thf(70,axiom,((! [A:a,B:a]: ((less @ A @ B) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_local_Oless__imp__neq)). 52.41/15.44 thf(452,plain,((! [A:a,B:a]: ((less @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 52.41/15.44 thf(207,axiom,((! [A:a,B:a,C:a]: ((inf @ A @ (modula1144073633_aux_a @ inf @ sup @ B @ C @ A)) = (inf @ A @ (sup @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_local_Oc__meet__e)). 52.41/15.44 thf(920,plain,((! [A:a,B:a,C:a]: ((inf @ A @ (modula1144073633_aux_a @ (inf) @ (sup) @ B @ C @ A)) = (inf @ A @ (sup @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 52.41/15.44 thf(65,axiom,((! [A:a,B:a]: ((~ (less @ B @ A)) <= (less @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_local_Oless__asym)). 52.41/15.44 thf(439,plain,((! [A:a,B:a]: ((less @ A @ B) => (~ (less @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 52.41/15.44 thf(128,axiom,((! [A:a,B:a,C:a]: ((modula1144073633_aux_a @ inf @ sup @ A @ B @ C) = (modula1144073633_aux_a @ inf @ sup @ C @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_local_Oe__b__c__a)). 52.41/15.44 thf(678,plain,((! [A:a,B:a,C:a]: ((modula1144073633_aux_a @ (inf) @ (sup) @ A @ B @ C) = (modula1144073633_aux_a @ (inf) @ (sup) @ C @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 52.41/15.44 thf(8,axiom,((! [A:a,B:a,C:a]: (((less @ A @ C) <= (B = C)) <= (less @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_local_Oord__less__eq__trans)). 52.41/15.44 thf(270,plain,((! [A:a,B:a,C:a]: ((less @ A @ B) => ((B = C) => (less @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 52.41/15.44 thf(209,axiom,(((sup @ x @ (inf @ y @ z)) != (inf @ y @ (sup @ x @ z)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2)). 52.41/15.44 thf(925,plain,((~ ((sup @ x @ (inf @ y @ z)) = (inf @ y @ (sup @ x @ z))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 52.41/15.44 thf(40,axiom,((! [A:a,B:a,C:a]: (((less @ B @ C) => (less @ A @ C)) <= (less @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_local_Oorder_Ostrict__trans)). 52.41/15.44 thf(366,plain,((! [A:a,B:a,C:a]: ((less @ A @ B) => ((less @ B @ C) => (less @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 52.41/15.44 thf(140,axiom,((! [A:a,B:a]: ((~ (less @ A @ B)) => ((less_eq @ A @ B) = (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_local_Oantisym__conv1)). 52.41/15.44 thf(714,plain,((! [A:a,B:a]: ((~ (less @ A @ B)) => ((less_eq @ A @ B) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 52.41/15.44 thf(9,axiom,((! [A:(a > (a > a)),B:a,C:a,D:a]: ((abel_semigroup_a @ A) => ((A @ B @ (A @ C @ D)) = (A @ C @ (A @ B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_abel__semigroup_Oleft__commute)). 52.41/15.44 thf(275,plain,((! [A:(a > (a > a)),B:a,C:a,D:a]: ((abel_semigroup_a @ (A)) => ((A @ B @ (A @ C @ D)) = (A @ C @ (A @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 52.41/15.44 thf(276,plain,((! [A:(a > (a > a))]: ((abel_semigroup_a @ (A)) => (! [B:a,C:a,D:a]: ((A @ B @ (A @ C @ D)) = (A @ C @ (A @ B @ D))))))),inference(miniscope,[status(thm)],[275])). 52.41/15.44 thf(277,plain,(! [D:a,C:a,B:a,A:(a > (a > a))] : ((~ (abel_semigroup_a @ (A))) | ((A @ B @ (A @ C @ D)) = (A @ C @ (A @ B @ D))))),inference(cnf,[status(esa)],[276])). 52.41/15.44 thf(278,plain,(! [D:a,C:a,B:a,A:(a > (a > a))] : (((A @ B @ (A @ C @ D)) = (A @ C @ (A @ B @ D))) | (~ (abel_semigroup_a @ (A))))),inference(lifteq,[status(thm)],[277])). 52.41/15.44 thf(963,plain,(! [A:a] : ((less_eq @ A @ A))),inference(cnf,[status(esa)],[962])). 52.41/15.44 thf(1108,plain,(! [A:a] : (~ (($true)) | ((less_eq @ A @ A) != (less_eq @ x @ (sup @ (inf @ y @ (sup @ x @ z)) @ z))))),inference(paramod_ordered,[status(thm)],[963,256])). 52.41/15.44 thf(1109,plain,(! [A:a] : (((less_eq @ A @ A) != (less_eq @ x @ (sup @ (inf @ y @ (sup @ x @ z)) @ z))))),inference(simp,[status(thm)],[1108])). 52.41/15.44 thf(1110,plain,(! [A:a] : ((A != x) | (A != (sup @ (inf @ y @ (sup @ x @ z)) @ z)))),inference(simp,[status(thm)],[1109])). 52.41/15.44 thf(1111,plain,(((sup @ (inf @ y @ (sup @ x @ z)) @ z) != x)),inference(simp,[status(thm)],[1110])). 52.41/15.44 thf(1172,plain,(! [D:a,C:a,B:a,A:(a > (a > a))] : ((~ (abel_semigroup_a @ (A))) | ((A @ B @ (A @ C @ D)) != x) | ((A @ C @ (A @ B @ D)) != (sup @ (inf @ y @ (sup @ x @ z)) @ z)))),inference(paramod_ordered,[status(thm)],[278,1111])). 52.41/15.44 thf(1591,plain,(! [A:a] : ((~ (abel_semigroup_a @ (^ [B:a,C:a]: (sup @ B @ z)))) | ((sup @ A @ z) != x))),inference(pre_uni,[status(thm)],[1172:[bind(A, $thf(^ [E:a,F:a]: (sup @ E @ z))),bind(B, $thf(B)),bind(C, $thf(inf @ y @ (sup @ x @ z))),bind(D, $thf(D))]])). 52.41/15.44 thf(1636,plain,(! [A:a] : ((~ (abel_semigroup_a @ (^ [B:a,C:a]: (sup @ B @ z)))) | ((sup @ A @ z) != x))),inference(simp,[status(thm)],[1591])). 52.41/15.44 thf(165,axiom,((((=) @ a) = (^ [A:a,B:a]: ((less_eq @ A @ B) & (less_eq @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_local_Oorder_Oeq__iff)). 52.41/15.44 thf(798,plain,((((=) @ a) = (^ [A:a,B:a]: ((less_eq @ A @ B) & (less_eq @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 52.41/15.44 thf(253,axiom,((! [A:a,B:a]: ((A = B) => (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_local_Oeq__refl)). 52.41/15.44 thf(1057,plain,((! [A:a,B:a]: ((A = B) => (less_eq @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])). 52.41/15.44 thf(197,axiom,((! [A:a,B:a,C:a]: ((modula1936294176_aux_a @ inf @ sup @ A @ B @ C) = (sup @ (sup @ (inf @ A @ B) @ (inf @ B @ C)) @ (inf @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_local_Od__aux__def)). 52.41/15.44 thf(894,plain,((! [A:a,B:a,C:a]: ((modula1936294176_aux_a @ (inf) @ (sup) @ A @ B @ C) = (sup @ (sup @ (inf @ A @ B) @ (inf @ B @ C)) @ (inf @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 52.41/15.44 thf(240,axiom,((! [A:a,B:a,C:a]: ((less_eq @ (sup @ A @ B) @ C) = ((less_eq @ B @ C) & (less_eq @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_local_Osup_Obounded__iff)). 52.41/15.44 thf(1021,plain,((! [A:a,B:a,C:a]: ((less_eq @ (sup @ A @ B) @ C) = ((less_eq @ B @ C) & (less_eq @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 52.41/15.44 thf(247,axiom,((! [A:a,B:a]: ((less_eq @ A @ B) <= (less @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_local_Odual__order_Ostrict__implies__order)). 52.41/15.44 thf(1042,plain,((! [A:a,B:a]: ((less @ A @ B) => (less_eq @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])). 52.41/15.44 thf(302,plain,(! [A:(a > (a > a))] : ((~ (abel_semigroup_a @ (A))) | (semigroup_a @ (A)))),inference(cnf,[status(esa)],[301])). 52.41/15.44 thf(173,axiom,((! [A:a,B:a]: ((less_eq @ A @ B) = ((less @ A @ B) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_local_Ole__less)). 52.41/15.44 thf(820,plain,((! [A:a,B:a]: ((less_eq @ A @ B) = ((less @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 52.41/15.44 thf(16,axiom,((! [A:a,B:a,C:a]: ((less @ A @ B) => ((less @ A @ C) <= (less @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_local_Oless__trans)). 52.41/15.44 thf(295,plain,((! [A:a,B:a,C:a]: ((less @ A @ B) => ((less @ B @ C) => (less @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 52.41/15.44 thf(296,plain,((! [A:a,B:a]: ((less @ A @ B) => (! [C:a]: ((less @ B @ C) => (less @ A @ C)))))),inference(miniscope,[status(thm)],[295])). 52.41/15.44 thf(297,plain,(! [C:a,B:a,A:a] : ((~ (less @ A @ B)) | (~ (less @ B @ C)) | (less @ A @ C))),inference(cnf,[status(esa)],[296])). 52.41/15.44 thf(62,axiom,((! [A:a]: ~ (less @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_local_Oless__irrefl)). 52.41/15.44 thf(429,plain,((! [A:a]: ~ (less @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 52.41/15.44 thf(4,axiom,((! [A:(a > (a > a))]: ((semigroup_a @ A) <= (! [B:a,C:a,D:a]: ((A @ (A @ B @ C) @ D) = (A @ B @ (A @ C @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_semigroup_Ointro)). 52.41/15.44 thf(260,plain,((! [A:(a > (a > a))]: ((! [B:a,C:a,D:a]: ((A @ (A @ B @ C) @ D) = (A @ B @ (A @ C @ D)))) => (semigroup_a @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 52.41/15.44 thf(185,axiom,((! [A:a,B:a]: ((inf @ A @ (inf @ A @ B)) = (inf @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_local_Oinf__left__idem)). 52.41/15.44 thf(862,plain,((! [A:a,B:a]: ((inf @ A @ (inf @ A @ B)) = (inf @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 52.41/15.44 thf(55,axiom,((! [A:(a > (a > a)),B:a,C:a]: ((abel_semigroup_a @ A) => ((A @ B @ C) = (A @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_abel__semigroup_Ocommute)). 52.41/15.44 thf(407,plain,((! [A:(a > (a > a)),B:a,C:a]: ((abel_semigroup_a @ (A)) => ((A @ B @ C) = (A @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 52.41/15.44 thf(132,axiom,((! [A:a,B:a]: ((less_eq @ A @ B) = (A = (inf @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_local_Oinf_Oorder__iff)). 52.41/15.44 thf(693,plain,((! [A:a,B:a]: ((less_eq @ A @ B) = (A = (inf @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 52.41/15.44 thf(182,axiom,((! [A:(a > (a > a)),B:a,C:a]: (((! [D:a,E:a]: (less_eq @ E @ (A @ D @ E))) => (((sup @ B @ C) = (A @ B @ C)) <= (! [D:a,E:a,F:a]: ((less_eq @ E @ D) => ((less_eq @ F @ D) => (less_eq @ (A @ E @ F) @ D)))))) <= (! [D:a,E:a]: (less_eq @ D @ (A @ D @ E)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_local_Osup__unique)). 52.41/15.44 thf(847,plain,((! [A:(a > (a > a)),B:a,C:a]: ((! [D:a,E:a]: (less_eq @ D @ (A @ D @ E))) => ((! [D:a,E:a]: (less_eq @ E @ (A @ D @ E))) => ((! [D:a,E:a,F:a]: ((less_eq @ E @ D) => ((less_eq @ F @ D) => (less_eq @ (A @ E @ F) @ D)))) => ((sup @ B @ C) = (A @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 52.41/15.44 thf(38,axiom,((modula1373251614_aux_a = modula1373251614_aux_a)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_lattice_Ob__aux_Ocong)). 52.41/15.44 thf(361,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 52.41/15.44 thf(110,axiom,((! [A:a,B:a,C:a]: (((less_eq @ A @ C) => (less_eq @ A @ (inf @ B @ C))) <= (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_local_Oinf_OboundedI)). 52.41/15.44 thf(625,plain,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => ((less_eq @ A @ C) => (less_eq @ A @ (inf @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 52.41/15.44 thf(29,axiom,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a]: (((B @ D @ E) = ((A @ D @ E) = D)) <= (semilattice_order_a @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_semilattice__order_Oabsorb__iff1)). 52.41/15.44 thf(329,plain,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a]: ((semilattice_order_a @ (A) @ (B) @ (C)) => ((B @ D @ E) = ((A @ D @ E) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 52.41/15.44 thf(242,axiom,((! [A:a]: ((sup @ A @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_local_Osup_Oidem)). 52.41/15.44 thf(1027,plain,((! [A:a]: ((sup @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])). 52.41/15.44 thf(150,axiom,((! [A:a,B:a,C:a]: (((less_eq @ A @ C) <= (less_eq @ B @ C)) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_local_Oord__eq__le__trans)). 52.41/15.44 thf(757,plain,((! [A:a,B:a,C:a]: ((A = B) => ((less_eq @ B @ C) => (less_eq @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 52.41/15.44 thf(224,axiom,((! [A:a,B:a]: ((inf @ A @ (inf @ A @ B)) = (inf @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_local_Oinf_Oleft__idem)). 52.41/15.44 thf(974,plain,((! [A:a,B:a]: ((inf @ A @ (inf @ A @ B)) = (inf @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 52.41/15.44 thf(64,axiom,((! [A:a,B:a]: ((less @ A @ B) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_local_Oorder_Ostrict__implies__not__eq)). 52.41/15.44 thf(435,plain,((! [A:a,B:a]: ((less @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 52.41/15.44 thf(95,axiom,((! [A:a]: ((inf @ A @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_local_Oinf_Oidem)). 52.41/15.44 thf(575,plain,((! [A:a]: ((inf @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 52.41/15.44 thf(576,plain,(! [A:a] : (((inf @ A @ A) = A))),inference(cnf,[status(esa)],[575])). 52.41/15.44 thf(577,plain,(! [A:a] : (((inf @ A @ A) = A))),inference(lifteq,[status(thm)],[576])). 52.41/15.44 thf(190,axiom,((abel_semigroup_a @ inf)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_local_Oinf_Oabel__semigroup__axioms)). 52.41/15.44 thf(876,plain,((abel_semigroup_a @ (inf))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 52.41/15.44 thf(926,plain,((~ ((sup @ x @ (inf @ y @ z)) = (inf @ y @ (sup @ x @ z))))),inference(polarity_switch,[status(thm)],[925])). 52.41/15.44 thf(927,plain,(((sup @ x @ (inf @ y @ z)) != (inf @ y @ (sup @ x @ z)))),inference(lifteq,[status(thm)],[926])). 52.41/15.44 thf(1263,plain,(! [D:a,C:a,B:a,A:(a > (a > a))] : ((~ (abel_semigroup_a @ (A))) | ((A @ B @ (A @ C @ D)) != (inf @ y @ (sup @ x @ z))) | ((A @ C @ (A @ B @ D)) != (sup @ x @ (inf @ y @ z))))),inference(paramod_ordered,[status(thm)],[278,927])). 52.41/15.44 thf(1413,plain,(! [A:a] : ((~ (abel_semigroup_a @ (^ [B:a,C:a]: (B)))) | (A != (inf @ y @ (sup @ x @ z))))),inference(pre_uni,[status(thm)],[1263:[bind(A, $thf(^ [E:a,F:a]: (E))),bind(B, $thf(B)),bind(C, $thf(sup @ x @ (inf @ y @ z)))]])). 52.41/15.44 thf(1417,plain,((~ (abel_semigroup_a @ (^ [A:a,B:a]: (A))))),inference(pattern_uni,[status(thm)],[1413:[bind(A, $thf(inf @ y @ (sup @ x @ z)))]])). 52.41/15.44 thf(1755,plain,(~ (($true)) | ((abel_semigroup_a @ (inf)) != (abel_semigroup_a @ (^ [A:a,B:a]: (A))))),inference(paramod_ordered,[status(thm)],[876,1417])). 52.41/15.44 thf(1756,plain,(((abel_semigroup_a @ (inf)) != (abel_semigroup_a @ (^ [A:a,B:a]: (A))))),inference(simp,[status(thm)],[1755])). 52.41/15.44 thf(1758,plain,(((inf) != (^ [A:a,B:a]: (A)))),inference(simp,[status(thm)],[1756])). 52.41/15.44 thf(1984,plain,(((inf @ sk43 @ sk44) != sk43)),inference(func_ext,[status(esa)],[1758])). 52.41/15.44 thf(2058,plain,(! [A:a] : ((A != sk43) | ((inf @ A @ A) != (inf @ sk43 @ sk44)))),inference(paramod_ordered,[status(thm)],[577,1984])). 52.41/15.44 thf(2078,plain,((sk43 != sk43) | (sk44 != sk43)),inference(simp,[status(thm)],[2058])). 52.41/15.44 thf(2112,plain,((sk44 != sk43)),inference(simp,[status(thm)],[2078])). 52.41/15.44 thf(139,axiom,((! [A:a,B:a,C:a]: (((inf @ A @ (sup @ B @ C)) = (sup @ (inf @ A @ B) @ (inf @ A @ C))) <= (! [D:a,E:a,F:a]: ((sup @ D @ (inf @ E @ F)) = (inf @ (sup @ D @ E) @ (sup @ D @ F))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_local_Odistrib__imp2)). 52.41/15.44 thf(710,plain,((! [A:a,B:a,C:a]: ((! [D:a,E:a,F:a]: ((sup @ D @ (inf @ E @ F)) = (inf @ (sup @ D @ E) @ (sup @ D @ F)))) => ((inf @ A @ (sup @ B @ C)) = (sup @ (inf @ A @ B) @ (inf @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 52.41/15.44 thf(71,axiom,((! [A:a,B:a,C:a]: ((modula1373251614_aux_a @ inf @ sup @ A @ B @ C) = (sup @ (inf @ B @ (modula1144073633_aux_a @ inf @ sup @ A @ B @ C)) @ (modula1936294176_aux_a @ inf @ sup @ A @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_local_Ob__aux__def)). 52.41/15.44 thf(456,plain,((! [A:a,B:a,C:a]: ((modula1373251614_aux_a @ (inf) @ (sup) @ A @ B @ C) = (sup @ (inf @ B @ (modula1144073633_aux_a @ (inf) @ (sup) @ A @ B @ C)) @ (modula1936294176_aux_a @ (inf) @ (sup) @ A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 52.41/15.44 thf(180,axiom,((! [A:a,B:a]: (less_eq @ (inf @ A @ B) @ B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_local_Oinf_Ocobounded2)). 52.41/15.44 thf(842,plain,((! [A:a,B:a]: (less_eq @ (inf @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 52.41/15.44 thf(96,axiom,((! [A:a,B:a]: (((A != B) => (less @ A @ B)) <= (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_local_Ole__neq__trans)). 52.41/15.44 thf(578,plain,((! [A:a,B:a]: ((less_eq @ A @ B) => ((~ (A = B)) => (less @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 52.41/15.44 thf(134,axiom,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => (less_eq @ A @ (sup @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_local_Osup_OcoboundedI2)). 52.41/15.44 thf(697,plain,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => (less_eq @ A @ (sup @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 52.41/15.44 thf(125,axiom,((abel_semigroup_a @ sup)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_local_Osup_Oabel__semigroup__axioms)). 52.41/15.44 thf(671,plain,((abel_semigroup_a @ (sup))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 52.41/15.44 thf(1753,plain,(~ (($true)) | ((abel_semigroup_a @ (sup)) != (abel_semigroup_a @ (^ [A:a,B:a]: (A))))),inference(paramod_ordered,[status(thm)],[671,1417])). 52.41/15.44 thf(1754,plain,(((abel_semigroup_a @ (sup)) != (abel_semigroup_a @ (^ [A:a,B:a]: (A))))),inference(simp,[status(thm)],[1753])). 52.41/15.44 thf(1757,plain,(((sup) != (^ [A:a,B:a]: (A)))),inference(simp,[status(thm)],[1754])). 52.41/15.44 thf(1983,plain,(((sup @ sk41 @ sk42) != sk41)),inference(func_ext,[status(esa)],[1757])). 52.41/15.44 thf(107,axiom,((! [A:a,B:a]: ((sup @ A @ (sup @ A @ B)) = (sup @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_local_Osup__left__idem)). 52.41/15.44 thf(615,plain,((! [A:a,B:a]: ((sup @ A @ (sup @ A @ B)) = (sup @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 52.41/15.44 thf(255,axiom,((! [A:a]: (less_eq @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_local_Oorder__refl)). 52.41/15.44 thf(1064,plain,((! [A:a]: (less_eq @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])). 52.41/15.44 thf(144,axiom,((! [A:a,B:a,C:a,D:a]: (((less_eq @ (sup @ A @ C) @ (sup @ B @ D)) <= (less_eq @ C @ D)) <= (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_local_Osup__mono)). 52.41/15.44 thf(725,plain,((! [A:a,B:a,C:a,D:a]: ((less_eq @ A @ B) => ((less_eq @ C @ D) => (less_eq @ (sup @ A @ C) @ (sup @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 52.41/15.44 thf(54,axiom,((! [A:a,B:a]: ((less @ A @ B) => (B != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_local_Odual__order_Ostrict__implies__not__eq)). 52.41/15.44 thf(403,plain,((! [A:a,B:a]: ((less @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 52.41/15.44 thf(37,axiom,((! [A:a,B:a,C:a]: (((less @ A @ C) <= (less @ B @ C)) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_local_Oord__eq__less__trans)). 52.41/15.44 thf(356,plain,((! [A:a,B:a,C:a]: ((A = B) => ((less @ B @ C) => (less @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 52.41/15.44 thf(59,axiom,((modula1144073633_aux_a = modula1144073633_aux_a)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_lattice_Oe__aux_Ocong)). 52.41/15.44 thf(420,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 52.41/15.44 thf(79,axiom,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => (less_eq @ A @ (sup @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_local_Ole__supI2)). 52.41/15.44 thf(499,plain,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => (less_eq @ A @ (sup @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 52.41/15.44 thf(32,axiom,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a]: ((semilattice_order_a @ A @ B @ C) => ((B @ D @ E) => (D = (A @ D @ E)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_semilattice__order_OorderE)). 52.41/15.44 thf(339,plain,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a]: ((semilattice_order_a @ (A) @ (B) @ (C)) => ((B @ D @ E) => (D = (A @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 52.41/15.44 thf(88,axiom,((! [A:a,B:a,C:a]: (((less_eq @ C @ B) => (less_eq @ (sup @ A @ C) @ B)) <= (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_local_Osup_OboundedI)). 52.41/15.44 thf(554,plain,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => ((less_eq @ C @ B) => (less_eq @ (sup @ A @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 52.41/15.44 thf(124,axiom,((! [A:a,B:a]: ((~ (less @ B @ A)) <= (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_local_OleD)). 52.41/15.44 thf(669,plain,((! [A:a,B:a]: ((less_eq @ A @ B) => (~ (less @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 52.41/15.44 thf(246,axiom,((! [A:a,B:a,C:a]: ((less @ (inf @ C @ A) @ B) <= (less @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_local_Oless__infI2)). 52.41/15.44 thf(1039,plain,((! [A:a,B:a,C:a]: ((less @ A @ B) => (less @ (inf @ C @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])). 52.41/15.44 thf(109,axiom,((! [A:a,B:a,C:a]: ((modula581031071_aux_a @ inf @ sup @ A @ B @ C) = (modula17988509_aux_a @ inf @ sup @ C @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_local_Oc__a)). 52.41/15.44 thf(622,plain,((! [A:a,B:a,C:a]: ((modula581031071_aux_a @ (inf) @ (sup) @ A @ B @ C) = (modula17988509_aux_a @ (inf) @ (sup) @ C @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 52.41/15.44 thf(116,axiom,((lattic1885654924_set_a @ inf)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_local_OInf__fin_Osemilattice__set__axioms)). 52.41/15.44 thf(647,plain,((lattic1885654924_set_a @ (inf))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 52.41/15.44 thf(228,axiom,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => ((less_eq @ A @ C) <= (B = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_local_Oord__le__eq__trans)). 52.41/15.44 thf(985,plain,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => ((B = C) => (less_eq @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 52.41/15.44 thf(119,axiom,((! [A:a,B:a,C:a]: ((less @ (inf @ A @ C) @ B) <= (less @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_local_Oless__infI1)). 52.41/15.44 thf(654,plain,((! [A:a,B:a,C:a]: ((less @ A @ B) => (less @ (inf @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 52.41/15.44 thf(2202,plain,(! [E:a,D:a,C:(a > (a > $o)),B:(a > (a > $o)),A:(a > (a > a))] : ((~ (D = E) & (D = (A @ D @ E))) | (~ (semilattice_order_a @ (A) @ (B) @ (C))) | ((abel_semigroup_a @ (inf)) != (C @ D @ E)))),inference(paramod_ordered,[status(thm)],[876,289])). 52.41/15.44 thf(2217,plain,(! [D:a,C:a,B:(a > (a > $o)),A:(a > (a > a))] : ((~ (C = D) & (C = (A @ C @ D))) | (~ (semilattice_order_a @ (A) @ (B) @ (^ [E:a,F:a]: (abel_semigroup_a @ inf)))))),inference(pre_uni,[status(thm)],[2202:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(^ [F:a,G:a]: (abel_semigroup_a @ inf))),bind(D, $thf(D)),bind(E, $thf(E))]])). 52.41/15.44 thf(2338,plain,(! [D:a,C:a,B:(a > (a > $o)),A:(a > (a > a))] : (((~ (C = D) | ~ (semilattice_order_a @ (A) @ (B) @ (^ [E:a,F:a]: (abel_semigroup_a @ inf)))) & ((C = (A @ C @ D)) | ~ (semilattice_order_a @ (A) @ (B) @ (^ [E:a,F:a]: (abel_semigroup_a @ inf))))))),inference(cnf,[status(esa)],[2217])). 52.41/15.44 thf(2339,plain,(! [D:a,C:a,B:(a > (a > $o)),A:(a > (a > a))] : ((~ (C = D)) | (~ (semilattice_order_a @ (A) @ (B) @ (^ [E:a,F:a]: (abel_semigroup_a @ inf)))))),inference(cnfConj,[status(thm)],[2338])). 52.41/15.44 thf(2341,plain,(! [D:a,C:a,B:(a > (a > $o)),A:(a > (a > a))] : ((C != D) | (~ (semilattice_order_a @ (A) @ (B) @ (^ [E:a,F:a]: (abel_semigroup_a @ inf)))))),inference(lifteq,[status(thm)],[2339])). 52.41/15.44 thf(2342,plain,(! [B:(a > (a > $o)),A:(a > (a > a))] : ((~ (semilattice_order_a @ (A) @ (B) @ (^ [C:a,D:a]: (abel_semigroup_a @ inf)))))),inference(simp,[status(thm)],[2341])). 52.41/15.44 thf(3819,plain,(! [B:(a > (a > $o)),A:(a > (a > a))] : ((~ (semilattice_order_a @ (A) @ (B) @ (^ [C:a,D:a]: (($true))))))),inference(rewrite,[status(thm)],[2342,876])). 52.41/15.44 thf(142,axiom,((! [A:a,B:a]: (condit1001553558elow_a @ less_eq @ (set_gr1491433118Than_a @ less @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_local_Obdd__below__Ioo)). 52.41/15.44 thf(720,plain,((! [A:a,B:a]: (condit1001553558elow_a @ (less_eq) @ (set_gr1491433118Than_a @ (less) @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 52.41/15.44 thf(721,plain,(! [B:a,A:a] : ((condit1001553558elow_a @ (less_eq) @ (set_gr1491433118Than_a @ (less) @ A @ B)))),inference(cnf,[status(esa)],[720])). 52.41/15.44 thf(157,axiom,((! [A:a,B:a]: ((less @ A @ B) => (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_local_Oless__imp__le)). 52.41/15.44 thf(779,plain,((! [A:a,B:a]: ((less @ A @ B) => (less_eq @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 52.41/15.44 thf(42,axiom,((! [A:a,B:a]: ((~ (less @ B @ A)) <= (less @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_local_Oless__not__sym)). 52.41/15.44 thf(371,plain,((! [A:a,B:a]: ((less @ A @ B) => (~ (less @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 52.41/15.44 thf(33,axiom,((! [A:(a > (a > a)),B:a,C:a,D:a]: ((semigroup_a @ A) => ((A @ (A @ B @ C) @ D) = (A @ B @ (A @ C @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_semigroup_Oassoc)). 52.41/15.44 thf(343,plain,((! [A:(a > (a > a)),B:a,C:a,D:a]: ((semigroup_a @ (A)) => ((A @ (A @ B @ C) @ D) = (A @ B @ (A @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 52.41/15.44 thf(213,axiom,((! [A:a,B:a,C:a]: ((less @ A @ B) => ((less_eq @ C @ A) => (less @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_local_Odual__order_Ostrict__trans2)). 52.41/15.44 thf(938,plain,((! [A:a,B:a,C:a]: ((less @ A @ B) => ((less_eq @ C @ A) => (less @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 52.41/15.44 thf(168,axiom,((! [A:a,B:a]: ((less_eq @ A @ B) => ((sup @ A @ B) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_local_Osup__absorb2)). 52.41/15.44 thf(805,plain,((! [A:a,B:a]: ((less_eq @ A @ B) => ((sup @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 52.41/15.44 thf(82,axiom,((! [A:a,B:a,C:a]: ((less @ A @ B) => ((less @ A @ C) <= (less_eq @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_local_Oorder_Ostrict__trans2)). 52.41/15.44 thf(508,plain,((! [A:a,B:a,C:a]: ((less @ A @ B) => ((less_eq @ B @ C) => (less @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 52.41/15.44 thf(23,axiom,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a,F:a]: (((C @ D @ E) => (C @ (A @ D @ F) @ E)) <= (semilattice_order_a @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_semilattice__order_Ostrict__coboundedI1)). 52.41/15.44 thf(311,plain,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a,F:a]: ((semilattice_order_a @ (A) @ (B) @ (C)) => ((C @ D @ E) => (C @ (A @ D @ F) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 52.41/15.44 thf(120,axiom,((! [A:a,B:a]: ((less_eq @ A @ B) = ((less @ A @ B) | (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_local_Odual__order_Oorder__iff__strict)). 52.41/15.44 thf(657,plain,((! [A:a,B:a]: ((less_eq @ A @ B) = ((less @ A @ B) | (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 52.41/15.44 thf(252,axiom,((! [A:a,B:a]: (((sup @ B @ A) = B) <= (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_local_Osup__absorb1)). 52.41/15.44 thf(1054,plain,((! [A:a,B:a]: ((less_eq @ A @ B) => ((sup @ B @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])). 52.41/15.44 thf(84,axiom,((! [A:a,B:a,C:a]: ((less @ (inf @ C @ A) @ B) <= (less @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_local_Oinf_Ostrict__coboundedI2)). 52.41/15.44 thf(530,plain,((! [A:a,B:a,C:a]: ((less @ A @ B) => (less @ (inf @ C @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 52.41/15.44 thf(195,axiom,((! [A:a,B:a]: ((modula1727524044comp_a @ less_eq @ A @ B) = (~ (less_eq @ A @ B) & ~ (less_eq @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_local_Oincomp__def)). 52.41/15.44 thf(888,plain,((! [A:a,B:a]: ((modula1727524044comp_a @ (less_eq) @ A @ B) = (~ (less_eq @ A @ B) & ~ (less_eq @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 52.41/15.44 thf(155,axiom,((! [A:a,B:a,C:a]: ((less_eq @ A @ (sup @ B @ C)) <= (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_local_Osup_OcoboundedI1)). 52.41/15.44 thf(773,plain,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => (less_eq @ A @ (sup @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 52.41/15.44 thf(163,axiom,((! [A:a,B:a]: ((sup @ A @ (sup @ A @ B)) = (sup @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_local_Osup_Oleft__idem)). 52.41/15.44 thf(794,plain,((! [A:a,B:a]: ((sup @ A @ (sup @ A @ B)) = (sup @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 52.41/15.44 thf(17,axiom,((modula1936294176_aux_a = modula1936294176_aux_a)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_lattice_Od__aux_Ocong)). 52.41/15.44 thf(298,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 52.41/15.44 thf(108,axiom,((! [A:a,B:a,C:a]: ((! [D:a,E:a,F:a]: ((inf @ D @ (sup @ E @ F)) = (sup @ (inf @ D @ E) @ (inf @ D @ F)))) => ((sup @ A @ (inf @ B @ C)) = (inf @ (sup @ A @ B) @ (sup @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_local_Odistrib__imp1)). 52.41/15.44 thf(618,plain,((! [A:a,B:a,C:a]: ((! [D:a,E:a,F:a]: ((inf @ D @ (sup @ E @ F)) = (sup @ (inf @ D @ E) @ (inf @ D @ F)))) => ((sup @ A @ (inf @ B @ C)) = (inf @ (sup @ A @ B) @ (sup @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 52.41/15.44 thf(61,axiom,((! [A:(a > (a > a)),B:a]: (((A @ B @ B) = B) <= (semilattice_a @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_semilattice_Oidem)). 52.41/15.44 thf(425,plain,((! [A:(a > (a > a)),B:a]: ((semilattice_a @ (A)) => ((A @ B @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 52.41/15.44 thf(183,axiom,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => (less_eq @ A @ (sup @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_local_Ole__supI1)). 52.41/15.44 thf(856,plain,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => (less_eq @ A @ (sup @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 52.41/15.44 thf(10,axiom,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a,F:a]: ((semilattice_order_a @ A @ B @ C) => ((B @ (A @ F @ D) @ E) <= (B @ D @ E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_semilattice__order_OcoboundedI2)). 52.41/15.44 thf(279,plain,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a,F:a]: ((semilattice_order_a @ (A) @ (B) @ (C)) => ((B @ D @ E) => (B @ (A @ F @ D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 52.41/15.44 thf(130,axiom,((! [A:a,B:a]: ((less @ A @ B) = ((A != B) & (less_eq @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_local_Oorder_Ostrict__iff__order)). 52.41/15.44 thf(689,plain,((! [A:a,B:a]: ((less @ A @ B) = (~ (A = B) & (less_eq @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 52.41/15.44 thf(98,axiom,((! [A:a,B:a]: ((less @ A @ B) = ((less_eq @ A @ B) & (B != A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_local_Odual__order_Ostrict__iff__order)). 52.41/15.44 thf(584,plain,((! [A:a,B:a]: ((less @ A @ B) = ((less_eq @ A @ B) & ~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 52.41/15.44 thf(235,axiom,((! [A:a,B:a]: ((less @ A @ B) = ((A != B) & (A = (inf @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_local_Oinf_Ostrict__order__iff)). 52.41/15.44 thf(1007,plain,((! [A:a,B:a]: ((less @ A @ B) = (~ (A = B) & (A = (inf @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 52.41/15.44 thf(218,axiom,((! [A:a,B:a]: (less_eq @ A @ (sup @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_local_Osup__ge2)). 52.41/15.44 thf(958,plain,((! [A:a,B:a]: (less_eq @ A @ (sup @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 52.41/15.44 thf(280,plain,((! [A:(a > (a > a)),B:(a > (a > $o))]: ((? [C:(a > (a > $o))]: (semilattice_order_a @ (A) @ (B) @ (C))) => (! [C:a,D:a]: ((B @ C @ D) => (! [E:a]: (B @ (A @ E @ C) @ D))))))),inference(miniscope,[status(thm)],[279])). 52.41/15.44 thf(281,plain,(! [F:a,E:a,D:a,C:(a > (a > $o)),B:(a > (a > $o)),A:(a > (a > a))] : ((~ (semilattice_order_a @ (A) @ (B) @ (C))) | (~ (B @ D @ E)) | (B @ (A @ F @ D) @ E))),inference(cnf,[status(esa)],[280])). 52.41/15.44 thf(2213,plain,(! [C:a,B:(a > (a > $o)),A:(a > (a > a))] : ((~ (semilattice_order_a @ (A) @ (B) @ (^ [D:a,E:a]: (less_eq @ D @ y)))) | (~ (x = C) & (x = (A @ x @ C))))),inference(pre_uni,[status(thm)],[2188:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(^ [F:a,G:a]: (less_eq @ F @ y))),bind(D, $thf(x)),bind(E, $thf(E))]])). 52.41/15.44 thf(2314,plain,(! [C:a,B:(a > (a > $o)),A:(a > (a > a))] : (((~ (semilattice_order_a @ (A) @ (B) @ (^ [D:a,E:a]: (less_eq @ D @ y))) | ~ (x = C)) & (~ (semilattice_order_a @ (A) @ (B) @ (^ [D:a,E:a]: (less_eq @ D @ y))) | (x = (A @ x @ C)))))),inference(cnf,[status(esa)],[2213])). 52.41/15.44 thf(2315,plain,(! [C:a,B:(a > (a > $o)),A:(a > (a > a))] : ((~ (semilattice_order_a @ (A) @ (B) @ (^ [D:a,E:a]: (less_eq @ D @ y)))) | (~ (x = C)))),inference(cnfConj,[status(thm)],[2314])). 52.41/15.44 thf(2317,plain,(! [C:a,B:(a > (a > $o)),A:(a > (a > a))] : ((x != C) | (~ (semilattice_order_a @ (A) @ (B) @ (^ [D:a,E:a]: (less_eq @ D @ y)))))),inference(lifteq,[status(thm)],[2315])). 52.41/15.44 thf(2318,plain,(! [B:(a > (a > $o)),A:(a > (a > a))] : ((~ (semilattice_order_a @ (A) @ (B) @ (^ [C:a,D:a]: (less_eq @ C @ y)))))),inference(simp,[status(thm)],[2317])). 52.41/15.44 thf(2655,plain,(! [B:(a > (a > $o)),A:(a > (a > a))] : (~ (($true)) | ((semilattice_order_a @ (inf) @ (less_eq) @ (less)) != (semilattice_order_a @ (A) @ (B) @ (^ [C:a,D:a]: (less_eq @ C @ y)))))),inference(paramod_ordered,[status(thm)],[884,2318])). 52.41/15.44 thf(2656,plain,(! [B:(a > (a > $o)),A:(a > (a > a))] : (((semilattice_order_a @ (inf) @ (less_eq) @ (less)) != (semilattice_order_a @ (A) @ (B) @ (^ [C:a,D:a]: (less_eq @ C @ y)))))),inference(simp,[status(thm)],[2655])). 52.41/15.44 thf(2670,plain,(! [B:(a > (a > $o)),A:(a > (a > a))] : (((inf) != (A)) | ((less_eq) != (B)) | ((less) != (^ [C:a,D:a]: (less_eq @ C @ y))))),inference(simp,[status(thm)],[2656])). 52.41/15.44 thf(2690,plain,(((less) != (^ [A:a,B:a]: (less_eq @ A @ y)))),inference(simp,[status(thm)],[2670])). 52.41/15.44 thf(2695,plain,(((less_eq @ sk45 @ y) != (less @ sk45 @ sk46))),inference(func_ext,[status(esa)],[2690])). 52.41/15.44 thf(258,plain,(! [B:(a > $o),A:(a > $o)] : ((~ ((A @ (sk1 @ (B) @ (A))) = (B @ (sk1 @ (B) @ (A))))) | ((collect_a @ (A)) = (collect_a @ (B))))),inference(cnf,[status(esa)],[257])). 52.41/15.44 thf(259,plain,(! [B:(a > $o),A:(a > $o)] : (((A @ (sk1 @ (B) @ (A))) != (B @ (sk1 @ (B) @ (A)))) | ((collect_a @ (A)) = (collect_a @ (B))))),inference(lifteq,[status(thm)],[258])). 52.41/15.44 thf(175,axiom,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => (less_eq @ (inf @ A @ C) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_local_Oinf_OcoboundedI1)). 52.41/15.44 thf(826,plain,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => (less_eq @ (inf @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 52.41/15.44 thf(49,axiom,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o))]: ((lattic655834328_set_a @ A @ B @ C) => (semilattice_order_a @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_semilattice__order__set_Oaxioms_I1_J)). 52.41/15.44 thf(391,plain,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o))]: ((lattic655834328_set_a @ (A) @ (B) @ (C)) => (semilattice_order_a @ (A) @ (B) @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 52.41/15.44 thf(160,axiom,((! [A:a,B:a]: ((sup @ A @ B) = (sup @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_local_Osup_Ocommute)). 52.41/15.44 thf(787,plain,((! [A:a,B:a]: ((sup @ A @ B) = (sup @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 52.41/15.44 thf(334,plain,(! [A:set_a] : (((collect_a @ (^ [B:a]: (member_a @ B @ A))) = A))),inference(cnf,[status(esa)],[333])). 52.41/15.44 thf(335,plain,(! [A:set_a] : (((collect_a @ (^ [B:a]: (member_a @ B @ A))) = A))),inference(lifteq,[status(thm)],[334])). 52.41/15.44 thf(137,axiom,((! [A:set_a]: ((condit1627435690bove_a @ less_eq @ A) = (? [B:a]: ! [C:a]: ((less_eq @ C @ B) <= (member_a @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_local_Obdd__above__def)). 52.41/15.44 thf(704,plain,((! [A:set_a]: ((condit1627435690bove_a @ (less_eq) @ A) = (? [B:a]: ! [C:a]: ((member_a @ C @ A) => (less_eq @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 52.41/15.44 thf(216,axiom,((! [A:a,B:a]: (((less_eq @ B @ A) => (B = A)) <= (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_local_Odual__order_Oantisym)). 52.41/15.44 thf(947,plain,((! [A:a,B:a]: ((less_eq @ A @ B) => ((less_eq @ B @ A) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 52.41/15.44 thf(348,plain,(! [B:a,A:a] : ((~ (less @ A @ B)) | (~ (B = A)))),inference(cnf,[status(esa)],[347])). 52.41/15.44 thf(349,plain,(! [B:a,A:a] : ((B != A) | (~ (less @ A @ B)))),inference(lifteq,[status(thm)],[348])). 52.41/15.44 thf(350,plain,(! [A:a] : ((~ (less @ A @ A)))),inference(simp,[status(thm)],[349])). 52.41/15.44 thf(126,axiom,((! [A:a,B:a,C:a]: (((less_eq @ A @ (inf @ B @ C)) <= (less_eq @ A @ C)) <= (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_local_Oinf__greatest)). 52.41/15.44 thf(672,plain,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => ((less_eq @ A @ C) => (less_eq @ A @ (inf @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 52.41/15.44 thf(199,axiom,((! [A:a,B:a,C:a]: ((modula581031071_aux_a @ inf @ sup @ A @ B @ C) = (sup @ (inf @ C @ (modula1144073633_aux_a @ inf @ sup @ A @ B @ C)) @ (modula1936294176_aux_a @ inf @ sup @ A @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_local_Oc__aux__def)). 52.41/15.44 thf(900,plain,((! [A:a,B:a,C:a]: ((modula581031071_aux_a @ (inf) @ (sup) @ A @ B @ C) = (sup @ (inf @ C @ (modula1144073633_aux_a @ (inf) @ (sup) @ A @ B @ C)) @ (modula1936294176_aux_a @ (inf) @ (sup) @ A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 52.41/15.44 thf(129,axiom,((! [A:a,B:a]: ((((min_a @ less_eq @ A @ B) = A) <= (less_eq @ A @ B)) & ((~ (less_eq @ A @ B)) => ((min_a @ less_eq @ A @ B) = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_local_Omin__def)). 52.41/15.44 thf(681,plain,((! [A:a,B:a]: (((less_eq @ A @ B) => ((min_a @ (less_eq) @ A @ B) = A)) & ((~ (less_eq @ A @ B)) => ((min_a @ (less_eq) @ A @ B) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 52.41/15.44 thf(159,axiom,((! [A:a,B:a,C:a]: ((less @ A @ B) => (less @ A @ (sup @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_local_Osup_Ostrict__coboundedI2)). 52.41/15.44 thf(784,plain,((! [A:a,B:a,C:a]: ((less @ A @ B) => (less @ A @ (sup @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 52.41/15.44 thf(250,axiom,((! [A:a,B:a]: ((less_eq @ A @ B) = ((inf @ A @ B) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_local_Oinf_Oabsorb__iff1)). 52.41/15.44 thf(1048,plain,((! [A:a,B:a]: ((less_eq @ A @ B) = ((inf @ A @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])). 52.41/15.44 thf(229,axiom,((! [A:a,B:a]: ((less_eq @ A @ B) <= (A = (inf @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_local_Oinf_OorderI)). 52.41/15.44 thf(990,plain,((! [A:a,B:a]: ((A = (inf @ A @ B)) => (less_eq @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 52.41/15.44 thf(192,axiom,((! [A:a,B:a,C:a]: ((less_eq @ A @ (inf @ B @ C)) => (~ ((~ (less_eq @ A @ C)) <= (less_eq @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_local_Oinf_OboundedE)). 52.41/15.44 thf(880,plain,((! [A:a,B:a,C:a]: ((less_eq @ A @ (inf @ B @ C)) => (~ ((less_eq @ A @ B) => (~ (less_eq @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 52.41/15.44 thf(20,axiom,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a,F:a,G:a]: ((semilattice_order_a @ A @ B @ C) => (((B @ F @ G) => (B @ (A @ D @ F) @ (A @ E @ G))) <= (B @ D @ E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_semilattice__order_Omono)). 52.41/15.44 thf(303,plain,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a,F:a,G:a]: ((semilattice_order_a @ (A) @ (B) @ (C)) => ((B @ D @ E) => ((B @ F @ G) => (B @ (A @ D @ F) @ (A @ E @ G))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 52.41/15.44 thf(152,axiom,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => ((less_eq @ A @ C) => (less_eq @ A @ (inf @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_local_Ole__infI)). 52.41/15.44 thf(764,plain,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => ((less_eq @ A @ C) => (less_eq @ A @ (inf @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 52.41/15.44 thf(226,axiom,((! [A:a,B:a,C:a]: ((sup @ A @ (sup @ B @ C)) = (sup @ B @ (sup @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_local_Osup__left__commute)). 52.41/15.44 thf(979,plain,((! [A:a,B:a,C:a]: ((sup @ A @ (sup @ B @ C)) = (sup @ B @ (sup @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 52.41/15.44 thf(39,axiom,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a]: ((semilattice_order_a @ A @ B @ C) => ((B @ D @ E) = ((A @ E @ D) = D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_semilattice__order_Oabsorb__iff2)). 52.41/15.44 thf(362,plain,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a]: ((semilattice_order_a @ (A) @ (B) @ (C)) => ((B @ D @ E) = ((A @ E @ D) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 52.41/15.44 thf(69,axiom,((modula1727524044comp_a = modula1727524044comp_a)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_lattice_Oincomp_Ocong)). 52.41/15.44 thf(451,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 52.41/15.44 thf(148,axiom,((! [A:a,B:a]: ((sup @ A @ B) = (sup @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_local_Osup__commute)). 52.41/15.44 thf(737,plain,((! [A:a,B:a]: ((sup @ A @ B) = (sup @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 52.41/15.44 thf(26,axiom,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a]: ((((A @ D @ E) = D) <= (B @ D @ E)) <= (semilattice_order_a @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_semilattice__order_Oabsorb1)). 52.41/15.44 thf(318,plain,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a]: ((semilattice_order_a @ (A) @ (B) @ (C)) => ((B @ D @ E) => ((A @ D @ E) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 52.41/15.44 thf(112,axiom,((! [A:a,B:a,C:a]: ((modula17988509_aux_a @ inf @ sup @ A @ B @ C) = (sup @ (inf @ A @ (modula1144073633_aux_a @ inf @ sup @ A @ B @ C)) @ (modula1936294176_aux_a @ inf @ sup @ A @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_local_Oa__aux__def)). 52.41/15.44 thf(631,plain,((! [A:a,B:a,C:a]: ((modula17988509_aux_a @ (inf) @ (sup) @ A @ B @ C) = (sup @ (inf @ A @ (modula1144073633_aux_a @ (inf) @ (sup) @ A @ B @ C)) @ (modula1936294176_aux_a @ (inf) @ (sup) @ A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 52.41/15.44 thf(87,axiom,((! [A:a,B:a]: (less_eq @ (inf @ A @ B) @ B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_local_Oinf__le2)). 52.41/15.44 thf(552,plain,((! [A:a,B:a]: (less_eq @ (inf @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 52.41/15.44 thf(105,axiom,((! [A:a,B:a,C:a]: (((less_eq @ A @ C) <= (less_eq @ B @ C)) <= (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_local_Oorder_Otrans)). 52.41/15.44 thf(609,plain,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => ((less_eq @ B @ C) => (less_eq @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 52.41/15.44 thf(799,plain,(((^ [A:a,B:a]: ((less_eq @ A @ B) & (less_eq @ B @ A))) = ((=) @ a))),inference(lifteq,[status(thm)],[798])). 52.41/15.44 thf(75,axiom,((! [A:(a > $o),B:a]: ((A @ B) => (((least_a @ less_eq @ A) = B) <= (! [C:a]: ((A @ C) => (less_eq @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_local_OLeast__equality)). 52.41/15.44 thf(483,plain,((! [A:(a > $o),B:a]: ((A @ B) => ((! [C:a]: ((A @ C) => (less_eq @ B @ C))) => ((least_a @ (less_eq) @ (A)) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 52.41/15.44 thf(135,axiom,((! [A:a,B:a]: ((less_eq @ A @ B) => ((inf @ A @ B) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_local_Oinf__absorb1)). 52.41/15.44 thf(700,plain,((! [A:a,B:a]: ((less_eq @ A @ B) => ((inf @ A @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 52.41/15.44 thf(2711,plain,(! [A:a] : ((A != sk41) | ((sup @ A @ A) != (sup @ sk41 @ sk42)))),inference(paramod_ordered,[status(thm)],[1020,1983])). 52.41/15.44 thf(2769,plain,((sk41 != sk41) | (sk42 != sk41)),inference(simp,[status(thm)],[2711])). 52.41/15.44 thf(2785,plain,((sk42 != sk41)),inference(simp,[status(thm)],[2769])). 52.41/15.44 thf(221,axiom,((! [A:a,B:a]: ((A != B) => ((less_eq @ A @ B) => (less @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_local_Oorder_Onot__eq__order__implies__strict)). 52.41/15.44 thf(964,plain,((! [A:a,B:a]: ((~ (A = B)) => ((less_eq @ A @ B) => (less @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 52.41/15.44 thf(3483,plain,(((less_eq @ x @ sk49) != (less @ sk49 @ sk50))),inference(func_ext,[status(esa)],[3463])). 52.41/15.44 thf(170,axiom,((! [A:a,B:a]: (((less_eq @ B @ A) => (less @ B @ A)) <= (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_local_Odual__order_Onot__eq__order__implies__strict)). 52.41/15.44 thf(811,plain,((! [A:a,B:a]: ((~ (A = B)) => ((less_eq @ B @ A) => (less @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 52.41/15.44 thf(48,axiom,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a]: ((semilattice_order_a @ A @ B @ C) => (((A @ E @ D) = D) <= (B @ D @ E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_semilattice__order_Oabsorb2)). 52.41/15.44 thf(387,plain,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a]: ((semilattice_order_a @ (A) @ (B) @ (C)) => ((B @ D @ E) => ((A @ E @ D) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 52.41/15.44 thf(211,axiom,((! [A:a,B:a,C:a]: ((inf @ A @ (modula1144073633_aux_a @ inf @ sup @ A @ B @ C)) = (inf @ A @ (sup @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_local_Oa__meet__e)). 52.41/15.44 thf(932,plain,((! [A:a,B:a,C:a]: ((inf @ A @ (modula1144073633_aux_a @ (inf) @ (sup) @ A @ B @ C)) = (inf @ A @ (sup @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 52.41/15.44 thf(254,axiom,((! [A:a,B:a,C:a]: ((less_eq @ A @ (inf @ B @ C)) = ((less_eq @ A @ B) & (less_eq @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_local_Ole__inf__iff)). 52.41/15.44 thf(1061,plain,((! [A:a,B:a,C:a]: ((less_eq @ A @ (inf @ B @ C)) = ((less_eq @ A @ B) & (less_eq @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])). 52.41/15.44 thf(204,axiom,((((=) @ a) = (^ [A:a,B:a]: ((less_eq @ A @ B) & (less_eq @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_local_Odual__order_Oeq__iff)). 52.41/15.44 thf(912,plain,((((=) @ a) = (^ [A:a,B:a]: ((less_eq @ A @ B) & (less_eq @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 52.41/15.44 thf(248,axiom,((semilattice_a @ sup)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_local_Osup_Osemilattice__axioms)). 52.41/15.44 thf(1044,plain,((semilattice_a @ (sup))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])). 52.41/15.44 thf(238,axiom,((! [A:a,B:a,C:a]: ((modula1936294176_aux_a @ inf @ sup @ A @ B @ C) = (modula1936294176_aux_a @ inf @ sup @ C @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_local_Od__b__c__a)). 52.41/15.44 thf(1015,plain,((! [A:a,B:a,C:a]: ((modula1936294176_aux_a @ (inf) @ (sup) @ A @ B @ C) = (modula1936294176_aux_a @ (inf) @ (sup) @ C @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 52.41/15.44 thf(21,axiom,((modula397570059tice_a = modula397570059tice_a)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_lattice_ON5__lattice_Ocong)). 52.41/15.44 thf(306,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 52.41/15.44 thf(18,axiom,((! [A:a,B:a]: ((~ (less @ B @ A)) <= (less @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_local_Odual__order_Oasym)). 52.41/15.44 thf(299,plain,((! [A:a,B:a]: ((less @ A @ B) => (~ (less @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 52.41/15.44 thf(202,axiom,((less @ (sup @ x @ (inf @ y @ z)) @ (inf @ y @ (sup @ x @ z)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3)). 52.41/15.44 thf(908,plain,((less @ (sup @ x @ (inf @ y @ z)) @ (inf @ y @ (sup @ x @ z)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 52.41/15.44 thf(300,plain,(! [B:a,A:a] : ((~ (less @ A @ B)) | (~ (less @ B @ A)))),inference(cnf,[status(esa)],[299])). 52.41/15.44 thf(1100,plain,(! [B:a,A:a] : (~ (($true)) | (~ (less @ B @ A)) | ((less @ (sup @ x @ (inf @ y @ z)) @ (inf @ y @ (sup @ x @ z))) != (less @ A @ B)))),inference(paramod_ordered,[status(thm)],[908,300])). 52.41/15.44 thf(1101,plain,(! [B:a,A:a] : ((~ (less @ B @ A)) | ((less @ (sup @ x @ (inf @ y @ z)) @ (inf @ y @ (sup @ x @ z))) != (less @ A @ B)))),inference(simp,[status(thm)],[1100])). 52.41/15.44 thf(1102,plain,((~ (less @ (inf @ y @ (sup @ x @ z)) @ (sup @ x @ (inf @ y @ z))))),inference(pattern_uni,[status(thm)],[1101:[bind(A, $thf(sup @ x @ (inf @ y @ z))),bind(B, $thf(inf @ y @ (sup @ x @ z)))]])). 52.41/15.44 thf(81,axiom,((! [A:a,B:a,C:a]: ((less @ A @ B) => (less @ A @ (sup @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_local_Osup_Ostrict__coboundedI1)). 52.41/15.44 thf(505,plain,((! [A:a,B:a,C:a]: ((less @ A @ B) => (less @ A @ (sup @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 52.41/15.44 thf(187,axiom,((! [A:a,B:a,C:a]: ((modula1373251614_aux_a @ inf @ sup @ A @ B @ C) = (modula17988509_aux_a @ inf @ sup @ B @ C @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_local_Ob__a)). 52.41/15.44 thf(868,plain,((! [A:a,B:a,C:a]: ((modula1373251614_aux_a @ (inf) @ (sup) @ A @ B @ C) = (modula17988509_aux_a @ (inf) @ (sup) @ B @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 52.41/15.44 thf(143,axiom,((! [A:a,B:a]: ((less @ A @ B) = ((B = (sup @ B @ A)) & (B != A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_local_Osup_Ostrict__order__iff)). 52.41/15.44 thf(722,plain,((! [A:a,B:a]: ((less @ A @ B) = ((B = (sup @ B @ A)) & ~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 52.41/15.44 thf(127,axiom,((! [A:a,B:a,C:a]: ((less @ A @ B) => (less @ (inf @ A @ C) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_local_Oinf_Ostrict__coboundedI1)). 52.41/15.44 thf(675,plain,((! [A:a,B:a,C:a]: ((less @ A @ B) => (less @ (inf @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 52.41/15.44 thf(215,axiom,((! [A:a,B:a]: ((inf @ A @ (sup @ A @ B)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_local_Oinf__sup__absorb)). 52.41/15.44 thf(944,plain,((! [A:a,B:a]: ((inf @ A @ (sup @ A @ B)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 52.41/15.44 thf(122,axiom,((! [A:a,B:a,C:a]: ((sup @ A @ (sup @ B @ C)) = (sup @ B @ (sup @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_local_Osup_Oleft__commute)). 52.41/15.44 thf(663,plain,((! [A:a,B:a,C:a]: ((sup @ A @ (sup @ B @ C)) = (sup @ B @ (sup @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 52.41/15.44 thf(117,axiom,((! [A:a,B:a]: (((inf @ B @ A) = A) <= (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_local_Oinf_Oabsorb2)). 52.41/15.44 thf(648,plain,((! [A:a,B:a]: ((less_eq @ A @ B) => ((inf @ B @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 52.41/15.44 thf(36,axiom,((semigroup_a = (^ [A:(a > (a > a))]: ! [B:a,C:a,D:a]: ((A @ (A @ B @ C) @ D) = (A @ B @ (A @ C @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_semigroup__def)). 52.41/15.44 thf(354,plain,(((semigroup_a) = (^ [A:(a > (a > a))]: ! [B:a,C:a,D:a]: ((A @ (A @ B @ C) @ D) = (A @ B @ (A @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 52.41/15.44 thf(355,plain,(((semigroup_a) = (^ [A:(a > (a > a))]: ! [B:a,C:a,D:a]: ((A @ (A @ B @ C) @ D) = (A @ B @ (A @ C @ D)))))),inference(lifteq,[status(thm)],[354])). 52.41/15.44 thf(174,axiom,((! [A:a,B:a]: (((inf @ B @ A) = A) <= (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_local_Oinf__absorb2)). 52.41/15.44 thf(823,plain,((! [A:a,B:a]: ((less_eq @ A @ B) => ((inf @ B @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 52.41/15.44 thf(156,axiom,((! [A:a,B:a,C:a]: ((less @ A @ B) => (less @ A @ (sup @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_local_Oless__supI2)). 52.41/15.44 thf(776,plain,((! [A:a,B:a,C:a]: ((less @ A @ B) => (less @ A @ (sup @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 52.41/15.44 thf(89,axiom,((! [A:a,B:a,C:a]: ((inf @ (inf @ A @ B) @ C) = (inf @ A @ (inf @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_local_Oinf_Oassoc)). 52.41/15.44 thf(557,plain,((! [A:a,B:a,C:a]: ((inf @ (inf @ A @ B) @ C) = (inf @ A @ (inf @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 52.41/15.44 thf(11,axiom,((modula1376131916tice_a = modula1376131916tice_a)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_lattice_OM5__lattice_Ocong)). 52.41/15.44 thf(282,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 52.41/15.44 thf(138,axiom,((! [A:a,B:a]: ((B = (sup @ B @ A)) <= (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_local_Osup_OorderE)). 52.41/15.44 thf(707,plain,((! [A:a,B:a]: ((less_eq @ A @ B) => (B = (sup @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 52.41/15.44 thf(5,axiom,((! [A:(a > (a > a))]: ((lattic1885654924_set_a @ A) <= (semilattice_a @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_semilattice__set_Ointro)). 52.41/15.44 thf(263,plain,((! [A:(a > (a > a))]: ((semilattice_a @ (A)) => (lattic1885654924_set_a @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 52.41/15.44 thf(230,axiom,((! [A:a,B:a]: (less_eq @ (inf @ A @ B) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_local_Oinf_Ocobounded1)). 52.41/15.44 thf(993,plain,((! [A:a,B:a]: (less_eq @ (inf @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 52.41/15.44 thf(57,axiom,((! [A:a,B:a]: ((A != B) <= (less @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_local_Oless__imp__not__eq)). 52.41/15.44 thf(414,plain,((! [A:a,B:a]: ((less @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 52.41/15.44 thf(223,axiom,((! [A:a,B:a]: (((sup @ A @ B) = B) <= (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_local_Osup_Oabsorb2)). 52.41/15.44 thf(971,plain,((! [A:a,B:a]: ((less_eq @ A @ B) => ((sup @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 52.41/15.44 thf(162,axiom,((! [A:a,B:a]: ((less_eq @ A @ B) => ((less_eq @ B @ A) => (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_local_Oantisym)). 52.41/15.44 thf(791,plain,((! [A:a,B:a]: ((less_eq @ A @ B) => ((less_eq @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 52.41/15.44 thf(66,axiom,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a,F:a]: (((B @ D @ (A @ E @ F)) => (~ ((~ (B @ D @ F)) <= (B @ D @ E)))) <= (semilattice_order_a @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_semilattice__order_OboundedE)). 52.41/15.44 thf(441,plain,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a,F:a]: ((semilattice_order_a @ (A) @ (B) @ (C)) => ((B @ D @ (A @ E @ F)) => (~ ((B @ D @ E) => (~ (B @ D @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 52.41/15.44 thf(141,axiom,((! [A:a,B:a,C:a]: ((inf @ A @ (inf @ B @ C)) = (inf @ B @ (inf @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_local_Oinf__left__commute)). 52.41/15.44 thf(717,plain,((! [A:a,B:a,C:a]: ((inf @ A @ (inf @ B @ C)) = (inf @ B @ (inf @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 52.41/15.44 thf(80,axiom,((! [A:a,B:a]: (((less_eq @ B @ A) = (B = A)) <= (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_local_Oantisym__conv)). 52.41/15.44 thf(502,plain,((! [A:a,B:a]: ((less_eq @ A @ B) => ((less_eq @ B @ A) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 52.41/15.44 thf(169,axiom,((! [A:a,B:a]: ((less_eq @ A @ B) = ((inf @ A @ B) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_local_Ole__iff__inf)). 52.41/15.44 thf(808,plain,((! [A:a,B:a]: ((less_eq @ A @ B) = ((inf @ A @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 52.41/15.44 thf(201,axiom,((semigroup_a @ inf)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_local_Oinf_Osemigroup__axioms)). 52.41/15.44 thf(907,plain,((semigroup_a @ (inf))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 52.41/15.44 thf(31,axiom,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a,F:a]: (((B @ D @ E) => ((B @ D @ (A @ E @ F)) <= (B @ D @ F))) <= (semilattice_order_a @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_semilattice__order_OboundedI)). 52.41/15.44 thf(336,plain,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a,F:a]: ((semilattice_order_a @ (A) @ (B) @ (C)) => ((B @ D @ E) => ((B @ D @ F) => (B @ D @ (A @ E @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 52.41/15.44 thf(136,axiom,((lattice_a @ inf @ less_eq @ less @ sup)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)). 52.41/15.44 thf(703,plain,((lattice_a @ (inf) @ (less_eq) @ (less) @ (sup))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 52.41/15.44 thf(47,axiom,((modula1962211574trib_a = modula1962211574trib_a)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_lattice_Ono__distrib_Ocong)). 52.41/15.44 thf(386,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 52.41/15.44 thf(24,axiom,((! [A:(a > (a > a))]: ((semilattice_a @ A) <= (lattic1885654924_set_a @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_semilattice__set_Oaxioms)). 52.41/15.44 thf(314,plain,((! [A:(a > (a > a))]: ((lattic1885654924_set_a @ (A)) => (semilattice_a @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 52.41/15.44 thf(102,axiom,((! [A:a,B:a]: (less_eq @ A @ (sup @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_local_Osup__ge1)). 52.41/15.44 thf(595,plain,((! [A:a,B:a]: (less_eq @ A @ (sup @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 52.41/15.44 thf(106,axiom,((! [A:a,B:a,C:a]: ((modula1936294176_aux_a @ inf @ sup @ A @ B @ C) = (modula1936294176_aux_a @ inf @ sup @ B @ C @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_local_Od__c__a__b)). 52.41/15.44 thf(612,plain,((! [A:a,B:a,C:a]: ((modula1936294176_aux_a @ (inf) @ (sup) @ A @ B @ C) = (modula1936294176_aux_a @ (inf) @ (sup) @ B @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 52.41/15.44 thf(184,axiom,((! [A:a,B:a,C:a]: ((sup @ (sup @ A @ B) @ C) = (sup @ A @ (sup @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_local_Osup__assoc)). 52.41/15.44 thf(859,plain,((! [A:a,B:a,C:a]: ((sup @ (sup @ A @ B) @ C) = (sup @ A @ (sup @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 52.41/15.44 thf(67,axiom,((modula581031071_aux_a = modula581031071_aux_a)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_lattice_Oc__aux_Ocong)). 52.41/15.44 thf(446,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 52.41/15.44 thf(93,axiom,((! [A:a,B:a]: ((less_eq @ A @ B) => ((sup @ B @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_local_Osup_Oabsorb1)). 52.41/15.44 thf(571,plain,((! [A:a,B:a]: ((less_eq @ A @ B) => ((sup @ B @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 52.41/15.44 thf(200,axiom,((! [A:a,B:a,C:a]: ((less_eq @ (sup @ A @ B) @ C) => (~ ((less_eq @ A @ C) => (~ (less_eq @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_local_Osup_OboundedE)). 52.41/15.44 thf(903,plain,((! [A:a,B:a,C:a]: ((less_eq @ (sup @ A @ B) @ C) => (~ ((less_eq @ A @ C) => (~ (less_eq @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 52.41/15.44 thf(97,axiom,((! [A:a,B:a,C:a]: ((modula1144073633_aux_a @ inf @ sup @ A @ B @ C) = (inf @ (inf @ (sup @ A @ B) @ (sup @ B @ C)) @ (sup @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_local_Oe__aux__def)). 52.41/15.44 thf(581,plain,((! [A:a,B:a,C:a]: ((modula1144073633_aux_a @ (inf) @ (sup) @ A @ B @ C) = (inf @ (inf @ (sup @ A @ B) @ (sup @ B @ C)) @ (sup @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 52.41/15.44 thf(77,axiom,((! [A:a,B:a]: ((less @ A @ B) = (~ (less_eq @ B @ A) & (less_eq @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_local_Oless__le__not__le)). 52.41/15.44 thf(495,plain,((! [A:a,B:a]: ((less @ A @ B) = (~ (less_eq @ B @ A) & (less_eq @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 52.41/15.44 thf(196,axiom,((! [A:a,B:a]: ((sup @ A @ (inf @ A @ B)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_local_Osup__inf__absorb)). 52.41/15.44 thf(891,plain,((! [A:a,B:a]: ((sup @ A @ (inf @ A @ B)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 52.41/15.44 thf(2997,plain,((less_eq @ sk45 @ y) | (less @ sk45 @ sk46)),inference(bool_ext,[status(thm)],[2695])). 52.41/15.44 thf(236,axiom,((! [A:a,B:a,C:a]: ((modula397570059tice_a @ inf @ less @ sup @ A @ B @ C) = (((inf @ A @ C) = (inf @ B @ C)) & ((sup @ A @ C) = (sup @ B @ C)) & (less @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_local_ON5__lattice__def)). 52.41/15.44 thf(1010,plain,((! [A:a,B:a,C:a]: ((modula397570059tice_a @ (inf) @ (less) @ (sup) @ A @ B @ C) = (((inf @ A @ C) = (inf @ B @ C)) & ((sup @ A @ C) = (sup @ B @ C)) & (less @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 52.41/15.44 thf(181,axiom,((! [A:a,B:a]: ((sup @ (sup @ A @ B) @ B) = (sup @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_local_Osup_Oright__idem)). 52.41/15.44 thf(844,plain,((! [A:a,B:a]: ((sup @ (sup @ A @ B) @ B) = (sup @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 52.41/15.44 thf(100,axiom,((! [A:a,B:a,C:a]: ((less @ A @ B) => (less @ A @ (sup @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_local_Oless__supI1)). 52.41/15.44 thf(588,plain,((! [A:a,B:a,C:a]: ((less @ A @ B) => (less @ A @ (sup @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 52.41/15.44 thf(219,axiom,((((=) @ a) = (^ [A:a,B:a]: ((less_eq @ B @ A) & (less_eq @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_local_Oeq__iff)). 52.41/15.44 thf(960,plain,((((=) @ a) = (^ [A:a,B:a]: ((less_eq @ B @ A) & (less_eq @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 52.41/15.44 thf(961,plain,(((^ [A:a,B:a]: ((less_eq @ B @ A) & (less_eq @ A @ B))) = ((=) @ a))),inference(lifteq,[status(thm)],[960])). 52.41/15.44 thf(35,axiom,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a]: ((B @ (A @ D @ E) @ D) <= (semilattice_order_a @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_semilattice__order_Ocobounded1)). 52.41/15.44 thf(351,plain,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a]: ((semilattice_order_a @ (A) @ (B) @ (C)) => (B @ (A @ D @ E) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 52.41/15.44 thf(158,axiom,((! [A:a,B:a]: ((less_eq @ A @ B) = ((sup @ A @ B) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_local_Osup_Oabsorb__iff2)). 52.41/15.44 thf(781,plain,((! [A:a,B:a]: ((less_eq @ A @ B) = ((sup @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 52.41/15.44 thf(231,axiom,((! [A:a,B:a,C:a]: ((less_eq @ A @ (inf @ B @ C)) = ((less_eq @ A @ B) & (less_eq @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_local_Oinf_Obounded__iff)). 52.41/15.44 thf(995,plain,((! [A:a,B:a,C:a]: ((less_eq @ A @ (inf @ B @ C)) = ((less_eq @ A @ B) & (less_eq @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 52.41/15.44 thf(146,axiom,((! [A:a,B:a]: ((less_eq @ A @ B) => ((~ (less @ A @ B)) = (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_local_Oantisym__conv2)). 52.41/15.44 thf(731,plain,((! [A:a,B:a]: ((less_eq @ A @ B) => ((~ (less @ A @ B)) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 52.41/15.44 thf(58,axiom,((! [A:a,B:a]: ((~ (less @ B @ A)) <= (less @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_local_Oless__asym_H)). 52.41/15.44 thf(418,plain,((! [A:a,B:a]: ((less @ A @ B) => (~ (less @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 52.41/15.44 thf(243,axiom,((! [A:set_a]: ((condit1001553558elow_a @ less_eq @ A) = (? [B:a]: ! [C:a]: ((less_eq @ B @ C) <= (member_a @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_local_Obdd__below__def)). 52.41/15.44 thf(1030,plain,((! [A:set_a]: ((condit1001553558elow_a @ (less_eq) @ A) = (? [B:a]: ! [C:a]: ((member_a @ C @ A) => (less_eq @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 52.41/15.44 thf(92,axiom,((! [A:a,B:a]: ((A = (sup @ A @ B)) => (less_eq @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_local_Osup_OorderI)). 52.41/15.44 thf(568,plain,((! [A:a,B:a]: ((A = (sup @ A @ B)) => (less_eq @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 52.41/15.44 thf(46,axiom,((! [A:a,B:a,C:$o]: ((less @ A @ B) => ((C) <= (less @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_local_Oless__imp__triv)). 52.41/15.44 thf(383,plain,((! [A:a,B:a,C:$o]: ((less @ A @ B) => ((less @ B @ A) => (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 52.41/15.44 thf(177,axiom,((! [A:a,B:a]: ((less_eq @ A @ B) => ((inf @ A @ B) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_local_Oinf_Oabsorb1)). 52.41/15.44 thf(832,plain,((! [A:a,B:a]: ((less_eq @ A @ B) => ((inf @ A @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 52.41/15.44 thf(86,axiom,((! [A:(a > $o),B:a,C:(a > $o)]: (((! [D:a]: ((less_eq @ D @ B) <= (A @ D))) => ((! [D:a]: ((A @ D) => ((! [E:a]: ((less_eq @ E @ D) <= (A @ E))) => (C @ D)))) => (C @ (greatest_a @ less_eq @ A)))) <= (A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_local_OGreatestI2__order)). 52.41/15.44 thf(536,plain,((! [A:(a > $o),B:a,C:(a > $o)]: ((A @ B) => ((! [D:a]: ((A @ D) => (less_eq @ D @ B))) => ((! [D:a]: ((A @ D) => ((! [E:a]: ((A @ E) => (less_eq @ E @ D))) => (C @ D)))) => (C @ (greatest_a @ (less_eq) @ (A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 52.41/15.44 thf(249,axiom,((! [A:a]: ((inf @ A @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_local_Oinf__idem)). 52.41/15.44 thf(1045,plain,((! [A:a]: ((inf @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])). 52.41/15.44 thf(166,axiom,((! [A:a,B:a]: ((inf @ A @ B) = (inf @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_local_Oinf_Ocommute)). 52.41/15.44 thf(800,plain,((! [A:a,B:a]: ((inf @ A @ B) = (inf @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 52.41/15.44 thf(205,axiom,((! [A:a,B:a,C:a]: ((modula1376131916tice_a @ inf @ less @ sup @ A @ B @ C) = (((inf @ A @ B) = (inf @ B @ C)) & (less @ (inf @ A @ B) @ (sup @ A @ B)) & ((sup @ C @ A) = (sup @ B @ C)) & ((sup @ A @ B) = (sup @ B @ C)) & ((inf @ C @ A) = (inf @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_local_OM5__lattice__def)). 52.41/15.44 thf(914,plain,((! [A:a,B:a,C:a]: ((modula1376131916tice_a @ (inf) @ (less) @ (sup) @ A @ B @ C) = (((inf @ A @ B) = (inf @ B @ C)) & (less @ (inf @ A @ B) @ (sup @ A @ B)) & ((sup @ C @ A) = (sup @ B @ C)) & ((sup @ A @ B) = (sup @ B @ C)) & ((inf @ C @ A) = (inf @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 52.41/15.44 thf(68,axiom,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a]: ((semilattice_order_a @ A @ B @ C) => ((B @ D @ E) = (D = (A @ D @ E)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_semilattice__order_Oorder__iff)). 52.41/15.44 thf(447,plain,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a]: ((semilattice_order_a @ (A) @ (B) @ (C)) => ((B @ D @ E) = (D = (A @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 52.41/15.44 thf(63,axiom,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a,F:a]: ((semilattice_order_a @ A @ B @ C) => ((C @ D @ E) => (C @ (A @ F @ D) @ E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_semilattice__order_Ostrict__coboundedI2)). 52.41/15.44 thf(432,plain,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a,F:a]: ((semilattice_order_a @ (A) @ (B) @ (C)) => ((C @ D @ E) => (C @ (A @ F @ D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 52.41/15.44 thf(222,axiom,((! [A:a,B:a,C:a]: ((less_eq @ A @ (inf @ B @ C)) => (~ ((less_eq @ A @ B) => (~ (less_eq @ A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_local_Ole__infE)). 52.41/15.44 thf(967,plain,((! [A:a,B:a,C:a]: ((less_eq @ A @ (inf @ B @ C)) => (~ ((less_eq @ A @ B) => (~ (less_eq @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 52.41/15.44 thf(161,axiom,((lattic1885654924_set_a @ sup)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_local_OSup__fin_Osemilattice__set__axioms)). 52.41/15.44 thf(790,plain,((lattic1885654924_set_a @ (sup))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 52.41/15.44 thf(186,axiom,((! [A:a,B:a,C:a]: ((sup @ A @ (modula1936294176_aux_a @ inf @ sup @ B @ A @ C)) = (sup @ A @ (inf @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_local_Ob__join__d)). 52.41/15.44 thf(865,plain,((! [A:a,B:a,C:a]: ((sup @ A @ (modula1936294176_aux_a @ (inf) @ (sup) @ B @ A @ C)) = (sup @ A @ (inf @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 52.41/15.44 thf(43,axiom,((! [A:a]: ~ (less @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_local_Oorder_Oirrefl)). 52.41/15.44 thf(373,plain,((! [A:a]: ~ (less @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 52.41/15.44 thf(217,axiom,((! [A:a,B:a]: (((less_eq @ A @ B) => ((max_a @ less_eq @ A @ B) = B)) & ((~ (less_eq @ A @ B)) => ((max_a @ less_eq @ A @ B) = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_local_Omax__def)). 52.41/15.44 thf(950,plain,((! [A:a,B:a]: (((less_eq @ A @ B) => ((max_a @ (less_eq) @ A @ B) = B)) & ((~ (less_eq @ A @ B)) => ((max_a @ (less_eq) @ A @ B) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 52.41/15.44 thf(178,axiom,((! [A:a,B:a,C:a]: ((~ ((less @ A @ C) => (~ (less @ B @ C)))) <= (less @ (sup @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_local_Osup_Ostrict__boundedE)). 52.41/15.44 thf(835,plain,((! [A:a,B:a,C:a]: ((less @ (sup @ A @ B) @ C) => (~ ((less @ A @ C) => (~ (less @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 52.41/15.44 thf(261,plain,(! [A:(a > (a > a))] : ((~ ((A @ (A @ (sk2 @ (A)) @ (sk3 @ (A))) @ (sk4 @ (A))) = (A @ (sk2 @ (A)) @ (A @ (sk3 @ (A)) @ (sk4 @ (A)))))) | (semigroup_a @ (A)))),inference(cnf,[status(esa)],[260])). 52.41/15.44 thf(262,plain,(! [A:(a > (a > a))] : (((A @ (A @ (sk2 @ (A)) @ (sk3 @ (A))) @ (sk4 @ (A))) != (A @ (sk2 @ (A)) @ (A @ (sk3 @ (A)) @ (sk4 @ (A))))) | (semigroup_a @ (A)))),inference(lifteq,[status(thm)],[261])). 52.41/15.44 thf(28,axiom,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a,F:a]: ((semilattice_order_a @ A @ B @ C) => ((B @ D @ E) => (B @ (A @ D @ F) @ E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_semilattice__order_OcoboundedI1)). 52.41/15.44 thf(326,plain,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o)),D:a,E:a,F:a]: ((semilattice_order_a @ (A) @ (B) @ (C)) => ((B @ D @ E) => (B @ (A @ D @ F) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 52.41/15.44 thf(294,plain,(! [F:a,E:a,D:a,C:(a > (a > $o)),B:(a > (a > $o)),A:(a > (a > a))] : ((~ (semilattice_order_a @ (A) @ (B) @ (C))) | (~ (C @ D @ (A @ E @ F))) | (C @ D @ F))),inference(cnfConj,[status(thm)],[292])). 52.41/15.44 thf(133,axiom,((finite40241356em_a_a @ sup)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_local_Ocomp__fun__idem__sup)). 52.41/15.44 thf(696,plain,((finite40241356em_a_a @ (sup))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 52.41/15.44 thf(12,axiom,((modula17988509_aux_a = modula17988509_aux_a)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_lattice_Oa__aux_Ocong)). 52.41/15.44 thf(283,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 52.41/15.44 thf(210,axiom,((! [A:a,B:a,C:a]: ((less_eq @ (sup @ A @ B) @ C) => (~ ((~ (less_eq @ B @ C)) <= (less_eq @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_local_Ole__supE)). 52.41/15.44 thf(928,plain,((! [A:a,B:a,C:a]: ((less_eq @ (sup @ A @ B) @ C) => (~ ((less_eq @ A @ C) => (~ (less_eq @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])). 52.41/15.44 thf(198,axiom,((! [A:a,B:a,C:a]: (((less_eq @ C @ A) => (less_eq @ C @ B)) <= (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_local_Odual__order_Otrans)). 52.41/15.44 thf(897,plain,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => ((less_eq @ C @ A) => (less_eq @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 52.41/15.44 thf(153,axiom,((! [A:a,B:a,C:a]: ((less @ A @ B) => ((less @ A @ C) <= (less_eq @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_local_Oless__le__trans)). 52.41/15.44 thf(767,plain,((! [A:a,B:a,C:a]: ((less @ A @ B) => ((less_eq @ B @ C) => (less @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 52.41/15.44 thf(244,axiom,((! [A:a,B:a,C:a]: ((less_eq @ (sup @ A @ B) @ C) = ((less_eq @ A @ C) & (less_eq @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_local_Ole__sup__iff)). 52.41/15.44 thf(1033,plain,((! [A:a,B:a,C:a]: ((less_eq @ (sup @ A @ B) @ C) = ((less_eq @ A @ C) & (less_eq @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])). 52.41/15.44 thf(53,axiom,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o))]: ((semilattice_a @ A) <= (semilattice_order_a @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_semilattice__order_Oaxioms_I1_J)). 52.41/15.44 thf(400,plain,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o))]: ((semilattice_order_a @ (A) @ (B) @ (C)) => (semilattice_a @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 52.41/15.44 thf(114,axiom,((! [A:a,B:a]: ((inf @ (inf @ A @ B) @ B) = (inf @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_local_Oinf_Oright__idem)). 52.41/15.44 thf(635,plain,((! [A:a,B:a]: ((inf @ (inf @ A @ B) @ B) = (inf @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 52.41/15.44 thf(72,axiom,((! [A:(a > $o),B:a,C:(a > $o)]: (((! [D:a]: ((A @ D) => (less_eq @ B @ D))) => ((C @ (least_a @ less_eq @ A)) <= (! [D:a]: ((A @ D) => ((C @ D) <= (! [E:a]: ((less_eq @ D @ E) <= (A @ E)))))))) <= (A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_local_OLeastI2__order)). 52.41/15.44 thf(459,plain,((! [A:(a > $o),B:a,C:(a > $o)]: ((A @ B) => ((! [D:a]: ((A @ D) => (less_eq @ B @ D))) => ((! [D:a]: ((A @ D) => ((! [E:a]: ((A @ E) => (less_eq @ D @ E))) => (C @ D)))) => (C @ (least_a @ (less_eq) @ (A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 52.41/15.44 thf(3394,plain,((less_eq @ sk48 @ y) | (less @ sk47 @ sk48)),inference(bool_ext,[status(thm)],[3382])). 52.41/15.44 thf(188,axiom,((! [A:a,B:a]: (less_eq @ (inf @ A @ B) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_local_Oinf__le1)). 52.41/15.44 thf(871,plain,((! [A:a,B:a]: (less_eq @ (inf @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 52.41/15.44 thf(41,axiom,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o))]: (((lattic655834328_set_a @ A @ B @ C) <= (lattic1885654924_set_a @ A)) <= (semilattice_order_a @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_semilattice__order__set_Ointro)). 52.41/15.44 thf(369,plain,((! [A:(a > (a > a)),B:(a > (a > $o)),C:(a > (a > $o))]: ((semilattice_order_a @ (A) @ (B) @ (C)) => ((lattic1885654924_set_a @ (A)) => (lattic655834328_set_a @ (A) @ (B) @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 52.41/15.44 thf(51,axiom,((! [A:a,B:a]: ((~ (less @ B @ A)) <= (less @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_local_Oless__imp__not__less)). 52.41/15.44 thf(395,plain,((! [A:a,B:a]: ((less @ A @ B) => (~ (less @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 52.41/15.44 thf(179,axiom,((! [A:a,B:a,C:a,D:a]: (((less_eq @ C @ D) => (less_eq @ (sup @ A @ C) @ (sup @ B @ D))) <= (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_local_Osup_Omono)). 52.41/15.44 thf(839,plain,((! [A:a,B:a,C:a,D:a]: ((less_eq @ A @ B) => ((less_eq @ C @ D) => (less_eq @ (sup @ A @ C) @ (sup @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 52.41/15.44 thf(145,axiom,((! [A:a,B:a,C:a]: ((modula1144073633_aux_a @ inf @ sup @ A @ B @ C) = (modula1144073633_aux_a @ inf @ sup @ B @ C @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_local_Oe__c__a__b)). 52.41/15.44 thf(728,plain,((! [A:a,B:a,C:a]: ((modula1144073633_aux_a @ (inf) @ (sup) @ A @ B @ C) = (modula1144073633_aux_a @ (inf) @ (sup) @ B @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 52.41/15.44 thf(149,axiom,((! [A:(a > $o)]: ((A @ (least_a @ less_eq @ A)) <= (? [B:a]: (! [C:a]: ((C = B) <= (! [D:a]: ((A @ D) => (less_eq @ C @ D)) & (A @ C))) & ! [C:a]: ((A @ C) => (less_eq @ B @ C)) & (A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_local_OLeast1I)). 52.41/15.44 thf(740,plain,((! [A:(a > $o)]: ((? [B:a]: (! [C:a]: ((! [D:a]: ((A @ D) => (less_eq @ C @ D)) & (A @ C)) => (C = B)) & ! [C:a]: ((A @ C) => (less_eq @ B @ C)) & (A @ B))) => (A @ (least_a @ (less_eq) @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 52.41/15.44 thf(227,axiom,((! [A:a,B:a,C:a]: (((less_eq @ A @ C) <= (less_eq @ B @ C)) <= (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_local_Oorder__trans)). 52.41/15.44 thf(982,plain,((! [A:a,B:a,C:a]: ((less_eq @ A @ B) => ((less_eq @ B @ C) => (less_eq @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 52.41/15.44 thf(234,axiom,((! [A:a,B:a]: ((less_eq @ A @ B) = (B = (sup @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_local_Osup_Oorder__iff)). 52.41/15.44 thf(1004,plain,((! [A:a,B:a]: ((less_eq @ A @ B) = (B = (sup @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 52.41/15.44 thf(27,axiom,((! [A:(a > (a > a)),B:a,C:a]: ((semilattice_a @ A) => ((A @ (A @ B @ C) @ C) = (A @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_semilattice_Oright__idem)). 52.41/15.44 thf(322,plain,((! [A:(a > (a > a)),B:a,C:a]: ((semilattice_a @ (A)) => ((A @ (A @ B @ C) @ C) = (A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 52.41/15.44 thf(167,axiom,((! [A:a,B:a]: ((less @ A @ B) => (less_eq @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_local_Oorder_Ostrict__implies__order)). 52.41/15.44 thf(803,plain,((! [A:a,B:a]: ((less @ A @ B) => (less_eq @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 52.41/15.44 thf(212,axiom,((! [A:a,B:a]: ((less_eq @ A @ B) = ((inf @ B @ A) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_local_Oinf_Oabsorb__iff2)). 52.41/15.44 thf(935,plain,((! [A:a,B:a]: ((less_eq @ A @ B) = ((inf @ B @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 52.41/15.44 thf(208,axiom,((! [A:a,B:a,C:a]: (less_eq @ (sup @ A @ (inf @ B @ C)) @ (inf @ (sup @ A @ B) @ (sup @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_local_Odistrib__sup__le)). 52.41/15.44 thf(923,plain,((! [A:a,B:a,C:a]: (less_eq @ (sup @ A @ (inf @ B @ C)) @ (inf @ (sup @ A @ B) @ (sup @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 52.41/15.44 thf(90,axiom,((! [A:set_a,B:a]: ((! [C:a]: ((member_a @ C @ A) => (less_eq @ B @ C))) => (condit1001553558elow_a @ less_eq @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_local_Obdd__belowI)). 52.41/15.44 thf(560,plain,((! [A:set_a,B:a]: ((! [C:a]: ((member_a @ C @ A) => (less_eq @ B @ C))) => (condit1001553558elow_a @ (less_eq) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 52.41/15.44 thf(4734,plain,(($false)),inference(e,[status(thm)],[1036,1024,347,962,941,666,909,333,628,977,762,1073,873,379,511,269,597,3382,533,797,814,829,1001,885,301,565,651,257,587,917,817,638,3463,421,606,289,316,1013,284,770,475,492,591,376,1136,1051,480,1020,574,397,634,734,293,660,998,411,265,877,692,307,452,920,439,678,270,925,366,714,1636,798,1057,894,1021,1042,302,820,297,429,275,260,862,407,693,847,361,625,329,1027,757,974,2332,435,2112,710,456,842,578,697,1983,615,1064,1111,725,403,356,420,499,256,884,339,554,669,1039,622,393,647,985,654,3819,721,1984,779,371,343,938,805,508,311,657,1054,530,888,773,794,298,618,425,3079,856,279,689,584,1007,286,958,281,2695,259,826,577,391,787,498,335,704,947,350,672,900,681,784,1048,990,880,303,764,979,362,451,737,318,631,552,609,799,483,700,2785,964,3483,811,387,932,1061,912,1044,1015,306,299,1102,505,1066,278,868,722,675,1758,944,2318,663,927,648,1018,355,823,776,557,295,282,707,263,993,414,971,791,441,717,502,808,907,336,703,386,314,595,612,876,859,446,571,671,903,581,495,2325,891,2997,1010,844,588,961,963,351,781,995,731,418,1030,568,383,832,536,1045,800,290,914,300,447,432,967,790,1757,865,373,950,835,262,326,294,268,696,720,283,928,897,767,1033,400,960,635,575,459,908,3394,871,369,395,839,728,740,982,1004,322,803,354,935,923,2690,560,1417])). 52.41/15.44 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p 52.41/15.44 % [INFO] Killing All external provers ... 0.19/15.57 EOF