0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : java -Xss128m -Xmx4g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar %s -t %d -p --atp cvc4=/export/starexec/sandbox/solver/bin/externals/cvc4 --atp e=/export/starexec/sandbox/solver/bin/externals/eprover --atp iprover=/export/starexec/sandbox/solver/bin/externals/iprover 0.03/0.23 % Computer : n019.star.cs.uiowa.edu 0.03/0.23 % Model : x86_64 x86_64 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.23 % Memory : 32218.625MB 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.23 % CPULimit : 300 0.03/0.23 % DateTime : Sat Jul 14 05:56:24 CDT 2018 0.03/0.23 % CPUTime : 9.75/3.78 % [INFO] Running in sequential loop mode. 10.39/4.00 % [CONFIG] Using configuration: timeout(300) with strategy 10.67/4.08 % [INFO] iprover registered as external prover. 10.67/4.08 % [INFO] e registered as external prover. 10.67/4.08 % [INFO] cvc4 registered as external prover. 10.67/4.09 % [INFO] Parsing finished. Scanning for conjecture ... 10.92/4.19 % [INFO] Found a conjecture and 532 axioms. Running axiom selection ... 11.65/4.36 % [INFO] Axiom selection finished. Selected 532 axioms (removed 0 axioms). 13.34/4.92 % [INFO] Type checking passed. Searching for refutation ... 31.12/10.81 % [INFO] Killing All external provers ... 31.12/10.82 % Time passed: 10488ms 31.12/10.82 % Effective reasoning time: 7032ms 31.12/10.82 % Solved by strategy 31.12/10.84 % Axioms used in derivation (532): fact_add__le__less__mono, fact_order__le__neq__trans, fact_Nat_Oadd__0__right, fact_xt1_I1_J, fact_le__SucI, fact_Pi__I, fact_insertCI, fact_card__image__le, arity_fun__Orderings_Oorder, fact_nat_Osimps_I3_J, fact_surj__f__inv__f, arity_Nat__Onat__Groups_Ocancel__semigroup__add, fact_pos__add__strict, fact_n_I2_J, fact_add__strict__right__mono, fact_Ints__odd__nonzero, fact_less__eq__nat_Osimps_I2_J, fact_inj__imp__surj__inv, fact_subset__UNIV, fact_nat__add__left__commute, fact_order__le__less__trans, fact_inv__into__into, fact_insert__iff, fact_image__insert, fact__C1_C, fact_le__eq__less__or__eq, fact_nat__less__cases, fact_Pi__mono, arity_prod__Finite__Set_Ofinite, fact_IIA__def, fact_one__is__add, fact_surjh, fact_xt1_I4_J, fact_termination__basic__simps_I5_J, fact_insert__subset, fact_unanimity__def, fact_trans__less__add1, fact_injD, fact__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096, fact_less__imp__le__nat, arity_Nat__Onat__Orderings_Oorder, fact_add__leD1, arity_sum__Finite__Set_Ofinite, fact__096_Ia_M_Ab_J_A_126_058_ALba_096, fact_Suc__mono, arity_Nat__Onat__Groups_Oordered__comm__monoid__add, fact_less__nat__zero__code, fact_nat_Osize_I4_J, fact_linorder__not__le, fact_finite, fact_add__less__mono, fact_insertI1, fact_order__less__asym_H, fact_third__alt, fact_order__eq__refl, arity_Nat__Onat__Rings_Ozero__neq__one, fact_folding__image__simple_Oeq__fold__g, fact_in__mktop, fact_add__right__imp__eq, fact_inj__image__mem__iff, fact_Pi__anti__mono, fact_linorder__antisym__conv2, fact_finite__range__imageI, fact_measures__lesseq, arity_HOL__Obool__Orderings_Opreorder, fact_nat__add__right__cancel, fact_PiProf, fact_gr0__conv__Suc, fact_in__mkbot, fact_linorder__neqE, fact_leI, fact_assms_I1_J, fact_Suc__le__mono, fact_surj__iff__all, help_c__fequal__2, fact_le__neq__implies__less, fact_add__pos__nonneg, fact_finite__code, fact_zero__le__one, fact_finite__Plus__UNIV__iff, fact_below__Lin, fact_nat__add__left__cancel__less, fact_pred__equals__eq2, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, help_c__fFalse__1, fact_linorder__antisym__conv3, fact_add__strict__increasing2, fact_order__less__imp__not__eq, fact_linorder__neqE__linordered__idom, help_c__COMBC__1, fact_image__image, fact__C4_C, fact_add__le__imp__le__left, fact__096_B_Bthesis_O_A_I_B_Be_O_Adistinct_A_091c_M_Ad_M_Ae_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_card__eq__UNIV__imp__eq__UNIV, fact_add__increasing2, arity_Option__Ooption__Finite__Set_Ofinite, fact_list_Osimps_I3_J, fact_linorder__antisym__conv1, fact_add__nonneg__eq__0__iff, fact_inv__into__image__cancel, fact_measures__less, fact_splice_Osimps_I3_J, fact_equalityD2, fact_even__less__0__iff, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_add__0__left, fact_add__mono, fact_predicate2D, fact_gr0I, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact__096c_A_126_061_Ad_096, fact_add__0__iff, fact_le__funD, fact_add__right__mono, fact_le__fun__def, fact_finite__Prod__UNIV, fact_finite__UNIV, fact_Pi__mem, fact_inj__on__inv__into, fact_splice_Osimps_I2_J, fact_le__iff__add, fact_one__reorient, fact_list_Osize_I2_J, fact_top__apply, help_c__COMBS__1, arity_HOL__Obool__Orderings_Otop, fact_xt1_I9_J, fact_less__add__eq__less, help_c__COMBI__1, fact_linorder__less__linear, fact_order__less__imp__not__less, fact_add__lessD1, fact_add__le__mono1, fact_less__eq__nat_Osimps_I1_J, fact_lessI, fact_ord__less__eq__trans, fact_in__mono, fact_zero__reorient, fact_termination__basic__simps_I4_J, fact_card__image, fact_nat_Oinject, fact__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096, fact_mkbot__Lin, fact_not__add__less2, fact_less__or__eq__imp__le, fact_list_Osimps_I2_J, fact_in__measure, fact_Suc__less__SucD, fact_funcset__mem, fact_top1I, fact_rev__image__eqI, fact_add__0__right, fact_card__bij, fact_Suc__leI, fact_add__neg__nonpos, fact_subset__iff__psubset__eq, fact_in__finite__psubset, fact_inj__on__contraD, fact_not__less__less__Suc__eq, fact_finite__imageD, fact_card__Plus__conv__if, fact_UNIV__I, fact_le__add2, fact_inj__on__strict__subset, fact_xt1_I10_J, fact_less__irrefl__nat, fact_order__antisym, arity_Nat__Onat__Orderings_Opreorder, fact_finite__indi, fact_finite__surj, fact_Suc__lessD, fact_order__less__imp__not__eq2, fact_Suc__n__not__le__n, fact_order__refl, fact_not__less0, fact_card__psubset, fact_dictator__def, fact_add__left__imp__eq, fact_trans__less__add2, fact_less__Suc__eq__le, fact_xt1_I5_J, fact_insert__code, fact_card_Oinsert, fact_add__leD2, fact_Ints__0, arity_Nat__Onat__Rings_Ocomm__semiring__1, fact_inj__on__id2, fact_less__zeroE, fact_termination__basic__simps_I2_J, fact_not__one__less__zero, fact_not__less__eq, fact_insert__image, fact_nat_Osimps_I2_J, fact_zero__le__double__add__iff__zero__le__single__add, fact_nat__neq__iff, fact_less__imp__neq, fact_xt1_I8_J, fact_finite__PlusD_I2_J, fact_predicate1D, fact_less__not__refl3, fact__C2_C, fact_add__right__cancel, fact_add__less__cancel__left, fact_add__left__cancel, fact_eq__mem, fact_distinct_Osimps_I1_J, fact_finite__UNIV__card__ge__0, fact_nat__size, fact_subset__insertI, fact_notin__Lin__iff, fact_xt1_I3_J, fact_inj__eq, fact_nat__add__left__cancel__le, fact_double__zero__sym, arity_HOL__Obool__Orderings_Oord, fact__096a_A_126_061_Ab_096, fact_finite__insert, fact_one__neq__zero, fact_insert__absorb2, fact_card__def, fact_list_Oinject, fact_insertI2, fact_less__Suc__eq__0__disj, fact_le__Suc__eq, fact_insert__absorb, fact_finite__fun__UNIVD1, fact_add__strict__mono, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_inj__image__eq__iff, fact_subset__insert, fact__096Lba_A_058_ALin_096, fact_rev__finite__subset, arity_Nat__Onat__Groups_Ocomm__monoid__add, fact_eqset__imp__iff, fact_same__fstI, fact_less__antisym, fact_order__neq__le__trans, fact_not__one__le__zero, fact_Suc__le__eq, fact_range__composition, fact_equalityD1, fact_finite__option__UNIV, fact_subset__image__iff, fact_le__funE, fact_inj__on__def, fact_inj__on__iff, arity_Nat__Onat__Orderings_Oord, arity_Nat__Onat__Groups_Omonoid__add, arity_fun__Orderings_Opreorder, fact_less__eq__Suc__le, fact_less__add__Suc2, fact_insert__commute, fact_in__below, fact_inv__image__comp, fact_folding__image__simple_Oinsert, help_c__fequal__1, fact_in__above, fact_nat_Osize_I1_J, fact_range__ex1__eq, fact_finite__imageI, fact_ord__le__eq__trans, fact_linorder__neq__iff, fact_not__Cons__self, fact_mlex__leq, arity_Nat__Onat__Groups_Oordered__ab__semigroup__add, fact_set__mp, fact_psubset__card__mono, fact_injh, fact_linorder__neqE__nat, fact_not__less__iff__gr__or__eq, fact_mktop__Lin, fact__096_Ib_M_Aa_J_A_126_058_ALab_096, fact_card__ge__0__finite, fact_psubsetD, arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add, fact_inj__image__subset__iff, arity_Nat__Onat__Groups_Ozero, fact_add__is__1, fact_card__insert__if, fact_order__less__le, fact__096Lab_A_058_ALin_096, fact_card__Plus, fact_add__nonneg__pos, fact_add__less__cancel__right, fact_add__nonpos__nonpos, fact_Ints__double__eq__0__iff, fact_subset__inj__on, fact_Suc__le__lessD, fact_set__eq__subset, fact_add__increasing, fact_not__add__less1, fact_Nitpick_Orefl_H__def, fact_inv__into__injective, fact_psubset__trans, fact_xt1_I12_J, fact_pred__subset__eq, arity_Product____Type__Ounit__Finite__Set_Ofinite, fact_n_I3_J, fact_Suc__inject, arity_fun__Orderings_Oord, fact_equalityI, fact_subset__refl, fact_ext, fact_order__less__not__sym, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, arity_fun__Finite__Set_Ofinite, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_zero__less__double__add__iff__zero__less__single__add, arity_HOL__Obool__Orderings_Oorder, fact_linorder__le__less__linear, fact_Suc__neq__Zero, fact_card__mono, fact_add__eq__self__zero, fact_nat__add__left__cancel, fact_endo__inj__surj, fact_Prof__def, fact_Ints__1, fact_less__le__not__le, arity_Nat__Onat__Orderings_Olinorder, fact_PiE, fact_n__not__Suc__n, fact_nat__le__linear, fact_inv__into__f__f, fact_linorder__le__cases, fact_assms_I3_J, fact_Pi__UNIV, fact_in__measures_I2_J, fact_card__UNIV__unit, fact_order__less__le__trans, help_c__COMBB__1, fact_rangeI, fact_not__leE, fact_leD, fact_add__strict__left__mono, fact_insert__ident, fact_add__Suc, fact_order__less__asym, fact_add__gr__0, arity_fun__Orderings_Otop, fact_mlex__less, fact_psubset__imp__subset, fact_nat_Osize_I2_J, fact_funcset__id, fact_set__rev__mp, fact_card__insert__disjoint, fact_add__less__imp__less__right, fact_ex__nat__less__eq, arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le, fact_eq__mem__trans, fact_inj__on__iff__eq__card, fact_Suc__eq__plus1__left, fact_Zero__not__Suc, fact_inv__f__f, fact_list_Osimps_I5_J, fact_pigeonhole, fact_not__Cons__self2, fact_Suc__leD, fact_zero__less__one, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_add_Ocomm__neutral, fact_image__surj__f__inv__f, fact_rev__predicate2D, fact_linorder__linear, fact_less__eq__Suc__le__raw, fact_less__trans__Suc, fact_xt1_I6_J, fact_le__refl, fact_nat__add__assoc, fact_subset__insertI2, arity_HOL__Obool__Finite__Set_Ofinite, fact_less__not__refl2, fact_inj__fun, fact_le__add1, fact_trans__le__add2, fact_linorder__not__less, fact_less__add__Suc1, fact_all__nat__less__eq, fact_add__neg__neg, fact_nat__case__Suc, fact_less__fun__def, fact_rev__predicate1D, fact_One__nat__def, fact_in__lex__prod, fact_add__is__0, fact_Ints__odd__less__0, fact_termination__basic__simps_I3_J, fact_image__inv__into__cancel, fact_add__less__imp__less__left, fact_inv__f__eq, fact__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact__096P_A_058_AProf_096, fact_le__imp__less__Suc, fact_in__measures_I1_J, fact_xt1_I2_J, fact_add__pos__pos, fact_add__0, fact_equalityE, fact_add__nonneg__nonneg, fact_Suc__eq__plus1, fact_in__rel__def, fact_image__iff, fact_Lin__irrefl, fact_subset__psubset__trans, fact_card__seteq, fact_finite__fun__UNIVD2, fact_card__inj, fact_Zero__neq__Suc, fact_order__eq__iff, arity_Nat__Onat__Groups_Oab__semigroup__add, arity_Nat__Onat__Rings_Olinordered__semidom, fact_add__le__cancel__right, fact_add__left__mono, fact_pairwise__neutrality, fact__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_096, fact_not__less__eq__eq, fact_double__add__le__zero__iff__single__add__le__zero, fact_less__not__refl, fact_insert__mono, fact_ord__eq__less__trans, fact_le0, fact_ex__least__nat__less, fact_card_Oeq__fold__g, fact_le__trans, fact_equalityCE, fact_gr__implies__not0, fact_finite_OinsertI, help_c__COMBK__1, fact_add__less__le__mono, fact_dist, fact_Ints__add, fact_image__eqI, fact_less__add__one, fact_inj__on__add__nat, fact_subsetD, fact_top__greatest, fact_zero__neq__one, fact_less__Suc__eq, fact_nat__add__commute, fact_above__Lin, fact_Suc__less__eq, fact_splice__Nil2, fact_eq__card__imp__inj__on, fact_psubset__eq, fact_add__leE, fact_range__eqI, fact_u, arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add, fact_image__ident, fact__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_G_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_096, fact_zero__less__Suc, fact_dictatorI, fact_eq__imp__le, fact_finite__surj__inj, fact_inv__into__f__eq, fact_image__mono, fact_plus__nat_Oadd__0, fact__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_059_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_order__le__imp__less__or__eq, fact_nat_Osize_I3_J, fact_add__strict__increasing, fact_insertE, fact_inj__Suc, fact_add__nonpos__neg, fact_list_Osimps_I4_J, fact__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_058_AProf_096, fact_finite__PlusD_I1_J, fact_le__SucE, fact_le__less__Suc__eq, fact_inj__onD, fact_splice_Osimps_I1_J, fact_order__antisym__conv, fact_n_I1_J, fact_neq0__conv, fact_Suc__n__not__n, fact_f__inv__into__f, fact_subset__trans, fact_le__antisym, fact_trans__le__add1, fact_eqelem__imp__iff, fact_card__infinite, fact_pred__equals__eq, fact_double__eq__0__iff, fact_le__0__eq, fact_finite__UNIV__surj__inj, fact_psubset__subset__trans, fact_order__less__imp__le, fact_termination__basic__simps_I1_J, fact_less__iff__Suc__add, fact_finite__subset, fact_order__less__trans, fact_finite__UNIV__inj__surj, fact_zero__less__two, fact__C3_C, fact_add__le__imp__le__right, fact_order__less__irrefl, fact_add__le__mono, fact_less__Suc0, fact_order__le__less, fact__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_iso__tuple__UNIV__I, arity_Nat__Onat__Groups_Oone, fact_mem__def, fact_add__imp__eq, arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_nat__less__le, fact_list_Osize_I1_J, fact_pred__subset__eq2, fact_card__insert__le, fact_less__SucE, fact_linorder__cases, fact_add__less__mono1, fact_add__le__cancel__left, fact_xt1_I11_J, fact_ord__eq__le__trans, fact_finite__Plus, fact_double__add__less__zero__iff__single__add__less__zero, fact_ab__semigroup__add__class_Oadd__ac_I1_J, fact_add__Suc__shift, fact_less__SucI, fact_Suc__not__Zero, fact_surj__imp__inj__inv, fact_xt1_I7_J, fact_order__trans, fact_Suc__lessI, fact_add__Suc__right, fact_image__inv__f__f, fact_finite__Plus__iff, fact_const__Lin__Prof, fact_UNIV__Plus__UNIV, fact_imageI 31.12/10.85 % No. of inferences in proof: 1068 31.12/10.85 % No. of processed clauses: 8 31.12/10.85 % No. of generated clauses: 0 31.12/10.85 % No. of forward subsumed clauses: 0 31.12/10.85 % No. of backward subsumed clauses: 0 31.12/10.85 % No. of ground rewrite rules in store: 5 31.12/10.85 % No. of non-ground rewrite rules in store: 0 31.12/10.85 % No. of positive (non-rewrite) units in store: 0 31.12/10.85 % No. of negative (non-rewrite) units in store: 2 31.12/10.85 % No. of choice functions detected: 0 31.12/10.85 % No. of choice instantiations: 0 31.12/10.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 10488 ms resp. 7032 ms w/o parsing 32.13/11.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p 32.13/11.36 thf(tc_Arrow__Order__Mirabelle_Oalt_type, type, tc_Arrow__Order__Mirabelle_Oalt: $i). 32.13/11.36 thf(tc_prod_type, type, tc_prod: ($i > ($i > $i))). 32.13/11.36 thf(c_member_type, type, c_member: ($i > $i)). 32.13/11.36 thf(c_Product__Type_OPair_type, type, c_Product__Type_OPair: ($i > ($i > $i))). 32.13/11.36 thf(v_c_____type, type, v_c____: $i). 32.13/11.36 thf(hAPP_type, type, hAPP: ($i > ($i > $i))). 32.13/11.36 thf(v_d_____type, type, v_d____: $i). 32.13/11.36 thf(v_P_____type, type, v_P____: $i). 32.13/11.36 thf(hBOOL_type, type, hBOOL: ($i > $o)). 32.13/11.36 thf(tc_Nat_Onat_type, type, tc_Nat_Onat: $i). 32.13/11.36 thf(c_Orderings_Oord__class_Oless_type, type, c_Orderings_Oord__class_Oless: ($i > $i)). 32.13/11.36 thf(v_h_____type, type, v_h____: $i). 32.13/11.36 thf(v_n_____type, type, v_n____: $i). 32.13/11.36 thf(c_Arrow__Order__Mirabelle_Omktop_type, type, c_Arrow__Order__Mirabelle_Omktop: $i). 32.13/11.36 thf(v_e_____type, type, v_e____: $i). 32.13/11.36 thf(c_Arrow__Order__Mirabelle_Oabove_type, type, c_Arrow__Order__Mirabelle_Oabove: $i). 32.13/11.36 thf(c_Arrow__Order__Mirabelle_Omkbot_type, type, c_Arrow__Order__Mirabelle_Omkbot: $i). 32.13/11.36 thf(tc_HOL_Obool_type, type, tc_HOL_Obool: $i). 32.13/11.36 thf(class_Orderings_Opreorder_type, type, class_Orderings_Opreorder: ($i > $o)). 32.13/11.36 thf(tc_fun_type, type, tc_fun: ($i > ($i > $i))). 32.13/11.36 thf(c_Orderings_Otop__class_Otop_type, type, c_Orderings_Otop__class_Otop: ($i > $i)). 32.13/11.36 thf(c_Set_Oimage_type, type, c_Set_Oimage: ($i > ($i > ($i > ($i > $i))))). 32.13/11.36 thf(c_Hilbert__Choice_Oinv__into_type, type, c_Hilbert__Choice_Oinv__into: ($i > ($i > ($i > ($i > $i))))). 32.13/11.36 thf(class_Finite__Set_Ofinite_type, type, class_Finite__Set_Ofinite: ($i > $o)). 32.13/11.36 thf(c_Finite__Set_Ofinite_type, type, c_Finite__Set_Ofinite: ($i > ($i > $o))). 32.13/11.36 thf(tc_Arrow__Order__Mirabelle_Oindi_type, type, tc_Arrow__Order__Mirabelle_Oindi: $i). 32.13/11.36 thf(c_Groups_Oone__class_Oone_type, type, c_Groups_Oone__class_Oone: ($i > $i)). 32.13/11.36 thf(class_Groups_Oone_type, type, class_Groups_Oone: ($i > $o)). 32.13/11.36 thf(c_Fun_Oinj__on_type, type, c_Fun_Oinj__on: ($i > ($i > ($i > ($i > $o))))). 32.13/11.36 thf(v_F_type, type, v_F: $i). 32.13/11.36 thf(c_Arrow__Order__Mirabelle_OIIA_type, type, c_Arrow__Order__Mirabelle_OIIA: ($i > $o)). 32.13/11.36 thf(tc_sum_type, type, tc_sum: ($i > ($i > $i))). 32.13/11.36 thf(c_Sum__Type_OPlus_type, type, c_Sum__Type_OPlus: ($i > ($i > ($i > ($i > $i))))). 32.13/11.36 thf(c_Finite__Set_Ocard_type, type, c_Finite__Set_Ocard: ($i > ($i > $i))). 32.13/11.36 thf(c_List_Olist_ONil_type, type, c_List_Olist_ONil: ($i > $i)). 32.13/11.36 thf(c_List_Osplice_type, type, c_List_Osplice: ($i > ($i > ($i > $i)))). 32.13/11.36 thf(tc_Option_Ooption_type, type, tc_Option_Ooption: ($i > $i)). 32.13/11.36 thf(c_List_Olist_OCons_type, type, c_List_Olist_OCons: ($i > ($i > ($i > $i)))). 32.13/11.36 thf(class_Orderings_Oorder_type, type, class_Orderings_Oorder: ($i > $o)). 32.13/11.36 thf(c_Set_Oinsert_type, type, c_Set_Oinsert: ($i > ($i > ($i > $i)))). 32.13/11.36 thf(class_Orderings_Otop_type, type, class_Orderings_Otop: ($i > $o)). 32.13/11.36 thf(class_Orderings_Oord_type, type, class_Orderings_Oord: ($i > $o)). 32.13/11.36 thf(c_Arrow__Order__Mirabelle_Ounanimity_type, type, c_Arrow__Order__Mirabelle_Ounanimity: ($i > $o)). 32.13/11.36 thf(class_Groups_Ozero_type, type, class_Groups_Ozero: ($i > $o)). 32.13/11.36 thf(c_Groups_Ozero__class_Ozero_type, type, c_Groups_Ozero__class_Ozero: ($i > $i)). 32.13/11.36 thf(c_List_Odistinct_type, type, c_List_Odistinct: ($i > ($i > $o))). 32.13/11.36 thf(class_Rings_Ozero__neq__one_type, type, class_Rings_Ozero__neq__one: ($i > $o)). 32.13/11.36 thf(tc_Product__Type_Ounit_type, type, tc_Product__Type_Ounit: $i). 32.13/11.36 thf(c_COMBI_type, type, c_COMBI: ($i > $i)). 32.13/11.36 thf(c_List_Olist_Olist__case_type, type, c_List_Olist_Olist__case: ($i > ($i > ($i > ($i > ($i > $i)))))). 32.13/11.36 thf(c_COMBB_type, type, c_COMBB: ($i > ($i > ($i > ($i > $i))))). 32.13/11.36 thf(v_b_____type, type, v_b____: $i). 32.13/11.36 thf(v_a_____type, type, v_a____: $i). 32.13/11.36 thf(c_Groups_Oplus__class_Oplus_type, type, c_Groups_Oplus__class_Oplus: ($i > $i)). 32.13/11.36 thf(class_Groups_Oordered__ab__semigroup__add__imp__le_type, type, class_Groups_Oordered__ab__semigroup__add__imp__le: ($i > $o)). 32.13/11.36 thf(c_Nat_OSuc_type, type, c_Nat_OSuc: $i). 32.13/11.36 thf(c_Orderings_Oord__class_Oless__eq_type, type, c_Orderings_Oord__class_Oless__eq: ($i > ($i > $i))). 32.13/11.36 thf(class_Groups_Oordered__comm__monoid__add_type, type, class_Groups_Oordered__comm__monoid__add: ($i > $o)). 32.13/11.36 thf(c_Arrow__Order__Mirabelle_OLin_type, type, c_Arrow__Order__Mirabelle_OLin: $i). 32.13/11.36 thf(class_Groups_Ocancel__semigroup__add_type, type, class_Groups_Ocancel__semigroup__add: ($i > $o)). 32.13/11.36 thf(class_Rings_Ocomm__semiring__1_type, type, class_Rings_Ocomm__semiring__1: ($i > $o)). 32.13/11.36 thf(c_COMBC_type, type, c_COMBC: ($i > ($i > ($i > $i)))). 32.13/11.36 thf(c_If_type, type, c_If: ($i > $i)). 32.13/11.36 thf(v_Lab_____type, type, v_Lab____: $i). 32.13/11.36 thf(v_Lba_____type, type, v_Lba____: $i). 32.13/11.36 thf(c_COMBK_type, type, c_COMBK: ($i > ($i > $i))). 32.13/11.36 thf(c_FuncSet_OPi_type, type, c_FuncSet_OPi: ($i > ($i > ($i > ($i > $i))))). 32.13/11.36 thf(c_fequal_type, type, c_fequal: $i). 32.13/11.36 thf(c_Wellfounded_Omlex__prod_type, type, c_Wellfounded_Omlex__prod: ($i > ($i > ($i > $i)))). 32.13/11.36 thf(c_Arrow__Order__Mirabelle_OProf_type, type, c_Arrow__Order__Mirabelle_OProf: $i). 32.13/11.36 thf(class_Groups_Olinordered__ab__group__add_type, type, class_Groups_Olinordered__ab__group__add: ($i > $o)). 32.13/11.36 thf(c_List_Omeasures_type, type, c_List_Omeasures: ($i > ($i > $i))). 32.13/11.36 thf(c_COMBS_type, type, c_COMBS: ($i > ($i > ($i > ($i > ($i > $i)))))). 32.13/11.36 thf(c_SetInterval_Oord__class_OatLeastLessThan_type, type, c_SetInterval_Oord__class_OatLeastLessThan: ($i > ($i > ($i > $i)))). 32.13/11.36 thf(c_List_Olist_Olist__size_type, type, c_List_Olist_Olist__size: ($i > ($i > ($i > $i)))). 32.13/11.36 thf(c_Arrow__Order__Mirabelle_Odictator_type, type, c_Arrow__Order__Mirabelle_Odictator: ($i > ($i > $o))). 32.13/11.36 thf(class_Groups_Oordered__cancel__ab__semigroup__add_type, type, class_Groups_Oordered__cancel__ab__semigroup__add: ($i > $o)). 32.13/11.36 thf(class_Orderings_Olinorder_type, type, class_Orderings_Olinorder: ($i > $o)). 32.13/11.36 thf(class_Groups_Omonoid__add_type, type, class_Groups_Omonoid__add: ($i > $o)). 32.13/11.36 thf(class_Groups_Ocomm__monoid__add_type, type, class_Groups_Ocomm__monoid__add: ($i > $o)). 32.13/11.36 thf(class_Rings_Olinordered__semidom_type, type, class_Rings_Olinordered__semidom: ($i > $o)). 32.13/11.36 thf(class_Groups_Oordered__ab__semigroup__add_type, type, class_Groups_Oordered__ab__semigroup__add: ($i > $o)). 32.13/11.36 thf(c_Finite__Set_Ofolding__image__simple_type, type, c_Finite__Set_Ofolding__image__simple: ($i > ($i > ($i > ($i > ($i > ($i > $o))))))). 32.13/11.36 thf(c_Finite__Set_Ofold__image_type, type, c_Finite__Set_Ofold__image: ($i > ($i > ($i > ($i > ($i > ($i > $i))))))). 32.13/11.36 thf(c_Recdef_Osame__fst_type, type, c_Recdef_Osame__fst: ($i > ($i > ($i > ($i > $i))))). 32.13/11.36 thf(c_Int_Oring__1__class_OInts_type, type, c_Int_Oring__1__class_OInts: ($i > $i)). 32.13/11.36 thf(class_Rings_Oring__1_type, type, class_Rings_Oring__1: ($i > $o)). 32.13/11.36 thf(c_fFalse_type, type, c_fFalse: $i). 32.13/11.36 thf(c_Nat_Onat_Onat__case_type, type, c_Nat_Onat_Onat__case: ($i > ($i > ($i > ($i > $i))))). 32.13/11.36 thf(c_Arrow__Order__Mirabelle_Obelow_type, type, c_Arrow__Order__Mirabelle_Obelow: ($i > ($i > ($i > $i)))). 32.13/11.36 thf(class_Rings_Olinordered__idom_type, type, class_Rings_Olinordered__idom: ($i > $o)). 32.13/11.36 thf(class_Groups_Oab__semigroup__add_type, type, class_Groups_Oab__semigroup__add: ($i > $o)). 32.13/11.36 thf(c_Nat_Osize__class_Osize_type, type, c_Nat_Osize__class_Osize: ($i > ($i > $i))). 32.13/11.36 thf(class_Int_Oring__char__0_type, type, class_Int_Oring__char__0: ($i > $o)). 32.13/11.36 thf(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_type, type, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: ($i > $o)). 32.13/11.36 thf(c_Nat_Onat_Onat__size_type, type, c_Nat_Onat_Onat__size: ($i > $i)). 32.13/11.36 thf(class_Groups_Ocancel__ab__semigroup__add_type, type, class_Groups_Ocancel__ab__semigroup__add: ($i > $o)). 32.13/11.36 thf(c_Nitpick_Orefl_H_type, type, c_Nitpick_Orefl_H: ($i > ($i > $o))). 32.13/11.36 thf(c_Wellfounded_Olex__prod_type, type, c_Wellfounded_Olex__prod: ($i > ($i > ($i > ($i > $i))))). 32.13/11.36 thf(c_Wellfounded_Ofinite__psubset_type, type, c_Wellfounded_Ofinite__psubset: ($i > $i)). 32.13/11.36 thf(c_Wellfounded_Omeasure_type, type, c_Wellfounded_Omeasure: ($i > ($i > $i))). 32.13/11.36 thf(c_FunDef_Oin__rel_type, type, c_FunDef_Oin__rel: ($i > ($i > ($i > ($i > ($i > $o)))))). 32.13/11.36 thf(113,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ B)) @ A) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc)). 32.13/11.36 thf(892,plain,((! [A:$i,B:$i,C:$i]: ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ B)) @ A) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 32.13/11.36 thf(231,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((class_Groups_Oordered__cancel__ab__semigroup__add @ E) => (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ E) @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ E) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ D) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ C) @ A)))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ E @ D) @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__less__mono)). 32.13/11.36 thf(1337,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((class_Groups_Oordered__cancel__ab__semigroup__add @ E) => (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ E) @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ E) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ D) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ C) @ A)))) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ E @ D) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 32.13/11.36 thf(436,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((A = B) <= ((hAPP @ C @ A) = (hAPP @ C @ B))) <= (c_Fun_Oinj__on @ E @ D @ C @ (c_Orderings_Otop__class_Otop @ (tc_fun @ E @ tc_HOL_Obool)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_injD)). 32.13/11.36 thf(2094,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((A = B) | ~ ((hAPP @ C @ A) = (hAPP @ C @ B)) | ~ (c_Fun_Oinj__on @ E @ D @ C @ (c_Orderings_Otop__class_Otop @ (tc_fun @ E @ tc_HOL_Obool)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[436])). 32.13/11.36 thf(146,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((hAPP @ C @ B) = (hAPP @ C @ A)) <=> (A = B)) <= (c_Fun_Oinj__on @ E @ D @ C @ (c_Orderings_Otop__class_Otop @ (tc_fun @ E @ tc_HOL_Obool)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__eq)). 32.13/11.36 thf(1024,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((((hAPP @ C @ B) = (hAPP @ C @ A)) => (A = B)) & ((A = B) => ((hAPP @ C @ B) = (hAPP @ C @ A)))) | ~ (c_Fun_Oinj__on @ E @ D @ C @ (c_Orderings_Otop__class_Otop @ (tc_fun @ E @ tc_HOL_Obool)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 32.13/11.36 thf(178,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ A) @ B)) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (c_Finite__Set_Ocard @ C @ B)) @ (c_Finite__Set_Ocard @ C @ A))) => (B = A))) <= (c_Finite__Set_Ofinite @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__seteq)). 32.13/11.36 thf(1168,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ A) @ B)) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (c_Finite__Set_Ocard @ C @ B)) @ (c_Finite__Set_Ocard @ C @ A))) => (B = A))) | ~ (c_Finite__Set_Ofinite @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 32.13/11.36 thf(481,axiom,((! [A:$i,B:$i,C:$i]: ((c_Finite__Set_Ofinite @ C @ B) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ A) @ B)) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ C @ tc_HOL_Obool)) @ A) @ B)) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Finite__Set_Ocard @ C @ A)) @ (c_Finite__Set_Ocard @ C @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__psubset)). 32.13/11.36 thf(2306,plain,((! [A:$i,B:$i,C:$i]: ((c_Finite__Set_Ofinite @ C @ B) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ A) @ B)) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ C @ tc_HOL_Obool)) @ A) @ B)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Finite__Set_Ocard @ C @ A)) @ (c_Finite__Set_Ocard @ C @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[481])). 32.13/11.36 thf(491,axiom,((class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add)). 32.13/11.36 thf(2336,plain,((class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[491])). 32.13/11.36 thf(406,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((c_Fun_Oinj__on @ F @ E @ D @ C) => (((A = (hAPP @ D @ B)) => (B = (hAPP @ (c_Hilbert__Choice_Oinv__into @ F @ E @ C @ D) @ A))) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ F) @ B) @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__f__eq)). 32.13/11.36 thf(1995,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((c_Fun_Oinj__on @ F @ E @ D @ C) => (((A = (hAPP @ D @ B)) => (B = (hAPP @ (c_Hilbert__Choice_Oinv__into @ F @ E @ C @ D) @ A))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ F) @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[406])). 32.13/11.36 thf(118,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ E @ D)) @ (hAPP @ E @ C))) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ B @ B)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ B @ B) @ D) @ C)) @ (c_List_Omeasures @ B @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ B @ B)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ B @ B) @ D) @ C)) @ (c_List_Omeasures @ B @ (c_List_Olist_OCons @ (tc_fun @ B @ tc_Nat_Onat) @ E @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_measures__lesseq)). 32.13/11.36 thf(909,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ E @ D)) @ (hAPP @ E @ C))) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ B @ B)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ B @ B) @ D) @ C)) @ (c_List_Omeasures @ B @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ B @ B)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ B @ B) @ D) @ C)) @ (c_List_Omeasures @ B @ (c_List_Olist_OCons @ (tc_fun @ B @ tc_Nat_Onat) @ E @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 32.13/11.36 thf(28,axiom,((! [A:$i,B:$i,C:$i]: ((c_List_Olist_OCons @ B @ A @ C) != C))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Cons__self)). 32.13/11.36 thf(628,plain,((! [A:$i,B:$i,C:$i]: ~ ((c_List_Olist_OCons @ B @ A @ C) = C))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 32.13/11.36 thf(147,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ E) @ D) @ C)) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ E) @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ E) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ D) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ C) @ A))))) <= (class_Groups_Oordered__cancel__ab__semigroup__add @ E)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__mono)). 32.13/11.36 thf(1031,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ E) @ D) @ C)) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ E) @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ E) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ D) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ C) @ A))))) | ~ (class_Groups_Oordered__cancel__ab__semigroup__add @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 32.13/11.36 thf(512,axiom,(((c_Groups_Oone__class_Oone @ tc_Nat_Onat) = (c_Finite__Set_Ocard @ tc_Product__Type_Ounit @ (c_Orderings_Otop__class_Otop @ (tc_fun @ tc_Product__Type_Ounit @ tc_HOL_Obool))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__UNIV__unit)). 32.13/11.36 thf(2463,plain,(((c_Groups_Oone__class_Oone @ tc_Nat_Onat) = (c_Finite__Set_Ocard @ tc_Product__Type_Ounit @ (c_Orderings_Otop__class_Otop @ (tc_fun @ tc_Product__Type_Ounit @ tc_HOL_Obool))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[512])). 32.13/11.36 thf(225,axiom,((c_Fun_Oinj__on @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ v_h____ @ (c_Orderings_Otop__class_Otop @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_injh)). 32.13/11.36 thf(1315,plain,((c_Fun_Oinj__on @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ v_h____ @ (c_Orderings_Otop__class_Otop @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])). 32.13/11.36 thf(525,axiom,((! [A:$i,B:$i]: ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ A) @ B) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute)). 32.13/11.36 thf(2499,plain,((! [A:$i,B:$i]: ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ A) @ B) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[525])). 32.13/11.36 thf(519,axiom,((! [A:$i,B:$i,C:$i]: (((B = A) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A))) <= (class_Orderings_Opreorder @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__refl)). 32.13/11.36 thf(2480,plain,((! [A:$i,B:$i,C:$i]: (((B = A) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A))) | ~ (class_Orderings_Opreorder @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[519])). 32.13/11.36 thf(126,axiom,((! [A:$i,B:$i,C:$i]: ((B = C) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ A @ tc_HOL_Obool) @ B) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD2)). 32.13/11.36 thf(941,plain,((! [A:$i,B:$i,C:$i]: ((B = C) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ A @ tc_HOL_Obool) @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 32.13/11.36 thf(182,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ D @ tc_HOL_Obool)) @ C) @ A))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ D @ tc_HOL_Obool)) @ C) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__subset__trans)). 32.13/11.36 thf(1179,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ D @ tc_HOL_Obool)) @ C) @ A))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ D @ tc_HOL_Obool)) @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 32.13/11.36 thf(4,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((c_Set_Oimage @ D @ C @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool))) = (c_Orderings_Otop__class_Otop @ (tc_fun @ C @ tc_HOL_Obool))) => ((c_Set_Oimage @ D @ C @ B @ (c_Set_Oimage @ C @ D @ (c_Hilbert__Choice_Oinv__into @ D @ C @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool)) @ B) @ A)) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__surj__f__inv__f)). 32.13/11.36 thf(555,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((c_Set_Oimage @ D @ C @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool))) = (c_Orderings_Otop__class_Otop @ (tc_fun @ C @ tc_HOL_Obool))) => ((c_Set_Oimage @ D @ C @ B @ (c_Set_Oimage @ C @ D @ (c_Hilbert__Choice_Oinv__into @ D @ C @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool)) @ B) @ A)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 32.13/11.36 thf(40,axiom,((class_Orderings_Oord @ tc_HOL_Obool)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord)). 32.13/11.36 thf(666,plain,((class_Orderings_Oord @ tc_HOL_Obool)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 32.13/11.36 thf(357,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ A) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ B)) <=> (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel)). 32.13/11.36 thf(1818,plain,((! [A:$i,B:$i,C:$i]: ((((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ A) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ B)) => (A = B)) & ((A = B) => ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ A) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[357])). 32.13/11.36 thf(217,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ A) @ B)) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ A) @ C))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ B))) <= (class_Orderings_Oorder @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I10_J)). 32.13/11.36 thf(1295,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ A) @ B)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ A) @ C)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ B)) | ~ (class_Orderings_Oorder @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 32.13/11.36 thf(394,axiom,((! [A:$i,B:$i]: ((A != (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr__implies__not0)). 32.13/11.36 thf(1950,plain,((! [A:$i,B:$i]: (~ (A = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[394])). 32.13/11.36 thf(498,axiom,((! [A:$i,B:$i]: ((hBOOL @ (c_Nat_Onat_Onat__case @ tc_HOL_Obool @ c_fFalse @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) <=> (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ B)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I2_J)). 32.13/11.36 thf(2363,plain,((! [A:$i,B:$i]: (((hBOOL @ (c_Nat_Onat_Onat__case @ tc_HOL_Obool @ c_fFalse @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ B)) @ A))) & ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ B)) @ A)) => (hBOOL @ (c_Nat_Onat_Onat__case @ tc_HOL_Obool @ c_fFalse @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[498])). 32.13/11.36 thf(431,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ B @ tc_HOL_Obool) @ A) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__UNIV)). 32.13/11.36 thf(2077,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ B @ tc_HOL_Obool) @ A) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[431])). 32.13/11.36 thf(483,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Groups_Oordered__comm__monoid__add @ D) => (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ B) @ A))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ (c_Groups_Ozero__class_Ozero @ D)) @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing)). 32.13/11.36 thf(2309,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Groups_Oordered__comm__monoid__add @ D) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A))) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ B) @ A)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ (c_Groups_Ozero__class_Ozero @ D)) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[483])). 32.13/11.36 thf(531,axiom,((! [A:$i,B:$i,C:$i]: ((c_Finite__Set_Ofinite @ C @ B) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (c_Finite__Set_Ocard @ C @ B)) @ (c_Finite__Set_Ocard @ C @ (c_Set_Oinsert @ C @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__le)). 32.13/11.36 thf(2512,plain,((! [A:$i,B:$i,C:$i]: ((c_Finite__Set_Ofinite @ C @ B) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (c_Finite__Set_Ocard @ C @ B)) @ (c_Finite__Set_Ocard @ C @ (c_Set_Oinsert @ C @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[531])). 32.13/11.36 thf(48,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((c_Fun_Oinj__on @ E @ D @ C @ (c_Orderings_Otop__class_Otop @ (tc_fun @ E @ tc_HOL_Obool))) => (((c_Set_Oimage @ E @ D @ C @ A) = (c_Set_Oimage @ E @ D @ C @ B)) <=> (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__eq__iff)). 32.13/11.36 thf(683,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((c_Fun_Oinj__on @ E @ D @ C @ (c_Orderings_Otop__class_Otop @ (tc_fun @ E @ tc_HOL_Obool))) => ((((c_Set_Oimage @ E @ D @ C @ A) = (c_Set_Oimage @ E @ D @ C @ B)) => (B = A)) & ((B = A) => ((c_Set_Oimage @ E @ D @ C @ A) = (c_Set_Oimage @ E @ D @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 32.13/11.36 thf(152,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J)). 32.13/11.36 thf(1068,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 32.13/11.36 thf(505,axiom,((! [A:$i]: ((! [B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ B) @ c_Arrow__Order__Mirabelle_OProf)) => (! [C:$i,D:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ C) @ D)) @ (hAPP @ A @ B))) <= (! [E:$i]: (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ C) @ D)) @ (hAPP @ B @ E)))))))) <=> (c_Arrow__Order__Mirabelle_Ounanimity @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unanimity__def)). 32.13/11.36 thf(2381,plain,((! [A:$i]: (((! [B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ B) @ c_Arrow__Order__Mirabelle_OProf)) => (! [C:$i,D:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ C) @ D)) @ (hAPP @ A @ B))) | ~ (! [E:$i]: (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ C) @ D)) @ (hAPP @ B @ E)))))))) => (c_Arrow__Order__Mirabelle_Ounanimity @ A)) & ((c_Arrow__Order__Mirabelle_Ounanimity @ A) => (! [B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ B) @ c_Arrow__Order__Mirabelle_OProf)) => (! [C:$i,D:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ C) @ D)) @ (hAPP @ A @ B))) | ~ (! [E:$i]: (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ C) @ D)) @ (hAPP @ B @ E)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[505])). 32.13/11.36 thf(428,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((c_Finite__Set_Ofinite @ C @ B) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ B) @ (c_Set_Oimage @ E @ C @ A @ D)))) <= (c_Finite__Set_Ofinite @ E @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj)). 32.13/11.36 thf(2062,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((c_Finite__Set_Ofinite @ C @ B) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ B) @ (c_Set_Oimage @ E @ C @ A @ D))) | ~ (c_Finite__Set_Ofinite @ E @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[428])). 32.13/11.36 thf(257,axiom,((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ v_a____) @ v_b____)) @ (hAPP @ v_F @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (c_COMBB @ tc_HOL_Obool @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_If @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool) @ (hAPP @ (c_COMBB @ tc_Nat_Onat @ (tc_fun @ tc_Nat_Onat @ tc_HOL_Obool) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat)) @ v_h____)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ v_n____) @ (c_Groups_Oone__class_Oone @ tc_Nat_Onat))))) @ v_Lab____)) @ v_Lba____))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n_I3_J)). 32.13/11.36 thf(1422,plain,((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ v_a____) @ v_b____)) @ (hAPP @ v_F @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (c_COMBB @ tc_HOL_Obool @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_If @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool) @ (hAPP @ (c_COMBB @ tc_Nat_Onat @ (tc_fun @ tc_Nat_Onat @ tc_HOL_Obool) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat)) @ v_h____)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ v_n____) @ (c_Groups_Oone__class_Oone @ tc_Nat_Onat))))) @ v_Lab____)) @ v_Lba____))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])). 32.13/11.36 thf(291,axiom,((! [A:$i,B:$i]: ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (hAPP @ c_Nat_OSuc @ B)) @ A) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__shift)). 32.13/11.36 thf(1569,plain,((! [A:$i,B:$i]: ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (hAPP @ c_Nat_OSuc @ B)) @ A) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[291])). 32.13/11.36 thf(329,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ B @ A) @ A)) <= (class_Orderings_Opreorder @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__refl)). 32.13/11.36 thf(1728,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ B @ A) @ A)) | ~ (class_Orderings_Opreorder @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[329])). 32.13/11.36 thf(109,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ (c_Groups_Ozero__class_Ozero @ C)) @ A)) => (((c_Groups_Ozero__class_Ozero @ C) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ B) @ A)) <=> (((c_Groups_Ozero__class_Ozero @ C) = A) & ((c_Groups_Ozero__class_Ozero @ C) = B)))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ (c_Groups_Ozero__class_Ozero @ C)) @ B))) <= (class_Groups_Oordered__comm__monoid__add @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff)). 32.13/11.36 thf(878,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ (c_Groups_Ozero__class_Ozero @ C)) @ A)) => ((((c_Groups_Ozero__class_Ozero @ C) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ B) @ A)) => (((c_Groups_Ozero__class_Ozero @ C) = A) & ((c_Groups_Ozero__class_Ozero @ C) = B))) & ((((c_Groups_Ozero__class_Ozero @ C) = A) & ((c_Groups_Ozero__class_Ozero @ C) = B)) => ((c_Groups_Ozero__class_Ozero @ C) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ B) @ A))))) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ (c_Groups_Ozero__class_Ozero @ C)) @ B)) | ~ (class_Groups_Oordered__comm__monoid__add @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 32.13/11.36 thf(399,axiom,((! [A:$i,B:$i,C:$i]: ((~ ((~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ A @ tc_HOL_Obool) @ B) @ C))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ A @ tc_HOL_Obool) @ C) @ B)))) <= (B = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityE)). 32.13/11.36 thf(1971,plain,((! [A:$i,B:$i,C:$i]: (~ (~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ A @ tc_HOL_Obool) @ B) @ C)) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ A @ tc_HOL_Obool) @ C) @ B))) | ~ (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[399])). 32.13/11.36 thf(349,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ B)) @ A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD1)). 32.13/11.36 thf(1793,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ B)) @ A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[349])). 32.13/11.36 thf(321,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ A) @ A))) <= (class_Orderings_Opreorder @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__irrefl)). 32.13/11.36 thf(1692,plain,((! [A:$i,B:$i]: (~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ A) @ A)) | ~ (class_Orderings_Opreorder @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[321])). 32.13/11.36 thf(221,axiom,((! [A:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ A) @ (c_Groups_Ozero__class_Ozero @ A)) @ (c_Int_Oring__1__class_OInts @ A))) <= (class_Rings_Oring__1 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__0)). 32.13/11.36 thf(1305,plain,((! [A:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ A) @ (c_Groups_Ozero__class_Ozero @ A)) @ (c_Int_Oring__1__class_OInts @ A))) | ~ (class_Rings_Oring__1 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 32.13/11.36 thf(17,axiom,((! [A:$i]: ((c_Finite__Set_Ofinite @ (tc_Option_Ooption @ A) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ (tc_Option_Ooption @ A) @ tc_HOL_Obool))) <=> (c_Finite__Set_Ofinite @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ A @ tc_HOL_Obool)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__option__UNIV)). 32.13/11.36 thf(597,plain,((! [A:$i]: (((c_Finite__Set_Ofinite @ (tc_Option_Ooption @ A) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ (tc_Option_Ooption @ A) @ tc_HOL_Obool))) => (c_Finite__Set_Ofinite @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ A @ tc_HOL_Obool)))) & ((c_Finite__Set_Ofinite @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ A @ tc_HOL_Obool))) => (c_Finite__Set_Ofinite @ (tc_Option_Ooption @ A) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ (tc_Option_Ooption @ A) @ tc_HOL_Obool))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 32.13/11.36 thf(263,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((D != E) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ C) @ c_Arrow__Order__Mirabelle_OLin)) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ B) @ A)) @ (c_Arrow__Order__Mirabelle_Obelow @ C @ E @ D))) <=> ((A != B) & ((A = E) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ B) @ D)) @ C))) & (((((A = D) | (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ A)) @ C))) <= (B = E)) & ((B != E) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ B) @ A)) @ C)))) <= (E != A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__below)). 32.13/11.36 thf(1437,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((~ (D = E)) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ C) @ c_Arrow__Order__Mirabelle_OLin)) => (((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ B) @ A)) @ (c_Arrow__Order__Mirabelle_Obelow @ C @ E @ D))) => (~ (A = B) & ((A = E) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ B) @ D)) @ C))) & ((((A = D) | (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ A)) @ C)) | ~ (B = E)) & ((~ (B = E)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ B) @ A)) @ C)))) | (E = A)))) & ((~ (A = B) & ((A = E) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ B) @ D)) @ C))) & ((((A = D) | (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ A)) @ C)) | ~ (B = E)) & ((~ (B = E)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ B) @ A)) @ C)))) | (E = A))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ B) @ A)) @ (c_Arrow__Order__Mirabelle_Obelow @ C @ E @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])). 32.13/11.36 thf(104,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ A) @ B))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J)). 32.13/11.36 thf(861,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ A) @ B))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 32.13/11.36 thf(180,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A))) <=> (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ B) @ A))) <= (class_Groups_Oordered__ab__semigroup__add__imp__le @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__left)). 32.13/11.36 thf(1173,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A))) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ B) @ A))) & ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ B) @ A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A))))) | ~ (class_Groups_Oordered__ab__semigroup__add__imp__le @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 32.13/11.36 thf(270,axiom,((! [A:$i,B:$i]: ((class_Rings_Olinordered__idom @ B) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ A) @ (c_Int_Oring__1__class_OInts @ B))) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ A) @ (c_Groups_Ozero__class_Ozero @ B))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ (c_Groups_Oone__class_Oone @ B)) @ A)) @ A)) @ (c_Groups_Ozero__class_Ozero @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__odd__less__0)). 32.13/11.36 thf(1486,plain,((! [A:$i,B:$i]: ((class_Rings_Olinordered__idom @ B) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ A) @ (c_Int_Oring__1__class_OInts @ B))) => (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ A) @ (c_Groups_Ozero__class_Ozero @ B))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ (c_Groups_Oone__class_Oone @ B)) @ A)) @ A)) @ (c_Groups_Ozero__class_Ozero @ B)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ (c_Groups_Oone__class_Oone @ B)) @ A)) @ A)) @ (c_Groups_Ozero__class_Ozero @ B))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ A) @ (c_Groups_Ozero__class_Ozero @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[270])). 32.13/11.36 thf(324,axiom,((! [A:$i,B:$i,C:$i]: ((c_Finite__Set_Ofinite @ C @ B) => ((((c_Finite__Set_Ocard @ C @ (c_Set_Oinsert @ C @ A @ B)) = (c_Finite__Set_Ocard @ C @ B)) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ A) @ B))) & ((~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ A) @ B))) => ((c_Finite__Set_Ocard @ C @ (c_Set_Oinsert @ C @ A @ B)) = (hAPP @ c_Nat_OSuc @ (c_Finite__Set_Ocard @ C @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__if)). 32.13/11.36 thf(1705,plain,((! [A:$i,B:$i,C:$i]: ((c_Finite__Set_Ofinite @ C @ B) => ((((c_Finite__Set_Ocard @ C @ (c_Set_Oinsert @ C @ A @ B)) = (c_Finite__Set_Ocard @ C @ B)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ A) @ B))) & ((~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ A) @ B))) => ((c_Finite__Set_Ocard @ C @ (c_Set_Oinsert @ C @ A @ B)) = (hAPP @ c_Nat_OSuc @ (c_Finite__Set_Ocard @ C @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[324])). 32.13/11.36 thf(347,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ A) @ B)) => (A = B)) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A))) <= (class_Orderings_Oorder @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I5_J)). 32.13/11.36 thf(1788,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ A) @ B)) => (A = B)) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)) | ~ (class_Orderings_Oorder @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[347])). 32.13/11.36 thf(375,axiom,((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ v_a____) @ v_b____)) @ v_Lab____))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096)). 32.13/11.36 thf(1867,plain,((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ v_a____) @ v_b____)) @ v_Lab____))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[375])). 32.13/11.36 thf(407,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((c_Fun_Oinj__on @ D @ C @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool))) => (c_Fun_Oinj__on @ D @ (tc_fun @ A @ C) @ (hAPP @ (c_COMBB @ C @ (tc_fun @ A @ C) @ D @ (c_COMBK @ C @ A)) @ B) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__fun)). 32.13/11.36 thf(1999,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((c_Fun_Oinj__on @ D @ C @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool))) => (c_Fun_Oinj__on @ D @ (tc_fun @ A @ C) @ (hAPP @ (c_COMBB @ C @ (tc_fun @ A @ C) @ D @ (c_COMBK @ C @ A)) @ B) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[407])). 32.13/11.36 thf(517,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top1I)). 32.13/11.36 thf(2476,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[517])). 32.13/11.36 thf(53,axiom,((! [A:$i,B:$i]: (A = (c_List_Osplice @ B @ A @ (c_List_Olist_ONil @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splice__Nil2)). 32.13/11.36 thf(698,plain,((! [A:$i,B:$i]: (A = (c_List_Osplice @ B @ A @ (c_List_Olist_ONil @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 32.13/11.36 thf(403,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ A)) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ A) @ B)))) <= (class_Groups_Oordered__ab__semigroup__add__imp__le @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__right)). 32.13/11.36 thf(1988,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ A)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ A) @ B))) | ~ (class_Groups_Oordered__ab__semigroup__add__imp__le @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[403])). 32.13/11.36 thf(68,axiom,((! [A:$i,B:$i]: ((c_Set_Oimage @ B @ B @ (c_COMBI @ B) @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__ident)). 32.13/11.36 thf(747,plain,((! [A:$i,B:$i]: ((c_Set_Oimage @ B @ B @ (c_COMBI @ B) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 32.13/11.36 thf(307,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ B) @ A)) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A)))) <= (class_Groups_Oordered__ab__semigroup__add__imp__le @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__left)). 32.13/11.36 thf(1640,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ B) @ A)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A))) | ~ (class_Groups_Oordered__ab__semigroup__add__imp__le @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[307])). 32.13/11.36 thf(127,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Groups_Oordered__ab__semigroup__add__imp__le @ D) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ A)) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ A) @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__right)). 32.13/11.36 thf(945,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Groups_Oordered__ab__semigroup__add__imp__le @ D) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ A)) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 32.13/11.36 thf(497,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hAPP @ B @ (hAPP @ (c_Hilbert__Choice_Oinv__into @ C @ E @ A @ B) @ D)) = D) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ D) @ (c_Set_Oimage @ C @ E @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_f__inv__into__f)). 32.13/11.36 thf(2360,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hAPP @ B @ (hAPP @ (c_Hilbert__Choice_Oinv__into @ C @ E @ A @ B) @ D)) = D) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ D) @ (c_Set_Oimage @ C @ E @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[497])). 32.13/11.36 thf(115,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ A))) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rev__mp)). 32.13/11.36 thf(898,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ A))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 32.13/11.36 thf(466,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((c_Finite__Set_Ofolding__image__simple @ G @ F @ E @ D @ C @ B) => (((hAPP @ B @ A) = (c_Finite__Set_Ofold__image @ G @ F @ E @ C @ D @ A)) <= (c_Finite__Set_Ofinite @ F @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oeq__fold__g)). 32.13/11.36 thf(2216,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: ((c_Finite__Set_Ofolding__image__simple @ G @ F @ E @ D @ C @ B) => (((hAPP @ B @ A) = (c_Finite__Set_Ofold__image @ G @ F @ E @ C @ D @ A)) | ~ (c_Finite__Set_Ofinite @ F @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[466])). 32.13/11.36 thf(523,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ F @ E)) @ D) @ (c_FuncSet_OPi @ F @ E @ C @ (hAPP @ (c_COMBK @ (tc_fun @ E @ tc_HOL_Obool) @ F) @ B)))) => (((((c_Finite__Set_Ofinite @ F @ C) => ((c_Finite__Set_Ofinite @ E @ B) => ((c_Finite__Set_Ocard @ E @ B) = (c_Finite__Set_Ocard @ F @ C)))) <= (c_Fun_Oinj__on @ E @ F @ A @ B)) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ E @ F)) @ A) @ (c_FuncSet_OPi @ E @ F @ B @ (hAPP @ (c_COMBK @ (tc_fun @ F @ tc_HOL_Obool) @ E) @ C))))) <= (c_Fun_Oinj__on @ F @ E @ D @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__bij)). 32.13/11.36 thf(2491,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ F @ E)) @ D) @ (c_FuncSet_OPi @ F @ E @ C @ (hAPP @ (c_COMBK @ (tc_fun @ E @ tc_HOL_Obool) @ F) @ B)))) => (((c_Finite__Set_Ofinite @ F @ C) => ((c_Finite__Set_Ofinite @ E @ B) => ((c_Finite__Set_Ocard @ E @ B) = (c_Finite__Set_Ocard @ F @ C)))) | ~ (c_Fun_Oinj__on @ E @ F @ A @ B) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ E @ F)) @ A) @ (c_FuncSet_OPi @ E @ F @ B @ (hAPP @ (c_COMBK @ (tc_fun @ F @ tc_HOL_Obool) @ E) @ C)))) | ~ (c_Fun_Oinj__on @ F @ E @ D @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[523])). 32.13/11.36 thf(201,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((((hAPP @ B @ E) = C) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ A) @ C) @ (c_Set_Oimage @ F @ A @ B @ D)))) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ F) @ E) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__image__eqI)). 32.13/11.36 thf(1243,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((((hAPP @ B @ E) = C) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ A) @ C) @ (c_Set_Oimage @ F @ A @ B @ D)))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ F) @ E) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 32.13/11.36 thf(166,axiom,((! [A:$i]: (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J)). 32.13/11.36 thf(1127,plain,((! [A:$i]: (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 32.13/11.36 thf(344,axiom,((! [A:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ A) @ (c_Groups_Oone__class_Oone @ A)) @ (c_Int_Oring__1__class_OInts @ A))) <= (class_Rings_Oring__1 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__1)). 32.13/11.36 thf(1782,plain,((! [A:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ A) @ (c_Groups_Oone__class_Oone @ A)) @ (c_Int_Oring__1__class_OInts @ A))) | ~ (class_Rings_Oring__1 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[344])). 32.13/11.36 thf(250,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ A))) <= (C = B)) <= (class_Orderings_Oord @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__eq__less__trans)). 32.13/11.36 thf(1391,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ A))) | ~ (C = B) | ~ (class_Orderings_Oord @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])). 32.13/11.36 thf(294,axiom,((! [A:$i,B:$i]: ((((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ (c_Groups_Oone__class_Oone @ B)) @ A)) @ A) != (c_Groups_Ozero__class_Ozero @ B)) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ A) @ (c_Int_Oring__1__class_OInts @ B)))) <= (class_Int_Oring__char__0 @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__odd__nonzero)). 32.13/11.36 thf(1576,plain,((! [A:$i,B:$i]: (~ ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ (c_Groups_Oone__class_Oone @ B)) @ A)) @ A) = (c_Groups_Ozero__class_Ozero @ B)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ A) @ (c_Int_Oring__1__class_OInts @ B))) | ~ (class_Int_Oring__char__0 @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[294])). 32.13/11.36 thf(76,axiom,((! [A:$i,B:$i,C:$i]: ((class_Groups_Oordered__comm__monoid__add @ C) => (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ (c_Groups_Ozero__class_Ozero @ C))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ B) @ A)) @ (c_Groups_Ozero__class_Ozero @ C)))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ (c_Groups_Ozero__class_Ozero @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__neg)). 32.13/11.36 thf(782,plain,((! [A:$i,B:$i,C:$i]: ((class_Groups_Oordered__comm__monoid__add @ C) => (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ (c_Groups_Ozero__class_Ozero @ C))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ B) @ A)) @ (c_Groups_Ozero__class_Ozero @ C)))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ (c_Groups_Ozero__class_Ozero @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 32.13/11.36 thf(414,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ A) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add2)). 32.13/11.36 thf(2020,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[414])). 32.13/11.36 thf(151,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((A != D) & ((A != C) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ B))) & ((C = A) => (C != D))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ (hAPP @ c_Arrow__Order__Mirabelle_Omktop @ B) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mktop)). 32.13/11.36 thf(1046,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((~ (A = D) & ((~ (A = C)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ B))) & ((C = A) => (~ (C = D)))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ (hAPP @ c_Arrow__Order__Mirabelle_Omktop @ B) @ A)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ (hAPP @ c_Arrow__Order__Mirabelle_Omktop @ B) @ A))) => (~ (A = D) & ((~ (A = C)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ B))) & ((C = A) => (~ (C = D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 32.13/11.36 thf(299,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ (tc_fun @ E @ C) @ tc_HOL_Obool) @ (c_FuncSet_OPi @ E @ C @ D @ B)) @ (c_FuncSet_OPi @ E @ C @ D @ A))) <= (! [F:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ (hAPP @ B @ F)) @ (hAPP @ A @ F))) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ F) @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__mono)). 32.13/11.36 thf(1601,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ (tc_fun @ E @ C) @ tc_HOL_Obool) @ (c_FuncSet_OPi @ E @ C @ D @ B)) @ (c_FuncSet_OPi @ E @ C @ D @ A))) | ~ (! [F:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ (hAPP @ B @ F)) @ (hAPP @ A @ F))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ F) @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[299])). 32.13/11.36 thf(328,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP @ B @ A)) => (? [C:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ A)) & ! [D:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D) @ C)) => (~ (hBOOL @ (hAPP @ B @ D)))) & (hBOOL @ (hAPP @ B @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ (c_Groups_Oone__class_Oone @ tc_Nat_Onat))))))) <= (~ (hBOOL @ (hAPP @ B @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__least__nat__less)). 32.13/11.36 thf(1724,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP @ B @ A)) => (? [C:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ A)) & ! [D:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D) @ C)) => (~ (hBOOL @ (hAPP @ B @ D)))) & (hBOOL @ (hAPP @ B @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ (c_Groups_Oone__class_Oone @ tc_Nat_Onat))))))) | (hBOOL @ (hAPP @ B @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[328])). 32.13/11.36 thf(352,axiom,((! [A:$i]: ((hAPP @ c_Nat_OSuc @ A) != A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n)). 32.13/11.36 thf(1803,plain,((! [A:$i]: ~ ((hAPP @ c_Nat_OSuc @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[352])). 32.13/11.36 thf(207,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))) => ((A = B) <=> (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq)). 32.13/11.36 thf(1265,plain,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))) => (((A = B) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ A)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ A))) => (A = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 32.13/11.36 thf(195,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ C) @ B)) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ A) @ C)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ A) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mono)). 32.13/11.36 thf(1228,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ C) @ B)) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ A) @ C)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 32.13/11.36 thf(33,axiom,((class_Finite__Set_Ofinite @ tc_HOL_Obool)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite)). 32.13/11.36 thf(651,plain,((class_Finite__Set_Ofinite @ tc_HOL_Obool)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 32.13/11.36 thf(489,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ A) @ B)) <=> (B = A))) <= (class_Orderings_Oorder @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym__conv)). 32.13/11.36 thf(2328,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)) => (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ A) @ B)) => (B = A)) & ((B = A) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ A) @ B))))) | ~ (class_Orderings_Oorder @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[489])). 32.13/11.36 thf(402,axiom,((! [A:$i,B:$i]: ((class_Groups_Omonoid__add @ B) => (A = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ (c_Groups_Ozero__class_Ozero @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__right)). 32.13/11.36 thf(1985,plain,((! [A:$i,B:$i]: ((class_Groups_Omonoid__add @ B) => (A = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ (c_Groups_Ozero__class_Ozero @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[402])). 32.13/11.36 thf(338,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl)). 32.13/11.36 thf(1760,plain,((! [A:$i]: ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[338])). 32.13/11.36 thf(493,axiom,((! [A:$i,B:$i]: ((c_List_Olist_Olist__size @ B @ A @ (c_List_Olist_ONil @ B)) = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osize_I1_J)). 32.13/11.36 thf(2339,plain,((! [A:$i,B:$i]: ((c_List_Olist_Olist__size @ B @ A @ (c_List_Olist_ONil @ B)) = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[493])). 32.13/11.36 thf(386,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ D) @ (c_Set_Oimage @ C @ E @ B @ A))) <=> (? [F:$i]: (((hAPP @ B @ F) = D) & (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ F) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__iff)). 32.13/11.36 thf(1907,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ D) @ (c_Set_Oimage @ C @ E @ B @ A))) => (? [F:$i]: (((hAPP @ B @ F) = D) & (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ F) @ A))))) & ((? [F:$i]: (((hAPP @ B @ F) = D) & (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ F) @ A)))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ D) @ (c_Set_Oimage @ C @ E @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[386])). 32.13/11.36 thf(372,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) <= (A != B)) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less)). 32.13/11.36 thf(1860,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) | (A = B) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[372])). 32.13/11.36 thf(14,axiom,((! [A:$i,B:$i]: ((class_Finite__Set_Ofinite @ B) => (c_Finite__Set_Ofinite @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite)). 32.13/11.36 thf(587,plain,((! [A:$i,B:$i]: ((class_Finite__Set_Ofinite @ B) => (c_Finite__Set_Ofinite @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 32.13/11.36 thf(24,axiom,((! [A:$i]: ((class_Finite__Set_Ofinite @ A) => (c_Finite__Set_Ofinite @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ A @ tc_HOL_Obool)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV)). 32.13/11.36 thf(619,plain,((! [A:$i]: ((class_Finite__Set_Ofinite @ A) => (c_Finite__Set_Ofinite @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ A @ tc_HOL_Obool)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 32.13/11.36 thf(276,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) <=> (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__le)). 32.13/11.36 thf(1511,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ A)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ A))) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[276])). 32.13/11.36 thf(84,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Orderings_Oorder @ D) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ B)) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ A) @ C)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ A) @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J)). 32.13/11.36 thf(802,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Orderings_Oorder @ D) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ B)) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ A) @ C)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 32.13/11.36 thf(224,axiom,((! [A:$i]: (c_Fun_Oinj__on @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Suc)). 32.13/11.36 thf(1313,plain,((! [A:$i]: (c_Fun_Oinj__on @ tc_Nat_Onat @ tc_Nat_Onat @ c_Nat_OSuc @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 32.13/11.36 thf(457,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ A @ tc_HOL_Obool) @ C) @ B)) <= (C = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD1)). 32.13/11.36 thf(2185,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ A @ tc_HOL_Obool) @ C) @ B)) | ~ (C = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[457])). 32.13/11.36 thf(522,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ B) @ (c_Set_Oimage @ F @ E @ C @ D))) => ((B = A) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ A) @ (c_Set_Oimage @ F @ E @ C @ D))))) <= ((hAPP @ (c_Hilbert__Choice_Oinv__into @ F @ E @ D @ C) @ B) = (hAPP @ (c_Hilbert__Choice_Oinv__into @ F @ E @ D @ C) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__injective)). 32.13/11.36 thf(2488,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ B) @ (c_Set_Oimage @ F @ E @ C @ D))) => ((B = A) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ A) @ (c_Set_Oimage @ F @ E @ C @ D))))) | ~ ((hAPP @ (c_Hilbert__Choice_Oinv__into @ F @ E @ D @ C) @ B) = (hAPP @ (c_Hilbert__Choice_Oinv__into @ F @ E @ D @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[522])). 32.13/11.36 thf(101,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc1)). 32.13/11.36 thf(853,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 32.13/11.36 thf(202,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__zero__code)). 32.13/11.36 thf(1247,plain,((! [A:$i]: ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 32.13/11.36 thf(227,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ A @ tc_HOL_Obool) @ C) @ B)) & (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ A @ tc_HOL_Obool) @ B) @ C))) <=> (C = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__eq__subset)). 32.13/11.36 thf(1319,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ A @ tc_HOL_Obool) @ C) @ B)) & (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ A @ tc_HOL_Obool) @ B) @ C))) => (C = B)) & ((C = B) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ A @ tc_HOL_Obool) @ C) @ B)) & (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ A @ tc_HOL_Obool) @ B) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 32.13/11.36 thf(502,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ C) @ B)) => ((hBOOL @ (hAPP @ B @ A)) <= (hBOOL @ (hAPP @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate1D)). 32.13/11.36 thf(2373,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ C) @ B)) => ((hBOOL @ (hAPP @ B @ A)) | ~ (hBOOL @ (hAPP @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[502])). 32.13/11.36 thf(19,axiom,((class_Orderings_Oorder @ tc_HOL_Obool)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder)). 32.13/11.36 thf(606,plain,((class_Orderings_Oorder @ tc_HOL_Obool)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 32.13/11.36 thf(235,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ A)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n)). 32.13/11.36 thf(1347,plain,((! [A:$i]: ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ A)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 32.13/11.36 thf(292,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ A)) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ B)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__lessD1)). 32.13/11.36 thf(1572,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ A)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ B)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[292])). 32.13/11.36 thf(141,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ B)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leI)). 32.13/11.36 thf(1013,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ B)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 32.13/11.36 thf(334,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ C) @ B)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ C) @ (c_Set_Oinsert @ D @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI2)). 32.13/11.36 thf(1741,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ C) @ B)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ C) @ (c_Set_Oinsert @ D @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[334])). 32.13/11.36 thf(534,axiom,((! [A:$i,B:$i,C:$i]: (((c_Set_Oinsert @ C @ B @ A) = A) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb)). 32.13/11.36 thf(2520,plain,((! [A:$i,B:$i,C:$i]: (((c_Set_Oinsert @ C @ B @ A) = A) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[534])). 32.13/11.36 thf(450,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ c_Nat_OSuc @ B)) @ (hAPP @ c_Nat_OSuc @ A))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mono)). 32.13/11.36 thf(2158,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ c_Nat_OSuc @ B)) @ (hAPP @ c_Nat_OSuc @ A))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[450])). 32.13/11.36 thf(416,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ A))) <=> (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le)). 32.13/11.36 thf(2024,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ A))) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A))) & ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[416])). 32.13/11.36 thf(480,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ A @ C)) @ (hAPP @ A @ B))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ D @ D)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ D @ D) @ C) @ B)) @ (c_Wellfounded_Omeasure @ D @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__measure)). 32.13/11.36 thf(2301,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ A @ C)) @ (hAPP @ A @ B))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ D @ D)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ D @ D) @ C) @ B)) @ (c_Wellfounded_Omeasure @ D @ A)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ D @ D)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ D @ D) @ C) @ B)) @ (c_Wellfounded_Omeasure @ D @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ A @ C)) @ (hAPP @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[480])). 32.13/11.36 thf(378,axiom,((! [A:$i,B:$i,C:$i]: (((~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A))) => ((A != B) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B)))) <= (class_Orderings_Olinorder @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__cases)). 32.13/11.36 thf(1875,plain,((! [A:$i,B:$i,C:$i]: (((~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A))) => ((~ (A = B)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B)))) | ~ (class_Orderings_Olinorder @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[378])). 32.13/11.36 thf(506,axiom,((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ v_b____) @ v_a____)) @ v_Lba____))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096)). 32.13/11.36 thf(2388,plain,((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ v_b____) @ v_a____)) @ v_Lba____))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[506])). 32.13/11.36 thf(197,axiom,((~ (! [A:$i]: ((~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ A) @ c_Arrow__Order__Mirabelle_OLin))) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ v_a____) @ v_b____)) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096)). 32.13/11.36 thf(1232,plain,((~ (! [A:$i]: (~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ A) @ c_Arrow__Order__Mirabelle_OLin)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ v_a____) @ v_b____)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 32.13/11.36 thf(456,axiom,((! [A:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ (hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)))) <=> (A = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc0)). 32.13/11.36 thf(2178,plain,((! [A:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ (hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)))) => (A = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))) & ((A = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ (hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[456])). 32.13/11.36 thf(271,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A)))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ (c_Groups_Ozero__class_Ozero @ D)) @ C))) <= (class_Rings_Olinordered__semidom @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__add__strict)). 32.13/11.36 thf(1489,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A)))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ (c_Groups_Ozero__class_Ozero @ D)) @ C)) | ~ (class_Rings_Olinordered__semidom @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[271])). 32.13/11.36 thf(122,axiom,((! [A:$i,B:$i]: ((? [C:$i]: ((hBOOL @ (hAPP @ A @ C)) & (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ B)))) <=> (? [C:$i]: ((hBOOL @ (hAPP @ A @ C)) & (hBOOL @ (hAPP @ (hAPP @ (c_member @ tc_Nat_Onat) @ C) @ (c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__nat__less__eq)). 32.13/11.36 thf(924,plain,((! [A:$i,B:$i]: (((? [C:$i]: ((hBOOL @ (hAPP @ A @ C)) & (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ B)))) => (? [C:$i]: ((hBOOL @ (hAPP @ A @ C)) & (hBOOL @ (hAPP @ (hAPP @ (c_member @ tc_Nat_Onat) @ C) @ (c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) @ B)))))) & ((? [C:$i]: ((hBOOL @ (hAPP @ A @ C)) & (hBOOL @ (hAPP @ (hAPP @ (c_member @ tc_Nat_Onat) @ C) @ (c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) @ B))))) => (? [C:$i]: ((hBOOL @ (hAPP @ A @ C)) & (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 32.13/11.36 thf(220,axiom,((! [A:$i]: ((A != (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0I)). 32.13/11.36 thf(1302,plain,((! [A:$i]: ((~ (A = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])). 32.13/11.36 thf(79,axiom,((! [A:$i]: (A != (hAPP @ c_Nat_OSuc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n)). 32.13/11.36 thf(789,plain,((! [A:$i]: ~ (A = (hAPP @ c_Nat_OSuc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 32.13/11.36 thf(440,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Groups_Oab__semigroup__add @ D) => ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ A) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ B) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J)). 32.13/11.36 thf(2105,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Groups_Oab__semigroup__add @ D) => ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ A) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[440])). 32.13/11.36 thf(355,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ (hAPP @ C @ B)) @ (c_Set_Oimage @ E @ D @ C @ A))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ B) @ A))) <= (c_Fun_Oinj__on @ E @ D @ C @ (c_Orderings_Otop__class_Otop @ (tc_fun @ E @ tc_HOL_Obool)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__mem__iff)). 32.13/11.36 thf(1811,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ (hAPP @ C @ B)) @ (c_Set_Oimage @ E @ D @ C @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ B) @ A))) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ (hAPP @ C @ B)) @ (c_Set_Oimage @ E @ D @ C @ A))))) | ~ (c_Fun_Oinj__on @ E @ D @ C @ (c_Orderings_Otop__class_Otop @ (tc_fun @ E @ tc_HOL_Obool)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[355])). 32.13/11.36 thf(230,axiom,((! [A:$i,B:$i]: ((B = A) <= ((hAPP @ c_Nat_OSuc @ B) = (hAPP @ c_Nat_OSuc @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject)). 32.13/11.36 thf(1334,plain,((! [A:$i,B:$i]: ((B = A) | ~ ((hAPP @ c_Nat_OSuc @ B) = (hAPP @ c_Nat_OSuc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 32.13/11.36 thf(371,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ F) @ A) @ C)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ (hAPP @ D @ A)) @ (hAPP @ B @ A)))) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ F @ E)) @ D) @ (c_FuncSet_OPi @ F @ E @ C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__mem)). 32.13/11.36 thf(1858,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ F) @ A) @ C)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ (hAPP @ D @ A)) @ (hAPP @ B @ A)))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ F @ E)) @ D) @ (c_FuncSet_OPi @ F @ E @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[371])). 32.13/11.36 thf(444,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ (hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ B) @ A))) <=> (((C != D) <= (D = A)) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ B)) <= (A != D)) & (A != C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mkbot)). 32.13/11.36 thf(2122,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ (hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ B) @ A))) => ((~ (C = D) | ~ (D = A)) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ B)) | (A = D)) & ~ (A = C))) & (((~ (C = D) | ~ (D = A)) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ B)) | (A = D)) & ~ (A = C)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ (hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[444])). 32.13/11.36 thf(400,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ B)) @ A)) <=> (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__eq)). 32.13/11.36 thf(1978,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ B)) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))) & ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ B)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[400])). 32.13/11.36 thf(477,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ (tc_fun @ C @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool))) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ (tc_fun @ C @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ B) @ A)) @ (c_Wellfounded_Ofinite__psubset @ C))) <=> ((c_Finite__Set_Ofinite @ C @ A) & (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ C @ tc_HOL_Obool)) @ B) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__finite__psubset)). 32.13/11.36 thf(2291,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ (tc_fun @ C @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool))) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ (tc_fun @ C @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ B) @ A)) @ (c_Wellfounded_Ofinite__psubset @ C))) => ((c_Finite__Set_Ofinite @ C @ A) & (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ C @ tc_HOL_Obool)) @ B) @ A)))) & (((c_Finite__Set_Ofinite @ C @ A) & (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ C @ tc_HOL_Obool)) @ B) @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ (tc_fun @ C @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool))) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ (tc_fun @ C @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ B) @ A)) @ (c_Wellfounded_Ofinite__psubset @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[477])). 32.13/11.36 thf(247,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ B @ B)) @ (c_COMBI @ B)) @ (c_FuncSet_OPi @ B @ B @ A @ (hAPP @ (c_COMBK @ (tc_fun @ B @ tc_HOL_Obool) @ B) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__id)). 32.13/11.36 thf(1383,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ B @ B)) @ (c_COMBI @ B)) @ (c_FuncSet_OPi @ B @ B @ A @ (hAPP @ (c_COMBK @ (tc_fun @ B @ tc_HOL_Obool) @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])). 32.13/11.36 thf(11,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((c_Finite__Set_Ofinite @ C @ A) & (c_Finite__Set_Ofinite @ D @ B)) <=> (c_Finite__Set_Ofinite @ (tc_sum @ D @ C) @ (c_Sum__Type_OPlus @ D @ C @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__iff)). 32.13/11.36 thf(574,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((c_Finite__Set_Ofinite @ C @ A) & (c_Finite__Set_Ofinite @ D @ B)) => (c_Finite__Set_Ofinite @ (tc_sum @ D @ C) @ (c_Sum__Type_OPlus @ D @ C @ B @ A))) & ((c_Finite__Set_Ofinite @ (tc_sum @ D @ C) @ (c_Sum__Type_OPlus @ D @ C @ B @ A)) => ((c_Finite__Set_Ofinite @ C @ A) & (c_Finite__Set_Ofinite @ D @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 32.13/11.36 thf(296,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Orderings_Oord @ D) => ((! [E:$i]: (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ (hAPP @ B @ E)) @ (hAPP @ A @ E)))) <=> (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ D) @ B) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__fun__def)). 32.13/11.36 thf(1581,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Orderings_Oord @ D) => (((! [E:$i]: (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ (hAPP @ B @ E)) @ (hAPP @ A @ E)))) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ D) @ B) @ A))) & ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ D) @ B) @ A)) => (! [E:$i]: (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ (hAPP @ B @ E)) @ (hAPP @ A @ E))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[296])). 32.13/11.36 thf(184,axiom,((! [A:$i,B:$i]: (((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)) <=> (((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) = B) & ((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__0)). 32.13/11.36 thf(1183,plain,((! [A:$i,B:$i]: ((((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)) => (((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) = B) & ((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) = A))) & ((((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) = B) & ((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) = A)) => ((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 32.13/11.36 thf(91,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C) @ B)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ A) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add2)). 32.13/11.36 thf(821,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C) @ B)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 32.13/11.36 thf(413,axiom,((! [A:$i,B:$i,C:$i]: ((c_Finite__Set_Ofinite @ C @ B) => (((c_Fun_Oinj__on @ C @ C @ A @ B) => (B = (c_Set_Oimage @ C @ C @ A @ B))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ (c_Set_Oimage @ C @ C @ A @ B)) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_endo__inj__surj)). 32.13/11.36 thf(2017,plain,((! [A:$i,B:$i,C:$i]: ((c_Finite__Set_Ofinite @ C @ B) => (((c_Fun_Oinj__on @ C @ C @ A @ B) => (B = (c_Set_Oimage @ C @ C @ A @ B))) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ (c_Set_Oimage @ C @ C @ A @ B)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[413])). 32.13/11.36 thf(18,axiom,((! [A:$i,B:$i,C:$i]: ((c_List_Olist_OCons @ C @ B @ A) != A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Cons__self2)). 32.13/11.36 thf(602,plain,((! [A:$i,B:$i,C:$i]: ~ ((c_List_Olist_OCons @ C @ B @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 32.13/11.36 thf(529,axiom,((! [A:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ A) @ c_Arrow__Order__Mirabelle_OLin)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (c_COMBK @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ tc_Arrow__Order__Mirabelle_Oindi) @ A)) @ c_Arrow__Order__Mirabelle_OProf))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_const__Lin__Prof)). 32.13/11.36 thf(2508,plain,((! [A:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ A) @ c_Arrow__Order__Mirabelle_OLin)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (c_COMBK @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ tc_Arrow__Order__Mirabelle_Oindi) @ A)) @ c_Arrow__Order__Mirabelle_OProf))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[529])). 32.13/11.36 thf(364,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)) | (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B)) | (B = A)) <= (class_Orderings_Olinorder @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__less__linear)). 32.13/11.36 thf(1843,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)) | (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B)) | (B = A) | ~ (class_Orderings_Olinorder @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[364])). 32.13/11.36 thf(244,axiom,((! [A:$i]: ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0)). 32.13/11.36 thf(1377,plain,((! [A:$i]: ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])). 32.13/11.36 thf(383,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__le__nat)). 32.13/11.36 thf(1896,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[383])). 32.13/11.36 thf(130,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) <= (B = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le)). 32.13/11.36 thf(956,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) | ~ (B = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 32.13/11.36 thf(381,axiom,((! [A:$i,B:$i]: ((! [C:$i]: ((hBOOL @ (hAPP @ A @ C)) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ B)))) <=> (! [C:$i]: ((hBOOL @ (hAPP @ A @ C)) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ tc_Nat_Onat) @ C) @ (c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nat__less__eq)). 32.13/11.36 thf(1886,plain,((! [A:$i,B:$i]: (((! [C:$i]: ((hBOOL @ (hAPP @ A @ C)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ B)))) => (! [C:$i]: ((hBOOL @ (hAPP @ A @ C)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ tc_Nat_Onat) @ C) @ (c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) @ B)))))) & ((! [C:$i]: ((hBOOL @ (hAPP @ A @ C)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ tc_Nat_Onat) @ C) @ (c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) @ B))))) => (! [C:$i]: ((hBOOL @ (hAPP @ A @ C)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[381])). 32.13/11.36 thf(164,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ B))) => ((~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ A))) => ((B = A) <=> ((c_Set_Oinsert @ D @ C @ A) = (c_Set_Oinsert @ D @ C @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__ident)). 32.13/11.36 thf(1119,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ B))) => ((~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ A))) => (((B = A) => ((c_Set_Oinsert @ D @ C @ A) = (c_Set_Oinsert @ D @ C @ B))) & (((c_Set_Oinsert @ D @ C @ A) = (c_Set_Oinsert @ D @ C @ B)) => (B = A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 32.13/11.36 thf(302,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ E) @ (c_Set_Oimage @ A @ B @ D @ (c_Orderings_Otop__class_Otop @ (tc_fun @ A @ tc_HOL_Obool))))) <= (E = (hAPP @ D @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__eqI)). 32.13/11.36 thf(1622,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ E) @ (c_Set_Oimage @ A @ B @ D @ (c_Orderings_Otop__class_Otop @ (tc_fun @ A @ tc_HOL_Obool))))) | ~ (E = (hAPP @ D @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[302])). 32.13/11.36 thf(73,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ (hAPP @ C @ B)) @ (c_Set_Oimage @ A @ D @ C @ (c_Orderings_Otop__class_Otop @ (tc_fun @ A @ tc_HOL_Obool))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rangeI)). 32.13/11.36 thf(774,plain,((! [A:$i,B:$i,C:$i,D:$i]: (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ (hAPP @ C @ B)) @ (c_Set_Oimage @ A @ D @ C @ (c_Orderings_Otop__class_Otop @ (tc_fun @ A @ tc_HOL_Obool))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 32.13/11.36 thf(471,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) <=> (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ B)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le)). 32.13/11.36 thf(2242,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ B)) @ A))) & ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ B)) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[471])). 32.13/11.36 thf(234,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ A) @ C)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ A) @ B))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ C) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__mp)). 32.13/11.36 thf(1345,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ A) @ C)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ A) @ B))) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 32.13/11.36 thf(254,axiom,((! [A:$i,B:$i,C:$i]: ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ C @ C)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ C @ C) @ B) @ A)) @ (c_List_Omeasures @ C @ (c_List_Olist_ONil @ (tc_fun @ C @ tc_Nat_Onat))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__measures_I1_J)). 32.13/11.36 thf(1405,plain,((! [A:$i,B:$i,C:$i]: ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ C @ C)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ C @ C) @ B) @ A)) @ (c_List_Omeasures @ C @ (c_List_Olist_ONil @ (tc_fun @ C @ tc_Nat_Onat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])). 32.13/11.36 thf(159,axiom,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Oorder @ C) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)) => (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2)). 32.13/11.36 thf(1104,plain,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Oorder @ C) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)) => (~ (A = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 32.13/11.36 thf(449,axiom,((~ (! [A:$i]: ((~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ A) @ c_Arrow__Order__Mirabelle_OLin))) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ v_b____) @ v_a____)) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096)). 32.13/11.36 thf(2154,plain,((~ (! [A:$i]: (~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ A) @ c_Arrow__Order__Mirabelle_OLin)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ v_b____) @ v_a____)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[449])). 32.13/11.36 thf(280,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ B) @ A)) <=> ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ C @ tc_HOL_Obool)) @ B) @ A)) | (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq)). 32.13/11.36 thf(1521,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ B) @ A)) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ C @ tc_HOL_Obool)) @ B) @ A)) | (B = A))) & (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ C @ tc_HOL_Obool)) @ B) @ A)) | (B = A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[280])). 32.13/11.36 thf(289,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ (c_Groups_Ozero__class_Ozero @ C)) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ (c_Groups_Ozero__class_Ozero @ C)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ B) @ A)))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ (c_Groups_Ozero__class_Ozero @ C)) @ B))) <= (class_Groups_Oordered__comm__monoid__add @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__nonneg)). 32.13/11.36 thf(1564,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ (c_Groups_Ozero__class_Ozero @ C)) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ (c_Groups_Ozero__class_Ozero @ C)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ B) @ A)))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ (c_Groups_Ozero__class_Ozero @ C)) @ B)) | ~ (class_Groups_Oordered__comm__monoid__add @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[289])). 32.13/11.36 thf(373,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ B) @ A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ A) @ C)))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ (c_Groups_Ozero__class_Ozero @ D)) @ C))) <= (class_Groups_Oordered__comm__monoid__add @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing2)). 32.13/11.36 thf(1863,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ B) @ A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ A) @ C)))) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ (c_Groups_Ozero__class_Ozero @ D)) @ C)) | ~ (class_Groups_Oordered__comm__monoid__add @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[373])). 32.13/11.36 thf(310,axiom,((! [A:$i,B:$i,C:$i]: ((c_Finite__Set_Ofinite @ C @ B) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ C @ tc_HOL_Obool)) @ A) @ B)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Finite__Set_Ocard @ C @ A)) @ (c_Finite__Set_Ocard @ C @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__card__mono)). 32.13/11.36 thf(1651,plain,((! [A:$i,B:$i,C:$i]: ((c_Finite__Set_Ofinite @ C @ B) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ C @ tc_HOL_Obool)) @ A) @ B)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Finite__Set_Ocard @ C @ A)) @ (c_Finite__Set_Ocard @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[310])). 32.13/11.36 thf(154,axiom,((! [A:$i,B:$i]: ((class_Groups_Omonoid__add @ B) => (A = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ (c_Groups_Ozero__class_Ozero @ B)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left)). 32.13/11.36 thf(1074,plain,((! [A:$i,B:$i]: ((class_Groups_Omonoid__add @ B) => (A = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ (c_Groups_Ozero__class_Ozero @ B)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 32.13/11.36 thf(300,axiom,((! [A:$i,B:$i,C:$i]: ((B = A) <=> ((hAPP @ (hAPP @ (c_COMBC @ C @ (tc_fun @ C @ tc_HOL_Obool) @ tc_HOL_Obool) @ (c_member @ C)) @ B) = (hAPP @ (hAPP @ (c_COMBC @ C @ (tc_fun @ C @ tc_HOL_Obool) @ tc_HOL_Obool) @ (c_member @ C)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq)). 32.13/11.36 thf(1604,plain,((! [A:$i,B:$i,C:$i]: (((B = A) => ((hAPP @ (hAPP @ (c_COMBC @ C @ (tc_fun @ C @ tc_HOL_Obool) @ tc_HOL_Obool) @ (c_member @ C)) @ B) = (hAPP @ (hAPP @ (c_COMBC @ C @ (tc_fun @ C @ tc_HOL_Obool) @ tc_HOL_Obool) @ (c_member @ C)) @ A))) & (((hAPP @ (hAPP @ (c_COMBC @ C @ (tc_fun @ C @ tc_HOL_Obool) @ tc_HOL_Obool) @ (c_member @ C)) @ B) = (hAPP @ (hAPP @ (c_COMBC @ C @ (tc_fun @ C @ tc_HOL_Obool) @ tc_HOL_Obool) @ (c_member @ C)) @ A)) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[300])). 32.13/11.36 thf(410,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ A) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc2)). 32.13/11.36 thf(2011,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[410])). 32.13/11.36 thf(120,axiom,((! [A:$i,B:$i]: ((((hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) != (c_Finite__Set_Ocard @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ A @ tc_HOL_Obool)))) => (c_Finite__Set_Ofinite @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)))) <= (c_Finite__Set_Ofinite @ (tc_fun @ B @ A) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ (tc_fun @ B @ A) @ tc_HOL_Obool)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD1)). 32.13/11.36 thf(920,plain,((! [A:$i,B:$i]: (((~ ((hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) = (c_Finite__Set_Ocard @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ A @ tc_HOL_Obool))))) => (c_Finite__Set_Ofinite @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)))) | ~ (c_Finite__Set_Ofinite @ (tc_fun @ B @ A) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ (tc_fun @ B @ A) @ tc_HOL_Obool)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 32.13/11.36 thf(461,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ F @ E)) @ D) @ (c_FuncSet_OPi @ F @ E @ C @ B))) => ((~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ (hAPP @ D @ A)) @ (hAPP @ B @ A)))) => (~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ F) @ A) @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PiE)). 32.13/11.36 thf(2204,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ F @ E)) @ D) @ (c_FuncSet_OPi @ F @ E @ C @ B))) => ((~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ (hAPP @ D @ A)) @ (hAPP @ B @ A)))) => (~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ F) @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[461])). 32.13/11.36 thf(46,axiom,((! [A:$i,B:$i]: (c_Fun_Oinj__on @ B @ B @ (c_COMBI @ B) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__id2)). 32.13/11.36 thf(678,plain,((! [A:$i,B:$i]: (c_Fun_Oinj__on @ B @ B @ (c_COMBI @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 32.13/11.36 thf(516,axiom,((! [A:$i,B:$i]: ((hAPP @ c_Nat_OSuc @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (hAPP @ c_Nat_OSuc @ B)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc)). 32.13/11.36 thf(2473,plain,((! [A:$i,B:$i]: ((hAPP @ c_Nat_OSuc @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (hAPP @ c_Nat_OSuc @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[516])). 32.13/11.36 thf(38,axiom,((! [A:$i,B:$i]: ((class_Orderings_Oorder @ B) => (class_Orderings_Oorder @ (tc_fun @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder)). 32.13/11.36 thf(661,plain,((! [A:$i,B:$i]: ((class_Orderings_Oorder @ B) => (class_Orderings_Oorder @ (tc_fun @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 32.13/11.36 thf(80,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ B) @ A)) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ C @ tc_HOL_Obool)) @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__imp__subset)). 32.13/11.36 thf(793,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ B) @ A)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ C @ tc_HOL_Obool)) @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 32.13/11.36 thf(453,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less0)). 32.13/11.36 thf(2164,plain,((! [A:$i]: ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[453])). 32.13/11.36 thf(174,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hAPP @ (hAPP @ (c_COMBC @ D @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ C @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ D @ (c_COMBC @ C @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ C @ (tc_prod @ D @ C)) @ (tc_fun @ C @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ D @ (c_COMBB @ (tc_prod @ D @ C) @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool) @ C @ (c_member @ (tc_prod @ D @ C)))) @ (c_Product__Type_OPair @ D @ C)))) @ B) = (hAPP @ (hAPP @ (c_COMBC @ D @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ C @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ D @ (c_COMBC @ C @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ C @ (tc_prod @ D @ C)) @ (tc_fun @ C @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ D @ (c_COMBB @ (tc_prod @ D @ C) @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool) @ C @ (c_member @ (tc_prod @ D @ C)))) @ (c_Product__Type_OPair @ D @ C)))) @ A)) <=> (B = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq2)). 32.13/11.36 thf(1153,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((hAPP @ (hAPP @ (c_COMBC @ D @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ C @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ D @ (c_COMBC @ C @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ C @ (tc_prod @ D @ C)) @ (tc_fun @ C @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ D @ (c_COMBB @ (tc_prod @ D @ C) @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool) @ C @ (c_member @ (tc_prod @ D @ C)))) @ (c_Product__Type_OPair @ D @ C)))) @ B) = (hAPP @ (hAPP @ (c_COMBC @ D @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ C @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ D @ (c_COMBC @ C @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ C @ (tc_prod @ D @ C)) @ (tc_fun @ C @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ D @ (c_COMBB @ (tc_prod @ D @ C) @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool) @ C @ (c_member @ (tc_prod @ D @ C)))) @ (c_Product__Type_OPair @ D @ C)))) @ A)) => (B = A)) & ((B = A) => ((hAPP @ (hAPP @ (c_COMBC @ D @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ C @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ D @ (c_COMBC @ C @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ C @ (tc_prod @ D @ C)) @ (tc_fun @ C @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ D @ (c_COMBB @ (tc_prod @ D @ C) @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool) @ C @ (c_member @ (tc_prod @ D @ C)))) @ (c_Product__Type_OPair @ D @ C)))) @ B) = (hAPP @ (hAPP @ (c_COMBC @ D @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ C @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ D @ (c_COMBC @ C @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ C @ (tc_prod @ D @ C)) @ (tc_fun @ C @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ D @ (c_COMBB @ (tc_prod @ D @ C) @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool) @ C @ (c_member @ (tc_prod @ D @ C)))) @ (c_Product__Type_OPair @ D @ C)))) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 32.13/11.36 thf(423,axiom,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Olinorder @ C) => (((A = B) <=> (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A))) <= (~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv1)). 32.13/11.36 thf(2047,plain,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Olinorder @ C) => ((((A = B) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A))) & ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)) => (A = B))) | (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[423])). 32.13/11.36 thf(387,axiom,((! [A:$i,B:$i]: ((hAPP @ c_Nat_OSuc @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right)). 32.13/11.36 thf(1915,plain,((! [A:$i,B:$i]: ((hAPP @ c_Nat_OSuc @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[387])). 32.13/11.36 thf(433,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ B) @ A)) <=> (hBOOL @ (hAPP @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def)). 32.13/11.36 thf(2083,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ B) @ A)) => (hBOOL @ (hAPP @ A @ B))) & ((hBOOL @ (hAPP @ A @ B)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[433])). 32.13/11.36 thf(376,axiom,((! [A:$i,B:$i]: ((c_Nitpick_Orefl_H @ B @ A) <=> (! [C:$i]: (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ B @ B)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ B @ B) @ C) @ C)) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Orefl_H__def)). 32.13/11.36 thf(1868,plain,((! [A:$i,B:$i]: (((c_Nitpick_Orefl_H @ B @ A) => (! [C:$i]: (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ B @ B)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ B @ B) @ C) @ C)) @ A)))) & ((! [C:$i]: (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ B @ B)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ B @ B) @ C) @ C)) @ A))) => (c_Nitpick_Orefl_H @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[376])). 32.13/11.36 thf(330,axiom,((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ v_F) @ (c_FuncSet_OPi @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ c_Arrow__Order__Mirabelle_OProf @ (hAPP @ (c_COMBK @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ tc_HOL_Obool) @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ c_Arrow__Order__Mirabelle_OLin))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I1_J)). 32.13/11.36 thf(1730,plain,((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ v_F) @ (c_FuncSet_OPi @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ c_Arrow__Order__Mirabelle_OProf @ (hAPP @ (c_COMBK @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ tc_HOL_Obool) @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ c_Arrow__Order__Mirabelle_OLin))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[330])). 32.13/11.36 thf(82,axiom,((class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add)). 32.13/11.36 thf(798,plain,((class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 32.13/11.36 thf(176,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (c_Finite__Set_Ocard @ B @ (c_Set_Oimage @ D @ B @ A @ C))) @ (c_Finite__Set_Ocard @ D @ C))) <= (c_Finite__Set_Ofinite @ D @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image__le)). 32.13/11.36 thf(1163,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (c_Finite__Set_Ocard @ B @ (c_Set_Oimage @ D @ B @ A @ C))) @ (c_Finite__Set_Ocard @ D @ C))) | ~ (c_Finite__Set_Ofinite @ D @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 32.13/11.36 thf(209,axiom,((! [A:$i,B:$i,C:$i]: ((c_Finite__Set_Ofinite @ C @ B) => ((c_Finite__Set_Ofinite @ C @ A) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ A) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__finite__subset)). 32.13/11.36 thf(1274,plain,((! [A:$i,B:$i,C:$i]: ((c_Finite__Set_Ofinite @ C @ B) => ((c_Finite__Set_Ofinite @ C @ A) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 32.13/11.36 thf(475,axiom,((! [A:$i]: ((c_Arrow__Order__Mirabelle_OIIA @ A) <=> (! [B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ B) @ c_Arrow__Order__Mirabelle_OProf)) => (! [C:$i]: ((! [D:$i,E:$i]: ((! [F:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ E)) @ (hAPP @ B @ F))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ E)) @ (hAPP @ C @ F))))) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ E)) @ (hAPP @ A @ B))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ E)) @ (hAPP @ A @ C)))))) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ C) @ c_Arrow__Order__Mirabelle_OProf))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IIA__def)). 32.13/11.36 thf(2264,plain,((! [A:$i]: (((c_Arrow__Order__Mirabelle_OIIA @ A) => (! [B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ B) @ c_Arrow__Order__Mirabelle_OProf)) => (! [C:$i]: (! [D:$i,E:$i]: ((! [F:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ E)) @ (hAPP @ B @ F))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ E)) @ (hAPP @ C @ F)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ E)) @ (hAPP @ C @ F))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ E)) @ (hAPP @ B @ F)))))) => (((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ E)) @ (hAPP @ A @ B))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ E)) @ (hAPP @ A @ C)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ E)) @ (hAPP @ A @ C))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ E)) @ (hAPP @ A @ B)))))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ C) @ c_Arrow__Order__Mirabelle_OProf))))))) & ((! [B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ B) @ c_Arrow__Order__Mirabelle_OProf)) => (! [C:$i]: (! [D:$i,E:$i]: ((! [F:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ E)) @ (hAPP @ B @ F))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ E)) @ (hAPP @ C @ F)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ E)) @ (hAPP @ C @ F))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ E)) @ (hAPP @ B @ F)))))) => (((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ E)) @ (hAPP @ A @ B))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ E)) @ (hAPP @ A @ C)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ E)) @ (hAPP @ A @ C))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ E)) @ (hAPP @ A @ B)))))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ C) @ c_Arrow__Order__Mirabelle_OProf)))))) => (c_Arrow__Order__Mirabelle_OIIA @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[475])). 32.13/11.36 thf(385,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((D = C) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ A) @ C)) <=> (hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ A) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eqset__imp__iff)). 32.13/11.36 thf(1900,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((D = C) => (((hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ A) @ C)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ A) @ D))) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ A) @ D)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[385])). 32.13/11.36 thf(93,axiom,((! [A:$i,B:$i]: ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2)). 32.13/11.36 thf(825,plain,((! [A:$i,B:$i]: ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 32.13/11.36 thf(145,axiom,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))) => (B = A)) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucE)). 32.13/11.36 thf(1021,plain,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))) => (B = A)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 32.13/11.36 thf(149,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ A) @ B)) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ A) @ C))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ C) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subsetD)). 32.13/11.36 thf(1042,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ A) @ B)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ A) @ C)) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 32.13/11.36 thf(279,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ D) @ (c_Set_Oimage @ C @ E @ B @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ (hAPP @ (c_Hilbert__Choice_Oinv__into @ C @ E @ A @ B) @ D)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__into)). 32.13/11.36 thf(1519,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ D) @ (c_Set_Oimage @ C @ E @ B @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ (hAPP @ (c_Hilbert__Choice_Oinv__into @ C @ E @ A @ B) @ D)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[279])). 32.13/11.36 thf(239,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ (c_Set_Oinsert @ D @ A @ B))) <= ((~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ B))) => (C = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertCI)). 32.13/11.36 thf(1355,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ (c_Set_Oinsert @ D @ A @ B))) | ~ ((~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ B))) => (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 32.13/11.36 thf(316,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ A) @ (c_Groups_Ozero__class_Ozero @ B))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ A)) @ (c_Groups_Ozero__class_Ozero @ B)))) <= (class_Rings_Olinordered__idom @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__less__0__iff)). 32.13/11.36 thf(1676,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ A) @ (c_Groups_Ozero__class_Ozero @ B))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ A)) @ (c_Groups_Ozero__class_Ozero @ B)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ A)) @ (c_Groups_Ozero__class_Ozero @ B))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ A) @ (c_Groups_Ozero__class_Ozero @ B))))) | ~ (class_Rings_Olinordered__idom @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[316])). 32.13/11.36 thf(446,axiom,((class_Groups_Ozero @ tc_Nat_Onat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero)). 32.13/11.36 thf(2147,plain,((class_Groups_Ozero @ tc_Nat_Onat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[446])). 32.13/11.36 thf(7,axiom,((! [A:$i,B:$i]: (((A = (c_Groups_Oone__class_Oone @ B)) <=> ((c_Groups_Oone__class_Oone @ B) = A)) <= (class_Groups_Oone @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__reorient)). 32.13/11.36 thf(561,plain,((! [A:$i,B:$i]: ((((A = (c_Groups_Oone__class_Oone @ B)) => ((c_Groups_Oone__class_Oone @ B) = A)) & (((c_Groups_Oone__class_Oone @ B) = A) => (A = (c_Groups_Oone__class_Oone @ B)))) | ~ (class_Groups_Oone @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 32.13/11.36 thf(51,axiom,((! [A:$i,B:$i]: ((class_Orderings_Otop @ B) => (class_Orderings_Otop @ (tc_fun @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Otop)). 32.13/11.36 thf(693,plain,((! [A:$i,B:$i]: ((class_Orderings_Otop @ B) => (class_Orderings_Otop @ (tc_fun @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 32.13/11.36 thf(199,axiom,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Oorder @ C) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)) <= (B != A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I11_J)). 32.13/11.36 thf(1238,plain,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Oorder @ C) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)) | (B = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 32.13/11.36 thf(258,axiom,((! [A:$i,B:$i,C:$i]: (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ B) @ (c_Set_Oinsert @ C @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI)). 32.13/11.36 thf(1423,plain,((! [A:$i,B:$i,C:$i]: (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ B) @ (c_Set_Oinsert @ C @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])). 32.13/11.36 thf(391,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((C = D) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ C) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ D) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem__trans)). 32.13/11.36 thf(1938,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((C = D) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ C) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ D) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[391])). 32.13/11.36 thf(362,axiom,((! [A:$i]: (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (c_COMBB @ tc_HOL_Obool @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_If @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool) @ (hAPP @ (c_COMBB @ tc_Nat_Onat @ (tc_fun @ tc_Nat_Onat @ tc_HOL_Obool) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat)) @ v_h____)) @ A))) @ v_Lab____)) @ v_Lba____)) @ c_Arrow__Order__Mirabelle_OProf)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PiProf)). 32.13/11.36 thf(1837,plain,((! [A:$i]: (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (c_COMBB @ tc_HOL_Obool @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_If @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool) @ (hAPP @ (c_COMBB @ tc_Nat_Onat @ (tc_fun @ tc_Nat_Onat @ tc_HOL_Obool) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat)) @ v_h____)) @ A))) @ v_Lab____)) @ v_Lba____)) @ c_Arrow__Order__Mirabelle_OProf)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[362])). 32.13/11.36 thf(242,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Orderings_Opreorder @ D) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ B)) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ A)) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ B) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__trans)). 32.13/11.36 thf(1365,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Orderings_Opreorder @ D) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ B)) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ A)) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])). 32.13/11.36 thf(27,axiom,((! [A:$i,B:$i]: ((c_Sum__Type_OPlus @ B @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ A @ tc_HOL_Obool))) = (c_Orderings_Otop__class_Otop @ (tc_fun @ (tc_sum @ B @ A) @ tc_HOL_Obool))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__Plus__UNIV)). 32.13/11.36 thf(625,plain,((! [A:$i,B:$i]: ((c_Sum__Type_OPlus @ B @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ A @ tc_HOL_Obool))) = (c_Orderings_Otop__class_Otop @ (tc_fun @ (tc_sum @ B @ A) @ tc_HOL_Obool))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 32.13/11.36 thf(286,axiom,((! [A:$i,B:$i]: ((((hAPP @ c_Nat_OSuc @ B) != A) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ c_Nat_OSuc @ B)) @ A))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessI)). 32.13/11.36 thf(1555,plain,((! [A:$i,B:$i]: (((~ ((hAPP @ c_Nat_OSuc @ B) = A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ c_Nat_OSuc @ B)) @ A))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[286])). 32.13/11.36 thf(319,axiom,((! [A:$i,B:$i]: ((class_Groups_Ocomm__monoid__add @ B) => ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ (c_Groups_Ozero__class_Ozero @ B)) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral)). 32.13/11.36 thf(1687,plain,((! [A:$i,B:$i]: ((class_Groups_Ocomm__monoid__add @ B) => ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ (c_Groups_Ozero__class_Ozero @ B)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[319])). 32.13/11.36 thf(430,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ (hAPP @ c_Nat_OSuc @ A))) <=> ((B = (hAPP @ c_Nat_OSuc @ A)) | (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__eq)). 32.13/11.36 thf(2068,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ (hAPP @ c_Nat_OSuc @ A))) => ((B = (hAPP @ c_Nat_OSuc @ A)) | (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)))) & (((B = (hAPP @ c_Nat_OSuc @ A)) | (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A))) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ (hAPP @ c_Nat_OSuc @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[430])). 32.13/11.36 thf(459,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ B)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ A)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1)). 32.13/11.36 thf(2200,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ B)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ A)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[459])). 32.13/11.36 thf(111,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ E @ D)) @ (hAPP @ E @ C))) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ B @ B)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ B @ B) @ D) @ C)) @ (c_Wellfounded_Omlex__prod @ B @ E @ A))) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ B @ B)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ B @ B) @ D) @ C)) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__leq)). 32.13/11.36 thf(889,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ E @ D)) @ (hAPP @ E @ C))) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ B @ B)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ B @ B) @ D) @ C)) @ (c_Wellfounded_Omlex__prod @ B @ E @ A))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ B @ B)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ B @ B) @ D) @ C)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 32.13/11.36 thf(312,axiom,((! [A:$i]: ((c_Nat_Osize__class_Osize @ tc_Nat_Onat @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__size)). 32.13/11.36 thf(1656,plain,((! [A:$i]: ((c_Nat_Osize__class_Osize @ tc_Nat_Onat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[312])). 32.13/11.36 thf(465,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((c_Fun_Oinj__on @ F @ E @ D @ C) => (((hBOOL @ (hAPP @ (hAPP @ (c_member @ F) @ B) @ C)) => (((hAPP @ D @ A) != (hAPP @ D @ B)) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ F) @ A) @ C)))) <= (B != A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__contraD)). 32.13/11.36 thf(2213,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((c_Fun_Oinj__on @ F @ E @ D @ C) => (((hBOOL @ (hAPP @ (hAPP @ (c_member @ F) @ B) @ C)) => (~ ((hAPP @ D @ A) = (hAPP @ D @ B)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ F) @ A) @ C)))) | (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[465])). 32.13/11.36 thf(187,axiom,((! [A:$i,B:$i]: ((c_Arrow__Order__Mirabelle_Odictator @ B @ A) <=> (! [C:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ C) @ c_Arrow__Order__Mirabelle_OProf)) => ((hAPP @ B @ C) = (hAPP @ C @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dictator__def)). 32.13/11.36 thf(1195,plain,((! [A:$i,B:$i]: (((c_Arrow__Order__Mirabelle_Odictator @ B @ A) => (! [C:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ C) @ c_Arrow__Order__Mirabelle_OProf)) => ((hAPP @ B @ C) = (hAPP @ C @ A))))) & ((! [C:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ C) @ c_Arrow__Order__Mirabelle_OProf)) => ((hAPP @ B @ C) = (hAPP @ C @ A)))) => (c_Arrow__Order__Mirabelle_Odictator @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 32.13/11.36 thf(464,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ E @ D)) @ C) @ (c_FuncSet_OPi @ E @ D @ B @ (hAPP @ (c_COMBK @ (tc_fun @ D @ tc_HOL_Obool) @ E) @ A)))) => ((c_Fun_Oinj__on @ E @ D @ C @ B) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (c_Finite__Set_Ocard @ E @ B)) @ (c_Finite__Set_Ocard @ D @ A))) <= (c_Finite__Set_Ofinite @ D @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__inj)). 32.13/11.36 thf(2211,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ E @ D)) @ C) @ (c_FuncSet_OPi @ E @ D @ B @ (hAPP @ (c_COMBK @ (tc_fun @ D @ tc_HOL_Obool) @ E) @ A)))) => ((c_Fun_Oinj__on @ E @ D @ C @ B) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (c_Finite__Set_Ocard @ E @ B)) @ (c_Finite__Set_Ocard @ D @ A))) | ~ (c_Finite__Set_Ofinite @ D @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[464])). 32.13/11.36 thf(495,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ (c_Groups_Ozero__class_Ozero @ C)) @ B)) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ (c_Groups_Ozero__class_Ozero @ C)) @ A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ (c_Groups_Ozero__class_Ozero @ C)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ B) @ A))))) <= (class_Groups_Oordered__comm__monoid__add @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__nonneg)). 32.13/11.36 thf(2344,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ (c_Groups_Ozero__class_Ozero @ C)) @ B)) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ (c_Groups_Ozero__class_Ozero @ C)) @ A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ (c_Groups_Ozero__class_Ozero @ C)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ B) @ A))))) | ~ (class_Groups_Oordered__comm__monoid__add @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[495])). 32.13/11.36 thf(485,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Finite__Set_Ocard @ D @ (c_Set_Oimage @ C @ D @ B @ A))) @ (c_Finite__Set_Ocard @ C @ A))) => (~ (c_Fun_Oinj__on @ C @ D @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pigeonhole)). 32.13/11.36 thf(2313,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Finite__Set_Ocard @ D @ (c_Set_Oimage @ C @ D @ B @ A))) @ (c_Finite__Set_Ocard @ C @ A))) => (~ (c_Fun_Oinj__on @ C @ D @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[485])). 32.13/11.36 thf(215,axiom,((class_Groups_Oone @ tc_Nat_Onat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone)). 32.13/11.36 thf(1291,plain,((class_Groups_Oone @ tc_Nat_Onat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 32.13/11.36 thf(57,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((c_Set_Oinsert @ D @ B @ (c_Set_Oinsert @ D @ C @ A)) = (c_Set_Oinsert @ D @ C @ (c_Set_Oinsert @ D @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__commute)). 32.13/11.36 thf(710,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((c_Set_Oinsert @ D @ B @ (c_Set_Oinsert @ D @ C @ A)) = (c_Set_Oinsert @ D @ C @ (c_Set_Oinsert @ D @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 32.13/11.36 thf(134,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) <=> (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ B)) @ (hAPP @ c_Nat_OSuc @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__mono)). 32.13/11.36 thf(974,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ B)) @ (hAPP @ c_Nat_OSuc @ A)))) & ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ B)) @ (hAPP @ c_Nat_OSuc @ A))) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 32.13/11.36 thf(240,axiom,((! [A:$i,B:$i]: (((c_Finite__Set_Ocard @ B @ A) = (c_Finite__Set_Ofold__image @ tc_Nat_Onat @ B @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (hAPP @ (c_COMBK @ tc_Nat_Onat @ B) @ (c_Groups_Oone__class_Oone @ tc_Nat_Onat)) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) @ A)) <= (c_Finite__Set_Ofinite @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oeq__fold__g)). 32.13/11.36 thf(1360,plain,((! [A:$i,B:$i]: (((c_Finite__Set_Ocard @ B @ A) = (c_Finite__Set_Ofold__image @ tc_Nat_Onat @ B @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (hAPP @ (c_COMBK @ tc_Nat_Onat @ B) @ (c_Groups_Oone__class_Oone @ tc_Nat_Onat)) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) @ A)) | ~ (c_Finite__Set_Ofinite @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 32.13/11.36 thf(236,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ B @ B)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ B @ B) @ D) @ C)) @ (c_List_Omeasures @ B @ (c_List_Olist_OCons @ (tc_fun @ B @ tc_Nat_Onat) @ E @ A)))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ E @ D)) @ (hAPP @ E @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_measures__less)). 32.13/11.36 thf(1350,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ B @ B)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ B @ B) @ D) @ C)) @ (c_List_Omeasures @ B @ (c_List_Olist_OCons @ (tc_fun @ B @ tc_Nat_Onat) @ E @ A)))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ E @ D)) @ (hAPP @ E @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 32.13/11.36 thf(401,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ B) @ A)) => ((c_Finite__Set_Ofinite @ C @ B) <= (c_Finite__Set_Ofinite @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__subset)). 32.13/11.36 thf(1983,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ B) @ A)) => ((c_Finite__Set_Ofinite @ C @ B) | ~ (c_Finite__Set_Ofinite @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[401])). 32.13/11.36 thf(443,axiom,((! [A:$i,B:$i,C:$i]: (((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ B) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ A) @ B)) <=> (A = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel)). 32.13/11.36 thf(2115,plain,((! [A:$i,B:$i,C:$i]: ((((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ B) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ A) @ B)) => (A = C)) & ((A = C) => ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ B) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[443])). 32.13/11.36 thf(438,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ B @ tc_HOL_Obool) @ D) @ A)) => (hBOOL @ (hAPP @ A @ C))) <= (hBOOL @ (hAPP @ D @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate1D)). 32.13/11.36 thf(2100,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ B @ tc_HOL_Obool) @ D) @ A)) => (hBOOL @ (hAPP @ A @ C))) | ~ (hBOOL @ (hAPP @ D @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[438])). 32.13/11.36 thf(367,axiom,((class_Groups_Omonoid__add @ tc_Nat_Onat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add)). 32.13/11.36 thf(1851,plain,((class_Groups_Omonoid__add @ tc_Nat_Onat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[367])). 32.13/11.36 thf(282,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ c_fequal @ B) @ A)) | (B != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__2)). 32.13/11.36 thf(1534,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ c_fequal @ B) @ A)) | ~ (B = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[282])). 32.13/11.36 thf(143,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ B @ B)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ B @ B) @ D) @ C)) @ (c_Wellfounded_Omlex__prod @ B @ E @ A))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ E @ D)) @ (hAPP @ E @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__less)). 32.13/11.36 thf(1017,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ B @ B)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ B @ B) @ D) @ C)) @ (c_Wellfounded_Omlex__prod @ B @ E @ A))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ E @ D)) @ (hAPP @ E @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 32.13/11.36 thf(161,axiom,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Olinorder @ C) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ A) @ B)) <=> (~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__less)). 32.13/11.36 thf(1111,plain,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Olinorder @ C) => (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ A) @ B)) => (~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)))) & ((~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A))) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 32.13/11.36 thf(62,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((A = (c_Set_Oimage @ C @ D @ (c_Hilbert__Choice_Oinv__into @ D @ C @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool)) @ B) @ (c_Set_Oimage @ D @ C @ B @ A))) <= (c_Fun_Oinj__on @ D @ C @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__image__comp)). 32.13/11.36 thf(725,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((A = (c_Set_Oimage @ C @ D @ (c_Hilbert__Choice_Oinv__into @ D @ C @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool)) @ B) @ (c_Set_Oimage @ D @ C @ B @ A))) | ~ (c_Fun_Oinj__on @ D @ C @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 32.13/11.36 thf(259,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((c_Nat_Onat_Onat__case @ D @ C @ B @ (hAPP @ c_Nat_OSuc @ A)) = (hAPP @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__Suc)). 32.13/11.36 thf(1425,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((c_Nat_Onat_Onat__case @ D @ C @ B @ (hAPP @ c_Nat_OSuc @ A)) = (hAPP @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])). 32.13/11.36 thf(284,axiom,((! [A:$i,B:$i]: ((B != A) <=> ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) | (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff)). 32.13/11.36 thf(1540,plain,((! [A:$i,B:$i]: (((~ (B = A)) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) | (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ B)))) & (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) | (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ B))) => (~ (B = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[284])). 32.13/11.36 thf(379,axiom,((! [A:$i,B:$i]: ((class_Groups_Olinordered__ab__group__add @ B) => (((c_Groups_Ozero__class_Ozero @ B) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ A)) <=> (A = (c_Groups_Ozero__class_Ozero @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__eq__0__iff)). 32.13/11.36 thf(1878,plain,((! [A:$i,B:$i]: ((class_Groups_Olinordered__ab__group__add @ B) => ((((c_Groups_Ozero__class_Ozero @ B) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ A)) => (A = (c_Groups_Ozero__class_Ozero @ B))) & ((A = (c_Groups_Ozero__class_Ozero @ B)) => ((c_Groups_Ozero__class_Ozero @ B) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[379])). 32.13/11.36 thf(252,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ F) @ B) @ C)) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ F) @ A) @ C)) => ((B = A) <=> ((hAPP @ D @ B) = (hAPP @ D @ A))))) <= (c_Fun_Oinj__on @ F @ E @ D @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff)). 32.13/11.36 thf(1397,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ F) @ B) @ C)) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ F) @ A) @ C)) => (((B = A) => ((hAPP @ D @ B) = (hAPP @ D @ A))) & (((hAPP @ D @ B) = (hAPP @ D @ A)) => (B = A))))) | ~ (c_Fun_Oinj__on @ F @ E @ D @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])). 32.13/11.36 thf(273,axiom,((! [A:$i,B:$i]: (((hAPP @ c_Nat_OSuc @ A) = (hAPP @ c_Nat_OSuc @ B)) <=> (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject)). 32.13/11.36 thf(1493,plain,((! [A:$i,B:$i]: ((((hAPP @ c_Nat_OSuc @ A) = (hAPP @ c_Nat_OSuc @ B)) => (A = B)) & ((A = B) => ((hAPP @ c_Nat_OSuc @ A) = (hAPP @ c_Nat_OSuc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[273])). 32.13/11.36 thf(318,axiom,((! [A:$i]: ((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) != (hAPP @ c_Nat_OSuc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc)). 32.13/11.36 thf(1683,plain,((! [A:$i]: ~ ((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) = (hAPP @ c_Nat_OSuc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[318])). 32.13/11.36 thf(228,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ (c_Groups_Ozero__class_Ozero @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ A))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ (c_Groups_Ozero__class_Ozero @ B)) @ A))) <= (class_Groups_Olinordered__ab__group__add @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add)). 32.13/11.36 thf(1329,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ (c_Groups_Ozero__class_Ozero @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ (c_Groups_Ozero__class_Ozero @ B)) @ A))) & ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ (c_Groups_Ozero__class_Ozero @ B)) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ (c_Groups_Ozero__class_Ozero @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ A))))) | ~ (class_Groups_Olinordered__ab__group__add @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 32.13/11.36 thf(175,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ A)) <= (B != C)) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ (c_Set_Oinsert @ D @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertE)). 32.13/11.36 thf(1160,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ A)) | (B = C) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ (c_Set_Oinsert @ D @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 32.13/11.36 thf(392,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (hAPP @ c_Arrow__Order__Mirabelle_Omktop @ B) @ A)) @ c_Arrow__Order__Mirabelle_OLin)) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ B) @ c_Arrow__Order__Mirabelle_OLin))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mktop__Lin)). 32.13/11.36 thf(1942,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (hAPP @ c_Arrow__Order__Mirabelle_Omktop @ B) @ A)) @ c_Arrow__Order__Mirabelle_OLin)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ B) @ c_Arrow__Order__Mirabelle_OLin))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[392])). 32.13/11.36 thf(313,axiom,((! [A:$i]: (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ (hAPP @ c_Nat_OSuc @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessI)). 32.13/11.36 thf(1659,plain,((! [A:$i]: (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ (hAPP @ c_Nat_OSuc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[313])). 32.13/11.36 thf(488,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((c_FunDef_Oin__rel @ E @ D @ C @ B @ A) <=> (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ E @ D)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ E @ D) @ B) @ A)) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rel__def)). 32.13/11.36 thf(2323,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((c_FunDef_Oin__rel @ E @ D @ C @ B @ A) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ E @ D)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ E @ D) @ B) @ A)) @ C))) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ E @ D)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ E @ D) @ B) @ A)) @ C)) => (c_FunDef_Oin__rel @ E @ D @ C @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[488])). 32.13/11.36 thf(216,axiom,((! [A:$i,B:$i]: (A = (hAPP @ (c_COMBI @ B) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1)). 32.13/11.36 thf(1292,plain,((! [A:$i,B:$i]: (A = (hAPP @ (c_COMBI @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 32.13/11.36 thf(3,axiom,((class_Orderings_Opreorder @ tc_HOL_Obool)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder)). 32.13/11.36 thf(554,plain,((class_Orderings_Opreorder @ tc_HOL_Obool)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 32.13/11.36 thf(70,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((c_List_Olist_OCons @ E @ D @ C) = (c_List_Olist_OCons @ E @ B @ A)) <=> ((D = B) & (C = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Oinject)). 32.13/11.36 thf(753,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((c_List_Olist_OCons @ E @ D @ C) = (c_List_Olist_OCons @ E @ B @ A)) => ((D = B) & (C = A))) & (((D = B) & (C = A)) => ((c_List_Olist_OCons @ E @ D @ C) = (c_List_Olist_OCons @ E @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 32.13/11.36 thf(31,axiom,((! [A:$i,B:$i]: (((class_Finite__Set_Ofinite @ B) & (class_Finite__Set_Ofinite @ A)) => (class_Finite__Set_Ofinite @ (tc_fun @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Finite__Set_Ofinite)). 32.13/11.36 thf(642,plain,((! [A:$i,B:$i]: (((class_Finite__Set_Ofinite @ B) & (class_Finite__Set_Ofinite @ A)) => (class_Finite__Set_Ofinite @ (tc_fun @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 32.13/11.36 thf(424,axiom,((class_Rings_Ozero__neq__one @ tc_Nat_Onat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one)). 32.13/11.36 thf(2053,plain,((class_Rings_Ozero__neq__one @ tc_Nat_Onat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[424])). 32.13/11.36 thf(297,axiom,((class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct)). 32.13/11.36 thf(1584,plain,((class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[297])). 32.13/11.36 thf(348,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J)). 32.13/11.36 thf(1791,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A))) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[348])). 32.13/11.36 thf(441,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Groups_Ocancel__semigroup__add @ D) => (((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ A) @ B)) => (A = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__imp__eq)). 32.13/11.36 thf(2108,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Groups_Ocancel__semigroup__add @ D) => (((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ A) @ B)) => (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[441])). 32.13/11.36 thf(419,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C) @ B)) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C) @ A)) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans)). 32.13/11.36 thf(2038,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C) @ B)) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C) @ A)) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[419])). 32.13/11.36 thf(189,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((c_Fun_Oinj__on @ E @ C @ (c_Hilbert__Choice_Oinv__into @ C @ E @ A @ B) @ D) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ E @ tc_HOL_Obool) @ D) @ (c_Set_Oimage @ C @ E @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__inv__into)). 32.13/11.36 thf(1207,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((c_Fun_Oinj__on @ E @ C @ (c_Hilbert__Choice_Oinv__into @ C @ E @ A @ B) @ D) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ E @ tc_HOL_Obool) @ D) @ (c_Set_Oimage @ C @ E @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 32.13/11.36 thf(309,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((D = C) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ D) @ A)) <=> (hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ C) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eqelem__imp__iff)). 32.13/11.36 thf(1644,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((D = C) => (((hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ D) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ C) @ A))) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ C) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ D) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[309])). 32.13/11.36 thf(301,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (hAPP @ A @ B) @ C)) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ B))) => (((hBOOL @ (hAPP @ (hAPP @ A @ B) @ C)) <= ((hBOOL @ (hAPP @ (hAPP @ A @ B) @ C)) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ C)))) <= ((hBOOL @ (hAPP @ (hAPP @ A @ B) @ C)) <= (C = B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases)). 32.13/11.36 thf(1612,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (hAPP @ A @ B) @ C)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ B))) => ((hBOOL @ (hAPP @ (hAPP @ A @ B) @ C)) | ~ ((hBOOL @ (hAPP @ (hAPP @ A @ B) @ C)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ C))) | ~ ((hBOOL @ (hAPP @ (hAPP @ A @ B) @ C)) | ~ (C = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[301])). 32.13/11.36 thf(256,axiom,((! [A:$i,B:$i,C:$i]: ((c_Finite__Set_Ofinite @ C @ B) => (((c_Finite__Set_Ocard @ C @ (c_Set_Oinsert @ C @ A @ B)) = (hAPP @ c_Nat_OSuc @ (c_Finite__Set_Ocard @ C @ B))) <= (~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ A) @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__disjoint)). 32.13/11.36 thf(1419,plain,((! [A:$i,B:$i,C:$i]: ((c_Finite__Set_Ofinite @ C @ B) => (((c_Finite__Set_Ocard @ C @ (c_Set_Oinsert @ C @ A @ B)) = (hAPP @ c_Nat_OSuc @ (c_Finite__Set_Ocard @ C @ B))) | (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])). 32.13/11.36 thf(97,axiom,((! [A:$i,B:$i,C:$i]: ((A = B) <=> (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ B) @ (hAPP @ c_fequal @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem)). 32.13/11.36 thf(837,plain,((! [A:$i,B:$i,C:$i]: (((A = B) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ B) @ (hAPP @ c_fequal @ A)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ B) @ (hAPP @ c_fequal @ A))) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 32.13/11.36 thf(358,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ A) @ (c_Int_Oring__1__class_OInts @ B))) => (((c_Groups_Ozero__class_Ozero @ B) = A) <=> ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ A) = (c_Groups_Ozero__class_Ozero @ B)))) <= (class_Int_Oring__char__0 @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__double__eq__0__iff)). 32.13/11.36 thf(1825,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ A) @ (c_Int_Oring__1__class_OInts @ B))) => ((((c_Groups_Ozero__class_Ozero @ B) = A) => ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ A) = (c_Groups_Ozero__class_Ozero @ B))) & (((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ A) = (c_Groups_Ozero__class_Ozero @ B)) => ((c_Groups_Ozero__class_Ozero @ B) = A)))) | ~ (class_Int_Oring__char__0 @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[358])). 32.13/11.36 thf(162,axiom,((! [A:$i,B:$i]: ((? [C:$i]: (c_List_Odistinct @ tc_Arrow__Order__Mirabelle_Oalt @ (c_List_Olist_OCons @ tc_Arrow__Order__Mirabelle_Oalt @ B @ (c_List_Olist_OCons @ tc_Arrow__Order__Mirabelle_Oalt @ A @ (c_List_Olist_OCons @ tc_Arrow__Order__Mirabelle_Oalt @ C @ (c_List_Olist_ONil @ tc_Arrow__Order__Mirabelle_Oalt)))))) <= (B != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_third__alt)). 32.13/11.36 thf(1114,plain,((! [A:$i,B:$i]: (? [C:$i]: (c_List_Odistinct @ tc_Arrow__Order__Mirabelle_Oalt @ (c_List_Olist_OCons @ tc_Arrow__Order__Mirabelle_Oalt @ B @ (c_List_Olist_OCons @ tc_Arrow__Order__Mirabelle_Oalt @ A @ (c_List_Olist_OCons @ tc_Arrow__Order__Mirabelle_Oalt @ C @ (c_List_Olist_ONil @ tc_Arrow__Order__Mirabelle_Oalt))))) | (B = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 32.13/11.36 thf(139,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((E != F) => ((D != C) => ((C != F) => (((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ B) @ c_Arrow__Order__Mirabelle_OProf)) => ((((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ v_F @ A))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ F) @ E)) @ (hAPP @ v_F @ B)))) <= (! [G:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ A @ G))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ F) @ E)) @ (hAPP @ B @ G)))))) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ A) @ c_Arrow__Order__Mirabelle_OProf)))) <= (D != E))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C2_C)). 32.13/11.36 thf(997,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((~ (E = F)) => ((~ (D = C)) => ((~ (C = F)) => (((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ B) @ c_Arrow__Order__Mirabelle_OProf)) => ((((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ v_F @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ F) @ E)) @ (hAPP @ v_F @ B)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ F) @ E)) @ (hAPP @ v_F @ B))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ v_F @ A))))) | ~ (! [G:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ A @ G))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ F) @ E)) @ (hAPP @ B @ G)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ F) @ E)) @ (hAPP @ B @ G))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ A @ G)))))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ A) @ c_Arrow__Order__Mirabelle_OProf)))) | (D = E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 32.13/11.36 thf(157,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ B) @ A)) => ((B = A) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ A) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityI)). 32.13/11.36 thf(1099,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ B) @ A)) => ((B = A) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 32.13/11.36 thf(137,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ B @ D)) @ (hAPP @ B @ C))) | ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ E @ E)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ E @ E) @ D) @ C)) @ (c_List_Omeasures @ E @ A))) & ((hAPP @ B @ C) = (hAPP @ B @ D)))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ E @ E)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ E @ E) @ D) @ C)) @ (c_List_Omeasures @ E @ (c_List_Olist_OCons @ (tc_fun @ E @ tc_Nat_Onat) @ B @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__measures_I2_J)). 32.13/11.36 thf(985,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ B @ D)) @ (hAPP @ B @ C))) | ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ E @ E)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ E @ E) @ D) @ C)) @ (c_List_Omeasures @ E @ A))) & ((hAPP @ B @ C) = (hAPP @ B @ D)))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ E @ E)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ E @ E) @ D) @ C)) @ (c_List_Omeasures @ E @ (c_List_Olist_OCons @ (tc_fun @ E @ tc_Nat_Onat) @ B @ A))))) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ E @ E)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ E @ E) @ D) @ C)) @ (c_List_Omeasures @ E @ (c_List_Olist_OCons @ (tc_fun @ E @ tc_Nat_Onat) @ B @ A)))) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ B @ D)) @ (hAPP @ B @ C))) | ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ E @ E)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ E @ E) @ D) @ C)) @ (c_List_Omeasures @ E @ A))) & ((hAPP @ B @ C) = (hAPP @ B @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 32.13/11.36 thf(54,axiom,((! [A:$i,B:$i]: ((((c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)) = (c_Set_Oimage @ B @ B @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)))) <= (c_Fun_Oinj__on @ B @ B @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)))) <= (c_Finite__Set_Ofinite @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__inj__surj)). 32.13/11.36 thf(701,plain,((! [A:$i,B:$i]: (((c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)) = (c_Set_Oimage @ B @ B @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)))) | ~ (c_Fun_Oinj__on @ B @ B @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool))) | ~ (c_Finite__Set_Ofinite @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 32.13/11.36 thf(173,axiom,((! [A:$i]: ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ A) @ (c_Groups_Oone__class_Oone @ tc_Nat_Onat)) = (hAPP @ c_Nat_OSuc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1)). 32.13/11.36 thf(1150,plain,((! [A:$i]: ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ A) @ (c_Groups_Oone__class_Oone @ tc_Nat_Onat)) = (hAPP @ c_Nat_OSuc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 32.13/11.36 thf(265,axiom,((~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ v_a____) @ v_b____)) @ v_Lba____)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_Ia_M_Ab_J_A_126_058_ALba_096)). 32.13/11.36 thf(1478,plain,((~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ v_a____) @ v_b____)) @ v_Lba____)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[265])). 32.13/11.36 thf(218,axiom,((! 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[A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ E @ E)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ E @ E) @ D) @ C)) @ (hAPP @ B @ F))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ (tc_prod @ A @ E) @ (tc_prod @ A @ E))) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ (tc_prod @ A @ E) @ (tc_prod @ A @ E)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ A @ E) @ F) @ D)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ A @ E) @ F) @ C))) @ (c_Recdef_Osame__fst @ A @ E @ G @ B)))) | ~ (hBOOL @ (hAPP @ G @ F))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 32.13/11.36 thf(281,axiom,((! [A:$i,B:$i,C:$i]: (((B != A) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A))) <= (class_Orderings_Oorder @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq)). 32.13/11.36 thf(1530,plain,((! [A:$i,B:$i,C:$i]: (~ (B = A) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)) | ~ (class_Orderings_Oorder @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[281])). 32.13/11.36 thf(246,axiom,((c_List_Odistinct @ tc_Arrow__Order__Mirabelle_Oalt @ (c_List_Olist_OCons @ tc_Arrow__Order__Mirabelle_Oalt @ v_c____ @ (c_List_Olist_OCons @ tc_Arrow__Order__Mirabelle_Oalt @ v_d____ @ (c_List_Olist_OCons @ tc_Arrow__Order__Mirabelle_Oalt @ v_e____ @ (c_List_Olist_ONil @ tc_Arrow__Order__Mirabelle_Oalt)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dist)). 32.13/11.36 thf(1382,plain,((c_List_Odistinct @ tc_Arrow__Order__Mirabelle_Oalt @ (c_List_Olist_OCons @ tc_Arrow__Order__Mirabelle_Oalt @ v_c____ @ (c_List_Olist_OCons @ tc_Arrow__Order__Mirabelle_Oalt @ v_d____ @ (c_List_Olist_OCons @ tc_Arrow__Order__Mirabelle_Oalt @ v_e____ @ (c_List_Olist_ONil @ tc_Arrow__Order__Mirabelle_Oalt)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])). 32.13/11.36 thf(359,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Groups_Oordered__cancel__ab__semigroup__add @ D) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ A) @ C)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ A) @ B))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__left__mono)). 32.13/11.36 thf(1831,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Groups_Oordered__cancel__ab__semigroup__add @ D) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ A) @ C)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ A) @ B))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[359])). 32.13/11.36 thf(35,axiom,((! [A:$i]: ((class_Finite__Set_Ofinite @ A) => (class_Finite__Set_Ofinite @ (tc_Option_Ooption @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite)). 32.13/11.36 thf(654,plain,((! [A:$i]: ((class_Finite__Set_Ofinite @ A) => (class_Finite__Set_Ofinite @ (tc_Option_Ooption @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 32.13/11.36 thf(185,axiom,((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ v_c____) @ v_d____)) @ (hAPP @ v_P____ @ (hAPP @ (c_Hilbert__Choice_Oinv__into @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ (c_Orderings_Otop__class_Otop @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool)) @ v_h____) @ v_n____))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_096)). 32.13/11.36 thf(1192,plain,((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ v_c____) @ v_d____)) @ (hAPP @ v_P____ @ (hAPP @ (c_Hilbert__Choice_Oinv__into @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ (c_Orderings_Otop__class_Otop @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool)) @ v_h____) @ v_n____))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 32.13/11.36 thf(513,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__zeroE)). 32.13/11.36 thf(2465,plain,((! [A:$i]: ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[513])). 32.13/11.36 thf(119,axiom,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Oorder @ C) => ((B = A) <=> ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ A) @ B)) & (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__iff)). 32.13/11.36 thf(911,plain,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Oorder @ C) => (((B = A) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ A) @ B)) & (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)))) & (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ A) @ B)) & (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A))) => (B = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 32.13/11.36 thf(527,axiom,((class_Orderings_Oorder @ tc_Nat_Onat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder)). 32.13/11.36 thf(2505,plain,((class_Orderings_Oorder @ tc_Nat_Onat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[527])). 32.13/11.36 thf(61,axiom,((! [A:$i,B:$i,C:$i]: ((c_List_Olist_ONil @ C) != (c_List_Olist_OCons @ C @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I2_J)). 32.13/11.36 thf(721,plain,((! [A:$i,B:$i,C:$i]: ~ ((c_List_Olist_ONil @ C) = (c_List_Olist_OCons @ C @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 32.13/11.36 thf(368,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)) | (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ A) @ B))) <= (class_Orderings_Olinorder @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__linear)). 32.13/11.36 thf(1852,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)) | (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ A) @ B)) | ~ (class_Orderings_Olinorder @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[368])). 32.13/11.36 thf(326,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ D) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ A))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ D) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono)). 32.13/11.36 thf(1720,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ D) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ A))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ D) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[326])). 32.13/11.36 thf(75,axiom,((! [A:$i]: ((c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ A)) = (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw)). 32.13/11.36 thf(779,plain,((! [A:$i]: ((c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ A)) = (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 32.13/11.36 thf(501,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A)) => (A = B)) <= (class_Groups_Ocancel__semigroup__add @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__imp__eq)). 32.13/11.36 thf(2370,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A)) => (A = B)) | ~ (class_Groups_Ocancel__semigroup__add @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[501])). 32.13/11.36 thf(370,axiom,((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ v_Lba____) @ c_Arrow__Order__Mirabelle_OLin))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096Lba_A_058_ALin_096)). 32.13/11.36 thf(1857,plain,((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ v_Lba____) @ c_Arrow__Order__Mirabelle_OLin))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[370])). 32.13/11.36 thf(356,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) => (B != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl2)). 32.13/11.36 thf(1814,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[356])). 32.13/11.36 thf(156,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((~ ((hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ A) @ C)) <= (~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ A) @ D))))) <= ((~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ A) @ C))) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ A) @ D)))) <= (C = D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityCE)). 32.13/11.36 thf(1086,plain,((! [A:$i,B:$i,C:$i,D:$i]: (~ ((hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ A) @ C)) | (hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ A) @ D))) | ~ (~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ A) @ C)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ A) @ D))) | ~ (C = D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 32.13/11.36 thf(200,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Orderings_Oorder @ D) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ B)) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ A) @ B)) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ A) @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J)). 32.13/11.36 thf(1241,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Orderings_Oorder @ D) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ B)) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ A) @ B)) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 32.13/11.36 thf(463,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((hBOOL @ (hAPP @ (hAPP @ D @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ C @ B) @ A))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ F @ (tc_fun @ E @ tc_HOL_Obool)) @ D) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate2D)). 32.13/11.36 thf(2208,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((hBOOL @ (hAPP @ (hAPP @ D @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ C @ B) @ A))) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ F @ (tc_fun @ E @ tc_HOL_Obool)) @ D) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[463])). 32.13/11.36 thf(421,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((class_Orderings_Oord @ E) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ E) @ C) @ B)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ E @ (hAPP @ C @ A)) @ (hAPP @ B @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funD)). 32.13/11.36 thf(2043,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((class_Orderings_Oord @ E) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ E) @ C) @ B)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ E @ (hAPP @ C @ A)) @ (hAPP @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[421])). 32.13/11.36 thf(426,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ B @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ A)) @ (c_Groups_Ozero__class_Ozero @ B))) <=> (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ B @ A) @ (c_Groups_Ozero__class_Ozero @ B)))) <= (class_Groups_Olinordered__ab__group__add @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero)). 32.13/11.36 thf(2057,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ B @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ A)) @ (c_Groups_Ozero__class_Ozero @ B))) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ B @ A) @ (c_Groups_Ozero__class_Ozero @ B)))) & ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ B @ A) @ (c_Groups_Ozero__class_Ozero @ B))) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ B @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ A)) @ (c_Groups_Ozero__class_Ozero @ B))))) | ~ (class_Groups_Olinordered__ab__group__add @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[426])). 32.13/11.36 thf(365,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((A = B) <= ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A))) <= (class_Groups_Ocancel__ab__semigroup__add @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__imp__eq)). 32.13/11.36 thf(1846,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((A = B) | ~ ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A)) | ~ (class_Groups_Ocancel__ab__semigroup__add @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[365])). 32.13/11.36 thf(499,axiom,((class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add)). 32.13/11.36 thf(2368,plain,((class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[499])). 32.13/11.36 thf(5,axiom,((! [A:$i,B:$i]: ((class_Finite__Set_Ofinite @ B) => (c_Finite__Set_Ofinite @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__code)). 32.13/11.36 thf(558,plain,((! [A:$i,B:$i]: ((class_Finite__Set_Ofinite @ B) => (c_Finite__Set_Ofinite @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 32.13/11.36 thf(468,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ A)) <= (A = B)) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ B))) <= (class_Orderings_Oord @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__less__eq__trans)). 32.13/11.36 thf(2221,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ A)) | ~ (A = B) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ B)) | ~ (class_Orderings_Oord @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[468])). 32.13/11.36 thf(458,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ H @ H)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ H @ H) @ F) @ D)) @ B)) | ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ G @ G)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ G @ G) @ E) @ C)) @ A)) & (F = D))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ (tc_prod @ H @ G) @ (tc_prod @ H @ G))) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ (tc_prod @ H @ G) @ (tc_prod @ H @ G)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ H @ G) @ F) @ E)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ H @ G) @ D) @ C))) @ (c_Wellfounded_Olex__prod @ H @ G @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__lex__prod)). 32.13/11.36 thf(2189,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: ((((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ H @ H)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ H @ H) @ F) @ D)) @ B)) | ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ G @ G)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ G @ G) @ E) @ C)) @ A)) & (F = D))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ (tc_prod @ H @ G) @ (tc_prod @ H @ G))) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ (tc_prod @ H @ G) @ (tc_prod @ H @ G)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ H @ G) @ F) @ E)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ H @ G) @ D) @ C))) @ (c_Wellfounded_Olex__prod @ H @ G @ B @ A)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ (tc_prod @ H @ G) @ (tc_prod @ H @ G))) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ (tc_prod @ H @ G) @ (tc_prod @ H @ G)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ H @ G) @ F) @ E)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ H @ G) @ D) @ C))) @ (c_Wellfounded_Olex__prod @ H @ G @ B @ A))) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ H @ H)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ H @ H) @ F) @ D)) @ B)) | ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ G @ G)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ G @ G) @ E) @ C)) @ A)) & (F = D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[458])). 32.13/11.36 thf(129,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ (c_Set_Oimage @ E @ D @ C @ B)) @ (c_Set_Oimage @ E @ D @ C @ A))) <=> (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ E @ tc_HOL_Obool) @ B) @ A))) <= (c_Fun_Oinj__on @ E @ D @ C @ (c_Orderings_Otop__class_Otop @ (tc_fun @ E @ tc_HOL_Obool)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__subset__iff)). 32.13/11.36 thf(953,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ (c_Set_Oimage @ E @ D @ C @ B)) @ (c_Set_Oimage @ E @ D @ C @ A))) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ E @ tc_HOL_Obool) @ B) @ A))) & ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ E @ tc_HOL_Obool) @ B) @ A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ (c_Set_Oimage @ E @ D @ C @ B)) @ (c_Set_Oimage @ E @ D @ C @ A))))) | ~ (c_Fun_Oinj__on @ E @ D @ C @ (c_Orderings_Otop__class_Otop @ (tc_fun @ E @ tc_HOL_Obool)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 32.13/11.36 thf(60,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((c_Finite__Set_Ofinite @ D @ C) => ((c_Fun_Oinj__on @ D @ B @ A @ C) <= ((c_Finite__Set_Ocard @ D @ C) = (c_Finite__Set_Ocard @ B @ (c_Set_Oimage @ D @ B @ A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__card__imp__inj__on)). 32.13/11.36 thf(718,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((c_Finite__Set_Ofinite @ D @ C) => ((c_Fun_Oinj__on @ D @ B @ A @ C) | ~ ((c_Finite__Set_Ocard @ D @ C) = (c_Finite__Set_Ocard @ B @ (c_Set_Oimage @ D @ B @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 32.13/11.36 thf(211,axiom,((! [A:$i,B:$i]: (((class_Finite__Set_Ofinite @ A) & (class_Finite__Set_Ofinite @ B)) => (class_Finite__Set_Ofinite @ (tc_prod @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod__Finite__Set_Ofinite)). 32.13/11.36 thf(1278,plain,((! [A:$i,B:$i]: (((class_Finite__Set_Ofinite @ A) & (class_Finite__Set_Ofinite @ B)) => (class_Finite__Set_Ofinite @ (tc_prod @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 32.13/11.36 thf(169,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((A = C) | (hBOOL @ (hAPP @ B @ A))) <=> (hBOOL @ (hAPP @ (c_Set_Oinsert @ D @ C @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__code)). 32.13/11.36 thf(1135,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((A = C) | (hBOOL @ (hAPP @ B @ A))) => (hBOOL @ (hAPP @ (c_Set_Oinsert @ D @ C @ B) @ A))) & ((hBOOL @ (hAPP @ (c_Set_Oinsert @ D @ C @ B) @ A)) => ((A = C) | (hBOOL @ (hAPP @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 32.13/11.36 thf(408,axiom,((! [A:$i,B:$i,C:$i]: (((A != B) => ((~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B)))) <= (class_Rings_Olinordered__idom @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom)). 32.13/11.36 thf(2001,plain,((! [A:$i,B:$i,C:$i]: (((~ (A = B)) => ((~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B)))) | ~ (class_Rings_Olinordered__idom @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[408])). 32.13/11.36 thf(69,axiom,((! [A:$i]: (((c_Groups_Ozero__class_Ozero @ A) != (c_Groups_Oone__class_Oone @ A)) <= (class_Rings_Ozero__neq__one @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__neq__one)). 32.13/11.36 thf(750,plain,((! [A:$i]: (~ ((c_Groups_Ozero__class_Ozero @ A) = (c_Groups_Oone__class_Oone @ A)) | ~ (class_Rings_Ozero__neq__one @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 32.13/11.36 thf(171,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add1)). 32.13/11.36 thf(1146,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 32.13/11.36 thf(508,axiom,((! [A:$i,B:$i,C:$i]: (((~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A))) <=> ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B)) | (B = A))) <= (class_Orderings_Olinorder @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq)). 32.13/11.36 thf(2391,plain,((! [A:$i,B:$i,C:$i]: ((((~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A))) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B)) | (B = A))) & (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B)) | (B = A)) => (~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A))))) | ~ (class_Orderings_Olinorder @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[508])). 32.13/11.36 thf(323,axiom,((! [A:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))) <=> ((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__0__eq)). 32.13/11.36 thf(1698,plain,((! [A:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))) => ((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) = A)) & (((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) = A) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[323])). 32.13/11.36 thf(268,axiom,((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ v_n____) @ (c_Finite__Set_Ocard @ tc_Arrow__Order__Mirabelle_Oindi @ (c_Orderings_Otop__class_Otop @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n_I1_J)). 32.13/11.36 thf(1483,plain,((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ v_n____) @ (c_Finite__Set_Ocard @ tc_Arrow__Order__Mirabelle_Oindi @ (c_Orderings_Otop__class_Otop @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[268])). 32.13/11.36 thf(389,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((C = A) <=> ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ A) @ B) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B))) <= (class_Groups_Ocancel__semigroup__add @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__cancel)). 32.13/11.36 thf(1927,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((C = A) => ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ A) @ B) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B))) & (((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ A) @ B) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) => (C = A))) | ~ (class_Groups_Ocancel__semigroup__add @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[389])). 32.13/11.36 thf(49,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((c_Finite__Set_Ofinite @ B @ (c_Set_Oimage @ D @ B @ (hAPP @ (c_COMBB @ E @ B @ D @ A) @ C) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool)))) <= (c_Finite__Set_Ofinite @ E @ (c_Set_Oimage @ D @ E @ C @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__range__imageI)). 32.13/11.36 thf(689,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((c_Finite__Set_Ofinite @ B @ (c_Set_Oimage @ D @ B @ (hAPP @ (c_COMBB @ E @ B @ D @ A) @ C) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool)))) | ~ (c_Finite__Set_Ofinite @ E @ (c_Set_Oimage @ D @ E @ C @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 32.13/11.36 thf(503,axiom,((! [A:$i]: (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le0)). 32.13/11.36 thf(2376,plain,((! [A:$i]: (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[503])). 32.13/11.36 thf(305,axiom,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Olinorder @ C) => (((B = A) <=> (~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B)))) <= (~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv3)). 32.13/11.36 thf(1631,plain,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Olinorder @ C) => ((((B = A) => (~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B)))) & ((~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B))) => (B = A))) | (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[305])). 32.13/11.36 thf(65,axiom,((! [A:$i,B:$i,C:$i]: (((c_Set_Oimage @ C @ B @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ C @ tc_HOL_Obool))) = (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool))) <=> (! [D:$i]: (D = (hAPP @ A @ (hAPP @ (c_Hilbert__Choice_Oinv__into @ C @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ C @ tc_HOL_Obool)) @ A) @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__iff__all)). 32.13/11.36 thf(733,plain,((! [A:$i,B:$i,C:$i]: ((((c_Set_Oimage @ C @ B @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ C @ tc_HOL_Obool))) = (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool))) => (! [D:$i]: (D = (hAPP @ A @ (hAPP @ (c_Hilbert__Choice_Oinv__into @ C @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ C @ tc_HOL_Obool)) @ A) @ D))))) & ((! [D:$i]: (D = (hAPP @ A @ (hAPP @ (c_Hilbert__Choice_Oinv__into @ C @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ C @ tc_HOL_Obool)) @ A) @ D)))) => ((c_Set_Oimage @ C @ B @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ C @ tc_HOL_Obool))) = (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 32.13/11.36 thf(13,axiom,((! [A:$i,B:$i,C:$i]: ((c_Fun_Oinj__on @ C @ B @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ C @ tc_HOL_Obool))) => ((c_Orderings_Otop__class_Otop @ (tc_fun @ C @ tc_HOL_Obool)) = (c_Set_Oimage @ B @ C @ (c_Hilbert__Choice_Oinv__into @ C @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ C @ tc_HOL_Obool)) @ A) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__imp__surj__inv)). 32.13/11.36 thf(584,plain,((! [A:$i,B:$i,C:$i]: ((c_Fun_Oinj__on @ C @ B @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ C @ tc_HOL_Obool))) => ((c_Orderings_Otop__class_Otop @ (tc_fun @ C @ tc_HOL_Obool)) = (c_Set_Oimage @ B @ C @ (c_Hilbert__Choice_Oinv__into @ C @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ C @ tc_HOL_Obool)) @ A) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 32.13/11.36 thf(360,axiom,((class_Orderings_Opreorder @ tc_Nat_Onat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder)). 32.13/11.36 thf(1833,plain,((class_Orderings_Opreorder @ tc_Nat_Onat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[360])). 32.13/11.36 thf(469,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((E != D) => (((((((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ v_F @ A))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ E) @ D)) @ (hAPP @ v_F @ B)))) <= (! [F:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ E) @ D)) @ (hAPP @ B @ F))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ A @ F)))))) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ A) @ c_Arrow__Order__Mirabelle_OProf))) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ B) @ c_Arrow__Order__Mirabelle_OProf))) <= (E != C)) <= (D != C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C4_C)). 32.13/11.36 thf(2225,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((~ (E = D)) => ((((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ v_F @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ E) @ D)) @ (hAPP @ v_F @ B)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ E) @ D)) @ (hAPP @ v_F @ B))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ v_F @ A))))) | ~ (! [F:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ E) @ D)) @ (hAPP @ B @ F))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ A @ F)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ A @ F))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ E) @ D)) @ (hAPP @ B @ F)))))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ A) @ c_Arrow__Order__Mirabelle_OProf)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ B) @ c_Arrow__Order__Mirabelle_OProf)) | (E = C) | (D = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[469])). 32.13/11.36 thf(380,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)) | (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B))) <= (class_Orderings_Olinorder @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__less__linear)). 32.13/11.36 thf(1884,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)) | (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B)) | ~ (class_Orderings_Olinorder @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[380])). 32.13/11.36 thf(345,axiom,((class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add)). 32.13/11.36 thf(1784,plain,((class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[345])). 32.13/11.36 thf(249,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ B)) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ A)))) <= (class_Orderings_Opreorder @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__trans)). 32.13/11.36 thf(1389,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ B)) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ A)))) | ~ (class_Orderings_Opreorder @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])). 32.13/11.36 thf(165,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ E @ tc_HOL_Obool) @ D) @ C)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ (tc_fun @ E @ B) @ tc_HOL_Obool) @ (c_FuncSet_OPi @ E @ B @ C @ A)) @ (c_FuncSet_OPi @ E @ B @ D @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__anti__mono)). 32.13/11.36 thf(1125,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ E @ tc_HOL_Obool) @ D) @ C)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ (tc_fun @ E @ B) @ tc_HOL_Obool) @ (c_FuncSet_OPi @ E @ B @ C @ A)) @ (c_FuncSet_OPi @ E @ B @ D @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 32.13/11.36 thf(336,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ c_Nat_OSuc @ B)) @ (hAPP @ c_Nat_OSuc @ A))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__eq)). 32.13/11.36 thf(1752,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ c_Nat_OSuc @ B)) @ (hAPP @ c_Nat_OSuc @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))) & ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ c_Nat_OSuc @ B)) @ (hAPP @ c_Nat_OSuc @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[336])). 32.13/11.36 thf(412,axiom,((class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add)). 32.13/11.36 thf(2016,plain,((class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[412])). 32.13/11.36 thf(532,axiom,((! [A:$i,B:$i,C:$i]: ((B != C) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (c_Arrow__Order__Mirabelle_Obelow @ A @ C @ B)) @ c_Arrow__Order__Mirabelle_OLin)) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ A) @ c_Arrow__Order__Mirabelle_OLin)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_below__Lin)). 32.13/11.36 thf(2514,plain,((! [A:$i,B:$i,C:$i]: ((~ (B = C)) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (c_Arrow__Order__Mirabelle_Obelow @ A @ C @ B)) @ c_Arrow__Order__Mirabelle_OLin)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ A) @ c_Arrow__Order__Mirabelle_OLin)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[532])). 32.13/11.36 thf(108,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ C) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ D) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ D) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less)). 32.13/11.36 thf(875,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ C) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ D) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ D) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 32.13/11.36 thf(253,axiom,((! [A:$i,B:$i,C:$i]: ((c_Finite__Set_Ofinite @ C @ B) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ A) @ B)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (c_Finite__Set_Ocard @ C @ A)) @ (c_Finite__Set_Ocard @ C @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__mono)). 32.13/11.36 thf(1403,plain,((! [A:$i,B:$i,C:$i]: ((c_Finite__Set_Ofinite @ C @ B) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ A) @ B)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (c_Finite__Set_Ocard @ C @ A)) @ (c_Finite__Set_Ocard @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])). 32.13/11.36 thf(350,axiom,((! [A:$i,B:$i,C:$i]: ((((B = A) <=> (~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A))) <= (class_Orderings_Olinorder @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv2)). 32.13/11.36 thf(1795,plain,((! [A:$i,B:$i,C:$i]: ((((B = A) => (~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)))) & ((~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A))) => (B = A))) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)) | ~ (class_Orderings_Olinorder @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[350])). 32.13/11.36 thf(509,axiom,((! [A:$i,B:$i]: (((((hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) = A) & ((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) = B)) | ((A = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) & ((hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) = B))) <=> ((hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__add)). 32.13/11.36 thf(2398,plain,((! [A:$i,B:$i]: ((((((hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) = A) & ((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) = B)) | ((A = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) & ((hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) = B))) => ((hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A))) & (((hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)) => ((((hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) = A) & ((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) = B)) | ((A = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) & ((hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) = B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[509])). 32.13/11.36 thf(204,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ B) @ A)) @ (c_Groups_Ozero__class_Ozero @ C))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ A) @ (c_Groups_Ozero__class_Ozero @ C)))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ (c_Groups_Ozero__class_Ozero @ C)))) <= (class_Groups_Oordered__comm__monoid__add @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__nonpos)). 32.13/11.36 thf(1256,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ B) @ A)) @ (c_Groups_Ozero__class_Ozero @ C))) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ A) @ (c_Groups_Ozero__class_Ozero @ C))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ (c_Groups_Ozero__class_Ozero @ C))) | ~ (class_Groups_Oordered__comm__monoid__add @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 32.13/11.36 thf(260,axiom,((! [A:$i,B:$i,C:$i]: (((c_Orderings_Otop__class_Otop @ C) = (hAPP @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ C)) @ A)) <= (class_Orderings_Otop @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__apply)). 32.13/11.36 thf(1428,plain,((! [A:$i,B:$i,C:$i]: (((c_Orderings_Otop__class_Otop @ C) = (hAPP @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ C)) @ A)) | ~ (class_Orderings_Otop @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])). 32.13/11.36 thf(124,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (hAPP @ C @ B)) @ (c_List_Olist_Olist__size @ D @ C @ A))) @ (hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))) = (c_List_Olist_Olist__size @ D @ C @ (c_List_Olist_OCons @ D @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osize_I2_J)). 32.13/11.36 thf(936,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (hAPP @ C @ B)) @ (c_List_Olist_Olist__size @ D @ C @ A))) @ (hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))) = (c_List_Olist_Olist__size @ D @ C @ (c_List_Olist_OCons @ D @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 32.13/11.36 thf(10,axiom,((! [A:$i,B:$i]: ((class_Orderings_Opreorder @ B) => (class_Orderings_Opreorder @ (tc_fun @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder)). 32.13/11.36 thf(572,plain,((! [A:$i,B:$i]: ((class_Orderings_Opreorder @ B) => (class_Orderings_Opreorder @ (tc_fun @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 32.13/11.36 thf(417,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)) <=> ((B != A) & (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)))) <= (class_Orderings_Oorder @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le)). 32.13/11.36 thf(2029,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)) => (~ (B = A) & (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)))) & ((~ (B = A) & (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)))) | ~ (class_Orderings_Oorder @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[417])). 32.13/11.36 thf(208,axiom,((! [A:$i,B:$i]: ((class_Groups_Olinordered__ab__group__add @ B) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ B @ (c_Groups_Ozero__class_Ozero @ B)) @ A)) <=> (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ B @ (c_Groups_Ozero__class_Ozero @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add)). 32.13/11.36 thf(1271,plain,((! [A:$i,B:$i]: ((class_Groups_Olinordered__ab__group__add @ B) => (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ B @ (c_Groups_Ozero__class_Ozero @ B)) @ A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ B @ (c_Groups_Ozero__class_Ozero @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ A)))) & ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ B @ (c_Groups_Ozero__class_Ozero @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ A))) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ B @ (c_Groups_Ozero__class_Ozero @ B)) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 32.13/11.36 thf(482,axiom,((class_Rings_Olinordered__semidom @ tc_Nat_Onat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom)). 32.13/11.36 thf(2308,plain,((class_Rings_Olinordered__semidom @ tc_Nat_Onat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[482])). 32.13/11.36 thf(58,axiom,((! [A:$i,B:$i]: ((((c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)) = A) <= ((c_Finite__Set_Ocard @ B @ A) = (c_Finite__Set_Ocard @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool))))) <= (c_Finite__Set_Ofinite @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV)). 32.13/11.36 thf(713,plain,((! [A:$i,B:$i]: (((c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)) = A) | ~ ((c_Finite__Set_Ocard @ B @ A) = (c_Finite__Set_Ocard @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)))) | ~ (c_Finite__Set_Ofinite @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 32.13/11.36 thf(374,axiom,((! [A:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ v_b____) @ v_a____)) @ (hAPP @ v_F @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (c_COMBB @ tc_HOL_Obool @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_If @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool) @ (hAPP @ (c_COMBB @ tc_Nat_Onat @ (tc_fun @ tc_Nat_Onat @ tc_HOL_Obool) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat)) @ v_h____)) @ A))) @ v_Lab____)) @ v_Lba____)))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A) @ v_n____))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n_I2_J)). 32.13/11.36 thf(1865,plain,((! [A:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ v_b____) @ v_a____)) @ (hAPP @ v_F @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (c_COMBB @ tc_HOL_Obool @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_If @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool) @ (hAPP @ (c_COMBB @ tc_Nat_Onat @ (tc_fun @ tc_Nat_Onat @ tc_HOL_Obool) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat)) @ v_h____)) @ A))) @ v_Lab____)) @ v_Lba____)))) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A) @ v_n____))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[374])). 32.13/11.36 thf(332,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ (hAPP @ c_Nat_OSuc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq)). 32.13/11.36 thf(1733,plain,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ (hAPP @ c_Nat_OSuc @ B)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ (hAPP @ c_Nat_OSuc @ B))) => (~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[332])). 32.13/11.36 thf(229,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ c_Nat_OSuc @ C)) @ A))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__trans__Suc)). 32.13/11.36 thf(1332,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ c_Nat_OSuc @ C)) @ A))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 32.13/11.36 thf(340,axiom,((~ (! [A:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ (c_Finite__Set_Ocard @ tc_Arrow__Order__Mirabelle_Oindi @ (c_Orderings_Otop__class_Otop @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool))))) => ((~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ v_a____) @ v_b____)) @ (hAPP @ v_F @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (c_COMBB @ tc_HOL_Obool @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_If @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool) @ (hAPP @ (c_COMBB @ tc_Nat_Onat @ (tc_fun @ tc_Nat_Onat @ tc_HOL_Obool) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat)) @ v_h____)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ A) @ (c_Groups_Oone__class_Oone @ tc_Nat_Onat))))) @ v_Lab____)) @ v_Lba____))))) <= (! [B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ v_b____) @ v_a____)) @ (hAPP @ v_F @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (c_COMBB @ tc_HOL_Obool @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_If @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool) @ (hAPP @ (c_COMBB @ tc_Nat_Onat @ (tc_fun @ tc_Nat_Onat @ tc_HOL_Obool) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat)) @ v_h____)) @ B))) @ v_Lab____)) @ v_Lba____)))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_059_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096)). 32.13/11.36 thf(1765,plain,((~ (! [A:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ (c_Finite__Set_Ocard @ tc_Arrow__Order__Mirabelle_Oindi @ (c_Orderings_Otop__class_Otop @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool))))) => (~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ v_a____) @ v_b____)) @ (hAPP @ v_F @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (c_COMBB @ tc_HOL_Obool @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_If @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool) @ (hAPP @ (c_COMBB @ tc_Nat_Onat @ (tc_fun @ tc_Nat_Onat @ tc_HOL_Obool) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat)) @ v_h____)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ A) @ (c_Groups_Oone__class_Oone @ tc_Nat_Onat))))) @ v_Lab____)) @ v_Lba____)))) | ~ (! [B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ v_b____) @ v_a____)) @ (hAPP @ v_F @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (c_COMBB @ tc_HOL_Obool @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_If @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool) @ (hAPP @ (c_COMBB @ tc_Nat_Onat @ (tc_fun @ tc_Nat_Onat @ tc_HOL_Obool) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat)) @ v_h____)) @ B))) @ v_Lab____)) @ v_Lba____)))) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[340])). 32.13/11.36 thf(85,axiom,((! [A:$i,B:$i,C:$i]: ((class_Rings_Ocomm__semiring__1 @ C) => ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ A) @ B) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J)). 32.13/11.36 thf(804,plain,((! [A:$i,B:$i,C:$i]: ((class_Rings_Ocomm__semiring__1 @ C) => ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ A) @ B) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 32.13/11.36 thf(205,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B)) <= (~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)))) <= (A != B)) <= (class_Orderings_Olinorder @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE)). 32.13/11.36 thf(1258,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B)) | (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)) | (A = B) | ~ (class_Orderings_Olinorder @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 32.13/11.36 thf(55,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((c_List_Olist_OCons @ E @ D @ (c_List_Olist_OCons @ E @ B @ (c_List_Osplice @ E @ C @ A))) = (c_List_Osplice @ E @ (c_List_Olist_OCons @ E @ D @ C) @ (c_List_Olist_OCons @ E @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splice_Osimps_I3_J)). 32.13/11.36 thf(704,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((c_List_Olist_OCons @ E @ D @ (c_List_Olist_OCons @ E @ B @ (c_List_Osplice @ E @ C @ A))) = (c_List_Osplice @ E @ (c_List_Olist_OCons @ E @ D @ C) @ (c_List_Olist_OCons @ E @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 32.13/11.36 thf(128,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ B) @ (c_FuncSet_OPi @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ c_Arrow__Order__Mirabelle_OProf @ (hAPP @ (c_COMBK @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ tc_HOL_Obool) @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ c_Arrow__Order__Mirabelle_OLin)))) => ((c_Arrow__Order__Mirabelle_Odictator @ B @ A) <= (! [C:$i]: ((! [D:$i,E:$i]: ((E != D) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ E)) @ (hAPP @ C @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ E)) @ (hAPP @ B @ C)))))) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ C) @ c_Arrow__Order__Mirabelle_OProf)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dictatorI)). 32.13/11.36 thf(947,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ B) @ (c_FuncSet_OPi @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ c_Arrow__Order__Mirabelle_OProf @ (hAPP @ (c_COMBK @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ tc_HOL_Obool) @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ c_Arrow__Order__Mirabelle_OLin)))) => ((c_Arrow__Order__Mirabelle_Odictator @ B @ A) | ~ (! [C:$i]: (! [D:$i,E:$i]: ((~ (E = D)) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ E)) @ (hAPP @ C @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ E)) @ (hAPP @ B @ C))))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ C) @ c_Arrow__Order__Mirabelle_OProf)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 32.13/11.37 thf(194,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: ((((~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ G) @ A) @ B))) => ((hAPP @ C @ (c_Set_Oinsert @ G @ A @ B)) = (hAPP @ (hAPP @ F @ (hAPP @ D @ A)) @ (hAPP @ C @ B)))) <= (c_Finite__Set_Ofinite @ G @ B)) <= (c_Finite__Set_Ofolding__image__simple @ H @ G @ F @ E @ D @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert)). 32.13/11.37 thf(1224,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i,G:$i,H:$i]: (((~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ G) @ A) @ B))) => ((hAPP @ C @ (c_Set_Oinsert @ G @ A @ B)) = (hAPP @ (hAPP @ F @ (hAPP @ D @ A)) @ (hAPP @ C @ B)))) | ~ (c_Finite__Set_Ofinite @ G @ B) | ~ (c_Finite__Set_Ofolding__image__simple @ H @ G @ F @ E @ D @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 32.13/11.37 thf(447,axiom,((! [A:$i]: ((hAPP @ c_Nat_OSuc @ A) != (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J)). 32.13/11.37 thf(2148,plain,((! [A:$i]: ~ ((hAPP @ c_Nat_OSuc @ A) = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[447])). 32.13/11.37 thf(530,axiom,(((c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) @ (c_Finite__Set_Ocard @ tc_Arrow__Order__Mirabelle_Oindi @ (c_Orderings_Otop__class_Otop @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool)))) = (c_Set_Oimage @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ v_h____ @ (c_Orderings_Otop__class_Otop @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surjh)). 32.13/11.37 thf(2510,plain,(((c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) @ (c_Finite__Set_Ocard @ tc_Arrow__Order__Mirabelle_Oindi @ (c_Orderings_Otop__class_Otop @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool)))) = (c_Set_Oimage @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ v_h____ @ (c_Orderings_Otop__class_Otop @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[530])). 32.13/11.37 thf(71,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl3)). 32.13/11.37 thf(764,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 32.13/11.37 thf(135,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((c_Finite__Set_Ofinite @ B @ A) => ((c_Finite__Set_Ocard @ (tc_sum @ D @ B) @ (c_Sum__Type_OPlus @ D @ B @ C @ A)) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (c_Finite__Set_Ocard @ D @ C)) @ (c_Finite__Set_Ocard @ B @ A)))) <= (c_Finite__Set_Ofinite @ D @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Plus)). 32.13/11.37 thf(979,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((c_Finite__Set_Ofinite @ B @ A) => ((c_Finite__Set_Ocard @ (tc_sum @ D @ B) @ (c_Sum__Type_OPlus @ D @ B @ C @ A)) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (c_Finite__Set_Ocard @ D @ C)) @ (c_Finite__Set_Ocard @ B @ A)))) | ~ (c_Finite__Set_Ofinite @ D @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 32.13/11.37 thf(496,axiom,((! [A:$i,B:$i]: ((? [C:$i]: (((hAPP @ c_Nat_OSuc @ C) = B) & (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ A))) | (B = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj)). 32.13/11.37 thf(2346,plain,((! [A:$i,B:$i]: (((? [C:$i]: (((hAPP @ c_Nat_OSuc @ C) = B) & (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ A))) | (B = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ A)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ A))) => (? [C:$i]: (((hAPP @ c_Nat_OSuc @ C) = B) & (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ A))) | (B = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[496])). 32.13/11.37 thf(432,axiom,((~ (! [A:$i]: ~ (c_List_Odistinct @ tc_Arrow__Order__Mirabelle_Oalt @ (c_List_Olist_OCons @ tc_Arrow__Order__Mirabelle_Oalt @ v_c____ @ (c_List_Olist_OCons @ tc_Arrow__Order__Mirabelle_Oalt @ v_d____ @ (c_List_Olist_OCons @ tc_Arrow__Order__Mirabelle_Oalt @ A @ (c_List_Olist_ONil @ tc_Arrow__Order__Mirabelle_Oalt)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Be_O_Adistinct_A_091c_M_Ad_M_Ae_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096)). 32.13/11.37 thf(2079,plain,((~ (! [A:$i]: ~ (c_List_Odistinct @ tc_Arrow__Order__Mirabelle_Oalt @ (c_List_Olist_OCons @ tc_Arrow__Order__Mirabelle_Oalt @ v_c____ @ (c_List_Olist_OCons @ tc_Arrow__Order__Mirabelle_Oalt @ v_d____ @ (c_List_Olist_OCons @ tc_Arrow__Order__Mirabelle_Oalt @ A @ (c_List_Olist_ONil @ tc_Arrow__Order__Mirabelle_Oalt)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[432])). 32.13/11.37 thf(484,axiom,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Opreorder @ C) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__le)). 32.13/11.37 thf(2311,plain,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Opreorder @ C) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[484])). 32.13/11.37 thf(190,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Orderings_Oorder @ D) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ B)) => ((C = A) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ A) @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I4_J)). 32.13/11.37 thf(1209,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Orderings_Oorder @ D) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ B)) => ((C = A) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 32.13/11.37 thf(116,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((c_Fun_Oinj__on @ E @ D @ C @ B) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ E @ tc_HOL_Obool) @ A) @ B)) => ((c_Set_Oimage @ D @ E @ (c_Hilbert__Choice_Oinv__into @ E @ D @ B @ C) @ (c_Set_Oimage @ E @ D @ C @ A)) = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__image__cancel)). 32.13/11.37 thf(900,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((c_Fun_Oinj__on @ E @ D @ C @ B) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ E @ tc_HOL_Obool) @ A) @ B)) => ((c_Set_Oimage @ D @ E @ (c_Hilbert__Choice_Oinv__into @ E @ D @ B @ C) @ (c_Set_Oimage @ E @ D @ C @ A)) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 32.13/11.37 thf(95,axiom,((! [A:$i,B:$i,C:$i]: (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ B) @ (c_Set_Oinsert @ C @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI1)). 32.13/11.37 thf(831,plain,((! [A:$i,B:$i,C:$i]: (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ B) @ (c_Set_Oinsert @ C @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 32.13/11.37 thf(255,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((! [E:$i]: ((! [F:$i]: (((E = F) <= ((hAPP @ B @ F) = (hAPP @ B @ E))) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ F) @ A)))) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ E) @ A)))) <=> (c_Fun_Oinj__on @ D @ C @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__def)). 32.13/11.37 thf(1408,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((! [E:$i]: (! [F:$i]: ((E = F) | ~ ((hAPP @ B @ F) = (hAPP @ B @ E)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ F) @ A))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ E) @ A)))) => (c_Fun_Oinj__on @ D @ C @ B @ A)) & ((c_Fun_Oinj__on @ D @ C @ B @ A) => (! [E:$i]: (! [F:$i]: ((E = F) | ~ ((hAPP @ B @ F) = (hAPP @ B @ E)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ F) @ A))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ E) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])). 32.13/11.37 thf(213,axiom,((! [A:$i,B:$i]: ((((c_Finite__Set_Ocard @ B @ A) = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) <= (~ (c_Finite__Set_Ofinite @ B @ A))) & (((c_Finite__Set_Ofold__image @ tc_Nat_Onat @ B @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (hAPP @ (c_COMBK @ tc_Nat_Onat @ B) @ (c_Groups_Oone__class_Oone @ tc_Nat_Onat)) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) @ A) = (c_Finite__Set_Ocard @ B @ A)) <= (c_Finite__Set_Ofinite @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__def)). 32.13/11.37 thf(1282,plain,((! [A:$i,B:$i]: ((((c_Finite__Set_Ocard @ B @ A) = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) | (c_Finite__Set_Ofinite @ B @ A)) & (((c_Finite__Set_Ofold__image @ tc_Nat_Onat @ B @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (hAPP @ (c_COMBK @ tc_Nat_Onat @ B) @ (c_Groups_Oone__class_Oone @ tc_Nat_Onat)) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) @ A) = (c_Finite__Set_Ocard @ B @ A)) | ~ (c_Finite__Set_Ofinite @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 32.13/11.37 thf(518,axiom,(((c_Nat_Osize__class_Osize @ tc_Nat_Onat @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I3_J)). 32.13/11.37 thf(2478,plain,(((c_Nat_Osize__class_Osize @ tc_Nat_Onat @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[518])). 32.13/11.37 thf(382,axiom,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ (c_Groups_Ozero__class_Ozero @ C)) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ (c_Groups_Ozero__class_Ozero @ C)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ B) @ A)))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ (c_Groups_Ozero__class_Ozero @ C)) @ B))) <= (class_Groups_Oordered__comm__monoid__add @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__pos)). 32.13/11.37 thf(1894,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ (c_Groups_Ozero__class_Ozero @ C)) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ (c_Groups_Ozero__class_Ozero @ C)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ B) @ A)))) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ (c_Groups_Ozero__class_Ozero @ C)) @ B)) | ~ (class_Groups_Oordered__comm__monoid__add @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[382])). 32.13/11.37 thf(77,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ A)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono1)). 32.13/11.37 thf(784,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ A)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A))) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 32.13/11.37 thf(163,axiom,((! [A:$i,B:$i,C:$i]: (((~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A))) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ A) @ B))) <= (class_Orderings_Olinorder @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leI)). 32.13/11.37 thf(1117,plain,((! [A:$i,B:$i,C:$i]: (((~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A))) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ A) @ B))) | ~ (class_Orderings_Olinorder @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 32.13/11.37 thf(293,axiom,((! [A:$i,B:$i,C:$i]: (((~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A))) <= (class_Orderings_Oorder @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I9_J)). 32.13/11.37 thf(1574,plain,((! [A:$i,B:$i,C:$i]: (~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)) | ~ (class_Orderings_Oorder @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[293])). 32.13/11.37 thf(140,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ B)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ (c_Set_Oinsert @ D @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI2)). 32.13/11.37 thf(1011,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ B)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ (c_Set_Oinsert @ D @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 32.13/11.37 thf(390,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A))) <=> (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ A)) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq)). 32.13/11.37 thf(1933,plain,((! [A:$i,B:$i]: (((~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A))) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ A)) @ B))) & ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ A)) @ B)) => (~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[390])). 32.13/11.37 thf(479,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ A) @ C)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ A) @ B))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ D @ tc_HOL_Obool)) @ C) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubsetD)). 32.13/11.37 thf(2299,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ A) @ C)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ A) @ B))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ D @ tc_HOL_Obool)) @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[479])). 32.13/11.37 thf(327,axiom,((! [A:$i,B:$i,C:$i]: (((~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B))) <= (class_Orderings_Olinorder @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__leE)). 32.13/11.37 thf(1722,plain,((! [A:$i,B:$i,C:$i]: (((~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B))) | ~ (class_Orderings_Olinorder @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[327])). 32.13/11.37 thf(170,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ A) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ (c_Groups_Oone__class_Oone @ B)))) <= (class_Rings_Olinordered__semidom @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__one)). 32.13/11.37 thf(1144,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ A) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ (c_Groups_Oone__class_Oone @ B)))) | ~ (class_Rings_Olinordered__semidom @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 32.13/11.37 thf(351,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Groups_Oordered__ab__semigroup__add @ D) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ B)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ A) @ C)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ A) @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__mono)). 32.13/11.37 thf(1801,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Groups_Oordered__ab__semigroup__add @ D) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ B)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ A) @ C)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[351])). 32.13/11.37 thf(504,axiom,((! 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[A:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ A)) <=> (A != (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neq0__conv)). 32.13/11.37 thf(863,plain,((! [A:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ A)) => (~ (A = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)))) & ((~ (A = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 32.13/11.37 thf(232,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ (c_Groups_Ozero__class_Ozero @ D)) @ C)) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ B) @ A)))) <= (class_Groups_Oordered__comm__monoid__add @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing)). 32.13/11.37 thf(1339,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ (c_Groups_Ozero__class_Ozero @ D)) @ C)) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A))) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ B) @ A)))) | ~ (class_Groups_Oordered__comm__monoid__add @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 32.13/11.37 thf(103,axiom,((v_c____ != v_d____)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096c_A_126_061_Ad_096)). 32.13/11.37 thf(858,plain,((~ (v_c____ = v_d____))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 32.13/11.37 thf(1,conjecture,((! 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[A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ (hAPP @ c_Nat_OSuc @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucI)). 32.13/11.37 thf(816,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ (hAPP @ c_Nat_OSuc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 32.13/11.37 thf(442,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)) <=> ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)) & ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ A) @ B)))) <= (class_Orderings_Opreorder @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le)). 32.13/11.37 thf(2111,plain,((! 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[A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) | (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[405])). 32.13/11.37 thf(331,axiom,((! [A:$i,B:$i]: (((c_Finite__Set_Ofinite @ (tc_prod @ B @ A) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ (tc_prod @ B @ A) @ tc_HOL_Obool))) <= (c_Finite__Set_Ofinite @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ A @ tc_HOL_Obool)))) <= (c_Finite__Set_Ofinite @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Prod__UNIV)). 32.13/11.37 thf(1731,plain,((! [A:$i,B:$i]: ((c_Finite__Set_Ofinite @ (tc_prod @ B @ A) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ (tc_prod @ B @ A) @ tc_HOL_Obool))) | ~ (c_Finite__Set_Ofinite @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ A @ tc_HOL_Obool))) | ~ (c_Finite__Set_Ofinite @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[331])). 32.13/11.37 thf(16,axiom,((! [A:$i,B:$i]: (A = (c_List_Osplice @ B @ (c_List_Olist_ONil @ B) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splice_Osimps_I1_J)). 32.13/11.37 thf(594,plain,((! [A:$i,B:$i]: (A = (c_List_Osplice @ B @ (c_List_Olist_ONil @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 32.13/11.37 thf(83,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((c_List_Olist_Olist__case @ F @ E @ D @ C @ (c_List_Olist_OCons @ E @ B @ A)) = (hAPP @ (hAPP @ C @ B) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I5_J)). 32.13/11.37 thf(799,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((c_List_Olist_Olist__case @ F @ E @ D @ C @ (c_List_Olist_OCons @ E @ B @ A)) = (hAPP @ (hAPP @ C @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 32.13/11.37 thf(25,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((c_Orderings_Otop__class_Otop @ (tc_fun @ C @ tc_HOL_Obool)) = (c_Set_Oimage @ D @ C @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool)))) => ((hAPP @ B @ (hAPP @ (c_Hilbert__Choice_Oinv__into @ D @ C @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool)) @ B) @ A)) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__f__inv__f)). 32.13/11.37 thf(621,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((c_Orderings_Otop__class_Otop @ (tc_fun @ C @ tc_HOL_Obool)) = (c_Set_Oimage @ D @ C @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool)))) => ((hAPP @ B @ (hAPP @ (c_Hilbert__Choice_Oinv__into @ D @ C @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool)) @ B) @ A)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 32.13/11.37 thf(99,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((hBOOL @ (hAPP @ (hAPP @ F @ E) @ D)) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ (tc_fun @ B @ tc_HOL_Obool)) @ F) @ A)) => (hBOOL @ (hAPP @ (hAPP @ A @ E) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate2D)). 32.13/11.37 thf(848,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((hBOOL @ (hAPP @ (hAPP @ F @ E) @ D)) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ (tc_fun @ B @ tc_HOL_Obool)) @ F) @ A)) => (hBOOL @ (hAPP @ (hAPP @ A @ E) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 32.13/11.37 thf(114,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((c_Set_Oinsert @ D @ (hAPP @ C @ B) @ (c_Set_Oimage @ E @ D @ C @ A)) = (c_Set_Oimage @ E @ D @ C @ (c_Set_Oinsert @ E @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__insert)). 32.13/11.37 thf(895,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((c_Set_Oinsert @ D @ (hAPP @ C @ B) @ (c_Set_Oimage @ E @ D @ C @ A)) = (c_Set_Oimage @ E @ D @ C @ (c_Set_Oinsert @ E @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 32.13/11.37 thf(473,axiom,((! [A:$i,B:$i,C:$i]: ((class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ C) => ((A = (c_Groups_Ozero__class_Ozero @ C)) <=> ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ B) @ A) = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff)). 32.13/11.37 thf(2252,plain,((! [A:$i,B:$i,C:$i]: ((class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ C) => (((A = (c_Groups_Ozero__class_Ozero @ C)) => ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ B) @ A) = B)) & (((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ B) @ A) = B) => (A = (c_Groups_Ozero__class_Ozero @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[473])). 32.13/11.37 thf(42,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((c_Fun_Oinj__on @ D @ C @ B @ A) => ((c_Finite__Set_Ocard @ C @ (c_Set_Oimage @ D @ C @ B @ A)) = (c_Finite__Set_Ocard @ D @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image)). 32.13/11.37 thf(668,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((c_Fun_Oinj__on @ D @ C @ B @ A) => ((c_Finite__Set_Ocard @ C @ (c_Set_Oimage @ D @ C @ B @ A)) = (c_Finite__Set_Ocard @ D @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 32.13/11.37 thf(123,axiom,((! [A:$i]: ((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) != (hAPP @ c_Nat_OSuc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J)). 32.13/11.37 thf(932,plain,((! [A:$i]: ~ ((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) = (hAPP @ c_Nat_OSuc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 32.13/11.37 thf(179,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((class_Groups_Oordered__ab__semigroup__add @ E) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ E @ D) @ C)) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ E @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ D) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ C) @ A))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ E @ B) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mono)). 32.13/11.37 thf(1171,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((class_Groups_Oordered__ab__semigroup__add @ E) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ E @ D) @ C)) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ E @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ D) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ C) @ A))) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ E @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 32.13/11.37 thf(510,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((D != E) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ C) @ c_Arrow__Order__Mirabelle_OLin)) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ B) @ A)) @ (hAPP @ (hAPP @ (hAPP @ c_Arrow__Order__Mirabelle_Oabove @ C) @ E) @ D))) <=> ((B != A) & ((((A != D) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ B) @ A)) @ C))) & (((E = B) | (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ B) @ E)) @ C))) <= (D = A))) <= (B != D)) & ((D = B) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ E) @ A)) @ C))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__above)). 32.13/11.37 thf(2418,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((~ (D = E)) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ C) @ c_Arrow__Order__Mirabelle_OLin)) => (((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ B) @ A)) @ (hAPP @ (hAPP @ (hAPP @ c_Arrow__Order__Mirabelle_Oabove @ C) @ E) @ D))) => (~ (B = A) & ((((~ (A = D)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ B) @ A)) @ C))) & ((E = B) | (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ B) @ E)) @ C)) | ~ (D = A))) | (B = D)) & ((D = B) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ E) @ A)) @ C))))) & ((~ (B = A) & ((((~ (A = D)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ B) @ A)) @ C))) & ((E = B) | (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ B) @ E)) @ C)) | ~ (D = A))) | (B = D)) & ((D = B) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ E) @ A)) @ C)))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ B) @ A)) @ (hAPP @ (hAPP @ (hAPP @ c_Arrow__Order__Mirabelle_Oabove @ C) @ E) @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[510])). 32.13/11.37 thf(191,axiom,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ A))) => (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__antisym)). 32.13/11.37 thf(1213,plain,((! [A:$i,B:$i]: ((~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ A))) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 32.13/11.37 thf(72,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ A)) | (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ B))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__gr__0)). 32.13/11.37 thf(768,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ A)) | (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ B))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A))) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ A)) | (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 32.13/11.37 thf(150,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ B)) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ A) @ C)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ A) @ B)))) <= (class_Orderings_Oorder @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J)). 32.13/11.37 thf(1044,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ B)) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ A) @ C)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ A) @ B)))) | ~ (class_Orderings_Oorder @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 32.13/11.37 thf(52,axiom,((! [A:$i,B:$i,C:$i]: ((c_List_Osplice @ C @ (c_List_Olist_OCons @ C @ B @ A) @ (c_List_Olist_ONil @ C)) = (c_List_Olist_OCons @ C @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_splice_Osimps_I2_J)). 32.13/11.37 thf(695,plain,((! [A:$i,B:$i,C:$i]: ((c_List_Osplice @ C @ (c_List_Olist_OCons @ C @ B @ A) @ (c_List_Olist_ONil @ C)) = (c_List_Olist_OCons @ C @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 32.13/11.37 thf(429,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Orderings_Oorder @ D) => ((C = B) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ A) @ B)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ A) @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I3_J)). 32.13/11.37 thf(2064,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Orderings_Oorder @ D) => ((C = B) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ A) @ B)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ A) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[429])). 32.13/11.37 thf(500,axiom,((class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1)). 32.13/11.37 thf(2369,plain,((class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[500])). 32.13/11.37 thf(142,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D) @ C)) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ D) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono)). 32.13/11.37 thf(1015,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D) @ C)) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ D) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 32.13/11.37 thf(181,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Groups_Oordered__ab__semigroup__add__imp__le @ D) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ A)) <=> (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ A) @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__right)). 32.13/11.37 thf(1176,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Groups_Oordered__ab__semigroup__add__imp__le @ D) => (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ A) @ B)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ A) @ B))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 32.13/11.37 thf(476,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((((hAPP @ D @ B) = (hAPP @ D @ A)) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ F) @ B) @ C)) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ F) @ A) @ C)) => (A = B)))) <= (c_Fun_Oinj__on @ F @ E @ D @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__onD)). 32.13/11.37 thf(2288,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((((hAPP @ D @ B) = (hAPP @ D @ A)) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ F) @ B) @ C)) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ F) @ A) @ C)) => (A = B)))) | ~ (c_Fun_Oinj__on @ F @ E @ D @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[476])). 32.13/11.37 thf(262,axiom,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Opreorder @ C) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)) => (~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym_H)). 32.13/11.37 thf(1435,plain,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Opreorder @ C) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)) => (~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])). 32.13/11.37 thf(415,axiom,((! [A:$i]: (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl)). 32.13/11.37 thf(2022,plain,((! [A:$i]: (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[415])). 32.13/11.37 thf(203,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ (c_Set_Oinsert @ D @ C @ B)) @ A)) <=> ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ B) @ A)) & (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__subset)). 32.13/11.37 thf(1250,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ (c_Set_Oinsert @ D @ C @ B)) @ A)) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ B) @ A)) & (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ A)))) & (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ B) @ A)) & (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ A))) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ (c_Set_Oinsert @ D @ C @ B)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 32.13/11.37 thf(158,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Orderings_Opreorder @ D) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ B)) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less__trans)). 32.13/11.37 thf(1102,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Orderings_Opreorder @ D) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ B)) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 32.13/11.37 thf(322,axiom,((! [A:$i]: ((hAPP @ c_Nat_OSuc @ A) != (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__not__Zero)). 32.13/11.37 thf(1694,plain,((! [A:$i]: ~ ((hAPP @ c_Nat_OSuc @ A) = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[322])). 32.13/11.37 thf(37,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((c_Finite__Set_Ofinite @ C @ A) <= (c_Finite__Set_Ofinite @ (tc_sum @ D @ C) @ (c_Sum__Type_OPlus @ D @ C @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I2_J)). 32.13/11.37 thf(658,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((c_Finite__Set_Ofinite @ C @ A) | ~ (c_Finite__Set_Ofinite @ (tc_sum @ D @ C) @ (c_Sum__Type_OPlus @ D @ C @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 32.13/11.37 thf(528,axiom,((~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ v_b____) @ v_a____)) @ v_Lab____)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_Ib_M_Aa_J_A_126_058_ALab_096)). 32.13/11.37 thf(2506,plain,((~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ v_b____) @ v_a____)) @ v_Lab____)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[528])). 32.13/11.37 thf(303,axiom,((! [A:$i,B:$i]: ((A = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ (c_Groups_Ozero__class_Ozero @ B))) <= (class_Rings_Ocomm__semiring__1 @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J)). 32.13/11.37 thf(1626,plain,((! [A:$i,B:$i]: ((A = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ (c_Groups_Ozero__class_Ozero @ B))) | ~ (class_Rings_Ocomm__semiring__1 @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[303])). 32.13/11.37 thf(425,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Rings_Ocomm__semiring__1 @ D) => ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A)) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ B) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J)). 32.13/11.37 thf(2054,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Rings_Ocomm__semiring__1 @ D) => ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A)) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[425])). 32.13/11.37 thf(470,axiom,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Oorder @ C) => (((A = B) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ A) @ B))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym)). 32.13/11.37 thf(2239,plain,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Oorder @ C) => ((A = B) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ A) @ B)) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[470])). 32.13/11.37 thf(45,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((c_Set_Oimage @ C @ D @ (c_Hilbert__Choice_Oinv__into @ D @ C @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool)) @ B) @ (c_Set_Oimage @ D @ C @ B @ A)) = A) <= (c_Fun_Oinj__on @ D @ C @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__inv__f__f)). 32.13/11.37 thf(675,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((c_Set_Oimage @ C @ D @ (c_Hilbert__Choice_Oinv__into @ D @ C @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool)) @ B) @ (c_Set_Oimage @ D @ C @ B @ A)) = A) | ~ (c_Fun_Oinj__on @ D @ C @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 32.13/11.37 thf(354,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ B) @ A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ C) @ A))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ C) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__trans)). 32.13/11.37 thf(1809,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ B) @ A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ C) @ A))) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[354])). 32.13/11.37 thf(377,axiom,((! [A:$i,B:$i,C:$i]: (((c_Fun_Oinj__on @ C @ C @ A @ B) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ B) @ (c_Set_Oimage @ C @ C @ A @ B)))) <= (c_Finite__Set_Ofinite @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj__inj)). 32.13/11.37 thf(1873,plain,((! [A:$i,B:$i,C:$i]: ((c_Fun_Oinj__on @ C @ C @ A @ B) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ B) @ (c_Set_Oimage @ C @ C @ A @ B))) | ~ (c_Finite__Set_Ofinite @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[377])). 32.13/11.37 thf(15,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((c_Fun_Oinj__on @ D @ B @ A @ C) <=> ((c_Finite__Set_Ocard @ B @ (c_Set_Oimage @ D @ B @ A @ C)) = (c_Finite__Set_Ocard @ D @ C))) <= (c_Finite__Set_Ofinite @ D @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__eq__card)). 32.13/11.37 thf(589,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((c_Fun_Oinj__on @ D @ B @ A @ C) => ((c_Finite__Set_Ocard @ B @ (c_Set_Oimage @ D @ B @ A @ C)) = (c_Finite__Set_Ocard @ D @ C))) & (((c_Finite__Set_Ocard @ B @ (c_Set_Oimage @ D @ B @ A @ C)) = (c_Finite__Set_Ocard @ D @ C)) => (c_Fun_Oinj__on @ D @ B @ A @ C))) | ~ (c_Finite__Set_Ofinite @ D @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 32.13/11.37 thf(81,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (hAPP @ (hAPP @ c_Arrow__Order__Mirabelle_Oabove @ A) @ C) @ B)) @ c_Arrow__Order__Mirabelle_OLin)) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ A) @ c_Arrow__Order__Mirabelle_OLin))) <= (B != C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_above__Lin)). 32.13/11.37 thf(795,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (hAPP @ (hAPP @ c_Arrow__Order__Mirabelle_Oabove @ A) @ C) @ B)) @ c_Arrow__Order__Mirabelle_OLin)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ A) @ c_Arrow__Order__Mirabelle_OLin)) | (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 32.13/11.37 thf(47,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (B = (c_List_Olist_Olist__case @ D @ C @ B @ A @ (c_List_Olist_ONil @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I4_J)). 32.13/11.37 thf(680,plain,((! [A:$i,B:$i,C:$i,D:$i]: (B = (c_List_Olist_Olist__case @ D @ C @ B @ A @ (c_List_Olist_ONil @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 32.13/11.37 thf(39,axiom,((! [A:$i]: (((c_Groups_Oone__class_Oone @ A) != (c_Groups_Ozero__class_Ozero @ A)) <= (class_Rings_Ozero__neq__one @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__neq__zero)). 32.13/11.37 thf(663,plain,((! [A:$i]: (~ ((c_Groups_Oone__class_Oone @ A) = (c_Groups_Ozero__class_Ozero @ A)) | ~ (class_Rings_Ozero__neq__one @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 32.13/11.37 thf(515,axiom,((! [A:$i]: ((class_Rings_Olinordered__semidom @ A) => (~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ A @ (c_Groups_Oone__class_Oone @ A)) @ (c_Groups_Ozero__class_Ozero @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__le__zero)). 32.13/11.37 thf(2471,plain,((! [A:$i]: ((class_Rings_Olinordered__semidom @ A) => (~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ A @ (c_Groups_Oone__class_Oone @ A)) @ (c_Groups_Ozero__class_Ozero @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[515])). 32.13/11.37 thf(511,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((C != D) => (((((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ v_F @ B))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ C) @ D)) @ (hAPP @ v_F @ A)))) <= (! [E:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ C) @ D)) @ (hAPP @ A @ E))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ B @ E)))))) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ A) @ c_Arrow__Order__Mirabelle_OProf))) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ B) @ c_Arrow__Order__Mirabelle_OProf)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C3_C)). 32.13/11.37 thf(2449,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((~ (C = D)) => ((((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ v_F @ B))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ C) @ D)) @ (hAPP @ v_F @ A)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ C) @ D)) @ (hAPP @ v_F @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ v_F @ B))))) | ~ (! [E:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ C) @ D)) @ (hAPP @ A @ E))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ B @ E)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ B @ E))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ C) @ D)) @ (hAPP @ A @ E)))))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ A) @ c_Arrow__Order__Mirabelle_OProf)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ B) @ c_Arrow__Order__Mirabelle_OProf)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[511])). 32.13/11.37 thf(88,axiom,((? [A:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ v_a____) @ v_b____)) @ (hAPP @ v_F @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (c_COMBB @ tc_HOL_Obool @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_If @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool) @ (hAPP @ (c_COMBB @ tc_Nat_Onat @ (tc_fun @ tc_Nat_Onat @ tc_HOL_Obool) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat)) @ v_h____)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ A) @ (c_Groups_Oone__class_Oone @ tc_Nat_Onat))))) @ v_Lab____)) @ v_Lba____)))) & ! [B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ v_b____) @ v_a____)) @ (hAPP @ v_F @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (c_COMBB @ tc_HOL_Obool @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_If @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool) @ (hAPP @ (c_COMBB @ tc_Nat_Onat @ (tc_fun @ tc_Nat_Onat @ tc_HOL_Obool) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat)) @ v_h____)) @ B))) @ v_Lab____)) @ v_Lba____)))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A))) & (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ (c_Finite__Set_Ocard @ tc_Arrow__Order__Mirabelle_Oindi @ (c_Orderings_Otop__class_Otop @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_G_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_096)). 32.13/11.37 thf(812,plain,((? [A:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ v_a____) @ v_b____)) @ (hAPP @ v_F @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (c_COMBB @ tc_HOL_Obool @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_If @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool) @ (hAPP @ (c_COMBB @ tc_Nat_Onat @ (tc_fun @ tc_Nat_Onat @ tc_HOL_Obool) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat)) @ v_h____)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ A) @ (c_Groups_Oone__class_Oone @ tc_Nat_Onat))))) @ v_Lab____)) @ v_Lba____)))) & ! [B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ v_b____) @ v_a____)) @ (hAPP @ v_F @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (c_COMBB @ tc_HOL_Obool @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_If @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool) @ (hAPP @ (c_COMBB @ tc_Nat_Onat @ (tc_fun @ tc_Nat_Onat @ tc_HOL_Obool) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat)) @ v_h____)) @ B))) @ v_Lab____)) @ v_Lba____)))) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A))) & (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ (c_Finite__Set_Ocard @ tc_Arrow__Order__Mirabelle_Oindi @ (c_Orderings_Otop__class_Otop @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 32.13/11.37 thf(404,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((c_Set_Oimage @ E @ D @ (hAPP @ (c_COMBB @ C @ D @ E @ B) @ A) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ E @ tc_HOL_Obool))) = (c_Set_Oimage @ C @ D @ B @ (c_Set_Oimage @ E @ C @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ E @ tc_HOL_Obool))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__composition)). 32.13/11.37 thf(1990,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((c_Set_Oimage @ E @ D @ (hAPP @ (c_COMBB @ C @ D @ E @ B) @ A) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ E @ tc_HOL_Obool))) = (c_Set_Oimage @ C @ D @ B @ (c_Set_Oimage @ E @ C @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ E @ tc_HOL_Obool))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[404])). 32.13/11.37 thf(23,axiom,((! [A:$i,B:$i]: ((class_Orderings_Oord @ (tc_fun @ A @ B)) <= (class_Orderings_Oord @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord)). 32.13/11.37 thf(617,plain,((! [A:$i,B:$i]: ((class_Orderings_Oord @ (tc_fun @ A @ B)) | ~ (class_Orderings_Oord @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 32.13/11.37 thf(460,axiom,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Opreorder @ C) => ((~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__less)). 32.13/11.37 thf(2202,plain,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Opreorder @ C) => (~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[460])). 32.13/11.37 thf(125,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ D) @ C)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ (hAPP @ A @ D)) @ (c_Set_Oimage @ E @ B @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_imageI)). 32.13/11.37 thf(939,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ D) @ C)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ (hAPP @ A @ D)) @ (c_Set_Oimage @ E @ B @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 32.13/11.37 thf(183,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ B @ tc_HOL_Obool) @ (c_Set_Oimage @ E @ B @ A @ D)) @ (c_Set_Oimage @ E @ B @ A @ C))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ E @ tc_HOL_Obool) @ D) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__mono)). 32.13/11.37 thf(1181,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ B @ tc_HOL_Obool) @ (c_Set_Oimage @ E @ B @ A @ D)) @ (c_Set_Oimage @ E @ B @ A @ C))) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ E @ tc_HOL_Obool) @ D) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 32.13/11.37 thf(92,axiom,((! [A:$i,B:$i]: (c_Fun_Oinj__on @ tc_Nat_Onat @ tc_Nat_Onat @ (hAPP @ (hAPP @ (c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat) @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat)) @ B) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__add__nat)). 32.13/11.37 thf(823,plain,((! [A:$i,B:$i]: (c_Fun_Oinj__on @ tc_Nat_Onat @ tc_Nat_Onat @ (hAPP @ (hAPP @ (c_COMBC @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Nat_Onat) @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat)) @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 32.13/11.37 thf(74,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ B) @ A))) <= (class_Groups_Oordered__ab__semigroup__add__imp__le @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__left)). 32.13/11.37 thf(776,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ B) @ A))) & ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A))))) | ~ (class_Groups_Oordered__ab__semigroup__add__imp__le @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 32.13/11.37 thf(341,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) <=> (? [C:$i]: ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ C) = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add)). 32.13/11.37 thf(1770,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) => (? [C:$i]: ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ C) = A))) & ((? [C:$i]: ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ C) = A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[341])). 32.13/11.37 thf(102,axiom,((! [A:$i,B:$i,C:$i]: ((~ ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C) @ A)) => (~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A))))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ B)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leE)). 32.13/11.37 thf(855,plain,((! [A:$i,B:$i,C:$i]: (~ ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C) @ A)) => (~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)))) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ B)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 32.13/11.37 thf(277,axiom,((class_Groups_Oab__semigroup__add @ tc_Nat_Onat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add)). 32.13/11.37 thf(1516,plain,((class_Groups_Oab__semigroup__add @ tc_Nat_Onat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[277])). 32.13/11.37 thf(153,axiom,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Oorder @ C) => ((B != A) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__neq)). 32.13/11.37 thf(1070,plain,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Oorder @ C) => (~ (B = A) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 32.13/11.37 thf(107,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ B) @ (c_Set_Oinsert @ D @ C @ A))) <=> (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ B) @ A))) <= (~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insert)). 32.13/11.39 thf(872,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ B) @ (c_Set_Oinsert @ D @ C @ A))) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ B) @ A))) & ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ B) @ A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ B) @ (c_Set_Oinsert @ D @ C @ A))))) | (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 32.13/11.39 thf(427,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C) @ B)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ A) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J)). 32.13/11.39 thf(2060,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C) @ B)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[427])). 32.13/11.39 thf(335,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) & (A != B)) <=> (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__le)). 32.13/11.39 thf(1743,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) & ~ (A = B)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))) & ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) & ~ (A = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[335])). 32.13/11.39 thf(56,axiom,((! [A:$i,B:$i,C:$i]: ((c_Fun_Oinj__on @ B @ C @ (c_Hilbert__Choice_Oinv__into @ C @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ C @ tc_HOL_Obool)) @ A) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool))) <= ((c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)) = (c_Set_Oimage @ C @ B @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ C @ tc_HOL_Obool))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__imp__inj__inv)). 32.13/11.39 thf(707,plain,((! [A:$i,B:$i,C:$i]: ((c_Fun_Oinj__on @ B @ C @ (c_Hilbert__Choice_Oinv__into @ C @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ C @ tc_HOL_Obool)) @ A) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool))) | ~ ((c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)) = (c_Set_Oimage @ C @ B @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ C @ tc_HOL_Obool))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 32.13/11.39 thf(290,axiom,((! [A:$i]: ((c_Nat_Osize__class_Osize @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ A)) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (c_Nat_Osize__class_Osize @ tc_Nat_Onat @ A)) @ (hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I4_J)). 32.13/11.39 thf(1566,plain,((! [A:$i]: ((c_Nat_Osize__class_Osize @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ A)) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (c_Nat_Osize__class_Osize @ tc_Nat_Onat @ A)) @ (hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[290])). 32.13/11.39 thf(455,axiom,((! [A:$i,B:$i,C:$i]: ((((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (c_Groups_Oone__class_Oone @ tc_Nat_Onat)) @ (c_Finite__Set_Ocard @ C @ B)) = (c_Finite__Set_Ocard @ C @ (c_Set_Oinsert @ C @ A @ B))) <= (~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ A) @ B)))) <= (c_Finite__Set_Ofinite @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oinsert)). 32.13/11.39 thf(2175,plain,((! [A:$i,B:$i,C:$i]: (((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (c_Groups_Oone__class_Oone @ tc_Nat_Onat)) @ (c_Finite__Set_Ocard @ C @ B)) = (c_Finite__Set_Ocard @ C @ (c_Set_Oinsert @ C @ A @ B))) | (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ A) @ B)) | ~ (c_Finite__Set_Ofinite @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[455])). 32.13/11.39 thf(343,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Groups_Oordered__ab__semigroup__add @ D) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ B) @ A))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__mono)). 32.13/11.39 thf(1780,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Groups_Oordered__ab__semigroup__add @ D) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ B) @ A))) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[343])). 32.13/11.39 thf(196,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Groups_Oordered__comm__monoid__add @ D) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ (c_Groups_Ozero__class_Ozero @ D)) @ C)) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ B) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing2)). 32.13/11.39 thf(1230,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Groups_Oordered__comm__monoid__add @ D) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ (c_Groups_Ozero__class_Ozero @ D)) @ C)) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 32.13/11.39 thf(269,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ B)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leD)). 32.13/11.39 thf(1484,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ B)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[269])). 32.13/11.39 thf(451,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((class_Orderings_Oord @ E) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ E @ (hAPP @ C @ A)) @ (hAPP @ B @ A))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ E) @ C) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funE)). 32.13/11.39 thf(2160,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((class_Orderings_Oord @ E) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ E @ (hAPP @ C @ A)) @ (hAPP @ B @ A))) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ E) @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[451])). 32.13/11.39 thf(44,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((c_Finite__Set_Ofinite @ D @ C) => ((c_Finite__Set_Ofinite @ (tc_sum @ D @ B) @ (c_Sum__Type_OPlus @ D @ B @ C @ A)) <= (c_Finite__Set_Ofinite @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus)). 32.13/11.39 thf(673,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((c_Finite__Set_Ofinite @ D @ C) => ((c_Finite__Set_Ofinite @ (tc_sum @ D @ B) @ (c_Sum__Type_OPlus @ D @ B @ C @ A)) | ~ (c_Finite__Set_Ofinite @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 32.13/11.39 thf(306,axiom,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Oorder @ C) => (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B)) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ A) @ B))) <= (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I12_J)). 32.13/11.39 thf(1637,plain,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Oorder @ C) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B)) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ A) @ B)) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[306])). 32.13/11.39 thf(346,axiom,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Oorder @ C) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)) | (A = B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq)). 32.13/11.39 thf(1785,plain,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Oorder @ C) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)) | (A = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[346])). 32.13/11.39 thf(492,axiom,((! [A:$i,B:$i]: ((c_Finite__Set_Ofinite @ B @ A) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ (c_Finite__Set_Ocard @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__ge__0__finite)). 32.13/11.39 thf(2337,plain,((! [A:$i,B:$i]: ((c_Finite__Set_Ofinite @ B @ A) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ (c_Finite__Set_Ocard @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[492])). 32.13/11.39 thf(467,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ c_Nat_OSuc @ B)) @ (hAPP @ c_Nat_OSuc @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__SucD)). 32.13/11.39 thf(2219,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ c_Nat_OSuc @ B)) @ (hAPP @ c_Nat_OSuc @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[467])). 32.13/11.39 thf(339,axiom,(((c_Nat_Onat_Onat__size @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I1_J)). 32.13/11.39 thf(1763,plain,(((c_Nat_Onat_Onat__size @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[339])). 32.13/11.39 thf(283,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ B)) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__lessD)). 32.13/11.39 thf(1538,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ c_Nat_OSuc @ B)) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[283])). 32.13/11.39 thf(521,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ B) @ c_Arrow__Order__Mirabelle_OLin)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ B) @ A)) @ c_Arrow__Order__Mirabelle_OLin))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mkbot__Lin)). 32.13/11.39 thf(2486,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ B) @ c_Arrow__Order__Mirabelle_OLin)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ B) @ A)) @ c_Arrow__Order__Mirabelle_OLin))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[521])). 32.13/11.39 thf(87,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Orderings_Oord @ D) => ((B = C) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ A)) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ B) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__eq__le__trans)). 32.13/11.39 thf(808,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Orderings_Oord @ D) => ((B = C) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ A)) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 32.13/11.39 thf(317,axiom,((! [A:$i,B:$i]: (((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) = A) <= (B = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero)). 32.13/11.39 thf(1679,plain,((! [A:$i,B:$i]: (((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) = A) | ~ (B = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[317])). 32.13/11.39 thf(168,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ C) @ c_Arrow__Order__Mirabelle_OLin)) => (((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ A) @ B)) @ C)) <=> (~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ B) @ A)) @ C)))) <= (B != A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_notin__Lin__iff)). 32.13/11.39 thf(1130,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ C) @ c_Arrow__Order__Mirabelle_OLin)) => ((((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ A) @ B)) @ C)) => (~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ B) @ A)) @ C)))) & ((~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ B) @ A)) @ C))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ A) @ B)) @ C)))) | (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 32.13/11.39 thf(295,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ A) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__I)). 32.13/11.39 thf(1579,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ A) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[295])). 32.13/11.39 thf(333,axiom,((! [A:$i,B:$i,C:$i]: ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute)). 32.13/11.39 thf(1738,plain,((! [A:$i,B:$i,C:$i]: ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[333])). 32.13/11.39 thf(514,axiom,((! [A:$i,B:$i]: ((((hAPP @ c_Nat_OSuc @ A) = B) <= (~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ (hAPP @ c_Nat_OSuc @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucE)). 32.13/11.39 thf(2468,plain,((! [A:$i,B:$i]: (((hAPP @ c_Nat_OSuc @ A) = B) | (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ (hAPP @ c_Nat_OSuc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[514])). 32.13/11.39 thf(472,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ B) @ A)) <=> (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ (tc_fun @ C @ tc_HOL_Obool)) @ (hAPP @ (hAPP @ (c_COMBC @ D @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ C @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ D @ (c_COMBC @ C @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ C @ (tc_prod @ D @ C)) @ (tc_fun @ C @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ D @ (c_COMBB @ (tc_prod @ D @ C) @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool) @ C @ (c_member @ (tc_prod @ D @ C)))) @ (c_Product__Type_OPair @ D @ C)))) @ B)) @ (hAPP @ (hAPP @ (c_COMBC @ D @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ C @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ D @ (c_COMBC @ C @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ C @ (tc_prod @ D @ C)) @ (tc_fun @ C @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ D @ (c_COMBB @ (tc_prod @ D @ C) @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool) @ C @ (c_member @ (tc_prod @ D @ C)))) @ (c_Product__Type_OPair @ D @ C)))) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq2)). 32.13/11.39 thf(2247,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ B) @ A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ (tc_fun @ C @ tc_HOL_Obool)) @ (hAPP @ (hAPP @ (c_COMBC @ D @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ C @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ D @ (c_COMBC @ C @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ C @ (tc_prod @ D @ C)) @ (tc_fun @ C @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ D @ (c_COMBB @ (tc_prod @ D @ C) @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool) @ C @ (c_member @ (tc_prod @ D @ C)))) @ (c_Product__Type_OPair @ D @ C)))) @ B)) @ (hAPP @ (hAPP @ (c_COMBC @ D @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ C @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ D @ (c_COMBC @ C @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ C @ (tc_prod @ D @ C)) @ (tc_fun @ C @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ D @ (c_COMBB @ (tc_prod @ D @ C) @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool) @ C @ (c_member @ (tc_prod @ D @ C)))) @ (c_Product__Type_OPair @ D @ C)))) @ A)))) & ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ (tc_fun @ C @ tc_HOL_Obool)) @ (hAPP @ (hAPP @ (c_COMBC @ D @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ C @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ D @ (c_COMBC @ C @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ C @ (tc_prod @ D @ C)) @ (tc_fun @ C @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ D @ (c_COMBB @ (tc_prod @ D @ C) @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool) @ C @ (c_member @ (tc_prod @ D @ C)))) @ (c_Product__Type_OPair @ D @ C)))) @ B)) @ (hAPP @ (hAPP @ (c_COMBC @ D @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ C @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ (tc_fun @ C @ tc_HOL_Obool)) @ D @ (c_COMBC @ C @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ C @ (tc_prod @ D @ C)) @ (tc_fun @ C @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool)) @ D @ (c_COMBB @ (tc_prod @ D @ C) @ (tc_fun @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ tc_HOL_Obool) @ C @ (c_member @ (tc_prod @ D @ C)))) @ (c_Product__Type_OPair @ D @ C)))) @ A))) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ (tc_prod @ D @ C) @ tc_HOL_Obool) @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[472])). 32.13/11.39 thf(67,axiom,((! [A:$i,B:$i]: ((c_Finite__Set_Ofinite @ (tc_fun @ B @ A) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ (tc_fun @ B @ A) @ tc_HOL_Obool))) => (c_Finite__Set_Ofinite @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ A @ tc_HOL_Obool)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD2)). 32.13/11.39 thf(744,plain,((! [A:$i,B:$i]: ((c_Finite__Set_Ofinite @ (tc_fun @ B @ A) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ (tc_fun @ B @ A) @ tc_HOL_Obool))) => (c_Finite__Set_Ofinite @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ A @ tc_HOL_Obool)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 32.13/11.39 thf(384,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__less__Suc)). 32.13/11.39 thf(1898,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[384])). 32.13/11.39 thf(366,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ E @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ E) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ D) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ C) @ A)))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ E) @ D) @ C))) <= (class_Groups_Oordered__cancel__ab__semigroup__add @ E)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__le__mono)). 32.13/11.39 thf(1849,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ E @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ E) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ D) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ C) @ A)))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ E) @ D) @ C)) | ~ (class_Groups_Oordered__cancel__ab__semigroup__add @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[366])). 32.13/11.39 thf(36,axiom,((! [A:$i]: (c_List_Odistinct @ A @ (c_List_Olist_ONil @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct_Osimps_I1_J)). 32.13/11.39 thf(656,plain,((! [A:$i]: (c_List_Odistinct @ A @ (c_List_Olist_ONil @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 32.13/11.39 thf(22,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((((hAPP @ (c_Hilbert__Choice_Oinv__into @ E @ D @ (c_Orderings_Otop__class_Otop @ (tc_fun @ E @ tc_HOL_Obool)) @ C) @ A) = B) <= (A = (hAPP @ C @ B))) <= (c_Fun_Oinj__on @ E @ D @ C @ (c_Orderings_Otop__class_Otop @ (tc_fun @ E @ tc_HOL_Obool)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__f__eq)). 32.13/11.39 thf(613,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hAPP @ (c_Hilbert__Choice_Oinv__into @ E @ D @ (c_Orderings_Otop__class_Otop @ (tc_fun @ E @ tc_HOL_Obool)) @ C) @ A) = B) | ~ (A = (hAPP @ C @ B)) | ~ (c_Fun_Oinj__on @ E @ D @ C @ (c_Orderings_Otop__class_Otop @ (tc_fun @ E @ tc_HOL_Obool)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 32.13/11.39 thf(193,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((hAPP @ (c_COMBS @ F @ E @ D @ C @ B) @ A) = (hAPP @ (hAPP @ C @ A) @ (hAPP @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBS__1)). 32.13/11.39 thf(1221,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((hAPP @ (c_COMBS @ F @ E @ D @ C @ B) @ A) = (hAPP @ (hAPP @ C @ A) @ (hAPP @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 32.13/11.39 thf(238,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ A))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucI)). 32.13/11.39 thf(1353,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ A))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 32.13/11.39 thf(395,axiom,((! [A:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ (c_Finite__Set_Ocard @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ A @ tc_HOL_Obool))))) <= (c_Finite__Set_Ofinite @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ A @ tc_HOL_Obool)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__card__ge__0)). 32.13/11.39 thf(1955,plain,((! [A:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ (c_Finite__Set_Ocard @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ A @ tc_HOL_Obool))))) | ~ (c_Finite__Set_Ofinite @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ A @ tc_HOL_Obool)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[395])). 32.13/11.39 thf(445,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ (c_Groups_Ozero__class_Ozero @ C))) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ A) @ (c_Groups_Ozero__class_Ozero @ C))) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ B) @ A)) @ (c_Groups_Ozero__class_Ozero @ C))))) <= (class_Groups_Oordered__comm__monoid__add @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__nonpos)). 32.13/11.39 thf(2145,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ (c_Groups_Ozero__class_Ozero @ C))) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ A) @ (c_Groups_Ozero__class_Ozero @ C))) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ B) @ A)) @ (c_Groups_Ozero__class_Ozero @ C))))) | ~ (class_Groups_Oordered__comm__monoid__add @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[445])). 32.13/11.39 thf(275,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) <=> (? [C:$i]: ((hAPP @ c_Nat_OSuc @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ C)) = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__Suc__add)). 32.13/11.39 thf(1504,plain,((! [A:$i,B:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) => (? [C:$i]: ((hAPP @ c_Nat_OSuc @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ C)) = A))) & ((? [C:$i]: ((hAPP @ c_Nat_OSuc @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ C)) = A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[275])). 32.13/11.39 thf(298,axiom,((! [A:$i,B:$i]: (((hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)) <=> (((A = (hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))) & (B = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))) | (((hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) = B) & (A = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__1)). 32.13/11.39 thf(1585,plain,((! [A:$i,B:$i]: ((((hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)) => (((A = (hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))) & (B = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))) | (((hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) = B) & (A = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))))) & ((((A = (hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))) & (B = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))) | (((hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) = B) & (A = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)))) => ((hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[298])). 32.13/11.39 thf(9,axiom,((c_Arrow__Order__Mirabelle_OIIA @ v_F)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I3_J)). 32.13/11.39 thf(571,plain,((c_Arrow__Order__Mirabelle_OIIA @ v_F)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 32.13/11.39 thf(21,axiom,((class_Orderings_Otop @ tc_HOL_Obool)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop)). 32.13/11.39 thf(612,plain,((class_Orderings_Otop @ tc_HOL_Obool)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 32.13/11.39 thf(98,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((hAPP @ (hAPP @ (hAPP @ (c_COMBC @ F @ E @ D) @ C) @ B) @ A) = (hAPP @ (hAPP @ C @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBC__1)). 32.13/11.39 thf(845,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((hAPP @ (hAPP @ (hAPP @ (c_COMBC @ F @ E @ D) @ C) @ B) @ A) = (hAPP @ (hAPP @ C @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 32.13/11.39 thf(411,axiom,((! [A:$i,B:$i]: ((A = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ (c_Groups_Ozero__class_Ozero @ B)) @ A)) <= (class_Groups_Ocomm__monoid__add @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0)). 32.13/11.39 thf(2013,plain,((! [A:$i,B:$i]: ((A = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ (c_Groups_Ozero__class_Ozero @ B)) @ A)) | ~ (class_Groups_Ocomm__monoid__add @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[411])). 32.13/11.39 thf(363,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Orderings_Oorder @ D) => (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ A) @ B)) <= (A = C)) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I2_J)). 32.13/11.39 thf(1839,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Orderings_Oorder @ D) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ A) @ B)) | ~ (A = C) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[363])). 32.13/11.39 thf(388,axiom,((! [A:$i,B:$i]: (((A = B) | (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))) <=> (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__eq__less__or__eq)). 32.13/11.39 thf(1918,plain,((! [A:$i,B:$i]: ((((A = B) | (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A))) & ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) => ((A = B) | (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[388])). 32.13/11.39 thf(226,axiom,((! [A:$i,B:$i]: ((A = B) | ~ (hBOOL @ (hAPP @ (hAPP @ c_fequal @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__1)). 32.13/11.39 thf(1316,plain,((! [A:$i,B:$i]: ((A = B) | ~ (hBOOL @ (hAPP @ (hAPP @ c_fequal @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 32.13/11.39 thf(434,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((! [F:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ F) @ D)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ (hAPP @ B @ F)) @ (hAPP @ A @ F))))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ E @ C)) @ B) @ (c_FuncSet_OPi @ E @ C @ D @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__I)). 32.13/11.39 thf(2088,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((! [F:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ F) @ D)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ (hAPP @ B @ F)) @ (hAPP @ A @ F))))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ E @ C)) @ B) @ (c_FuncSet_OPi @ E @ C @ D @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[434])). 32.13/11.39 thf(422,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)) => (~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B)))) <= (class_Orderings_Olinorder @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leD)). 32.13/11.39 thf(2045,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)) => (~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B)))) | ~ (class_Orderings_Olinorder @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[422])). 32.13/11.39 thf(397,axiom,((! [A:$i,B:$i]: ((~ (c_Finite__Set_Ofinite @ B @ A)) => ((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) = (c_Finite__Set_Ocard @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__infinite)). 32.13/11.39 thf(1966,plain,((! [A:$i,B:$i]: ((~ (c_Finite__Set_Ofinite @ B @ A)) => ((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) = (c_Finite__Set_Ocard @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[397])). 32.13/11.39 thf(43,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((c_Finite__Set_Ofinite @ D @ B) <= (c_Finite__Set_Ofinite @ (tc_sum @ D @ C) @ (c_Sum__Type_OPlus @ D @ C @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I1_J)). 32.13/11.39 thf(671,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((c_Finite__Set_Ofinite @ D @ B) | ~ (c_Finite__Set_Ofinite @ (tc_sum @ D @ C) @ (c_Sum__Type_OPlus @ D @ C @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 32.13/11.39 thf(361,axiom,((! [A:$i,B:$i]: ((class_Groups_Olinordered__ab__group__add @ B) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ A) @ (c_Groups_Ozero__class_Ozero @ B))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ A)) @ (c_Groups_Ozero__class_Ozero @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero)). 32.13/11.39 thf(1834,plain,((! [A:$i,B:$i]: ((class_Groups_Olinordered__ab__group__add @ B) => (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ A) @ (c_Groups_Ozero__class_Ozero @ B))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ A)) @ (c_Groups_Ozero__class_Ozero @ B)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ A)) @ (c_Groups_Ozero__class_Ozero @ B))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ B) @ A) @ (c_Groups_Ozero__class_Ozero @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[361])). 32.13/11.39 thf(117,axiom,((! [A:$i,B:$i]: ((((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ A) = (c_Groups_Ozero__class_Ozero @ B)) <=> (A = (c_Groups_Ozero__class_Ozero @ B))) <= (class_Groups_Olinordered__ab__group__add @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__zero__sym)). 32.13/11.39 thf(903,plain,((! [A:$i,B:$i]: (((((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ A) = (c_Groups_Ozero__class_Ozero @ B)) => (A = (c_Groups_Ozero__class_Ozero @ B))) & ((A = (c_Groups_Ozero__class_Ozero @ B)) => ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ A) @ A) = (c_Groups_Ozero__class_Ozero @ B)))) | ~ (class_Groups_Olinordered__ab__group__add @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 32.13/11.39 thf(12,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((c_Fun_Oinj__on @ D @ C @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool))) => ((hAPP @ (c_Hilbert__Choice_Oinv__into @ D @ C @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool)) @ B) @ (hAPP @ B @ A)) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__f__f)). 32.13/11.39 thf(581,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((c_Fun_Oinj__on @ D @ C @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool))) => ((hAPP @ (c_Hilbert__Choice_Oinv__into @ D @ C @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool)) @ B) @ (hAPP @ B @ A)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 32.13/11.39 thf(278,axiom,((c_Arrow__Order__Mirabelle_OProf = (c_FuncSet_OPi @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool)) @ (hAPP @ (c_COMBK @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ tc_HOL_Obool) @ tc_Arrow__Order__Mirabelle_Oindi) @ c_Arrow__Order__Mirabelle_OLin)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Prof__def)). 32.13/11.39 thf(1517,plain,((c_Arrow__Order__Mirabelle_OProf = (c_FuncSet_OPi @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool)) @ (hAPP @ (c_COMBK @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ tc_HOL_Obool) @ tc_Arrow__Order__Mirabelle_Oindi) @ c_Arrow__Order__Mirabelle_OLin)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[278])). 32.13/11.39 thf(192,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) <= ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) | (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__or__eq__imp__le)). 32.13/11.39 thf(1216,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) | ~ ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) | (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 32.13/11.39 thf(112,axiom,((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ v_P____) @ c_Arrow__Order__Mirabelle_OProf))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096P_A_058_AProf_096)). 32.13/11.39 thf(891,plain,((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ v_P____) @ c_Arrow__Order__Mirabelle_OProf))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 32.13/11.39 thf(494,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ B @ tc_HOL_Obool) @ A) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__refl)). 32.13/11.39 thf(2342,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ B @ tc_HOL_Obool) @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[494])). 32.13/11.39 thf(214,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ D @ tc_HOL_Obool)) @ C) @ B)) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ D @ tc_HOL_Obool)) @ C) @ A)) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ D @ tc_HOL_Obool)) @ B) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__trans)). 32.13/11.39 thf(1289,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ D @ tc_HOL_Obool)) @ C) @ B)) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ D @ tc_HOL_Obool)) @ C) @ A)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ D @ tc_HOL_Obool)) @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 32.13/11.39 thf(353,axiom,((! [A:$i]: ((class_Rings_Olinordered__semidom @ A) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ A) @ (c_Groups_Ozero__class_Ozero @ A)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ A) @ (c_Groups_Oone__class_Oone @ A)) @ (c_Groups_Oone__class_Oone @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__two)). 32.13/11.39 thf(1807,plain,((! [A:$i]: ((class_Rings_Olinordered__semidom @ A) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ A) @ (c_Groups_Ozero__class_Ozero @ A)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ A) @ (c_Groups_Oone__class_Oone @ A)) @ (c_Groups_Oone__class_Oone @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[353])). 32.13/11.39 thf(160,axiom,((! [A:$i,B:$i,C:$i]: (((~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B))) <= (class_Orderings_Olinorder @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__le)). 32.13/11.39 thf(1108,plain,((! [A:$i,B:$i,C:$i]: ((((~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B))) & ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B)) => (~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A))))) | ~ (class_Orderings_Olinorder @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 32.13/11.39 thf(210,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ (c_Set_Oinsert @ D @ A @ C)) @ (c_Set_Oinsert @ D @ A @ B))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ C) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__mono)). 32.13/11.39 thf(1276,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ (c_Set_Oinsert @ D @ A @ C)) @ (c_Set_Oinsert @ D @ A @ B))) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])). 32.13/11.39 thf(248,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ A)) <= (A = B)) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ B))) <= (class_Orderings_Oord @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__le__eq__trans)). 32.13/11.39 thf(1385,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ A)) | ~ (A = B) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ B)) | ~ (class_Orderings_Oord @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])). 32.13/11.39 thf(132,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ B) @ A)) & (A != B)) <=> (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ C @ tc_HOL_Obool)) @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__eq)). 32.13/11.39 thf(963,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ B) @ A)) & ~ (A = B)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ C @ tc_HOL_Obool)) @ B) @ A))) & ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ C @ tc_HOL_Obool)) @ B) @ A)) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ B) @ A)) & ~ (A = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 32.13/11.39 thf(454,axiom,((! [A:$i]: ((? [B:$i]: (A = (hAPP @ c_Nat_OSuc @ B))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc)). 32.13/11.39 thf(2167,plain,((! [A:$i]: (((? [B:$i]: (A = (hAPP @ c_Nat_OSuc @ B))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ A))) & ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ A)) => (? [B:$i]: (A = (hAPP @ c_Nat_OSuc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[454])). 32.13/11.39 thf(507,axiom,((! [A:$i,B:$i]: ((class_Orderings_Otop @ B) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ B @ A) @ (c_Orderings_Otop__class_Otop @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__greatest)). 32.13/11.39 thf(2389,plain,((! [A:$i,B:$i]: ((class_Orderings_Otop @ B) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ B @ A) @ (c_Orderings_Otop__class_Otop @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[507])). 32.13/11.39 thf(233,axiom,((! [A:$i]: ((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) != (hAPP @ c_Nat_OSuc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc)). 32.13/11.39 thf(1341,plain,((! [A:$i]: ~ ((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) = (hAPP @ c_Nat_OSuc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 32.13/11.39 thf(437,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ B)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ B) @ A)))) <= (class_Groups_Oordered__cancel__ab__semigroup__add @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__right__mono)). 32.13/11.39 thf(2098,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ B)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ B) @ A)))) | ~ (class_Groups_Oordered__cancel__ab__semigroup__add @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[437])). 32.13/11.39 thf(267,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ E @ tc_HOL_Obool) @ A) @ B)) => (c_Fun_Oinj__on @ E @ D @ C @ A)) <= (c_Fun_Oinj__on @ E @ D @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__inj__on)). 32.13/11.39 thf(1481,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ E @ tc_HOL_Obool) @ A) @ B)) => (c_Fun_Oinj__on @ E @ D @ C @ A)) | ~ (c_Fun_Oinj__on @ E @ D @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])). 32.13/11.39 thf(34,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((c_Finite__Set_Ofinite @ D @ C) => (c_Finite__Set_Ofinite @ B @ (c_Set_Oimage @ D @ B @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageI)). 32.13/11.39 thf(652,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((c_Finite__Set_Ofinite @ D @ C) => (c_Finite__Set_Ofinite @ B @ (c_Set_Oimage @ D @ B @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 32.13/11.39 thf(304,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Orderings_Opreorder @ D) => (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ A)) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ B) @ A))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le__trans)). 32.13/11.39 thf(1629,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Orderings_Opreorder @ D) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ A)) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ B) @ A)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[304])). 32.13/11.39 thf(409,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)) <=> ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)) | (A = B))) <= (class_Orderings_Oorder @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less)). 32.13/11.39 thf(2004,plain,((! [A:$i,B:$i,C:$i]: ((((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)) | (A = B))) & (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)) | (A = B)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)))) | ~ (class_Orderings_Oorder @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[409])). 32.13/11.39 thf(29,axiom,((! [A:$i,B:$i]: (((c_Finite__Set_Ofinite @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ A @ tc_HOL_Obool))) & (c_Finite__Set_Ofinite @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)))) <=> (c_Finite__Set_Ofinite @ (tc_sum @ B @ A) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ (tc_sum @ B @ A) @ tc_HOL_Obool)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__UNIV__iff)). 32.13/11.39 thf(632,plain,((! [A:$i,B:$i]: ((((c_Finite__Set_Ofinite @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ A @ tc_HOL_Obool))) & (c_Finite__Set_Ofinite @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)))) => (c_Finite__Set_Ofinite @ (tc_sum @ B @ A) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ (tc_sum @ B @ A) @ tc_HOL_Obool)))) & ((c_Finite__Set_Ofinite @ (tc_sum @ B @ A) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ (tc_sum @ B @ A) @ tc_HOL_Obool))) => ((c_Finite__Set_Ofinite @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ A @ tc_HOL_Obool))) & (c_Finite__Set_Ofinite @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 32.13/11.39 thf(369,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ A) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ B) @ A))) <= (class_Rings_Ocomm__semiring__1 @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J)). 32.13/11.39 thf(1854,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ A) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ B) @ A))) | ~ (class_Rings_Ocomm__semiring__1 @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[369])). 32.13/11.39 thf(64,axiom,((! [A:$i,B:$i,C:$i]: ((c_Finite__Set_Ofinite @ C @ (c_Set_Oinsert @ C @ A @ B)) <= (c_Finite__Set_Ofinite @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_OinsertI)). 32.13/11.39 thf(731,plain,((! [A:$i,B:$i,C:$i]: ((c_Finite__Set_Ofinite @ C @ (c_Set_Oinsert @ C @ A @ B)) | ~ (c_Finite__Set_Ofinite @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 32.13/11.39 thf(78,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ D) @ C)) => ((c_Set_Oinsert @ B @ (hAPP @ A @ D) @ (c_Set_Oimage @ E @ B @ A @ C)) = (c_Set_Oimage @ E @ B @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__image)). 32.13/11.39 thf(786,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ D) @ C)) => ((c_Set_Oinsert @ B @ (hAPP @ A @ D) @ (c_Set_Oimage @ E @ B @ A @ C)) = (c_Set_Oimage @ E @ B @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 32.13/11.39 thf(138,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((c_Fun_Oinj__on @ E @ D @ C @ B) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ E @ tc_HOL_Obool)) @ A) @ B)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ D @ tc_HOL_Obool)) @ (c_Set_Oimage @ E @ D @ C @ A)) @ (c_Set_Oimage @ E @ D @ C @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__strict__subset)). 32.13/11.39 thf(995,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((c_Fun_Oinj__on @ E @ D @ C @ B) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ E @ tc_HOL_Obool)) @ A) @ B)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ D @ tc_HOL_Obool)) @ (c_Set_Oimage @ E @ D @ C @ A)) @ (c_Set_Oimage @ E @ D @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 32.13/11.39 thf(287,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((hAPP @ (hAPP @ (c_COMBB @ F @ E @ D @ C) @ B) @ A) = (hAPP @ C @ (hAPP @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1)). 32.13/11.39 thf(1558,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((hAPP @ (hAPP @ (c_COMBB @ F @ E @ D @ C) @ B) @ A) = (hAPP @ C @ (hAPP @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[287])). 32.13/11.39 thf(448,axiom,((! [A:$i]: (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ (hAPP @ c_Nat_OSuc @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__Suc)). 32.13/11.39 thf(2152,plain,((! [A:$i]: (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) @ (hAPP @ c_Nat_OSuc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[448])). 32.13/11.39 thf(272,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ c_Nat_OSuc @ B)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessD)). 32.13/11.39 thf(1491,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ c_Nat_OSuc @ B)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[272])). 32.13/11.39 thf(8,axiom,((! [A:$i,B:$i]: ((c_Finite__Set_Ofinite @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool))) => (((c_Set_Oimage @ B @ B @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool))) = (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool))) => (c_Fun_Oinj__on @ B @ B @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__surj__inj)). 32.13/11.39 thf(568,plain,((! [A:$i,B:$i]: ((c_Finite__Set_Ofinite @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool))) => (((c_Set_Oimage @ B @ B @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool))) = (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool))) => (c_Fun_Oinj__on @ B @ B @ A @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 32.13/11.39 thf(342,axiom,((! [A:$i,B:$i]: ((! [C:$i]: ((hAPP @ B @ C) = (hAPP @ A @ C))) => (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext)). 32.13/11.39 thf(1777,plain,((! [A:$i,B:$i]: ((! [C:$i]: ((hAPP @ B @ C) = (hAPP @ A @ C))) => (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[342])). 32.13/11.39 thf(41,axiom,((class_Finite__Set_Ofinite @ tc_Product__Type_Ounit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Finite__Set_Ofinite)). 32.13/11.39 thf(667,plain,((class_Finite__Set_Ofinite @ tc_Product__Type_Ounit)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 32.13/11.39 thf(186,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J)). 32.13/11.39 thf(1193,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 32.13/11.39 thf(155,axiom,((! [A:$i,B:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) | (A = B)) <=> (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq)). 32.13/11.39 thf(1077,plain,((! [A:$i,B:$i]: ((((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) | (A = B)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ A)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ (hAPP @ c_Nat_OSuc @ A))) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) | (A = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 32.13/11.39 thf(452,axiom,(((hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) = (c_Groups_Oone__class_Oone @ tc_Nat_Onat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_One__nat__def)). 32.13/11.39 thf(2162,plain,(((hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) = (c_Groups_Oone__class_Oone @ tc_Nat_Onat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[452])). 32.13/11.39 thf(314,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((c_Fun_Oinj__on @ D @ C @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool))) => ((? [E:$i]: (! [F:$i]: ((E = F) <= (A = (hAPP @ B @ F))) & (A = (hAPP @ B @ E)))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ A) @ (c_Set_Oimage @ D @ C @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__ex1__eq)). 32.13/11.39 thf(1661,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((c_Fun_Oinj__on @ D @ C @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool))) => (((? [E:$i]: (! [F:$i]: ((E = F) | ~ (A = (hAPP @ B @ F))) & (A = (hAPP @ B @ E)))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ A) @ (c_Set_Oimage @ D @ C @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool)))))) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ A) @ (c_Set_Oimage @ D @ C @ B @ (c_Orderings_Otop__class_Otop @ (tc_fun @ D @ tc_HOL_Obool))))) => (? [E:$i]: (! [F:$i]: ((E = F) | ~ (A = (hAPP @ B @ F))) & (A = (hAPP @ B @ E))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[314])). 32.13/11.39 thf(418,axiom,((! [A:$i]: ((class_Rings_Olinordered__semidom @ A) => (~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ A) @ (c_Groups_Oone__class_Oone @ A)) @ (c_Groups_Ozero__class_Ozero @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__less__zero)). 32.13/11.39 thf(2036,plain,((! [A:$i]: ((class_Rings_Olinordered__semidom @ A) => (~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ A) @ (c_Groups_Oone__class_Oone @ A)) @ (c_Groups_Ozero__class_Ozero @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[418])). 32.13/11.39 thf(223,axiom,((! [A:$i]: ((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) != (hAPP @ c_Nat_OSuc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__neq__Zero)). 32.13/11.39 thf(1309,plain,((! [A:$i]: ~ ((c_Groups_Ozero__class_Ozero @ tc_Nat_Onat) = (hAPP @ c_Nat_OSuc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 32.13/11.39 thf(486,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) => ((B = A) <=> (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ (hAPP @ c_Nat_OSuc @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__less__Suc__eq)). 32.13/11.39 thf(2315,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) => (((B = A) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ (hAPP @ c_Nat_OSuc @ B)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ (hAPP @ c_Nat_OSuc @ B))) => (B = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[486])). 32.13/11.39 thf(524,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) <=> (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less)). 32.13/11.39 thf(2494,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ A)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[524])). 32.13/11.39 thf(59,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((c_Finite__Set_Ofinite @ C @ A) <= (c_Fun_Oinj__on @ C @ D @ B @ A)) <= (c_Finite__Set_Ofinite @ D @ (c_Set_Oimage @ C @ D @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageD)). 32.13/11.39 thf(716,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((c_Finite__Set_Ofinite @ C @ A) | ~ (c_Fun_Oinj__on @ C @ D @ B @ A) | ~ (c_Finite__Set_Ofinite @ D @ (c_Set_Oimage @ C @ D @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 32.13/11.39 thf(474,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Groups_Ocancel__semigroup__add @ D) => (((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) <=> (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__cancel)). 32.13/11.39 thf(2258,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Groups_Ocancel__semigroup__add @ D) => ((((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) => (A = B)) & ((A = B) => ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[474])). 32.13/11.39 thf(308,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ (c_Groups_Ozero__class_Ozero @ C))) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ B) @ A)) @ (c_Groups_Ozero__class_Ozero @ C))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ (c_Groups_Ozero__class_Ozero @ C))))) <= (class_Groups_Oordered__comm__monoid__add @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__neg)). 32.13/11.39 thf(1642,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ (c_Groups_Ozero__class_Ozero @ C))) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ B) @ A)) @ (c_Groups_Ozero__class_Ozero @ C))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ (c_Groups_Ozero__class_Ozero @ C))))) | ~ (class_Groups_Oordered__comm__monoid__add @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[308])). 32.13/11.39 thf(439,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP @ (hAPP @ (c_COMBK @ D @ C) @ B) @ A) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1)). 32.13/11.39 thf(2102,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hAPP @ (hAPP @ (c_COMBK @ D @ C) @ B) @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[439])). 32.13/11.39 thf(533,axiom,((! [A:$i,B:$i]: ((B != A) => ((~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat)). 32.13/11.39 thf(2517,plain,((! [A:$i,B:$i]: ((~ (B = A)) => ((~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ B) @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[533])). 32.13/11.39 thf(212,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ D @ tc_HOL_Obool)) @ C) @ A)) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ D @ tc_HOL_Obool)) @ B) @ A))) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ C) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__psubset__trans)). 32.13/11.39 thf(1280,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ D @ tc_HOL_Obool)) @ C) @ A)) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ D @ tc_HOL_Obool)) @ B) @ A)) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ D @ tc_HOL_Obool) @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 32.13/11.39 thf(396,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ A)) | (C = B)) <=> (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ (c_Set_Oinsert @ D @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__iff)). 32.13/11.39 thf(1957,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ A)) | (C = B)) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ (c_Set_Oinsert @ D @ B @ A)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ (c_Set_Oinsert @ D @ B @ A))) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ D) @ C) @ A)) | (C = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[396])). 32.13/11.39 thf(96,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ A) @ F) @ (c_Set_Oimage @ C @ A @ E @ B))) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ D) @ B))) <= ((hAPP @ E @ D) = F)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eqI)). 32.13/11.39 thf(833,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ A) @ F) @ (c_Set_Oimage @ C @ A @ E @ B))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ D) @ B)) | ~ ((hAPP @ E @ D) = F)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 32.13/11.39 thf(251,axiom,((~ (hBOOL @ c_fFalse))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fFalse__1)). 32.13/11.39 thf(1395,plain,((~ (hBOOL @ c_fFalse))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])). 32.13/11.39 thf(90,axiom,((! [A:$i,B:$i,C:$i]: ((c_Orderings_Otop__class_Otop @ (tc_fun @ (tc_fun @ C @ B) @ tc_HOL_Obool)) = (c_FuncSet_OPi @ C @ B @ A @ (hAPP @ (c_COMBK @ (tc_fun @ B @ tc_HOL_Obool) @ C) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__UNIV)). 32.13/11.39 thf(818,plain,((! [A:$i,B:$i,C:$i]: ((c_Orderings_Otop__class_Otop @ (tc_fun @ (tc_fun @ C @ B) @ tc_HOL_Obool)) = (c_FuncSet_OPi @ C @ B @ A @ (hAPP @ (c_COMBK @ (tc_fun @ B @ tc_HOL_Obool) @ C) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 32.13/11.39 thf(245,axiom,((! [A:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ A) @ (c_Groups_Ozero__class_Ozero @ A)) @ (c_Groups_Oone__class_Oone @ A))) <= (class_Rings_Olinordered__semidom @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__one)). 32.13/11.39 thf(1380,plain,((! [A:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ A) @ (c_Groups_Ozero__class_Ozero @ A)) @ (c_Groups_Oone__class_Oone @ A))) | ~ (class_Rings_Olinordered__semidom @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])). 32.13/11.39 thf(172,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ B)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ A) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2)). 32.13/11.39 thf(1148,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ B)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 32.13/11.39 thf(315,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A)) @ B) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ A)) <= (class_Rings_Ocomm__semiring__1 @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J)). 32.13/11.39 thf(1673,plain,((! [A:$i,B:$i,C:$i,D:$i]: (((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A)) @ B) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ A)) | ~ (class_Rings_Ocomm__semiring__1 @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[315])). 32.13/11.39 thf(337,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((c_Set_Oimage @ C @ E @ (hAPP @ (c_COMBB @ F @ E @ C @ D) @ B) @ A) = (c_Set_Oimage @ F @ E @ D @ (c_Set_Oimage @ C @ F @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__image)). 32.13/11.39 thf(1757,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((c_Set_Oimage @ C @ E @ (hAPP @ (c_COMBB @ F @ E @ C @ D) @ B) @ A) = (c_Set_Oimage @ F @ E @ D @ (c_Set_Oimage @ C @ F @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[337])). 32.13/11.39 thf(266,axiom,((class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Nat_Onat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le)). 32.13/11.39 thf(1480,plain,((class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Nat_Onat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])). 32.13/11.39 thf(241,axiom,((! [A:$i,B:$i,C:$i]: ((class_Rings_Oring__1 @ C) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ B) @ (c_Int_Oring__1__class_OInts @ C))) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ B) @ A)) @ (c_Int_Oring__1__class_OInts @ C))) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ A) @ (c_Int_Oring__1__class_OInts @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__add)). 32.13/11.39 thf(1363,plain,((! [A:$i,B:$i,C:$i]: ((class_Rings_Oring__1 @ C) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ B) @ (c_Int_Oring__1__class_OInts @ C))) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ B) @ A)) @ (c_Int_Oring__1__class_OInts @ C))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ C) @ A) @ (c_Int_Oring__1__class_OInts @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 32.13/11.39 thf(490,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ B)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1)). 32.13/11.39 thf(2334,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ B)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[490])). 32.13/11.39 thf(86,axiom,((class_Orderings_Oord @ tc_Nat_Onat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord)). 32.13/11.39 thf(807,plain,((class_Orderings_Oord @ tc_Nat_Onat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 32.13/11.39 thf(288,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((class_Rings_Ocomm__semiring__1 @ E) => ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ D) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ C) @ A)) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ D) @ C)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ B) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J)). 32.13/11.39 thf(1561,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((class_Rings_Ocomm__semiring__1 @ E) => ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ D) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ C) @ A)) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ D) @ C)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ E) @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[288])). 32.13/11.39 thf(148,axiom,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Olinorder @ C) => ((A != B) <=> ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)) | (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neq__iff)). 32.13/11.39 thf(1033,plain,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Olinorder @ C) => (((~ (A = B)) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)) | (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B)))) & (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)) | (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B))) => (~ (A = B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 32.13/11.39 thf(325,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: ((? [F:$i]: ((D = (c_Set_Oimage @ C @ E @ B @ F)) & (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ F) @ A)))) <=> (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ E @ tc_HOL_Obool) @ D) @ (c_Set_Oimage @ C @ E @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__image__iff)). 32.13/11.39 thf(1710,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((? [F:$i]: ((D = (c_Set_Oimage @ C @ E @ B @ F)) & (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ F) @ A)))) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ E @ tc_HOL_Obool) @ D) @ (c_Set_Oimage @ C @ E @ B @ A)))) & ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ E @ tc_HOL_Obool) @ D) @ (c_Set_Oimage @ C @ E @ B @ A))) => (? [F:$i]: ((D = (c_Set_Oimage @ C @ E @ B @ F)) & (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ F) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[325])). 32.13/11.39 thf(435,axiom,((! [A:$i,B:$i]: ((class_Rings_Ocomm__semiring__1 @ B) => ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ (c_Groups_Ozero__class_Ozero @ B)) @ A) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J)). 32.13/11.39 thf(2091,plain,((! [A:$i,B:$i]: ((class_Rings_Ocomm__semiring__1 @ B) => ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ B) @ (c_Groups_Ozero__class_Ozero @ B)) @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[435])). 32.13/11.39 thf(94,axiom,((! [A:$i]: ((hAPP @ c_Nat_OSuc @ A) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (c_Groups_Oone__class_Oone @ tc_Nat_Onat)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left)). 32.13/11.39 thf(828,plain,((! [A:$i]: ((hAPP @ c_Nat_OSuc @ A) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (c_Groups_Oone__class_Oone @ tc_Nat_Onat)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 32.13/11.39 thf(131,axiom,((! [A:$i,B:$i]: ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less1)). 32.13/11.39 thf(960,plain,((! [A:$i,B:$i]: ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ B) @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 32.13/11.39 thf(420,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ A) @ B))) <=> (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ A))) <= (class_Groups_Oordered__ab__semigroup__add__imp__le @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__right)). 32.13/11.39 thf(2040,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ A) @ B))) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ A))) & ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ C) @ A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ A) @ B))))) | ~ (class_Groups_Oordered__ab__semigroup__add__imp__le @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[420])). 32.13/11.39 thf(177,axiom,((! [A:$i]: ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat)). 32.13/11.39 thf(1165,plain,((! [A:$i]: ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat) @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 32.13/11.39 thf(110,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Rings_Ocomm__semiring__1 @ D) => ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ A) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ B) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J)). 32.13/11.39 thf(886,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Rings_Ocomm__semiring__1 @ D) => ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ A) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 32.13/11.39 thf(26,axiom,((c_Arrow__Order__Mirabelle_Ounanimity @ v_F)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_u)). 32.13/11.39 thf(624,plain,((c_Arrow__Order__Mirabelle_Ounanimity @ v_F)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 32.13/11.39 thf(63,axiom,((v_b____ != v_a____)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096a_A_126_061_Ab_096)). 32.13/11.39 thf(728,plain,((~ (v_b____ = v_a____))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 32.13/11.39 thf(66,axiom,((! [A:$i,B:$i,C:$i]: ((c_List_Olist_ONil @ C) != (c_List_Olist_OCons @ C @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I3_J)). 32.13/11.39 thf(740,plain,((! [A:$i,B:$i,C:$i]: ~ ((c_List_Olist_ONil @ C) = (c_List_Olist_OCons @ C @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 32.13/11.39 thf(198,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Groups_Oordered__ab__semigroup__add__imp__le @ D) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ B) @ A)) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__left)). 32.13/11.39 thf(1236,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Groups_Oordered__ab__semigroup__add__imp__le @ D) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ B) @ A)) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ D @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ B)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ D) @ C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 32.13/11.39 thf(526,axiom,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) => ((B = A) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym)). 32.13/11.39 thf(2502,plain,((! [A:$i,B:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) => ((B = A) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[526])). 32.13/11.39 thf(237,axiom,((class_Orderings_Olinorder @ tc_Nat_Onat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder)). 32.13/11.39 thf(1352,plain,((class_Orderings_Olinorder @ tc_Nat_Onat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 32.13/11.39 thf(167,axiom,((class_Groups_Ocomm__monoid__add @ tc_Nat_Onat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add)). 32.13/11.39 thf(1129,plain,((class_Groups_Ocomm__monoid__add @ tc_Nat_Onat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 32.13/11.39 thf(206,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((c_Set_Oimage @ F @ E @ D @ C) = B) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ E @ tc_HOL_Obool) @ A) @ B)) => ((c_Set_Oimage @ F @ E @ D @ (c_Set_Oimage @ E @ F @ (c_Hilbert__Choice_Oinv__into @ F @ E @ C @ D) @ A)) = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__inv__into__cancel)). 32.13/11.39 thf(1261,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((c_Set_Oimage @ F @ E @ D @ C) = B) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ E @ tc_HOL_Obool) @ A) @ B)) => ((c_Set_Oimage @ F @ E @ D @ (c_Set_Oimage @ E @ F @ (c_Hilbert__Choice_Oinv__into @ F @ E @ C @ D) @ A)) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 32.13/11.39 thf(144,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)) => (~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B)))) <= (class_Orderings_Opreorder @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__not__sym)). 32.13/11.39 thf(1019,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)) => (~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B)))) | ~ (class_Orderings_Opreorder @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 32.13/11.39 thf(32,axiom,((! [A:$i,B:$i]: ((class_Groups_Ozero @ B) => ((A = (c_Groups_Ozero__class_Ozero @ B)) <=> ((c_Groups_Ozero__class_Ozero @ B) = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__reorient)). 32.13/11.39 thf(644,plain,((! [A:$i,B:$i]: ((class_Groups_Ozero @ B) => (((A = (c_Groups_Ozero__class_Ozero @ B)) => ((c_Groups_Ozero__class_Ozero @ B) = A)) & (((c_Groups_Ozero__class_Ozero @ B) = A) => (A = (c_Groups_Ozero__class_Ozero @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 32.13/11.39 thf(285,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ B) @ A)) <=> (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ (hAPP @ (hAPP @ (c_COMBC @ C @ (tc_fun @ C @ tc_HOL_Obool) @ tc_HOL_Obool) @ (c_member @ C)) @ B)) @ (hAPP @ (hAPP @ (c_COMBC @ C @ (tc_fun @ C @ tc_HOL_Obool) @ tc_HOL_Obool) @ (c_member @ C)) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq)). 32.13/11.39 thf(1550,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ B) @ A)) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ (hAPP @ (hAPP @ (c_COMBC @ C @ (tc_fun @ C @ tc_HOL_Obool) @ tc_HOL_Obool) @ (c_member @ C)) @ B)) @ (hAPP @ (hAPP @ (c_COMBC @ C @ (tc_fun @ C @ tc_HOL_Obool) @ tc_HOL_Obool) @ (c_member @ C)) @ A)))) & ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ (hAPP @ (hAPP @ (c_COMBC @ C @ (tc_fun @ C @ tc_HOL_Obool) @ tc_HOL_Obool) @ (c_member @ C)) @ B)) @ (hAPP @ (hAPP @ (c_COMBC @ C @ (tc_fun @ C @ tc_HOL_Obool) @ tc_HOL_Obool) @ (c_member @ C)) @ A))) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ tc_HOL_Obool) @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[285])). 32.13/11.39 thf(274,axiom,((! [A:$i,B:$i,C:$i,D:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ C @ D)) @ B) @ A)) <=> ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ D) @ B) @ A)) & ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ D) @ A) @ B)))) <= (class_Orderings_Oord @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__fun__def)). 32.13/11.39 thf(1500,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ C @ D)) @ B) @ A)) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ D) @ B) @ A)) & ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ D) @ A) @ B)))) & (((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ D) @ B) @ A)) & ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ (tc_fun @ C @ D) @ A) @ B))) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ (tc_fun @ C @ D)) @ B) @ A)))) | ~ (class_Orderings_Oord @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[274])). 32.13/11.39 thf(100,axiom,((! [A:$i]: ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ A) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right)). 32.13/11.39 thf(850,plain,((! [A:$i]: ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ A) @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 32.13/11.39 thf(136,axiom,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) <= (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ B)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD2)). 32.13/11.39 thf(982,plain,((! [A:$i,B:$i,C:$i]: ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B) @ A)) | ~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ C) @ B)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 32.13/11.39 thf(261,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Orderings_Oorder @ D) => (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ A) @ B)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ A) @ C))) <= (B = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I1_J)). 32.13/11.39 thf(1431,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((class_Orderings_Oorder @ D) => (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ A) @ B)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ D) @ A) @ C))) | ~ (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])). 32.13/11.39 thf(219,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ A) @ B)) => (A = (hAPP @ (c_Hilbert__Choice_Oinv__into @ E @ D @ B @ C) @ (hAPP @ C @ A)))) <= (c_Fun_Oinj__on @ E @ D @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__f__f)). 32.13/11.39 thf(1299,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ E) @ A) @ B)) => (A = (hAPP @ (c_Hilbert__Choice_Oinv__into @ E @ D @ B @ C) @ (hAPP @ C @ A)))) | ~ (c_Fun_Oinj__on @ E @ D @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 32.13/11.39 thf(50,axiom,((! [A:$i,B:$i]: (((class_Finite__Set_Ofinite @ A) & (class_Finite__Set_Ofinite @ B)) => (class_Finite__Set_Ofinite @ (tc_sum @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum__Finite__Set_Ofinite)). 32.13/11.39 thf(691,plain,((! [A:$i,B:$i]: (((class_Finite__Set_Ofinite @ A) & (class_Finite__Set_Ofinite @ B)) => (class_Finite__Set_Ofinite @ (tc_sum @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 32.13/11.39 thf(520,axiom,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Olinorder @ C) => ((~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A))) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ A) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__cases)). 32.13/11.39 thf(2484,plain,((! [A:$i,B:$i,C:$i]: ((class_Orderings_Olinorder @ C) => ((~ (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A))) => (hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[520])). 32.13/11.39 thf(106,axiom,((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ v_Lab____) @ c_Arrow__Order__Mirabelle_OLin))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096Lab_A_058_ALin_096)). 32.13/11.39 thf(871,plain,((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ v_Lab____) @ c_Arrow__Order__Mirabelle_OLin))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 32.13/11.39 thf(20,axiom,((! [A:$i,B:$i,C:$i]: ((c_Finite__Set_Ofinite @ C @ A) <=> (c_Finite__Set_Ofinite @ C @ (c_Set_Oinsert @ C @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__insert)). 32.13/11.39 thf(607,plain,((! [A:$i,B:$i,C:$i]: (((c_Finite__Set_Ofinite @ C @ A) => (c_Finite__Set_Ofinite @ C @ (c_Set_Oinsert @ C @ B @ A))) & ((c_Finite__Set_Ofinite @ C @ (c_Set_Oinsert @ C @ B @ A)) => (c_Finite__Set_Ofinite @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 32.13/11.39 thf(487,axiom,((! [A:$i,B:$i]: (hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ A) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iso__tuple__UNIV__I)). 32.13/11.39 thf(2321,plain,((! [A:$i,B:$i]: (hBOOL @ (hAPP @ (hAPP @ (c_member @ B) @ A) @ (c_Orderings_Otop__class_Otop @ (tc_fun @ B @ tc_HOL_Obool)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[487])). 32.13/11.39 thf(311,axiom,((! [A:$i]: ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (c_Nat_Onat_Onat__size @ A)) @ (hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))) = (c_Nat_Onat_Onat__size @ (hAPP @ c_Nat_OSuc @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I2_J)). 32.13/11.39 thf(1653,plain,((! [A:$i]: ((hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (c_Nat_Onat_Onat__size @ A)) @ (hAPP @ c_Nat_OSuc @ (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat))) = (c_Nat_Onat_Onat__size @ (hAPP @ c_Nat_OSuc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[311])). 32.13/11.39 thf(393,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ B) @ c_Arrow__Order__Mirabelle_OProf)) => ((((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ F) @ E)) @ (hAPP @ v_F @ B))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ v_F @ A)))) <= (! [G:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ A @ G))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ F) @ E)) @ (hAPP @ B @ G)))))) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ A) @ c_Arrow__Order__Mirabelle_OProf)))) <= (C != D)) <= (F != E)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pairwise__neutrality)). 32.13/11.39 thf(1944,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ B) @ c_Arrow__Order__Mirabelle_OProf)) => ((((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ F) @ E)) @ (hAPP @ v_F @ B))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ v_F @ A)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ v_F @ A))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ F) @ E)) @ (hAPP @ v_F @ B))))) | ~ (! [G:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ A @ G))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ F) @ E)) @ (hAPP @ B @ G)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ F) @ E)) @ (hAPP @ B @ G))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ A @ G)))))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ A) @ c_Arrow__Order__Mirabelle_OProf)))) | (C = D) | (F = E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[393])). 32.13/11.39 thf(243,axiom,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((F != E) => ((C != D) => ((C != F) => (((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ B) @ c_Arrow__Order__Mirabelle_OProf)) => (((! [G:$i]: ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ A @ G))) <=> (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ F) @ E)) @ (hAPP @ B @ G))))) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ F) @ E)) @ (hAPP @ v_F @ B))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ v_F @ A))))) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ A) @ c_Arrow__Order__Mirabelle_OProf)))) <= (D != E))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C1_C)). 32.13/11.39 thf(1367,plain,((! [A:$i,B:$i,C:$i,D:$i,E:$i,F:$i]: ((~ (F = E)) => ((~ (C = D)) => ((~ (C = F)) => (((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ B) @ c_Arrow__Order__Mirabelle_OProf)) => (((! [G:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ A @ G))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ F) @ E)) @ (hAPP @ B @ G)))) & ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ F) @ E)) @ (hAPP @ B @ G))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ A @ G)))))) => ((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ F) @ E)) @ (hAPP @ v_F @ B))) => (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ D) @ C)) @ (hAPP @ v_F @ A))))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ A) @ c_Arrow__Order__Mirabelle_OProf)))) | (D = E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 32.13/11.39 thf(121,axiom,((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ tc_HOL_Obool @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_If @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool) @ (hAPP @ (c_COMBB @ tc_Nat_Onat @ (tc_fun @ tc_Nat_Onat @ tc_HOL_Obool) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat)) @ v_h____)) @ v_n____)) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ tc_Arrow__Order__Mirabelle_Oindi @ c_Arrow__Order__Mirabelle_Omktop) @ v_P____)) @ v_e____)) @ (c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ tc_HOL_Obool @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_If @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool) @ (hAPP @ (c_COMBB @ tc_Nat_Onat @ (tc_fun @ tc_Nat_Onat @ tc_HOL_Obool) @ tc_Arrow__Order__Mirabelle_Oindi @ c_fequal) @ v_h____)) @ v_n____)) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (c_COMBB @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ tc_Arrow__Order__Mirabelle_Oindi @ c_Arrow__Order__Mirabelle_Oabove) @ v_P____)) @ v_c____)) @ v_e____)) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ tc_Arrow__Order__Mirabelle_Oindi @ c_Arrow__Order__Mirabelle_Omkbot) @ v_P____)) @ v_e____)))) @ c_Arrow__Order__Mirabelle_OProf))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_058_AProf_096)). 32.13/11.39 thf(923,plain,((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ tc_HOL_Obool @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_If @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool) @ (hAPP @ (c_COMBB @ tc_Nat_Onat @ (tc_fun @ tc_Nat_Onat @ tc_HOL_Obool) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_Orderings_Oord__class_Oless @ tc_Nat_Onat)) @ v_h____)) @ v_n____)) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ tc_Arrow__Order__Mirabelle_Oindi @ c_Arrow__Order__Mirabelle_Omktop) @ v_P____)) @ v_e____)) @ (c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (c_COMBS @ tc_Arrow__Order__Mirabelle_Oindi @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ tc_HOL_Obool @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ tc_Arrow__Order__Mirabelle_Oindi @ (c_If @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Nat_Onat @ tc_HOL_Obool) @ (hAPP @ (c_COMBB @ tc_Nat_Onat @ (tc_fun @ tc_Nat_Onat @ tc_HOL_Obool) @ tc_Arrow__Order__Mirabelle_Oindi @ c_fequal) @ v_h____)) @ v_n____)) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ (hAPP @ (c_COMBB @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool))) @ tc_Arrow__Order__Mirabelle_Oindi @ c_Arrow__Order__Mirabelle_Oabove) @ v_P____)) @ v_c____)) @ v_e____)) @ (hAPP @ (hAPP @ (c_COMBC @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ (hAPP @ (c_COMBB @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool) @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ tc_Arrow__Order__Mirabelle_Oindi @ c_Arrow__Order__Mirabelle_Omkbot) @ v_P____)) @ v_e____)))) @ c_Arrow__Order__Mirabelle_OProf))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 32.13/11.39 thf(462,axiom,((! [A:$i,B:$i,C:$i]: ((class_Groups_Oordered__comm__monoid__add @ C) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ (c_Groups_Ozero__class_Ozero @ C)) @ B)) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ (c_Groups_Ozero__class_Ozero @ C)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ B) @ A))) <= (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ (c_Groups_Ozero__class_Ozero @ C)) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__pos)). 32.13/11.39 thf(2206,plain,((! [A:$i,B:$i,C:$i]: ((class_Groups_Oordered__comm__monoid__add @ C) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ (c_Groups_Ozero__class_Ozero @ C)) @ B)) => ((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ (c_Groups_Ozero__class_Ozero @ C)) @ (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ C) @ B) @ A))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ (c_Groups_Ozero__class_Ozero @ C)) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[462])). 32.13/11.39 thf(478,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ B) @ A)) @ C)) => (~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ A) @ B)) @ C)))) <= (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ C) @ c_Arrow__Order__Mirabelle_OLin))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Lin__irrefl)). 32.13/11.39 thf(2297,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ B) @ A)) @ C)) => (~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt)) @ (hAPP @ (hAPP @ (c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ A) @ B)) @ C)))) | ~ (hBOOL @ (hAPP @ (hAPP @ (c_member @ (tc_fun @ (tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt) @ tc_HOL_Obool)) @ C) @ c_Arrow__Order__Mirabelle_OLin))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[478])). 32.13/11.39 thf(6,axiom,((c_Finite__Set_Ofinite @ tc_Arrow__Order__Mirabelle_Oindi @ (c_Orderings_Otop__class_Otop @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__indi)). 32.13/11.39 thf(560,plain,((c_Finite__Set_Ofinite @ tc_Arrow__Order__Mirabelle_Oindi @ (c_Orderings_Otop__class_Otop @ (tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_HOL_Obool)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 32.13/11.39 thf(30,axiom,((! [A:$i,B:$i,C:$i]: ((c_Set_Oinsert @ C @ B @ (c_Set_Oinsert @ C @ B @ A)) = (c_Set_Oinsert @ C @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb2)). 32.13/11.39 thf(639,plain,((! [A:$i,B:$i,C:$i]: ((c_Set_Oinsert @ C @ B @ (c_Set_Oinsert @ C @ B @ A)) = (c_Set_Oinsert @ C @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 32.13/11.39 thf(188,axiom,((! [A:$i,B:$i,C:$i]: (((B != A) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)))) <= (class_Orderings_Oorder @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__neq__le__trans)). 32.13/11.39 thf(1204,plain,((! [A:$i,B:$i,C:$i]: (((~ (B = A)) => ((hBOOL @ (hAPP @ (c_Orderings_Oord__class_Oless__eq @ C @ B) @ A)) => (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)))) | ~ (class_Orderings_Oorder @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 32.13/11.39 thf(264,axiom,((! [A:$i,B:$i,C:$i,D:$i]: ((((c_Finite__Set_Ofinite @ B @ A) & (c_Finite__Set_Ofinite @ D @ C)) => ((c_Finite__Set_Ocard @ (tc_sum @ D @ B) @ (c_Sum__Type_OPlus @ D @ B @ C @ A)) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (c_Finite__Set_Ocard @ D @ C)) @ (c_Finite__Set_Ocard @ B @ A)))) & (((c_Finite__Set_Ocard @ (tc_sum @ D @ B) @ (c_Sum__Type_OPlus @ D @ B @ C @ A)) = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) <= (~ ((c_Finite__Set_Ofinite @ D @ C) & (c_Finite__Set_Ofinite @ B @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Plus__conv__if)). 32.13/11.39 thf(1468,plain,((! [A:$i,B:$i,C:$i,D:$i]: ((((c_Finite__Set_Ofinite @ B @ A) & (c_Finite__Set_Ofinite @ D @ C)) => ((c_Finite__Set_Ocard @ (tc_sum @ D @ B) @ (c_Sum__Type_OPlus @ D @ B @ C @ A)) = (hAPP @ (hAPP @ (c_Groups_Oplus__class_Oplus @ tc_Nat_Onat) @ (c_Finite__Set_Ocard @ D @ C)) @ (c_Finite__Set_Ocard @ B @ A)))) & (((c_Finite__Set_Ocard @ (tc_sum @ D @ B) @ (c_Sum__Type_OPlus @ D @ B @ C @ A)) = (c_Groups_Ozero__class_Ozero @ tc_Nat_Onat)) | ((c_Finite__Set_Ofinite @ D @ C) & (c_Finite__Set_Ofinite @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])). 32.13/11.39 thf(133,axiom,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)) => (~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B)))) <= (class_Orderings_Opreorder @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym)). 32.13/11.39 thf(972,plain,((! [A:$i,B:$i,C:$i]: (((hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ B) @ A)) => (~ (hBOOL @ (hAPP @ (hAPP @ (c_Orderings_Oord__class_Oless @ C) @ A) @ B)))) | ~ (class_Orderings_Opreorder @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 32.13/11.39 thf(2523,plain,($false),inference(e,[status(thm)],[892,1337,2094,1024,1168,2306,2336,1995,909,628,1031,2463,1315,2499,2480,941,1179,555,666,1818,1295,1950,2363,2077,2309,2512,683,1068,2381,2062,1422,1569,1728,878,1971,1793,1692,1305,597,1437,861,1173,1486,1705,1788,1867,1999,2476,698,1988,747,1640,945,2360,898,2216,2491,1243,1127,1782,1391,1576,782,2020,1046,1601,1724,1803,1265,1228,651,2328,1985,1760,2339,1907,1860,587,619,1511,802,1313,2185,2488,853,1247,1319,2373,606,1347,1572,1013,1741,2520,2158,2024,2301,1875,2388,1232,2178,1489,924,1302,789,2105,1811,1334,1858,2122,1978,2291,1383,574,1581,1183,821,2017,602,2508,1843,1377,1896,956,1886,1119,1622,774,2242,1345,1405,1104,2154,1521,1564,1863,1651,1074,1604,2011,920,2204,678,2473,661,793,2164,1153,2047,1915,2083,1868,1730,798,1163,1274,2264,1900,825,1021,1042,1519,1355,1676,2147,561,693,1238,1423,1938,1837,1365,625,1555,1687,2068,2200,889,1656,2213,1195,2211,2344,2313,1291,710,974,1360,1350,1983,2115,2100,1851,1534,1017,1111,725,1425,1540,1878,1397,1493,1683,1329,1160,1942,1659,2323,1292,554,753,642,2053,1584,1791,2108,2038,1207,1644,1612,1419,837,1825,1114,997,1099,985,701,1150,1478,1297,1530,1382,1831,654,1192,2465,911,2505,721,1852,1720,779,2370,1857,1814,1086,1241,2208,2043,2057,1846,2368,558,2221,2189,953,718,1278,1135,2001,750,1146,2391,1698,1483,1927,689,2376,1631,733,584,1833,2225,1884,1784,1389,1125,1752,2016,2514,875,1403,1795,2398,1256,1428,936,572,2029,1271,2308,713,1865,1733,1332,1765,804,1258,704,947,1224,2148,2510,764,979,2346,2079,2311,1209,900,831,1408,1282,2478,1894,784,1117,1574,1011,1933,2299,1722,1144,1801,2378,1690,1969,1307,863,1339,858,535,816,2111,1993,1731,594,799,621,848,895,2252,668,932,1171,2418,1213,768,1044,695,2064,2369,1015,1176,2288,1435,2022,1250,1102,1694,658,2506,1626,2054,2239,675,1809,1873,589,795,680,663,2471,2449,812,1990,617,2202,939,1181,823,776,1770,855,1516,1070,872,2060,1743,707,1566,2175,1780,1230,1484,2160,673,1637,1785,2337,2219,1763,1538,2486,808,1679,1130,1579,1738,2468,2247,744,1898,1849,656,613,1221,1353,1955,2145,1504,1585,571,612,845,2013,1839,1918,1316,2088,2045,1966,671,1834,903,581,1517,1216,891,2342,1289,1807,1108,1276,1385,963,2167,2389,1341,2098,1481,652,1629,2004,632,1854,731,786,995,1558,2152,1491,568,1777,667,1193,1077,2162,1661,2036,1309,2315,2494,716,2258,1642,2102,2517,1280,1957,833,1395,818,1380,1148,1673,1757,1480,1363,2334,807,1561,1033,1710,2091,828,960,2040,1165,886,624,728,740,1236,2502,1352,1129,1261,1019,644,1550,1500,850,982,1431,1299,691,2484,871,607,2321,1653,1944,1367,923,2206,2297,560,639,1204,1468,972])). 32.13/11.39 % SZS output end CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p 32.13/11.39 % [INFO] Killing All external provers ... 32.34/11.49 EOF