0.03/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.14 % Command : run_Leo-III %s %d 0.13/0.35 % Computer : n007.cluster.edu 0.13/0.35 % Model : x86_64 x86_64 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.35 % Memory : 8042.1875MB 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 1440 0.13/0.35 % WCLimit : 180 0.13/0.35 % DateTime : Mon Jul 3 03:44:43 EDT 2023 0.13/0.35 % CPUTime : 0.94/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 1.75/1.11 % [INFO] Parsing done (266ms). 1.75/1.12 % [INFO] Running in sequential loop mode. 2.45/1.32 % [INFO] eprover registered as external prover. 2.45/1.32 % [INFO] cvc4 registered as external prover. 2.45/1.32 % [INFO] Scanning for conjecture ... 2.59/1.40 % [INFO] Found a conjecture and 352 axioms. Running axiom selection ... 2.84/1.49 % [INFO] Axiom selection finished. Selected 256 axioms (removed 96 axioms). 3.49/1.65 % [INFO] Problem is higher-order (TPTP THF). 3.49/1.66 % [INFO] Type checking passed. 3.49/1.67 % [CONFIG] Using configuration: timeout(180) with strategy. Searching for refutation ... 13.66/4.09 % External prover 'e' found a proof! 13.66/4.09 % [INFO] Killing All external provers ... 13.66/4.09 % Time passed: 3568ms (effective reasoning time: 2965ms) 13.66/4.09 % Solved by strategy 13.66/4.09 % Axioms used in derivation (256): fact_264_sup__absorb2, fact_73_Un__iff, fact_104_insertI1, fact_80_equals0D, fact_271_sup_Oabsorb1, fact_262_sup__absorb2, fact_168_sup__bot_Oneutr__eq__iff, fact_124_insert__compr, fact_56_singleton__conv2, fact_166_sup__bot_Oleft__neutral, fact_177_sup_Oleft__idem, fact_64_Collect__empty__eq, fact_88_equalityD1, fact_279_sup_OorderI, fact_252_sup_Ocobounded1, fact_81_equals0I, fact_258_sup_OboundedI, fact_270_sup_Oabsorb2, fact_82_ex__in__conv, fact_26_sortLemmaR, fact_16_sortedTree_Osimps_I1_J, fact_49_minf_I6_J, fact_259_sup_OboundedE, fact_131_insert__not__empty, fact_148_Collect__conv__if2, fact_333_sup_Ostrict__coboundedI1, fact_46_complete__interval, fact_66_subsetI, fact_285_le__iff__sup, fact_57_singleton__conv, fact_59_Un__insert__left, fact_107_insert__ident, fact_115_bex__Un, fact_274_sup__unique, fact_306_sup__ge1, fact_156_sup__bot__left, fact_77_insert__subset, fact_134_subset__insert, fact_318_inf__sup__ord_I4_J, fact_340_order__refl, fact_117_Un__assoc, fact_152_insert__is__Un, fact_113_UnI1, fact_307_le__supI, fact_341_order__refl, fact_280_sup_OorderE, fact_11_minf_I7_J, fact_261_sup_OboundedE, fact_187_sup_Obounded__iff, fact_183_sup_Oidem, fact_63_all__not__in__conv, fact_70_insert__iff, fact_231_inf__sup__aci_I7_J, fact_179_sup__idem, fact_53_setOf_Osimps_I1_J, fact_151_subset__singleton__iff, fact_76_singletonI, fact_93_subset__trans, fact_227_inf__sup__aci_I6_J, fact_140_Un__least, fact_268_sup_Oabsorb2, fact_34_minf_I1_J, fact_324_less__supI2, fact_244_sup_Oabsorb__iff1, fact_86_equalityE, fact_23_Tree_Oexhaust, fact_91_subset__refl, fact_235_sup_OcoboundedI2, fact_38_sorted__distinct__pred__def, fact_304_sup__ge1, fact_203_sup_Oleft__commute, fact_1_rm__res, fact_36_h2, fact_233_inf__sup__aci_I8_J, fact_12_minf_I5_J, fact_288_sup__least, fact_90_subset__iff, fact_294_sup_Omono, fact_24_Tree_Oinduct, fact_95_Collect__mono__iff, fact_133_insert__mono, fact_112_UnE, fact_0_hLess, fact_138_Un__empty__right, fact_295_le__supI2, fact_173_sup__left__idem, fact_146_subset__Un__eq, fact_32_pinf_I5_J, fact_21_wrm_Osimps, fact_188_le__sup__iff, fact_40_wrm__set1, fact_55_singleton__insert__inj__eq, fact_289_sup__mono, fact_103_insertE, fact_13_minf_I4_J, fact_19_rm__set, fact_180_sup__idem, fact_18_binsert__sorted, fact_205_sup__commute, fact_208_sup_Ocommute, fact_110_insert__commute, fact_192_sup__bot_Oright__neutral, fact_255_sup_Oorder__iff, fact_214_sup_Oassoc, fact_44_Collect__cong, fact_121_Un__left__commute, fact_109_insert__eq__iff, fact_249_sup_Ocobounded2, fact_199_sup__left__commute, fact_111_mk__disjoint__insert, fact_230_inf__sup__aci_I7_J, fact_137_Un__empty__left, fact_291_sup__mono, fact_292_sup_Omono, fact_243_sup_Oabsorb__iff2, fact_75_empty__subsetI, fact_160_bot__eq__sup__iff, fact_277_sup_OorderI, fact_8_s2, fact_228_inf__sup__aci_I6_J, fact_176_sup_Oleft__idem, fact_30_pinf_I3_J, fact_310_le__supE, fact_153_Un__singleton__iff, fact_185_sup_Obounded__iff, fact_215_sup_Oassoc, fact_171_sup_Oright__idem, fact_247_sup_Ocobounded2, fact_312_le__supE, fact_147_Collect__conv__if, fact_6_ldef, fact_48_minf_I8_J, fact_129_singleton__iff, fact_238_sup_OcoboundedI1, fact_114_UnI2, fact_144_Un__absorb2, fact_5_wrm__res, fact_54_singleton__insert__inj__eq_H, fact_127_Collect__disj__eq, fact_142_Un__upper2, fact_125_insert__Collect, fact_265_sup__absorb1, fact_37_memb__spec, fact_256_sup_OboundedI, fact_20_binsert_Osimps_I1_J, fact_43_Collect__mem__eq, fact_246_sup_Oabsorb__iff1, fact_61_Un__empty, fact_67_subset__antisym, fact_60_Un__subset__iff, fact_240_sup_OcoboundedI1, fact_122_empty__def, fact_108_insert__absorb, fact_52_sorted__distinct, fact_209_sup_Ocommute, fact_74_subset__empty, fact_327_sup_Ostrict__boundedE, fact_69_insertCI, fact_309_le__supI, fact_58_Un__insert__right, fact_212_sup__assoc, fact_25_Tree_Odistinct_I1_J, fact_89_equalityD2, fact_65_empty__Collect__eq, fact_174_sup__left__idem, fact_105_insertI2, fact_336_sup_Ostrict__coboundedI2, fact_35_h1, fact_217_boolean__algebra__cancel_Osup2, fact_143_Un__absorb1, fact_220_boolean__algebra__cancel_Osup1, fact_162_sup__eq__bot__iff, fact_182_sup_Oidem, fact_158_sup__bot__right, fact_62_empty__iff, fact_300_le__supI1, fact_132_singleton__inject, fact_2_t2nTip, fact_218_boolean__algebra__cancel_Osup2, fact_234_inf__sup__aci_I8_J, fact_315_inf__sup__ord_I3_J, fact_27_sortLemmaL, fact_149_insert__def, fact_273_sup_Oabsorb1, fact_126_Un__def, fact_139_Un__mono, fact_84_in__mono, fact_225_inf__sup__aci_I5_J, fact_301_sup__ge2, fact_28_pinf_I1_J, fact_31_pinf_I4_J, fact_283_le__iff__sup, fact_3_Tree_Oinject, fact_50_pinf_I8_J, fact_14_minf_I3_J, fact_87_subset__eq, fact_120_Un__left__absorb, fact_330_sup_Ostrict__order__iff, fact_119_Un__commute, fact_282_sup_OorderE, fact_51_pinf_I6_J, fact_211_sup__assoc, fact_241_sup_Oabsorb__iff2, fact_313_inf__sup__ord_I3_J, fact_253_sup_Oorder__iff, fact_94_set__eq__subset, fact_141_Un__upper1, fact_9_binsert_Osimps_I2_J, fact_79_emptyE, fact_321_less__supI1, fact_200_sup__left__commute, fact_15_minf_I2_J, fact_202_sup_Oleft__commute, fact_92_Collect__mono, fact_4_s, fact_45_linorder__neqE__linordered__idom, fact_72_UnCI, fact_297_le__supI2, fact_250_sup_Ocobounded1, fact_224_inf__sup__aci_I5_J, fact_118_Un__absorb, fact_298_le__supI1, fact_29_pinf_I2_J, fact_33_pinf_I7_J, fact_22_sortedTree_Osimps_I2_J, fact_128_singletonD, fact_136_subset__insertI2, fact_123_Collect__subset, fact_154_singleton__Un__iff, fact_190_le__sup__iff, fact_71_insert__absorb2, fact_276_sup__unique, fact_303_sup__ge2, fact_130_doubleton__eq__iff, fact_42_mem__Collect__eq, fact_206_sup__commute, fact_106_Set_Oset__insert, fact_237_sup_OcoboundedI2, fact_145_subset__UnE, fact_339_the__elem__eq, fact_47_setOf_Osimps_I2_J, fact_164_sup__bot_Oeq__neutr__iff, fact_17_wrm__sort, fact_10_rm_Osimps, fact_85_subsetD, fact_267_sup__absorb1, fact_150_subset__singletonD, fact_135_subset__insertI, fact_39_l__scope, fact_286_sup__least, fact_170_sup_Oright__idem, fact_7_s1, fact_41_remove_Osimps_I1_J, fact_116_ball__Un, fact_221_boolean__algebra__cancel_Osup1, fact_316_inf__sup__ord_I4_J 13.66/4.09 % No. of inferences in proof: 516 13.66/4.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3568 ms resp. 2965 ms w/o parsing 14.28/4.23 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p 14.28/4.23 thf(binary1439146945Tree_a_type, type, binary1439146945Tree_a: $tType). 14.28/4.23 thf(set_a_type, type, set_a: $tType). 14.28/4.23 thf(int_type, type, int: $tType). 14.28/4.23 thf(a_type, type, a: $tType). 14.28/4.23 thf(binary717961607le_T_a_type, type, binary717961607le_T_a: (binary1439146945Tree_a > (a > (binary1439146945Tree_a > binary1439146945Tree_a)))). 14.28/4.23 thf(binary476621312_Tip_a_type, type, binary476621312_Tip_a: binary1439146945Tree_a). 14.28/4.23 thf(binary1226383794sert_a_type, type, binary1226383794sert_a: ((a > int) > (a > (binary1439146945Tree_a > binary1439146945Tree_a)))). 14.28/4.23 thf(binary2053421120memb_a_type, type, binary2053421120memb_a: ((a > int) > (a > (binary1439146945Tree_a > $o)))). 14.28/4.23 thf(binary1804682569move_a_type, type, binary1804682569move_a: ((a > int) > (a > (binary1439146945Tree_a > binary1439146945Tree_a)))). 14.28/4.23 thf(binary339557810e_rm_a_type, type, binary339557810e_rm_a: ((a > int) > (binary1439146945Tree_a > a))). 14.28/4.23 thf(binary945792244etOf_a_type, type, binary945792244etOf_a: (binary1439146945Tree_a > set_a)). 14.28/4.23 thf(binary1721989714Tree_a_type, type, binary1721989714Tree_a: ((a > int) > (binary1439146945Tree_a > $o))). 14.28/4.23 thf(binary670562003pred_a_type, type, binary670562003pred_a: ((a > int) > (a > (a > (binary1439146945Tree_a > $o))))). 14.28/4.23 thf(binary1217730267_wrm_a_type, type, binary1217730267_wrm_a: ((a > int) > (binary1439146945Tree_a > binary1439146945Tree_a))). 14.28/4.23 thf(sup_sup_int_type, type, sup_sup_int: (int > (int > int))). 14.28/4.23 thf(sup_sup_set_a_type, type, sup_sup_set_a: (set_a > (set_a > set_a))). 14.28/4.23 thf(bot_bot_set_a_type, type, bot_bot_set_a: set_a). 14.28/4.23 thf(ord_less_int_type, type, ord_less_int: (int > (int > $o))). 14.28/4.23 thf(ord_less_eq_int_type, type, ord_less_eq_int: (int > (int > $o))). 14.28/4.23 thf(ord_less_eq_set_a_type, type, ord_less_eq_set_a: (set_a > (set_a > $o))). 14.28/4.23 thf(collect_a_type, type, collect_a: ((a > $o) > set_a)). 14.28/4.23 thf(insert_a_type, type, insert_a: (a > (set_a > set_a))). 14.28/4.23 thf(the_elem_a_type, type, the_elem_a: (set_a > a)). 14.28/4.23 thf(member_a_type, type, member_a: (a > (set_a > $o))). 14.28/4.23 thf(h_type, type, h: (a > int)). 14.28/4.23 thf(l_type, type, l: a). 14.28/4.23 thf(t1_type, type, t1: binary1439146945Tree_a). 14.28/4.23 thf(t2_type, type, t2: binary1439146945Tree_a). 14.28/4.23 thf(x_type, type, x: a). 14.28/4.23 thf(244,axiom,((! [A:(int > $o),B:(int > $o),C:(int > $o),D:(int > $o)]: (((? [E:int]: ! [F:int]: (((C @ F) = (D @ F)) <= (ord_less_int @ F @ E))) => (? [E:int]: ! [F:int]: ((((A @ F) | (C @ F)) = ((B @ F) | (D @ F))) <= (ord_less_int @ F @ E)))) <= (? [E:int]: ! [F:int]: ((ord_less_int @ F @ E) => ((A @ F) = (B @ F))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_minf_I2_J)). 14.28/4.23 thf(1024,plain,((! [A:(int > $o),B:(int > $o),C:(int > $o),D:(int > $o)]: (((? [E:int]: ! [F:int]: (((C @ F) = (D @ F)) | ~ (ord_less_int @ F @ E))) => (? [E:int]: ! [F:int]: ((((A @ F) | (C @ F)) = ((B @ F) | (D @ F))) | ~ (ord_less_int @ F @ E)))) | ~ (? [E:int]: ! [F:int]: ((ord_less_int @ F @ E) => ((A @ F) = (B @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])). 14.28/4.23 thf(40,axiom,((! [A:set_a,B:set_a]: (((sup_sup_set_a @ A @ B) = B) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_sup__absorb2)). 14.28/4.23 thf(365,plain,((! [A:set_a,B:set_a]: (((sup_sup_set_a @ A @ B) = B) | ~ (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 14.28/4.23 thf(172,axiom,((! [A:a,B:set_a,C:a,D:set_a]: ((~ (member_a @ A @ B)) => ((((insert_a @ A @ B) = (insert_a @ C @ D)) = (((A != C) => (? [E:set_a]: ((B = (insert_a @ C @ E)) & ~ (member_a @ C @ E) & ~ (member_a @ A @ E) & (D = (insert_a @ A @ E))))) & ((A = C) => (B = D)))) <= (~ (member_a @ C @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_insert__eq__iff)). 14.28/4.23 thf(760,plain,((! [A:a,B:set_a,C:a,D:set_a]: ((~ (member_a @ A @ B)) => ((((insert_a @ A @ B) = (insert_a @ C @ D)) = (((~ (A = C)) => (? [E:set_a]: ((B = (insert_a @ C @ E)) & ~ (member_a @ C @ E) & ~ (member_a @ A @ E) & (D = (insert_a @ A @ E))))) & ((A = C) => (B = D)))) | (member_a @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 14.28/4.23 thf(33,axiom,((! [A:set_a,B:set_a]: (ord_less_eq_set_a @ A @ (sup_sup_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_inf__sup__ord_I3_J)). 14.28/4.23 thf(347,plain,((! [A:set_a,B:set_a]: (ord_less_eq_set_a @ A @ (sup_sup_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 14.28/4.23 thf(229,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ (sup_sup_int @ C @ B)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_sup_Ostrict__coboundedI2)). 14.28/4.23 thf(941,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ (sup_sup_int @ C @ B)) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 14.28/4.23 thf(79,axiom,((! [A:set_a,B:set_a]: (((sup_sup_set_a @ A @ B) = bot_bot_set_a) = ((B = bot_bot_set_a) & (A = bot_bot_set_a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_sup__eq__bot__iff)). 14.28/4.23 thf(481,plain,((! [A:set_a,B:set_a]: (((sup_sup_set_a @ A @ B) = bot_bot_set_a) = ((B = bot_bot_set_a) & (A = bot_bot_set_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 14.28/4.23 thf(135,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ A @ (sup_sup_int @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_le__supI2)). 14.28/4.23 thf(645,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ A @ (sup_sup_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 14.28/4.23 thf(215,axiom,((! [A:binary1439146945Tree_a,B:(a > int),C:binary1439146945Tree_a,D:a]: ((((binary339557810e_rm_a @ B @ (binary717961607le_T_a @ C @ D @ A)) = D) <= (A = binary476621312_Tip_a)) & ((A != binary476621312_Tip_a) => ((binary339557810e_rm_a @ B @ (binary717961607le_T_a @ C @ D @ A)) = (binary339557810e_rm_a @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_rm_Osimps)). 14.28/4.23 thf(892,plain,((! [A:binary1439146945Tree_a,B:(a > int),C:binary1439146945Tree_a,D:a]: ((((binary339557810e_rm_a @ (B) @ (binary717961607le_T_a @ C @ D @ A)) = D) | ~ (A = binary476621312_Tip_a)) & ((~ (A = binary476621312_Tip_a)) => ((binary339557810e_rm_a @ (B) @ (binary717961607le_T_a @ C @ D @ A)) = (binary339557810e_rm_a @ (B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 14.28/4.23 thf(55,axiom,((! [A:set_a,B:set_a]: (((sup_sup_set_a @ B @ A) = B) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_Un__absorb2)). 14.28/4.23 thf(408,plain,((! [A:set_a,B:set_a]: (((sup_sup_set_a @ B @ A) = B) | ~ (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 14.28/4.23 thf(93,axiom,((ord_less_eq_int = (^ [A:int,B:int]: (B = (sup_sup_int @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_sup_Oorder__iff)). 14.28/4.23 thf(523,plain,(((ord_less_eq_int) = (^ [A:int,B:int]: (B = (sup_sup_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 14.28/4.23 thf(147,axiom,((! [A:int,B:int,C:int,D:int]: ((A = (sup_sup_int @ B @ C)) => ((sup_sup_int @ A @ D) = (sup_sup_int @ B @ (sup_sup_int @ C @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_boolean__algebra__cancel_Osup1)). 14.28/4.23 thf(683,plain,((! [A:int,B:int,C:int,D:int]: ((A = (sup_sup_int @ B @ C)) => ((sup_sup_int @ A @ D) = (sup_sup_int @ B @ (sup_sup_int @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 14.28/4.23 thf(20,axiom,((! [A:set_a]: (ord_less_eq_set_a @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_subset__refl)). 14.28/4.23 thf(308,plain,((! [A:set_a]: (ord_less_eq_set_a @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 14.28/4.23 thf(66,axiom,((! [A:set_a]: (ord_less_eq_set_a @ bot_bot_set_a @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_empty__subsetI)). 14.28/4.23 thf(440,plain,((! [A:set_a]: (ord_less_eq_set_a @ bot_bot_set_a @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 14.28/4.23 thf(119,axiom,((binary670562003pred_a = (^ [A:(a > int),B:a,C:a,D:binary1439146945Tree_a]: (((member_a @ B @ (binary945792244etOf_a @ D)) & (member_a @ C @ (binary945792244etOf_a @ D)) & ((A @ B) = (A @ C)) & (binary1721989714Tree_a @ A @ D)) => (B = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_sorted__distinct__pred__def)). 14.28/4.23 thf(597,plain,(((binary670562003pred_a) = (^ [A:(a > int),B:a,C:a,D:binary1439146945Tree_a]: (((member_a @ B @ (binary945792244etOf_a @ D)) & (member_a @ C @ (binary945792244etOf_a @ D)) & ((A @ B) = (A @ C)) & (binary1721989714Tree_a @ A @ D)) => (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 14.28/4.23 thf(207,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((sup_sup_int @ B @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_sup__absorb1)). 14.28/4.23 thf(861,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((sup_sup_int @ B @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 14.28/4.23 thf(165,axiom,((! [A:int,B:int]: ((sup_sup_int @ A @ (sup_sup_int @ A @ B)) = (sup_sup_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_inf__sup__aci_I8_J)). 14.28/4.23 thf(741,plain,((! [A:int,B:int]: ((sup_sup_int @ A @ (sup_sup_int @ A @ B)) = (sup_sup_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 14.28/4.23 thf(254,axiom,((! [A:binary1439146945Tree_a,B:a,C:binary1439146945Tree_a,D:binary1439146945Tree_a,E:a,F:binary1439146945Tree_a]: (((binary717961607le_T_a @ A @ B @ C) = (binary717961607le_T_a @ D @ E @ F)) = ((B = E) & (C = F) & (A = D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_Tree_Oinject)). 14.28/4.23 thf(1073,plain,((! [A:binary1439146945Tree_a,B:a,C:binary1439146945Tree_a,D:binary1439146945Tree_a,E:a,F:binary1439146945Tree_a]: (((binary717961607le_T_a @ A @ B @ C) = (binary717961607le_T_a @ D @ E @ F)) = ((B = E) & (C = F) & (A = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])). 14.28/4.23 thf(156,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ (sup_sup_int @ B @ C)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_sup_OcoboundedI1)). 14.28/4.23 thf(715,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ (sup_sup_int @ B @ C)) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 14.28/4.23 thf(76,axiom,((! [A:set_a]: ((sup_sup_set_a @ A @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_sup_Oidem)). 14.28/4.23 thf(472,plain,((! [A:set_a]: ((sup_sup_set_a @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 14.28/4.23 thf(154,axiom,((! [A:set_a,B:set_a,C:set_a]: ((sup_sup_set_a @ (sup_sup_set_a @ A @ B) @ C) = (sup_sup_set_a @ A @ (sup_sup_set_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_sup_Oassoc)). 14.28/4.23 thf(709,plain,((! [A:set_a,B:set_a,C:set_a]: ((sup_sup_set_a @ (sup_sup_set_a @ A @ B) @ C) = (sup_sup_set_a @ A @ (sup_sup_set_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 14.28/4.23 thf(213,axiom,((! [A:binary1439146945Tree_a,B:a,C:binary1439146945Tree_a]: (binary476621312_Tip_a != (binary717961607le_T_a @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_Tree_Odistinct_I1_J)). 14.28/4.23 thf(885,plain,((! [A:binary1439146945Tree_a,B:a,C:binary1439146945Tree_a]: ~ (binary476621312_Tip_a = (binary717961607le_T_a @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 14.28/4.23 thf(137,axiom,((! [A:a,B:a]: ((A = B) <= (member_a @ A @ (insert_a @ B @ bot_bot_set_a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_singletonD)). 14.28/4.23 thf(651,plain,((! [A:a,B:a]: ((A = B) | ~ (member_a @ A @ (insert_a @ B @ bot_bot_set_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 14.28/4.23 thf(200,axiom,((! [A:a,B:a,C:a,D:a]: (((insert_a @ A @ (insert_a @ B @ bot_bot_set_a)) = (insert_a @ C @ (insert_a @ D @ bot_bot_set_a))) = (((A = C) & (B = D)) | ((A = D) & (B = C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_doubleton__eq__iff)). 14.28/4.23 thf(841,plain,((! [A:a,B:a,C:a,D:a]: (((insert_a @ A @ (insert_a @ B @ bot_bot_set_a)) = (insert_a @ C @ (insert_a @ D @ bot_bot_set_a))) = (((A = C) & (B = D)) | ((A = D) & (B = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 14.28/4.23 thf(58,axiom,((! [A:(a > $o),B:(a > $o)]: ((ord_less_eq_set_a @ (collect_a @ A) @ (collect_a @ B)) <= (! [C:a]: ((B @ C) <= (A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_Collect__mono)). 14.28/4.23 thf(417,plain,((! [A:(a > $o),B:(a > $o)]: ((ord_less_eq_set_a @ (collect_a @ (A)) @ (collect_a @ (B))) | ~ (! [C:a]: ((B @ C) | ~ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 14.28/4.23 thf(47,axiom,((ord_less_eq_set_a = (^ [A:set_a,B:set_a]: (B = (sup_sup_set_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_sup_Oorder__iff)). 14.28/4.23 thf(389,plain,(((ord_less_eq_set_a) = (^ [A:set_a,B:set_a]: (B = (sup_sup_set_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 14.28/4.23 thf(159,axiom,((! [A:a]: ~ (member_a @ A @ bot_bot_set_a))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_emptyE)). 14.28/4.23 thf(724,plain,((! [A:a]: ~ (member_a @ A @ bot_bot_set_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 14.28/4.23 thf(218,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ B @ C) => (ord_less_eq_int @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_pinf_I8_J)). 14.28/4.23 thf(917,plain,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ B @ C) => (ord_less_eq_int @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 14.28/4.23 thf(187,axiom,((! [A:a]: ((the_elem_a @ (insert_a @ A @ bot_bot_set_a)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_the__elem__eq)). 14.28/4.23 thf(802,plain,((! [A:a]: ((the_elem_a @ (insert_a @ A @ bot_bot_set_a)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 14.28/4.23 thf(204,axiom,((! [A:a]: ((collect_a @ (^ [B:a]: (B = A))) = (insert_a @ A @ bot_bot_set_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_singleton__conv)). 14.28/4.23 thf(853,plain,((! [A:a]: ((collect_a @ (^ [B:a]: (B = A))) = (insert_a @ A @ bot_bot_set_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 14.28/4.23 thf(212,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ C @ B) => (C != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_minf_I4_J)). 14.28/4.23 thf(881,plain,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ C @ B) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 14.28/4.23 thf(14,axiom,((! [A:(a > $o)]: (((collect_a @ A) = bot_bot_set_a) = (! [B:a]: ~ (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_Collect__empty__eq)). 14.28/4.23 thf(289,plain,((! [A:(a > $o)]: (((collect_a @ (A)) = bot_bot_set_a) = (! [B:a]: ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 14.28/4.23 thf(239,axiom,((binary1721989714Tree_a @ h @ t2)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_s2)). 14.28/4.23 thf(1013,plain,((binary1721989714Tree_a @ (h) @ t2)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 14.28/4.23 thf(175,axiom,((ord_less_eq_int = (^ [A:int,B:int]: ((sup_sup_int @ A @ B) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_sup_Oabsorb__iff2)). 14.28/4.23 thf(770,plain,(((ord_less_eq_int) = (^ [A:int,B:int]: ((sup_sup_int @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 14.28/4.23 thf(77,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ (sup_sup_int @ A @ C) @ B) <= (ord_less_eq_int @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_le__supI)). 14.28/4.23 thf(475,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ (sup_sup_int @ A @ C) @ B) | ~ (ord_less_eq_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 14.28/4.23 thf(25,axiom,((! [A:(set_a > (set_a > set_a)),B:set_a,C:set_a]: (((! [D:set_a,E:set_a]: (ord_less_eq_set_a @ E @ (A @ D @ E))) => ((! [D:set_a,E:set_a,F:set_a]: (((ord_less_eq_set_a @ F @ D) => (ord_less_eq_set_a @ (A @ E @ F) @ D)) <= (ord_less_eq_set_a @ E @ D))) => ((sup_sup_set_a @ B @ C) = (A @ B @ C)))) <= (! [D:set_a,E:set_a]: (ord_less_eq_set_a @ D @ (A @ D @ E)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_sup__unique)). 14.28/4.23 thf(321,plain,((! [A:(set_a > (set_a > set_a)),B:set_a,C:set_a]: (((! [D:set_a,E:set_a]: (ord_less_eq_set_a @ E @ (A @ D @ E))) => ((! [D:set_a,E:set_a,F:set_a]: (((ord_less_eq_set_a @ F @ D) => (ord_less_eq_set_a @ (A @ E @ F) @ D)) | ~ (ord_less_eq_set_a @ E @ D))) => ((sup_sup_set_a @ B @ C) = (A @ B @ C)))) | ~ (! [D:set_a,E:set_a]: (ord_less_eq_set_a @ D @ (A @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 14.28/4.23 thf(128,axiom,((! [A:int,B:int,C:int]: ((sup_sup_int @ (sup_sup_int @ A @ B) @ C) = (sup_sup_int @ A @ (sup_sup_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_sup__assoc)). 14.28/4.23 thf(623,plain,((! [A:int,B:int,C:int]: ((sup_sup_int @ (sup_sup_int @ A @ B) @ C) = (sup_sup_int @ A @ (sup_sup_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 14.28/4.23 thf(90,axiom,((! [A:int,B:int]: ((sup_sup_int @ A @ (sup_sup_int @ A @ B)) = (sup_sup_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_sup_Oleft__idem)). 14.28/4.23 thf(514,plain,((! [A:int,B:int]: ((sup_sup_int @ A @ (sup_sup_int @ A @ B)) = (sup_sup_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 14.28/4.23 thf(227,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ C @ A) <= (ord_less_int @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_minf_I5_J)). 14.28/4.23 thf(937,plain,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ C @ A) | ~ (ord_less_int @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 14.28/4.23 thf(110,axiom,((! [A:set_a]: ((sup_sup_set_a @ bot_bot_set_a @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_sup__bot_Oleft__neutral)). 14.28/4.23 thf(574,plain,((! [A:set_a]: ((sup_sup_set_a @ bot_bot_set_a @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 14.28/4.23 thf(36,axiom,((! [A:set_a,B:set_a,C:set_a,D:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ (sup_sup_set_a @ A @ C) @ (sup_sup_set_a @ B @ D)) <= (ord_less_eq_set_a @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_sup_Omono)). 14.28/4.23 thf(353,plain,((! [A:set_a,B:set_a,C:set_a,D:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ (sup_sup_set_a @ A @ C) @ (sup_sup_set_a @ B @ D)) | ~ (ord_less_eq_set_a @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 14.28/4.23 thf(209,axiom,((! [A:set_a,B:set_a,C:set_a,D:set_a]: ((A = (sup_sup_set_a @ B @ C)) => ((sup_sup_set_a @ D @ A) = (sup_sup_set_a @ B @ (sup_sup_set_a @ D @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_boolean__algebra__cancel_Osup2)). 14.28/4.23 thf(866,plain,((! [A:set_a,B:set_a,C:set_a,D:set_a]: ((A = (sup_sup_set_a @ B @ C)) => ((sup_sup_set_a @ D @ A) = (sup_sup_set_a @ B @ (sup_sup_set_a @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 14.28/4.23 thf(50,axiom,((! [A:set_a,B:set_a]: (ord_less_eq_set_a @ A @ (sup_sup_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_sup__ge1)). 14.28/4.23 thf(396,plain,((! [A:set_a,B:set_a]: (ord_less_eq_set_a @ A @ (sup_sup_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 14.28/4.23 thf(140,axiom,((! [A:a,B:a,C:set_a]: ((member_a @ A @ (insert_a @ B @ C)) => ((A != B) => (member_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_insertE)). 14.28/4.23 thf(660,plain,((! [A:a,B:a,C:set_a]: ((member_a @ A @ (insert_a @ B @ C)) => ((~ (A = B)) => (member_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 14.28/4.23 thf(56,axiom,((! [A:set_a]: ((collect_a @ (^ [B:a]: (member_a @ B @ A))) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_Collect__mem__eq)). 14.28/4.23 thf(411,plain,((! [A:set_a]: ((collect_a @ (^ [B:a]: (member_a @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 14.28/4.23 thf(5,axiom,((ord_less_eq_set_a = (^ [A:set_a,B:set_a]: ((sup_sup_set_a @ A @ B) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_subset__Un__eq)). 14.28/4.23 thf(265,plain,(((ord_less_eq_set_a) = (^ [A:set_a,B:set_a]: ((sup_sup_set_a @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 14.28/4.23 thf(22,axiom,((! [A:set_a,B:set_a]: (((sup_sup_set_a @ B @ A) = B) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_sup_Oabsorb1)). 14.28/4.23 thf(312,plain,((! [A:set_a,B:set_a]: (((sup_sup_set_a @ B @ A) = B) | ~ (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 14.28/4.23 thf(15,axiom,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ (sup_sup_set_a @ B @ C)) => (~ (! [D:set_a]: ((ord_less_eq_set_a @ D @ B) => (! [E:set_a]: ((A != (sup_sup_set_a @ D @ E)) <= (ord_less_eq_set_a @ E @ C))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_subset__UnE)). 14.28/4.23 thf(292,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ (sup_sup_set_a @ B @ C)) => (~ (! [D:set_a]: ((ord_less_eq_set_a @ D @ B) => (! [E:set_a]: (~ (A = (sup_sup_set_a @ D @ E)) | ~ (ord_less_eq_set_a @ E @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 14.28/4.23 thf(44,axiom,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ C @ B) => (ord_less_eq_set_a @ (sup_sup_set_a @ A @ C) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_sup__least)). 14.28/4.23 thf(380,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ C @ B) => (ord_less_eq_set_a @ (sup_sup_set_a @ A @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 14.28/4.23 thf(89,axiom,((! [A:int,B:int]: (ord_less_eq_int @ A @ (sup_sup_int @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_sup__ge2)). 14.28/4.23 thf(512,plain,((! [A:int,B:int]: (ord_less_eq_int @ A @ (sup_sup_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 14.28/4.23 thf(7,axiom,((! [A:set_a,B:set_a]: (ord_less_eq_set_a @ A @ (sup_sup_set_a @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_sup__ge2)). 14.28/4.23 thf(270,plain,((! [A:set_a,B:set_a]: (ord_less_eq_set_a @ A @ (sup_sup_set_a @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 14.28/4.23 thf(101,axiom,((sup_sup_set_a = (^ [A:set_a,B:set_a]: (sup_sup_set_a @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_sup__commute)). 14.28/4.23 thf(546,plain,(((sup_sup_set_a) = (^ [A:set_a,B:set_a]: (sup_sup_set_a @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 14.28/4.23 thf(190,axiom,((! [A:set_a]: ((? [B:a]: (member_a @ B @ A)) = (A != bot_bot_set_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_ex__in__conv)). 14.28/4.23 thf(810,plain,((! [A:set_a]: ((? [B:a]: (member_a @ B @ A)) = (~ (A = bot_bot_set_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 14.28/4.23 thf(97,axiom,((! [A:set_a,B:set_a]: ((sup_sup_set_a @ (sup_sup_set_a @ A @ B) @ B) = (sup_sup_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_sup_Oright__idem)). 14.28/4.23 thf(534,plain,((! [A:set_a,B:set_a]: ((sup_sup_set_a @ (sup_sup_set_a @ A @ B) @ B) = (sup_sup_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 14.28/4.23 thf(247,axiom,((! [A:(a > int),B:a]: ((binary1226383794sert_a @ A @ B @ binary476621312_Tip_a) = (binary717961607le_T_a @ binary476621312_Tip_a @ B @ binary476621312_Tip_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_binsert_Osimps_I1_J)). 14.28/4.23 thf(1047,plain,((! [A:(a > int),B:a]: ((binary1226383794sert_a @ (A) @ B @ binary476621312_Tip_a) = (binary717961607le_T_a @ binary476621312_Tip_a @ B @ binary476621312_Tip_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])). 14.28/4.23 thf(185,axiom,((sup_sup_int = (^ [A:int,B:int]: (sup_sup_int @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_sup__commute)). 14.28/4.23 thf(798,plain,(((sup_sup_int) = (^ [A:int,B:int]: (sup_sup_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 14.28/4.23 thf(167,axiom,((! [A:set_a]: ((sup_sup_set_a @ A @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_Un__absorb)). 14.28/4.23 thf(746,plain,((! [A:set_a]: ((sup_sup_set_a @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 14.28/4.23 thf(194,axiom,((! [A:set_a]: ((sup_sup_set_a @ A @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_sup__idem)). 14.28/4.23 thf(825,plain,((! [A:set_a]: ((sup_sup_set_a @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 14.28/4.23 thf(178,axiom,((! [A:int,B:int,C:int]: ((sup_sup_int @ (sup_sup_int @ A @ B) @ C) = (sup_sup_int @ A @ (sup_sup_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_sup_Oassoc)). 14.28/4.23 thf(778,plain,((! [A:int,B:int,C:int]: ((sup_sup_int @ (sup_sup_int @ A @ B) @ C) = (sup_sup_int @ A @ (sup_sup_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 14.28/4.23 thf(18,axiom,((! [A:(a > $o)]: ((bot_bot_set_a = (collect_a @ A)) = (! [B:a]: ~ (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_empty__Collect__eq)). 14.28/4.23 thf(302,plain,((! [A:(a > $o)]: ((bot_bot_set_a = (collect_a @ (A))) = (! [B:a]: ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 14.28/4.23 thf(16,axiom,((! [A:set_a,B:set_a,C:a]: ((ord_less_eq_set_a @ A @ B) => (ord_less_eq_set_a @ (insert_a @ C @ A) @ (insert_a @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_insert__mono)). 14.28/4.23 thf(297,plain,((! [A:set_a,B:set_a,C:a]: ((ord_less_eq_set_a @ A @ B) => (ord_less_eq_set_a @ (insert_a @ C @ A) @ (insert_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 14.28/4.23 thf(130,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ (sup_sup_int @ C @ B)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_sup_OcoboundedI2)). 14.28/4.23 thf(630,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ (sup_sup_int @ C @ B)) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 14.28/4.23 thf(62,axiom,((! [A:set_a,B:set_a]: (ord_less_eq_set_a @ A @ (sup_sup_set_a @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_sup_Ocobounded2)). 14.28/4.23 thf(429,plain,((! [A:set_a,B:set_a]: (ord_less_eq_set_a @ A @ (sup_sup_set_a @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 14.28/4.23 thf(9,axiom,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => ((sup_sup_set_a @ B @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_sup__absorb1)). 14.28/4.23 thf(275,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => ((sup_sup_set_a @ B @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 14.28/4.23 thf(161,axiom,((! [A:set_a,B:set_a]: (((sup_sup_set_a @ A @ B) = bot_bot_set_a) = ((B = bot_bot_set_a) & (A = bot_bot_set_a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_Un__empty)). 14.28/4.23 thf(729,plain,((! [A:set_a,B:set_a]: (((sup_sup_set_a @ A @ B) = bot_bot_set_a) = ((B = bot_bot_set_a) & (A = bot_bot_set_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 14.28/4.23 thf(3,axiom,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) <= (! [C:a]: ((member_a @ C @ B) <= (member_a @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_subsetI)). 14.28/4.23 thf(260,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) | ~ (! [C:a]: ((member_a @ C @ B) | ~ (member_a @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 14.28/4.23 thf(34,axiom,((ord_less_eq_set_a = (^ [A:set_a,B:set_a]: ((sup_sup_set_a @ A @ B) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_sup_Oabsorb__iff2)). 14.28/4.23 thf(349,plain,(((ord_less_eq_set_a) = (^ [A:set_a,B:set_a]: ((sup_sup_set_a @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 14.28/4.23 thf(211,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ B @ C) => (~ (ord_less_int @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_pinf_I5_J)). 14.28/4.23 thf(879,plain,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ B @ C) => (~ (ord_less_int @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 14.28/4.23 thf(26,axiom,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ C @ B) => (ord_less_eq_set_a @ (sup_sup_set_a @ A @ C) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_Un__least)). 14.28/4.23 thf(329,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ C @ B) => (ord_less_eq_set_a @ (sup_sup_set_a @ A @ C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 14.28/4.23 thf(142,axiom,((! [A:set_a,B:set_a,C:set_a]: ((sup_sup_set_a @ A @ (sup_sup_set_a @ B @ C)) = (sup_sup_set_a @ B @ (sup_sup_set_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_sup__left__commute)). 14.28/4.23 thf(665,plain,((! [A:set_a,B:set_a,C:set_a]: ((sup_sup_set_a @ A @ (sup_sup_set_a @ B @ C)) = (sup_sup_set_a @ B @ (sup_sup_set_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 14.28/4.23 thf(114,axiom,((! [A:binary1439146945Tree_a,B:(a > int)]: (((binary1721989714Tree_a @ B @ A) & (A != binary476621312_Tip_a)) => (binary1721989714Tree_a @ B @ (binary1217730267_wrm_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_wrm__sort)). 14.28/4.23 thf(583,plain,((! [A:binary1439146945Tree_a,B:(a > int)]: (((binary1721989714Tree_a @ (B) @ A) & ~ (A = binary476621312_Tip_a)) => (binary1721989714Tree_a @ (B) @ (binary1217730267_wrm_a @ (B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 14.28/4.23 thf(214,axiom,((t2 != binary476621312_Tip_a)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_t2nTip)). 14.28/4.23 thf(889,plain,((~ (t2 = binary476621312_Tip_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 14.28/4.23 thf(83,axiom,((! [A:a,B:set_a,C:set_a]: ((~ (member_a @ A @ B)) => ((~ (member_a @ A @ C)) => (((insert_a @ A @ B) = (insert_a @ A @ C)) = (B = C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_insert__ident)). 14.28/4.23 thf(493,plain,((! [A:a,B:set_a,C:set_a]: ((~ (member_a @ A @ B)) => ((~ (member_a @ A @ C)) => (((insert_a @ A @ B) = (insert_a @ A @ C)) = (B = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 14.28/4.23 thf(256,axiom,((! [A:(a > int),B:binary1439146945Tree_a,C:a,D:binary1439146945Tree_a]: ((binary1721989714Tree_a @ A @ (binary717961607le_T_a @ B @ C @ D)) = ((binary1721989714Tree_a @ A @ B) & ! [E:a]: ((member_a @ E @ (binary945792244etOf_a @ B)) => (ord_less_int @ (A @ E) @ (A @ C))) & (binary1721989714Tree_a @ A @ D) & ! [E:a]: ((ord_less_int @ (A @ C) @ (A @ E)) <= (member_a @ E @ (binary945792244etOf_a @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_sortedTree_Osimps_I2_J)). 14.28/4.23 thf(1079,plain,((! [A:(a > int),B:binary1439146945Tree_a,C:a,D:binary1439146945Tree_a]: ((binary1721989714Tree_a @ (A) @ (binary717961607le_T_a @ B @ C @ D)) = ((binary1721989714Tree_a @ (A) @ B) & ! [E:a]: ((member_a @ E @ (binary945792244etOf_a @ B)) => (ord_less_int @ (A @ E) @ (A @ C))) & (binary1721989714Tree_a @ (A) @ D) & ! [E:a]: ((ord_less_int @ (A @ C) @ (A @ E)) | ~ (member_a @ E @ (binary945792244etOf_a @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])). 14.28/4.23 thf(103,axiom,((! [A:(a > $o),B:a]: (((A @ B) => ((collect_a @ (^ [C:a]: ((A @ C) & (C = B)))) = (insert_a @ B @ bot_bot_set_a))) & (((collect_a @ (^ [C:a]: ((A @ C) & (C = B)))) = bot_bot_set_a) <= (~ (A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_Collect__conv__if)). 14.28/4.23 thf(551,plain,((! [A:(a > $o),B:a]: (((A @ B) => ((collect_a @ (^ [C:a]: ((A @ C) & (C = B)))) = (insert_a @ B @ bot_bot_set_a))) & (((collect_a @ (^ [C:a]: ((A @ C) & (C = B)))) = bot_bot_set_a) | (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 14.28/4.23 thf(13,axiom,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ B @ A) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_equalityD2)). 14.28/4.23 thf(285,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ B @ A) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 14.28/4.23 thf(202,axiom,((! [A:int,B:int]: ((B = (sup_sup_int @ B @ A)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_sup_OorderE)). 14.28/4.23 thf(847,plain,((! [A:int,B:int]: ((B = (sup_sup_int @ B @ A)) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 14.28/4.23 thf(107,axiom,((! [A:a,B:a]: (((insert_a @ A @ bot_bot_set_a) = (insert_a @ B @ bot_bot_set_a)) => (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_singleton__inject)). 14.28/4.23 thf(566,plain,((! [A:a,B:a]: (((insert_a @ A @ bot_bot_set_a) = (insert_a @ B @ bot_bot_set_a)) => (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 14.28/4.23 thf(80,axiom,((! [A:set_a,B:set_a]: ((sup_sup_set_a @ A @ (sup_sup_set_a @ A @ B)) = (sup_sup_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_sup__left__idem)). 14.28/4.23 thf(484,plain,((! [A:set_a,B:set_a]: ((sup_sup_set_a @ A @ (sup_sup_set_a @ A @ B)) = (sup_sup_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 14.28/4.23 thf(125,axiom,((! [A:a]: ~ (member_a @ A @ bot_bot_set_a))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_empty__iff)). 14.28/4.23 thf(615,plain,((! [A:a]: ~ (member_a @ A @ bot_bot_set_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 14.28/4.23 thf(53,axiom,((! [A:set_a,B:a]: (ord_less_eq_set_a @ A @ (insert_a @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_subset__insertI)). 14.28/4.23 thf(403,plain,((! [A:set_a,B:a]: (ord_less_eq_set_a @ A @ (insert_a @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 14.28/4.23 thf(37,axiom,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ (sup_sup_set_a @ A @ B) @ C) = ((ord_less_eq_set_a @ B @ C) & (ord_less_eq_set_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_le__sup__iff)). 14.28/4.23 thf(356,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ (sup_sup_set_a @ A @ B) @ C) = ((ord_less_eq_set_a @ B @ C) & (ord_less_eq_set_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 14.28/4.23 thf(59,axiom,((! [A:(a > $o),B:(a > $o)]: ((collect_a @ (^ [C:a]: ((A @ C) | (B @ C)))) = (sup_sup_set_a @ (collect_a @ A) @ (collect_a @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_Collect__disj__eq)). 14.28/4.23 thf(420,plain,((! [A:(a > $o),B:(a > $o)]: ((collect_a @ (^ [C:a]: ((A @ C) | (B @ C)))) = (sup_sup_set_a @ (collect_a @ (A)) @ (collect_a @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 14.28/4.23 thf(257,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((C != A) <= (ord_less_int @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_minf_I3_J)). 14.28/4.23 thf(1082,plain,((! [A:int]: ? [B:int]: ! [C:int]: (~ (C = A) | ~ (ord_less_int @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])). 14.28/4.23 thf(224,axiom,(((binary339557810e_rm_a @ h @ (binary717961607le_T_a @ t1 @ x @ t2)) = (binary339557810e_rm_a @ h @ t2))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_rm__res)). 14.28/4.23 thf(933,plain,(((binary339557810e_rm_a @ (h) @ (binary717961607le_T_a @ t1 @ x @ t2)) = (binary339557810e_rm_a @ (h) @ t2))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 14.28/4.23 thf(98,axiom,((! [A:(a > int),B:binary1439146945Tree_a,C:a]: ((binary1721989714Tree_a @ A @ (binary1226383794sert_a @ A @ C @ B)) <= (binary1721989714Tree_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_binsert__sorted)). 14.28/4.23 thf(537,plain,((! [A:(a > int),B:binary1439146945Tree_a,C:a]: ((binary1721989714Tree_a @ (A) @ (binary1226383794sert_a @ (A) @ C @ B)) | ~ (binary1721989714Tree_a @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 14.28/4.23 thf(134,axiom,((! [A:set_a,B:set_a]: ((bot_bot_set_a = (sup_sup_set_a @ A @ B)) = ((A = bot_bot_set_a) & (B = bot_bot_set_a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_bot__eq__sup__iff)). 14.28/4.23 thf(642,plain,((! [A:set_a,B:set_a]: ((bot_bot_set_a = (sup_sup_set_a @ A @ B)) = ((A = bot_bot_set_a) & (B = bot_bot_set_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 14.28/4.23 thf(241,axiom,((! [A:binary1439146945Tree_a,B:a,C:binary1439146945Tree_a]: ((binary945792244etOf_a @ (binary717961607le_T_a @ A @ B @ C)) = (sup_sup_set_a @ (sup_sup_set_a @ (binary945792244etOf_a @ A) @ (binary945792244etOf_a @ C)) @ (insert_a @ B @ bot_bot_set_a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_setOf_Osimps_I2_J)). 14.28/4.23 thf(1016,plain,((! [A:binary1439146945Tree_a,B:a,C:binary1439146945Tree_a]: ((binary945792244etOf_a @ (binary717961607le_T_a @ A @ B @ C)) = (sup_sup_set_a @ (sup_sup_set_a @ (binary945792244etOf_a @ A) @ (binary945792244etOf_a @ C)) @ (insert_a @ B @ bot_bot_set_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 14.28/4.23 thf(146,axiom,((! [A:a,B:set_a]: ((~ (! [C:set_a]: ((B = (insert_a @ A @ C)) => (member_a @ A @ C)))) <= (member_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_Set_Oset__insert)). 14.28/4.23 thf(679,plain,((! [A:a,B:set_a]: (~ (! [C:set_a]: ((B = (insert_a @ A @ C)) => (member_a @ A @ C))) | ~ (member_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 14.28/4.23 thf(153,axiom,((! [A:a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ (insert_a @ A @ B) @ C) = ((member_a @ A @ C) & (ord_less_eq_set_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_insert__subset)). 14.28/4.23 thf(706,plain,((! [A:a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ (insert_a @ A @ B) @ C) = ((member_a @ A @ C) & (ord_less_eq_set_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 14.28/4.23 thf(49,axiom,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ (sup_sup_set_a @ C @ B)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_le__supI2)). 14.28/4.23 thf(393,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ (sup_sup_set_a @ C @ B)) | ~ (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 14.28/4.23 thf(234,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_eq_int @ C @ A) <= (ord_less_int @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_minf_I6_J)). 14.28/4.23 thf(985,plain,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_eq_int @ C @ A) | ~ (ord_less_int @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 14.28/4.23 thf(164,axiom,((! [A:set_a,B:set_a,C:set_a]: ((sup_sup_set_a @ (sup_sup_set_a @ A @ B) @ C) = (sup_sup_set_a @ A @ (sup_sup_set_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_Un__assoc)). 14.28/4.23 thf(738,plain,((! [A:set_a,B:set_a,C:set_a]: ((sup_sup_set_a @ (sup_sup_set_a @ A @ B) @ C) = (sup_sup_set_a @ A @ (sup_sup_set_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 14.28/4.23 thf(138,axiom,((! [A:int,B:int]: ((sup_sup_int @ A @ (sup_sup_int @ A @ B)) = (sup_sup_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_sup__left__idem)). 14.28/4.23 thf(654,plain,((! [A:int,B:int]: ((sup_sup_int @ A @ (sup_sup_int @ A @ B)) = (sup_sup_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 14.28/4.23 thf(158,axiom,((! [A:set_a]: ((sup_sup_set_a @ A @ bot_bot_set_a) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_sup__bot_Oright__neutral)). 14.28/4.23 thf(721,plain,((! [A:set_a]: ((sup_sup_set_a @ A @ bot_bot_set_a) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 14.28/4.23 thf(108,axiom,((! [A:int,B:int]: (ord_less_eq_int @ A @ (sup_sup_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_inf__sup__ord_I3_J)). 14.28/4.23 thf(569,plain,((! [A:int,B:int]: (ord_less_eq_int @ A @ (sup_sup_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 14.28/4.23 thf(86,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (sup_sup_int @ A @ B) @ C) => (~ ((~ (ord_less_eq_int @ B @ C)) <= (ord_less_eq_int @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_le__supE)). 14.28/4.23 thf(503,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (sup_sup_int @ A @ B) @ C) => (~ (~ (ord_less_eq_int @ B @ C) | ~ (ord_less_eq_int @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 14.28/4.23 thf(252,axiom,((! [A:(int > $o),B:(int > $o),C:(int > $o),D:(int > $o)]: (((? [E:int]: ! [F:int]: (((C @ F) = (D @ F)) <= (ord_less_int @ E @ F))) => (? [E:int]: ! [F:int]: ((((A @ F) & (C @ F)) = ((D @ F) & (B @ F))) <= (ord_less_int @ E @ F)))) <= (? [E:int]: ! [F:int]: (((A @ F) = (B @ F)) <= (ord_less_int @ E @ F)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_pinf_I1_J)). 14.28/4.23 thf(1060,plain,((! [A:(int > $o),B:(int > $o),C:(int > $o),D:(int > $o)]: (((? [E:int]: ! [F:int]: (((C @ F) = (D @ F)) | ~ (ord_less_int @ E @ F))) => (? [E:int]: ! [F:int]: ((((A @ F) & (C @ F)) = ((D @ F) & (B @ F))) | ~ (ord_less_int @ E @ F)))) | ~ (? [E:int]: ! [F:int]: (((A @ F) = (B @ F)) | ~ (ord_less_int @ E @ F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])). 14.28/4.23 thf(248,axiom,((! [A:int,B:int]: ((A != B) => ((ord_less_int @ B @ A) <= (~ (ord_less_int @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_linorder__neqE__linordered__idom)). 14.28/4.23 thf(1050,plain,((! [A:int,B:int]: ((~ (A = B)) => ((ord_less_int @ B @ A) | (ord_less_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])). 14.28/4.23 thf(72,axiom,((! [A:int,B:int]: (ord_less_eq_int @ A @ (sup_sup_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_sup__ge1)). 14.28/4.23 thf(457,plain,((! [A:int,B:int]: (ord_less_eq_int @ A @ (sup_sup_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 14.28/4.23 thf(31,axiom,((ord_less_eq_set_a = (^ [A:set_a,B:set_a]: ! [C:a]: ((member_a @ C @ A) => (member_a @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_subset__eq)). 14.28/4.23 thf(343,plain,(((ord_less_eq_set_a) = (^ [A:set_a,B:set_a]: ! [C:a]: ((member_a @ C @ A) => (member_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 14.28/4.23 thf(183,axiom,((! [A:a,B:a,C:set_a]: (((insert_a @ A @ bot_bot_set_a) = (insert_a @ B @ C)) = ((B = A) & (ord_less_eq_set_a @ C @ (insert_a @ A @ bot_bot_set_a)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_singleton__insert__inj__eq)). 14.28/4.23 thf(792,plain,((! [A:a,B:a,C:set_a]: (((insert_a @ A @ bot_bot_set_a) = (insert_a @ B @ C)) = ((B = A) & (ord_less_eq_set_a @ C @ (insert_a @ A @ bot_bot_set_a)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 14.28/4.23 thf(258,axiom,((member_a @ l @ (sup_sup_set_a @ (sup_sup_set_a @ (insert_a @ x @ bot_bot_set_a) @ (binary945792244etOf_a @ t1)) @ (binary945792244etOf_a @ (binary1217730267_wrm_a @ h @ t2))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_l__scope)). 14.28/4.23 thf(1086,plain,((member_a @ l @ (sup_sup_set_a @ (sup_sup_set_a @ (insert_a @ x @ bot_bot_set_a) @ (binary945792244etOf_a @ t1)) @ (binary945792244etOf_a @ (binary1217730267_wrm_a @ (h) @ t2))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])). 14.28/4.23 thf(131,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ (sup_sup_int @ A @ C) @ B) <= (ord_less_eq_int @ C @ B)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_sup__least)). 14.28/4.23 thf(633,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (sup_sup_int @ A @ C) @ B) | ~ (ord_less_eq_int @ C @ B) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 14.28/4.23 thf(188,axiom,((! [A:set_a,B:set_a]: ((sup_sup_set_a @ A @ (sup_sup_set_a @ A @ B)) = (sup_sup_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_inf__sup__aci_I8_J)). 14.28/4.23 thf(805,plain,((! [A:set_a,B:set_a]: ((sup_sup_set_a @ A @ (sup_sup_set_a @ A @ B)) = (sup_sup_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 14.28/4.23 thf(139,axiom,((! [A:set_a,B:set_a,C:a]: (((sup_sup_set_a @ A @ B) = (insert_a @ C @ bot_bot_set_a)) = (((A = (insert_a @ C @ bot_bot_set_a)) & (B = bot_bot_set_a)) | ((B = (insert_a @ C @ bot_bot_set_a)) & (A = (insert_a @ C @ bot_bot_set_a))) | ((B = (insert_a @ C @ bot_bot_set_a)) & (A = bot_bot_set_a)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_Un__singleton__iff)). 14.28/4.23 thf(657,plain,((! [A:set_a,B:set_a,C:a]: (((sup_sup_set_a @ A @ B) = (insert_a @ C @ bot_bot_set_a)) = (((A = (insert_a @ C @ bot_bot_set_a)) & (B = bot_bot_set_a)) | ((B = (insert_a @ C @ bot_bot_set_a)) & (A = (insert_a @ C @ bot_bot_set_a))) | ((B = (insert_a @ C @ bot_bot_set_a)) & (A = bot_bot_set_a)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 14.28/4.23 thf(250,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ B @ C) => (C != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_pinf_I4_J)). 14.28/4.23 thf(1054,plain,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ B @ C) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])). 14.28/4.23 thf(51,axiom,((! [A:set_a,B:set_a,C:a]: ((ord_less_eq_set_a @ A @ B) => ((member_a @ C @ A) => (member_a @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_in__mono)). 14.28/4.23 thf(398,plain,((! [A:set_a,B:set_a,C:a]: ((ord_less_eq_set_a @ A @ B) => ((member_a @ C @ A) => (member_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 14.28/4.23 thf(104,axiom,((! [A:a,B:set_a,C:set_a]: (((~ (member_a @ A @ B)) => (member_a @ A @ C)) <= (member_a @ A @ (sup_sup_set_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_UnE)). 14.28/4.23 thf(558,plain,((! [A:a,B:set_a,C:set_a]: (((~ (member_a @ A @ B)) => (member_a @ A @ C)) | ~ (member_a @ A @ (sup_sup_set_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 14.28/4.23 thf(145,axiom,((! [A:set_a,B:a]: ((A = bot_bot_set_a) => (~ (member_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_equals0D)). 14.28/4.23 thf(674,plain,((! [A:set_a,B:a]: ((A = bot_bot_set_a) => (~ (member_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 14.28/4.23 thf(115,axiom,((! [A:int]: ((sup_sup_int @ A @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_sup__idem)). 14.28/4.23 thf(586,plain,((! [A:int]: ((sup_sup_int @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 14.28/4.23 thf(157,axiom,((! [A:a,B:set_a,C:set_a]: ((member_a @ A @ B) => (member_a @ A @ (sup_sup_set_a @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_UnI2)). 14.28/4.23 thf(718,plain,((! [A:a,B:set_a,C:set_a]: ((member_a @ A @ B) => (member_a @ A @ (sup_sup_set_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 14.28/4.23 thf(126,axiom,((! [A:int]: (ord_less_eq_int @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_order__refl)). 14.28/4.23 thf(618,plain,((! [A:int]: (ord_less_eq_int @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 14.28/4.23 thf(205,axiom,((sup_sup_set_a = (^ [A:set_a,B:set_a]: (sup_sup_set_a @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_sup_Ocommute)). 14.28/4.23 thf(856,plain,(((sup_sup_set_a) = (^ [A:set_a,B:set_a]: (sup_sup_set_a @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 14.28/4.23 thf(68,axiom,((! [A:set_a,B:set_a,C:a]: ((ord_less_eq_set_a @ A @ B) => (ord_less_eq_set_a @ A @ (insert_a @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_subset__insertI2)). 14.28/4.23 thf(444,plain,((! [A:set_a,B:set_a,C:a]: ((ord_less_eq_set_a @ A @ B) => (ord_less_eq_set_a @ A @ (insert_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 14.28/4.23 thf(42,axiom,((ord_less_eq_set_a = (^ [A:set_a,B:set_a]: ! [C:a]: ((member_a @ C @ B) <= (member_a @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_subset__iff)). 14.28/4.23 thf(375,plain,(((ord_less_eq_set_a) = (^ [A:set_a,B:set_a]: ! [C:a]: ((member_a @ C @ B) | ~ (member_a @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 14.28/4.23 thf(121,axiom,((sup_sup_set_a = (^ [A:set_a,B:set_a]: (sup_sup_set_a @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_inf__sup__aci_I5_J)). 14.28/4.23 thf(601,plain,(((sup_sup_set_a) = (^ [A:set_a,B:set_a]: (sup_sup_set_a @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 14.28/4.23 thf(60,axiom,((! [A:(a > $o),B:(a > $o)]: ((ord_less_eq_set_a @ (collect_a @ A) @ (collect_a @ B)) = (! [C:a]: ((B @ C) <= (A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_Collect__mono__iff)). 14.28/4.23 thf(423,plain,((! [A:(a > $o),B:(a > $o)]: ((ord_less_eq_set_a @ (collect_a @ (A)) @ (collect_a @ (B))) = (! [C:a]: ((B @ C) | ~ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 14.28/4.23 thf(162,axiom,((! [A:a,B:set_a,C:set_a]: ((sup_sup_set_a @ (insert_a @ A @ B) @ C) = (insert_a @ A @ (sup_sup_set_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_Un__insert__left)). 14.28/4.23 thf(732,plain,((! [A:a,B:set_a,C:set_a]: ((sup_sup_set_a @ (insert_a @ A @ B) @ C) = (insert_a @ A @ (sup_sup_set_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 14.28/4.23 thf(176,axiom,((! [A:a,B:set_a,C:set_a]: ((member_a @ A @ (sup_sup_set_a @ C @ B)) <= ((member_a @ A @ C) <= (~ (member_a @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_UnCI)). 14.28/4.23 thf(772,plain,((! [A:a,B:set_a,C:set_a]: ((member_a @ A @ (sup_sup_set_a @ C @ B)) | ~ ((member_a @ A @ C) | (member_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 14.28/4.23 thf(111,axiom,((! [A:a,B:set_a]: (member_a @ A @ (insert_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_insertI1)). 14.28/4.23 thf(577,plain,((! [A:a,B:set_a]: (member_a @ A @ (insert_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 14.28/4.23 thf(112,axiom,((sup_sup_set_a = (^ [A:set_a,B:set_a]: (collect_a @ (^ [C:a]: ((member_a @ C @ B) | (member_a @ C @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_Un__def)). 14.28/4.23 thf(579,plain,(((sup_sup_set_a) = (^ [A:set_a,B:set_a]: (collect_a @ (^ [C:a]: ((member_a @ C @ B) | (member_a @ C @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 14.28/4.23 thf(11,axiom,((ord_less_eq_set_a = (^ [A:set_a,B:set_a]: ((sup_sup_set_a @ B @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_sup_Oabsorb__iff1)). 14.28/4.23 thf(281,plain,(((ord_less_eq_set_a) = (^ [A:set_a,B:set_a]: ((sup_sup_set_a @ B @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 14.28/4.23 thf(1,conjecture,((ord_less_int @ (h @ l) @ (h @ (binary339557810e_rm_a @ h @ (binary717961607le_T_a @ t1 @ x @ t2))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)). 14.28/4.23 thf(2,negated_conjecture,((~ (ord_less_int @ (h @ l) @ (h @ (binary339557810e_rm_a @ h @ (binary717961607le_T_a @ t1 @ x @ t2)))))),inference(neg_conjecture,[status(cth)],[1])). 14.28/4.23 thf(259,plain,((~ (ord_less_int @ (h @ l) @ (h @ (binary339557810e_rm_a @ (h) @ (binary717961607le_T_a @ t1 @ x @ t2)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 14.28/4.23 thf(48,axiom,((ord_less_eq_set_a = (^ [A:set_a,B:set_a]: ((sup_sup_set_a @ A @ B) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_le__iff__sup)). 14.28/4.23 thf(391,plain,(((ord_less_eq_set_a) = (^ [A:set_a,B:set_a]: ((sup_sup_set_a @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 14.28/4.23 thf(226,axiom,((member_a @ l @ (binary945792244etOf_a @ (binary1217730267_wrm_a @ h @ (binary717961607le_T_a @ t1 @ x @ t2))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_ldef)). 14.28/4.23 thf(936,plain,((member_a @ l @ (binary945792244etOf_a @ (binary1217730267_wrm_a @ (h) @ (binary717961607le_T_a @ t1 @ x @ t2))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 14.28/4.23 thf(181,axiom,((! [A:(a > int),B:a]: ((binary1804682569move_a @ A @ B @ binary476621312_Tip_a) = binary476621312_Tip_a))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_remove_Osimps_I1_J)). 14.28/4.23 thf(787,plain,((! [A:(a > int),B:a]: ((binary1804682569move_a @ (A) @ B @ binary476621312_Tip_a) = binary476621312_Tip_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 14.28/4.23 thf(251,axiom,((ord_less_int = (^ [A:int,B:int]: ((B = (sup_sup_int @ B @ A)) & (B != A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_sup_Ostrict__order__iff)). 14.28/4.23 thf(1058,plain,(((ord_less_int) = (^ [A:int,B:int]: ((B = (sup_sup_int @ B @ A)) & ~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])). 14.28/4.23 thf(28,axiom,((! [A:set_a,B:set_a,C:set_a]: (((ord_less_eq_set_a @ C @ B) => (ord_less_eq_set_a @ (sup_sup_set_a @ A @ C) @ B)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_sup_OboundedI)). 14.28/4.23 thf(335,plain,((! [A:set_a,B:set_a,C:set_a]: (((ord_less_eq_set_a @ C @ B) => (ord_less_eq_set_a @ (sup_sup_set_a @ A @ C) @ B)) | ~ (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 14.28/4.23 thf(219,axiom,((! [A:binary1439146945Tree_a,B:(a > int)]: ((member_a @ (binary339557810e_rm_a @ B @ A) @ (binary945792244etOf_a @ A)) <= ((binary1721989714Tree_a @ B @ A) & (A != binary476621312_Tip_a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_rm__set)). 14.28/4.23 thf(919,plain,((! [A:binary1439146945Tree_a,B:(a > int)]: ((member_a @ (binary339557810e_rm_a @ (B) @ A) @ (binary945792244etOf_a @ A)) | ~ ((binary1721989714Tree_a @ (B) @ A) & ~ (A = binary476621312_Tip_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 14.28/4.23 thf(99,axiom,((! [A:a,B:set_a,C:a]: (((insert_a @ A @ B) = (insert_a @ C @ bot_bot_set_a)) = ((A = C) & (ord_less_eq_set_a @ B @ (insert_a @ C @ bot_bot_set_a)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_singleton__insert__inj__eq_H)). 14.28/4.23 thf(540,plain,((! [A:a,B:set_a,C:a]: (((insert_a @ A @ B) = (insert_a @ C @ bot_bot_set_a)) = ((A = C) & (ord_less_eq_set_a @ B @ (insert_a @ C @ bot_bot_set_a)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 14.28/4.23 thf(173,axiom,((! [A:set_a]: ((sup_sup_set_a @ A @ bot_bot_set_a) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_Un__empty__right)). 14.28/4.23 thf(764,plain,((! [A:set_a]: ((sup_sup_set_a @ A @ bot_bot_set_a) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 14.28/4.23 thf(216,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ (sup_sup_int @ B @ C)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_sup_Ostrict__coboundedI1)). 14.28/4.23 thf(900,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ (sup_sup_int @ B @ C)) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 14.28/4.23 thf(196,axiom,((! [A:int,B:int]: (ord_less_eq_int @ A @ (sup_sup_int @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_sup_Ocobounded2)). 14.28/4.23 thf(831,plain,((! [A:int,B:int]: (ord_less_eq_int @ A @ (sup_sup_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 14.28/4.23 thf(180,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ A @ (sup_sup_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_le__supI1)). 14.28/4.23 thf(784,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ A @ (sup_sup_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 14.28/4.23 thf(39,axiom,((! [A:a,B:(a > $o)]: ((member_a @ A @ (collect_a @ B)) = (B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_mem__Collect__eq)). 14.28/4.23 thf(362,plain,((! [A:a,B:(a > $o)]: ((member_a @ A @ (collect_a @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 14.28/4.23 thf(24,axiom,((! [A:set_a,B:set_a,C:a]: (((member_a @ C @ A) => (member_a @ C @ B)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_subsetD)). 14.28/4.23 thf(318,plain,((! [A:set_a,B:set_a,C:a]: (((member_a @ C @ A) => (member_a @ C @ B)) | ~ (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 14.28/4.23 thf(120,axiom,((! [A:(a > int)]: (binary1721989714Tree_a @ A @ binary476621312_Tip_a))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_sortedTree_Osimps_I1_J)). 14.28/4.23 thf(599,plain,((! [A:(a > int)]: (binary1721989714Tree_a @ (A) @ binary476621312_Tip_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 14.28/4.23 thf(43,axiom,((! [A:a,B:(a > $o)]: ((insert_a @ A @ (collect_a @ B)) = (collect_a @ (^ [C:a]: ((C != A) => (B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_insert__Collect)). 14.28/4.23 thf(377,plain,((! [A:a,B:(a > $o)]: ((insert_a @ A @ (collect_a @ (B))) = (collect_a @ (^ [C:a]: ((~ (C = A)) => (B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 14.28/4.23 thf(236,axiom,((! [A:(int > $o),B:(int > $o),C:(int > $o),D:(int > $o)]: (((? [E:int]: ! [F:int]: (((C @ F) = (D @ F)) <= (ord_less_int @ E @ F))) => (? [E:int]: ! [F:int]: ((ord_less_int @ E @ F) => (((A @ F) | (C @ F)) = ((D @ F) | (B @ F)))))) <= (? [E:int]: ! [F:int]: (((A @ F) = (B @ F)) <= (ord_less_int @ E @ F)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_pinf_I2_J)). 14.28/4.23 thf(990,plain,((! [A:(int > $o),B:(int > $o),C:(int > $o),D:(int > $o)]: (((? [E:int]: ! [F:int]: (((C @ F) = (D @ F)) | ~ (ord_less_int @ E @ F))) => (? [E:int]: ! [F:int]: ((ord_less_int @ E @ F) => (((A @ F) | (C @ F)) = ((D @ F) | (B @ F)))))) | ~ (? [E:int]: ! [F:int]: (((A @ F) = (B @ F)) | ~ (ord_less_int @ E @ F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 14.28/4.23 thf(88,axiom,((! [A:set_a,B:set_a,C:set_a]: ((sup_sup_set_a @ A @ (sup_sup_set_a @ B @ C)) = (sup_sup_set_a @ B @ (sup_sup_set_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_Un__left__commute)). 14.28/4.23 thf(509,plain,((! [A:set_a,B:set_a,C:set_a]: ((sup_sup_set_a @ A @ (sup_sup_set_a @ B @ C)) = (sup_sup_set_a @ B @ (sup_sup_set_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 14.28/4.23 thf(64,axiom,((! [A:set_a,B:set_a,C:set_a,D:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ C @ D) => (ord_less_eq_set_a @ (sup_sup_set_a @ A @ C) @ (sup_sup_set_a @ B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_sup__mono)). 14.28/4.23 thf(434,plain,((! [A:set_a,B:set_a,C:set_a,D:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ C @ D) => (ord_less_eq_set_a @ (sup_sup_set_a @ A @ C) @ (sup_sup_set_a @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 14.28/4.23 thf(171,axiom,((! [A:int,B:int]: (ord_less_eq_int @ A @ (sup_sup_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_sup_Ocobounded1)). 14.28/4.23 thf(758,plain,((! [A:int,B:int]: (ord_less_eq_int @ A @ (sup_sup_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 14.28/4.23 thf(118,axiom,((! [A:a,B:set_a,C:set_a]: ((member_a @ A @ (sup_sup_set_a @ B @ C)) = ((member_a @ A @ B) | (member_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Un__iff)). 14.28/4.23 thf(594,plain,((! [A:a,B:set_a,C:set_a]: ((member_a @ A @ (sup_sup_set_a @ B @ C)) = ((member_a @ A @ B) | (member_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 14.28/4.23 thf(129,axiom,((! [A:a,B:set_a]: ((insert_a @ A @ B) != bot_bot_set_a))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_insert__not__empty)). 14.28/4.23 thf(626,plain,((! [A:a,B:set_a]: ~ ((insert_a @ A @ B) = bot_bot_set_a))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 14.28/4.23 thf(243,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ A @ C) <= (ord_less_int @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_pinf_I7_J)). 14.28/4.23 thf(1022,plain,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ A @ C) | ~ (ord_less_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 14.28/4.23 thf(143,axiom,((! [A:int,B:int]: ((sup_sup_int @ (sup_sup_int @ A @ B) @ B) = (sup_sup_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_sup_Oright__idem)). 14.28/4.23 thf(668,plain,((! [A:int,B:int]: ((sup_sup_int @ (sup_sup_int @ A @ B) @ B) = (sup_sup_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 14.28/4.23 thf(74,axiom,((! [A:set_a,B:set_a,C:set_a]: ((sup_sup_set_a @ (sup_sup_set_a @ A @ B) @ C) = (sup_sup_set_a @ A @ (sup_sup_set_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_inf__sup__aci_I6_J)). 14.28/4.23 thf(462,plain,((! [A:set_a,B:set_a,C:set_a]: ((sup_sup_set_a @ (sup_sup_set_a @ A @ B) @ C) = (sup_sup_set_a @ A @ (sup_sup_set_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 14.28/4.23 thf(32,axiom,((((=) @ set_a) = (^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ B @ A) & (ord_less_eq_set_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_set__eq__subset)). 14.28/4.23 thf(345,plain,((((=) @ set_a) = (^ [A:set_a,B:set_a]: ((ord_less_eq_set_a @ B @ A) & (ord_less_eq_set_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 14.28/4.23 thf(206,axiom,((! [A:a,B:set_a,C:set_a]: ((member_a @ A @ (sup_sup_set_a @ B @ C)) <= (member_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_UnI1)). 14.28/4.23 thf(858,plain,((! [A:a,B:set_a,C:set_a]: ((member_a @ A @ (sup_sup_set_a @ B @ C)) | ~ (member_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 14.28/4.23 thf(151,axiom,((! [A:set_a,B:set_a,C:set_a]: ((sup_sup_set_a @ A @ (sup_sup_set_a @ B @ C)) = (sup_sup_set_a @ B @ (sup_sup_set_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_inf__sup__aci_I7_J)). 14.28/4.23 thf(700,plain,((! [A:set_a,B:set_a,C:set_a]: ((sup_sup_set_a @ A @ (sup_sup_set_a @ B @ C)) = (sup_sup_set_a @ B @ (sup_sup_set_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 14.28/4.23 thf(92,axiom,((! [A:int]: ((sup_sup_int @ A @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_sup_Oidem)). 14.28/4.23 thf(520,plain,((! [A:int]: ((sup_sup_int @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 14.28/4.23 thf(233,axiom,((! [A:(a > int),B:binary1439146945Tree_a,C:a,D:binary1439146945Tree_a]: ((binary1721989714Tree_a @ A @ (binary717961607le_T_a @ B @ C @ D)) => (binary1721989714Tree_a @ A @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_sortLemmaR)). 14.28/4.23 thf(983,plain,((! [A:(a > int),B:binary1439146945Tree_a,C:a,D:binary1439146945Tree_a]: ((binary1721989714Tree_a @ (A) @ (binary717961607le_T_a @ B @ C @ D)) => (binary1721989714Tree_a @ (A) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 14.28/4.23 thf(132,axiom,((! [A:a,B:set_a,C:set_a]: (((insert_a @ A @ bot_bot_set_a) = (sup_sup_set_a @ B @ C)) = (((B = bot_bot_set_a) & (C = (insert_a @ A @ bot_bot_set_a))) | ((C = bot_bot_set_a) & (B = (insert_a @ A @ bot_bot_set_a))) | ((C = (insert_a @ A @ bot_bot_set_a)) & (B = (insert_a @ A @ bot_bot_set_a))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_singleton__Un__iff)). 14.28/4.23 thf(636,plain,((! [A:a,B:set_a,C:set_a]: (((insert_a @ A @ bot_bot_set_a) = (sup_sup_set_a @ B @ C)) = (((B = bot_bot_set_a) & (C = (insert_a @ A @ bot_bot_set_a))) | ((C = bot_bot_set_a) & (B = (insert_a @ A @ bot_bot_set_a))) | ((C = (insert_a @ A @ bot_bot_set_a)) & (B = (insert_a @ A @ bot_bot_set_a))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 14.28/4.23 thf(10,axiom,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ (sup_sup_set_a @ A @ B) @ C) = ((ord_less_eq_set_a @ B @ C) & (ord_less_eq_set_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_sup_Obounded__iff)). 14.28/4.23 thf(278,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ (sup_sup_set_a @ A @ B) @ C) = ((ord_less_eq_set_a @ B @ C) & (ord_less_eq_set_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 14.28/4.23 thf(123,axiom,((! [A:set_a]: ((! [B:a]: ~ (member_a @ B @ A)) => (A = bot_bot_set_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_equals0I)). 14.28/4.23 thf(608,plain,((! [A:set_a]: ((! [B:a]: ~ (member_a @ B @ A)) => (A = bot_bot_set_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 14.28/4.23 thf(106,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (sup_sup_int @ A @ B) @ C) => (~ ((~ (ord_less_eq_int @ B @ C)) <= (ord_less_eq_int @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_sup_OboundedE)). 14.28/4.23 thf(563,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (sup_sup_int @ A @ B) @ C) => (~ (~ (ord_less_eq_int @ B @ C) | ~ (ord_less_eq_int @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 14.28/4.23 thf(237,axiom,((! [A:(a > int),B:a,C:a,D:binary1439146945Tree_a,E:binary1439146945Tree_a]: (((ord_less_int @ (A @ B) @ (A @ C)) => ((binary1226383794sert_a @ A @ B @ (binary717961607le_T_a @ D @ C @ E)) = (binary717961607le_T_a @ (binary1226383794sert_a @ A @ B @ D) @ C @ E))) & ((((ord_less_int @ (A @ C) @ (A @ B)) => ((binary1226383794sert_a @ A @ B @ (binary717961607le_T_a @ D @ C @ E)) = (binary717961607le_T_a @ D @ C @ (binary1226383794sert_a @ A @ B @ E)))) & (((binary1226383794sert_a @ A @ B @ (binary717961607le_T_a @ D @ C @ E)) = (binary717961607le_T_a @ D @ B @ E)) <= (~ (ord_less_int @ (A @ C) @ (A @ B))))) <= (~ (ord_less_int @ (A @ B) @ (A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_binsert_Osimps_I2_J)). 14.28/4.23 thf(1000,plain,((! [A:(a > int),B:a,C:a,D:binary1439146945Tree_a,E:binary1439146945Tree_a]: (((ord_less_int @ (A @ B) @ (A @ C)) => ((binary1226383794sert_a @ (A) @ B @ (binary717961607le_T_a @ D @ C @ E)) = (binary717961607le_T_a @ (binary1226383794sert_a @ (A) @ B @ D) @ C @ E))) & ((((ord_less_int @ (A @ C) @ (A @ B)) => ((binary1226383794sert_a @ (A) @ B @ (binary717961607le_T_a @ D @ C @ E)) = (binary717961607le_T_a @ D @ C @ (binary1226383794sert_a @ (A) @ B @ E)))) & (((binary1226383794sert_a @ (A) @ B @ (binary717961607le_T_a @ D @ C @ E)) = (binary717961607le_T_a @ D @ B @ E)) | (ord_less_int @ (A @ C) @ (A @ B)))) | (ord_less_int @ (A @ B) @ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 14.28/4.23 thf(6,axiom,((! [A:set_a,B:set_a,C:set_a]: ((~ ((~ (ord_less_eq_set_a @ B @ C)) <= (ord_less_eq_set_a @ A @ C))) <= (ord_less_eq_set_a @ (sup_sup_set_a @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_sup_OboundedE)). 14.28/4.23 thf(267,plain,((! [A:set_a,B:set_a,C:set_a]: (~ (~ (ord_less_eq_set_a @ B @ C) | ~ (ord_less_eq_set_a @ A @ C)) | ~ (ord_less_eq_set_a @ (sup_sup_set_a @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 14.28/4.23 thf(63,axiom,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ (sup_sup_set_a @ B @ C)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_le__supI1)). 14.28/4.23 thf(431,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ (sup_sup_set_a @ B @ C)) | ~ (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 14.28/4.23 thf(220,axiom,((binary1721989714Tree_a @ h @ t1)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_s1)). 14.28/4.23 thf(922,plain,((binary1721989714Tree_a @ (h) @ t1)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])). 14.28/4.23 thf(255,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ (sup_sup_int @ B @ C)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_less__supI1)). 14.28/4.23 thf(1076,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ (sup_sup_int @ B @ C)) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])). 14.28/4.23 thf(245,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ (sup_sup_int @ A @ B) @ C) => (~ ((~ (ord_less_int @ B @ C)) <= (ord_less_int @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_sup_Ostrict__boundedE)). 14.28/4.23 thf(1034,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (sup_sup_int @ A @ B) @ C) => (~ (~ (ord_less_int @ B @ C) | ~ (ord_less_int @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])). 14.28/4.23 thf(82,axiom,((! [A:set_a]: ((sup_sup_set_a @ bot_bot_set_a @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_Un__empty__left)). 14.28/4.23 thf(490,plain,((! [A:set_a]: ((sup_sup_set_a @ bot_bot_set_a @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 14.28/4.23 thf(61,axiom,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ B @ C) => (ord_less_eq_set_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_subset__trans)). 14.28/4.23 thf(426,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ B @ C) => (ord_less_eq_set_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 14.28/4.23 thf(116,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ C @ D) => (ord_less_eq_int @ (sup_sup_int @ A @ C) @ (sup_sup_int @ B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_sup_Omono)). 14.28/4.23 thf(589,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ C @ D) => (ord_less_eq_int @ (sup_sup_int @ A @ C) @ (sup_sup_int @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 14.28/4.23 thf(184,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((sup_sup_int @ A @ B) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_sup_Oabsorb2)). 14.28/4.23 thf(795,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((sup_sup_int @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 14.28/4.23 thf(222,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((~ (ord_less_int @ A @ C)) <= (ord_less_int @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_minf_I7_J)). 14.28/4.23 thf(927,plain,((! [A:int]: ? [B:int]: ! [C:int]: (~ (ord_less_int @ A @ C) | ~ (ord_less_int @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 14.28/4.23 thf(168,axiom,((! [A:int,B:int,C:int]: ((sup_sup_int @ A @ (sup_sup_int @ B @ C)) = (sup_sup_int @ B @ (sup_sup_int @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_inf__sup__aci_I7_J)). 14.28/4.23 thf(749,plain,((! [A:int,B:int,C:int]: ((sup_sup_int @ A @ (sup_sup_int @ B @ C)) = (sup_sup_int @ B @ (sup_sup_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 14.28/4.23 thf(228,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ B @ C) => (~ (ord_less_eq_int @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_pinf_I6_J)). 14.28/4.23 thf(939,plain,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ B @ C) => (~ (ord_less_eq_int @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 14.28/4.23 thf(198,axiom,((! [A:int,B:int]: ((A = (sup_sup_int @ A @ B)) => (ord_less_eq_int @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_sup_OorderI)). 14.28/4.23 thf(836,plain,((! [A:int,B:int]: ((A = (sup_sup_int @ A @ B)) => (ord_less_eq_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 14.28/4.23 thf(96,axiom,((! [A:set_a]: ((sup_sup_set_a @ bot_bot_set_a @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_sup__bot__left)). 14.28/4.23 thf(531,plain,((! [A:set_a]: ((sup_sup_set_a @ bot_bot_set_a @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 14.28/4.23 thf(230,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ C @ B) => (~ (ord_less_eq_int @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_minf_I8_J)). 14.28/4.23 thf(944,plain,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ C @ B) => (~ (ord_less_eq_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 14.28/4.23 thf(141,axiom,((ord_less_eq_int = (^ [A:int,B:int]: ((sup_sup_int @ A @ B) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_le__iff__sup)). 14.28/4.23 thf(663,plain,(((ord_less_eq_int) = (^ [A:int,B:int]: ((sup_sup_int @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 14.28/4.23 thf(102,axiom,((! [A:set_a,B:a,C:set_a]: ((sup_sup_set_a @ A @ (insert_a @ B @ C)) = (insert_a @ B @ (sup_sup_set_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_Un__insert__right)). 14.28/4.23 thf(548,plain,((! [A:set_a,B:a,C:set_a]: ((sup_sup_set_a @ A @ (insert_a @ B @ C)) = (insert_a @ B @ (sup_sup_set_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 14.28/4.23 thf(136,axiom,((! [A:a,B:a]: ((member_a @ A @ (insert_a @ B @ bot_bot_set_a)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_singleton__iff)). 14.28/4.23 thf(648,plain,((! [A:a,B:a]: ((member_a @ A @ (insert_a @ B @ bot_bot_set_a)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 14.28/4.23 thf(81,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((sup_sup_int @ B @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_sup_Oabsorb1)). 14.28/4.23 thf(487,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((sup_sup_int @ B @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 14.28/4.23 thf(94,axiom,((! [A:set_a,B:a]: ((ord_less_eq_set_a @ A @ (insert_a @ B @ bot_bot_set_a)) = ((A = bot_bot_set_a) | (A = (insert_a @ B @ bot_bot_set_a)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_subset__singleton__iff)). 14.28/4.23 thf(525,plain,((! [A:set_a,B:a]: ((ord_less_eq_set_a @ A @ (insert_a @ B @ bot_bot_set_a)) = ((A = bot_bot_set_a) | (A = (insert_a @ B @ bot_bot_set_a)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 14.28/4.23 thf(155,axiom,((! [A:set_a]: ((sup_sup_set_a @ A @ bot_bot_set_a) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_sup__bot__right)). 14.28/4.23 thf(712,plain,((! [A:set_a]: ((sup_sup_set_a @ A @ bot_bot_set_a) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 14.28/4.23 thf(253,axiom,(((! [A:a]: ((ord_less_int @ (h @ A) @ (h @ (binary339557810e_rm_a @ h @ t1))) <= (member_a @ A @ (binary945792244etOf_a @ (binary1217730267_wrm_a @ h @ t1))))) <= ((binary1721989714Tree_a @ h @ t1) & (t1 != binary476621312_Tip_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_h1)). 14.28/4.23 thf(1070,plain,((! [A:a]: ((ord_less_int @ (h @ A) @ (h @ (binary339557810e_rm_a @ (h) @ t1))) | ~ (member_a @ A @ (binary945792244etOf_a @ (binary1217730267_wrm_a @ (h) @ t1)))) | ~ ((binary1721989714Tree_a @ (h) @ t1) & ~ (t1 = binary476621312_Tip_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])). 14.28/4.23 thf(57,axiom,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => (ord_less_eq_set_a @ A @ (sup_sup_set_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_sup_OcoboundedI1)). 14.28/4.23 thf(414,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => (ord_less_eq_set_a @ A @ (sup_sup_set_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 14.28/4.23 thf(232,axiom,((! [A:int,B:int,C:(int > $o)]: ((ord_less_int @ A @ B) => ((C @ A) => ((? [D:int]: ((ord_less_eq_int @ A @ D) & (ord_less_eq_int @ D @ B) & ! [E:int]: ((C @ E) <= ((ord_less_eq_int @ A @ E) & (ord_less_int @ E @ D))) & ! [E:int]: ((ord_less_eq_int @ E @ D) <= (! [F:int]: (((ord_less_int @ F @ E) & (ord_less_eq_int @ A @ F)) => (C @ F)))))) <= (~ (C @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_complete__interval)). 14.28/4.23 thf(954,plain,((! [A:int,B:int,C:(int > $o)]: ((ord_less_int @ A @ B) => ((C @ A) => (? [D:int]: ((ord_less_eq_int @ A @ D) & (ord_less_eq_int @ D @ B) & ! [E:int]: ((C @ E) | ~ ((ord_less_eq_int @ A @ E) & (ord_less_int @ E @ D))) & ! [E:int]: ((ord_less_eq_int @ E @ D) | ~ (! [F:int]: (((ord_less_int @ F @ E) & (ord_less_eq_int @ A @ F)) => (C @ F))))) | (C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 14.28/4.23 thf(4,axiom,((! [A:set_a]: (ord_less_eq_set_a @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_order__refl)). 14.28/4.23 thf(263,plain,((! [A:set_a]: (ord_less_eq_set_a @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 14.28/4.23 thf(21,axiom,((! [A:set_a,B:set_a]: (ord_less_eq_set_a @ A @ (sup_sup_set_a @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_Un__upper2)). 14.28/4.23 thf(310,plain,((! [A:set_a,B:set_a]: (ord_less_eq_set_a @ A @ (sup_sup_set_a @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 14.28/4.23 thf(249,axiom,((ord_less_int @ (h @ l) @ (h @ (binary339557810e_rm_a @ h @ t2)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_hLess)). 14.28/4.23 thf(1053,plain,((ord_less_int @ (h @ l) @ (h @ (binary339557810e_rm_a @ (h) @ t2)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])). 14.28/4.23 thf(29,axiom,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ (sup_sup_set_a @ A @ B) @ C) = ((ord_less_eq_set_a @ B @ C) & (ord_less_eq_set_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_Un__subset__iff)). 14.28/4.23 thf(338,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ (sup_sup_set_a @ A @ B) @ C) = ((ord_less_eq_set_a @ B @ C) & (ord_less_eq_set_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 14.28/4.23 thf(189,axiom,((! [A:int,B:int]: (ord_less_eq_int @ A @ (sup_sup_int @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_inf__sup__ord_I4_J)). 14.28/4.23 thf(808,plain,((! [A:int,B:int]: (ord_less_eq_int @ A @ (sup_sup_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 14.28/4.23 thf(38,axiom,((! [A:set_a]: ((ord_less_eq_set_a @ A @ bot_bot_set_a) = (A = bot_bot_set_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_subset__empty)). 14.28/4.23 thf(359,plain,((! [A:set_a]: ((ord_less_eq_set_a @ A @ bot_bot_set_a) = (A = bot_bot_set_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 14.28/4.23 thf(166,axiom,((ord_less_eq_int = (^ [A:int,B:int]: ((sup_sup_int @ B @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_sup_Oabsorb__iff1)). 14.28/4.23 thf(744,plain,(((ord_less_eq_int) = (^ [A:int,B:int]: ((sup_sup_int @ B @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 14.28/4.23 thf(152,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ C @ B) => (ord_less_eq_int @ (sup_sup_int @ A @ C) @ B)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_sup_OboundedI)). 14.28/4.23 thf(703,plain,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ C @ B) => (ord_less_eq_int @ (sup_sup_int @ A @ C) @ B)) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 14.28/4.23 thf(208,axiom,((! [A:a]: (member_a @ A @ (insert_a @ A @ bot_bot_set_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_singletonI)). 14.28/4.23 thf(864,plain,((! [A:a]: (member_a @ A @ (insert_a @ A @ bot_bot_set_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 14.28/4.23 thf(160,axiom,((insert_a = (^ [A:a]: (sup_sup_set_a @ (collect_a @ (^ [B:a]: (B = A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_insert__def)). 14.28/4.23 thf(727,plain,(((insert_a) = (^ [A:a]: (sup_sup_set_a @ (collect_a @ (^ [B:a]: (B = A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 14.28/4.23 thf(46,axiom,((! [A:(a > $o),B:(a > $o)]: (((collect_a @ A) = (collect_a @ B)) <= (! [C:a]: ((A @ C) = (B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_Collect__cong)). 14.28/4.23 thf(386,plain,((! [A:(a > $o),B:(a > $o)]: (((collect_a @ (A)) = (collect_a @ (B))) | ~ (! [C:a]: ((A @ C) = (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 14.28/4.23 thf(109,axiom,((! [A:int,B:int,C:int]: ((sup_sup_int @ (sup_sup_int @ A @ B) @ C) = (sup_sup_int @ A @ (sup_sup_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_inf__sup__aci_I6_J)). 14.28/4.23 thf(571,plain,((! [A:int,B:int,C:int]: ((sup_sup_int @ (sup_sup_int @ A @ B) @ C) = (sup_sup_int @ A @ (sup_sup_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 14.28/4.23 thf(124,axiom,((! [A:set_a,B:set_a]: ((sup_sup_set_a @ A @ (sup_sup_set_a @ A @ B)) = (sup_sup_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_sup_Oleft__idem)). 14.28/4.23 thf(612,plain,((! [A:set_a,B:set_a]: ((sup_sup_set_a @ A @ (sup_sup_set_a @ A @ B)) = (sup_sup_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 14.28/4.23 thf(84,axiom,((! [A:a,B:set_a,C:set_a]: (((ord_less_eq_set_a @ B @ (insert_a @ A @ C)) = (ord_less_eq_set_a @ B @ C)) <= (~ (member_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_subset__insert)). 14.28/4.23 thf(497,plain,((! [A:a,B:set_a,C:set_a]: (((ord_less_eq_set_a @ B @ (insert_a @ A @ C)) = (ord_less_eq_set_a @ B @ C)) | (member_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 14.28/4.23 thf(75,axiom,((! [A:(a > $o),B:a]: ((((collect_a @ (^ [C:a]: ((B = C) & (A @ C)))) = bot_bot_set_a) <= (~ (A @ B))) & (((collect_a @ (^ [C:a]: ((B = C) & (A @ C)))) = (insert_a @ B @ bot_bot_set_a)) <= (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_Collect__conv__if2)). 14.28/4.23 thf(465,plain,((! [A:(a > $o),B:a]: ((((collect_a @ (^ [C:a]: ((B = C) & (A @ C)))) = bot_bot_set_a) | (A @ B)) & (((collect_a @ (^ [C:a]: ((B = C) & (A @ C)))) = (insert_a @ B @ bot_bot_set_a)) | ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 14.28/4.23 thf(70,axiom,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_equalityD1)). 14.28/4.23 thf(450,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 14.28/4.23 thf(144,axiom,((! [A:set_a,B:set_a]: (((sup_sup_set_a @ A @ B) = bot_bot_set_a) = ((A = bot_bot_set_a) & (B = bot_bot_set_a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_sup__bot_Oeq__neutr__iff)). 14.28/4.23 thf(671,plain,((! [A:set_a,B:set_a]: (((sup_sup_set_a @ A @ B) = bot_bot_set_a) = ((A = bot_bot_set_a) & (B = bot_bot_set_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 14.28/4.23 thf(113,axiom,((insert_a = (^ [A:a]: (sup_sup_set_a @ (insert_a @ A @ bot_bot_set_a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_insert__is__Un)). 14.28/4.23 thf(581,plain,(((insert_a) = (^ [A:a]: (sup_sup_set_a @ (insert_a @ A @ bot_bot_set_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 14.28/4.23 thf(238,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => (ord_less_int @ A @ (sup_sup_int @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_less__supI2)). 14.28/4.23 thf(1010,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => (ord_less_int @ A @ (sup_sup_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 14.28/4.23 thf(148,axiom,((! [A:set_a,B:set_a]: ((bot_bot_set_a = (sup_sup_set_a @ A @ B)) = ((A = bot_bot_set_a) & (B = bot_bot_set_a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_sup__bot_Oneutr__eq__iff)). 14.28/4.23 thf(688,plain,((! [A:set_a,B:set_a]: ((bot_bot_set_a = (sup_sup_set_a @ A @ B)) = ((A = bot_bot_set_a) & (B = bot_bot_set_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 14.28/4.23 thf(217,axiom,((! [A:(binary1439146945Tree_a > $o),B:binary1439146945Tree_a]: (((! [C:binary1439146945Tree_a,D:a,E:binary1439146945Tree_a]: (((A @ E) => (A @ (binary717961607le_T_a @ C @ D @ E))) <= (A @ C))) => (A @ B)) <= (A @ binary476621312_Tip_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_Tree_Oinduct)). 14.28/4.23 thf(903,plain,((! [A:(binary1439146945Tree_a > $o),B:binary1439146945Tree_a]: (((! [C:binary1439146945Tree_a,D:a,E:binary1439146945Tree_a]: (((A @ E) => (A @ (binary717961607le_T_a @ C @ D @ E))) | ~ (A @ C))) => (A @ B)) | ~ (A @ binary476621312_Tip_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 14.28/4.23 thf(41,axiom,((! [A:set_a,B:set_a]: ((A = B) => (~ ((ord_less_eq_set_a @ A @ B) => (~ (ord_less_eq_set_a @ B @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_equalityE)). 14.28/4.23 thf(368,plain,((! [A:set_a,B:set_a]: ((A = B) => (~ ((ord_less_eq_set_a @ A @ B) => (~ (ord_less_eq_set_a @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 14.28/4.23 thf(201,axiom,((! [A:int,B:int,C:int]: ((sup_sup_int @ A @ (sup_sup_int @ B @ C)) = (sup_sup_int @ B @ (sup_sup_int @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_sup_Oleft__commute)). 14.28/4.23 thf(844,plain,((! [A:int,B:int,C:int]: ((sup_sup_int @ A @ (sup_sup_int @ B @ C)) = (sup_sup_int @ B @ (sup_sup_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 14.28/4.23 thf(191,axiom,((! [A:set_a,B:set_a,C:set_a,D:set_a]: ((A = (sup_sup_set_a @ B @ C)) => ((sup_sup_set_a @ A @ D) = (sup_sup_set_a @ B @ (sup_sup_set_a @ C @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_boolean__algebra__cancel_Osup1)). 14.28/4.23 thf(813,plain,((! [A:set_a,B:set_a,C:set_a,D:set_a]: ((A = (sup_sup_set_a @ B @ C)) => ((sup_sup_set_a @ A @ D) = (sup_sup_set_a @ B @ (sup_sup_set_a @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 14.28/4.23 thf(91,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ (sup_sup_int @ A @ C) @ (sup_sup_int @ B @ D)) <= (ord_less_eq_int @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_sup__mono)). 14.28/4.23 thf(517,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ (sup_sup_int @ A @ C) @ (sup_sup_int @ B @ D)) | ~ (ord_less_eq_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 14.28/4.23 thf(231,axiom,((! [A:binary1439146945Tree_a,B:(a > int),C:binary1439146945Tree_a,D:a]: (((A = binary476621312_Tip_a) => ((binary1217730267_wrm_a @ B @ (binary717961607le_T_a @ C @ D @ A)) = C)) & ((A != binary476621312_Tip_a) => ((binary1217730267_wrm_a @ B @ (binary717961607le_T_a @ C @ D @ A)) = (binary717961607le_T_a @ C @ D @ (binary1217730267_wrm_a @ B @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_wrm_Osimps)). 14.28/4.23 thf(946,plain,((! [A:binary1439146945Tree_a,B:(a > int),C:binary1439146945Tree_a,D:a]: (((A = binary476621312_Tip_a) => ((binary1217730267_wrm_a @ (B) @ (binary717961607le_T_a @ C @ D @ A)) = C)) & ((~ (A = binary476621312_Tip_a)) => ((binary1217730267_wrm_a @ (B) @ (binary717961607le_T_a @ C @ D @ A)) = (binary717961607le_T_a @ C @ D @ (binary1217730267_wrm_a @ (B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 14.28/4.23 thf(35,axiom,((! [A:set_a,B:set_a]: (ord_less_eq_set_a @ A @ (sup_sup_set_a @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_inf__sup__ord_I4_J)). 14.28/4.23 thf(351,plain,((! [A:set_a,B:set_a]: (ord_less_eq_set_a @ A @ (sup_sup_set_a @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 14.28/4.23 thf(52,axiom,((! [A:(a > int),B:a,C:a,D:binary1439146945Tree_a]: (binary670562003pred_a @ A @ B @ C @ D))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_sorted__distinct)). 14.28/4.23 thf(401,plain,((! [A:(a > int),B:a,C:a,D:binary1439146945Tree_a]: (binary670562003pred_a @ (A) @ B @ C @ D))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 14.28/4.23 thf(179,axiom,((! [A:set_a,B:a]: (((A = bot_bot_set_a) | (A = (insert_a @ B @ bot_bot_set_a))) <= (ord_less_eq_set_a @ A @ (insert_a @ B @ bot_bot_set_a))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_subset__singletonD)). 14.28/4.23 thf(781,plain,((! [A:set_a,B:a]: ((A = bot_bot_set_a) | (A = (insert_a @ B @ bot_bot_set_a)) | ~ (ord_less_eq_set_a @ A @ (insert_a @ B @ bot_bot_set_a))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 14.28/4.23 thf(223,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ B @ C) => (C != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_pinf_I3_J)). 14.28/4.23 thf(929,plain,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ B @ C) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 14.28/4.23 thf(78,axiom,((! [A:set_a,B:set_a,C:(a > $o)]: ((? [D:a]: ((member_a @ D @ (sup_sup_set_a @ A @ B)) & (C @ D))) = (? [D:a]: ((C @ D) & (member_a @ D @ B)) | ? [D:a]: ((member_a @ D @ A) & (C @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_bex__Un)). 14.28/4.23 thf(478,plain,((! [A:set_a,B:set_a,C:(a > $o)]: ((? [D:a]: ((member_a @ D @ (sup_sup_set_a @ A @ B)) & (C @ D))) = (? [D:a]: ((C @ D) & (member_a @ D @ B)) | ? [D:a]: ((member_a @ D @ A) & (C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 14.28/4.23 thf(8,axiom,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => (B = (sup_sup_set_a @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_sup_OorderE)). 14.28/4.23 thf(272,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => (B = (sup_sup_set_a @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 14.28/4.23 thf(45,axiom,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ B @ A) <= (A = (sup_sup_set_a @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_sup_OorderI)). 14.28/4.23 thf(383,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ B @ A) | ~ (A = (sup_sup_set_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 14.28/4.23 thf(186,axiom,((sup_sup_int = (^ [A:int,B:int]: (sup_sup_int @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_inf__sup__aci_I5_J)). 14.28/4.23 thf(800,plain,(((sup_sup_int) = (^ [A:int,B:int]: (sup_sup_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 14.28/4.23 thf(17,axiom,((! [A:set_a,B:(a > $o)]: (ord_less_eq_set_a @ (collect_a @ (^ [C:a]: ((B @ C) & (member_a @ C @ A)))) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_Collect__subset)). 14.28/4.23 thf(300,plain,((! [A:set_a,B:(a > $o)]: (ord_less_eq_set_a @ (collect_a @ (^ [C:a]: ((B @ C) & (member_a @ C @ A)))) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 14.28/4.23 thf(127,axiom,((! [A:a,B:a,C:set_a]: ((insert_a @ A @ (insert_a @ B @ C)) = (insert_a @ B @ (insert_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_insert__commute)). 14.28/4.23 thf(620,plain,((! [A:a,B:a,C:set_a]: ((insert_a @ A @ (insert_a @ B @ C)) = (insert_a @ B @ (insert_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 14.28/4.23 thf(169,axiom,((! [A:a,B:set_a,C:a]: ((member_a @ A @ (insert_a @ C @ B)) <= (member_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_insertI2)). 14.28/4.23 thf(752,plain,((! [A:a,B:set_a,C:a]: ((member_a @ A @ (insert_a @ C @ B)) | ~ (member_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 14.28/4.23 thf(69,axiom,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => ((sup_sup_set_a @ A @ B) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_sup_Oabsorb2)). 14.28/4.23 thf(447,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => ((sup_sup_set_a @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 14.28/4.23 thf(23,axiom,((! [A:set_a,B:set_a,C:set_a]: (((ord_less_eq_set_a @ (sup_sup_set_a @ A @ C) @ B) <= (ord_less_eq_set_a @ C @ B)) <= (ord_less_eq_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_le__supI)). 14.28/4.23 thf(315,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ (sup_sup_set_a @ A @ C) @ B) | ~ (ord_less_eq_set_a @ C @ B) | ~ (ord_less_eq_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 14.28/4.23 thf(197,axiom,((! [A:binary1439146945Tree_a,B:(a > int)]: (((binary1721989714Tree_a @ B @ A) & (A != binary476621312_Tip_a)) => (ord_less_eq_set_a @ (binary945792244etOf_a @ (binary1217730267_wrm_a @ B @ A)) @ (binary945792244etOf_a @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_wrm__set1)). 14.28/4.23 thf(833,plain,((! [A:binary1439146945Tree_a,B:(a > int)]: (((binary1721989714Tree_a @ (B) @ A) & ~ (A = binary476621312_Tip_a)) => (ord_less_eq_set_a @ (binary945792244etOf_a @ (binary1217730267_wrm_a @ (B) @ A)) @ (binary945792244etOf_a @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 14.28/4.23 thf(192,axiom,((! [A:a,B:set_a]: ((member_a @ A @ B) => (? [C:set_a]: (~ (member_a @ A @ C) & (B = (insert_a @ A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_mk__disjoint__insert)). 14.28/4.23 thf(818,plain,((! [A:a,B:set_a]: ((member_a @ A @ B) => (? [C:set_a]: (~ (member_a @ A @ C) & (B = (insert_a @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 14.28/4.23 thf(54,axiom,((! [A:set_a,B:set_a,C:set_a]: ((~ ((~ (ord_less_eq_set_a @ B @ C)) <= (ord_less_eq_set_a @ A @ C))) <= (ord_less_eq_set_a @ (sup_sup_set_a @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_le__supE)). 14.28/4.23 thf(405,plain,((! [A:set_a,B:set_a,C:set_a]: (~ (~ (ord_less_eq_set_a @ B @ C) | ~ (ord_less_eq_set_a @ A @ C)) | ~ (ord_less_eq_set_a @ (sup_sup_set_a @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 14.28/4.23 thf(182,axiom,((sup_sup_int = (^ [A:int,B:int]: (sup_sup_int @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_sup_Ocommute)). 14.28/4.23 thf(790,plain,(((sup_sup_int) = (^ [A:int,B:int]: (sup_sup_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 14.28/4.23 thf(122,axiom,((! [A:a,B:set_a,C:a]: ((member_a @ A @ (insert_a @ C @ B)) <= ((A = C) <= (~ (member_a @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_insertCI)). 14.28/4.23 thf(603,plain,((! [A:a,B:set_a,C:a]: ((member_a @ A @ (insert_a @ C @ B)) | ~ ((A = C) | (member_a @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 14.28/4.23 thf(163,axiom,((! [A:a,B:set_a]: ((insert_a @ A @ (insert_a @ A @ B)) = (insert_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_insert__absorb2)). 14.28/4.23 thf(735,plain,((! [A:a,B:set_a]: ((insert_a @ A @ (insert_a @ A @ B)) = (insert_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 14.28/4.23 thf(19,axiom,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ B @ A) => (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_subset__antisym)). 14.28/4.23 thf(305,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 14.28/4.23 thf(30,axiom,((! [A:set_a,B:set_a]: (ord_less_eq_set_a @ A @ (sup_sup_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_sup_Ocobounded1)). 14.28/4.23 thf(341,plain,((! [A:set_a,B:set_a]: (ord_less_eq_set_a @ A @ (sup_sup_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 14.28/4.23 thf(87,axiom,((! [A:a,B:set_a]: ((member_a @ A @ B) => ((insert_a @ A @ B) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_insert__absorb)). 14.28/4.23 thf(506,plain,((! [A:a,B:set_a]: ((member_a @ A @ B) => ((insert_a @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 14.28/4.23 thf(65,axiom,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => (ord_less_eq_set_a @ A @ (sup_sup_set_a @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_sup_OcoboundedI2)). 14.28/4.23 thf(437,plain,((! [A:set_a,B:set_a,C:set_a]: ((ord_less_eq_set_a @ A @ B) => (ord_less_eq_set_a @ A @ (sup_sup_set_a @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 14.28/4.23 thf(174,axiom,((! [A:set_a,B:set_a,C:set_a]: ((sup_sup_set_a @ (sup_sup_set_a @ A @ B) @ C) = (sup_sup_set_a @ A @ (sup_sup_set_a @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_sup__assoc)). 14.28/4.23 thf(767,plain,((! [A:set_a,B:set_a,C:set_a]: ((sup_sup_set_a @ (sup_sup_set_a @ A @ B) @ C) = (sup_sup_set_a @ A @ (sup_sup_set_a @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 14.28/4.23 thf(195,axiom,((! [A:set_a]: ((! [B:a]: ~ (member_a @ B @ A)) = (A = bot_bot_set_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_all__not__in__conv)). 14.28/4.23 thf(828,plain,((! [A:set_a]: ((! [B:a]: ~ (member_a @ B @ A)) = (A = bot_bot_set_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 14.28/4.23 thf(150,axiom,((! [A:(a > int),B:binary1439146945Tree_a,C:a]: ((binary1721989714Tree_a @ A @ B) => ((binary2053421120memb_a @ A @ C @ B) = (member_a @ C @ (binary945792244etOf_a @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_memb__spec)). 14.28/4.23 thf(696,plain,((! [A:(a > int),B:binary1439146945Tree_a,C:a]: ((binary1721989714Tree_a @ (A) @ B) => ((binary2053421120memb_a @ (A) @ C @ B) = (member_a @ C @ (binary945792244etOf_a @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 14.28/4.23 thf(12,axiom,((! [A:set_a,B:set_a]: (ord_less_eq_set_a @ A @ (sup_sup_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_Un__upper1)). 14.28/4.23 thf(283,plain,((! [A:set_a,B:set_a]: (ord_less_eq_set_a @ A @ (sup_sup_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 14.28/4.23 thf(199,axiom,(((binary945792244etOf_a @ binary476621312_Tip_a) = bot_bot_set_a)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_setOf_Osimps_I1_J)). 14.28/4.23 thf(839,plain,(((binary945792244etOf_a @ binary476621312_Tip_a) = bot_bot_set_a)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 14.28/4.23 thf(235,axiom,((! [A:(a > int),B:binary1439146945Tree_a,C:a,D:binary1439146945Tree_a]: ((binary1721989714Tree_a @ A @ (binary717961607le_T_a @ B @ C @ D)) => (binary1721989714Tree_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_sortLemmaL)). 14.28/4.23 thf(987,plain,((! [A:(a > int),B:binary1439146945Tree_a,C:a,D:binary1439146945Tree_a]: ((binary1721989714Tree_a @ (A) @ (binary717961607le_T_a @ B @ C @ D)) => (binary1721989714Tree_a @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 14.28/4.23 thf(27,axiom,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => ((sup_sup_set_a @ A @ B) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_Un__absorb1)). 14.28/4.23 thf(332,plain,((! [A:set_a,B:set_a]: ((ord_less_eq_set_a @ A @ B) => ((sup_sup_set_a @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 14.28/4.23 thf(242,axiom,(((! [A:a]: ((member_a @ A @ (binary945792244etOf_a @ (binary1217730267_wrm_a @ h @ t2))) => (ord_less_int @ (h @ A) @ (h @ (binary339557810e_rm_a @ h @ t2))))) <= ((binary1721989714Tree_a @ h @ t2) & (t2 != binary476621312_Tip_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_h2)). 14.28/4.23 thf(1019,plain,((! [A:a]: ((member_a @ A @ (binary945792244etOf_a @ (binary1217730267_wrm_a @ (h) @ t2))) => (ord_less_int @ (h @ A) @ (h @ (binary339557810e_rm_a @ (h) @ t2)))) | ~ ((binary1721989714Tree_a @ (h) @ t2) & ~ (t2 = binary476621312_Tip_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])). 14.28/4.23 thf(95,axiom,((! [A:set_a,B:set_a,C:(a > $o)]: ((! [D:a]: ((member_a @ D @ (sup_sup_set_a @ A @ B)) => (C @ D))) = (! [D:a]: ((C @ D) <= (member_a @ D @ A)) & ! [D:a]: ((C @ D) <= (member_a @ D @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_ball__Un)). 14.28/4.23 thf(528,plain,((! [A:set_a,B:set_a,C:(a > $o)]: ((! [D:a]: ((member_a @ D @ (sup_sup_set_a @ A @ B)) => (C @ D))) = (! [D:a]: ((C @ D) | ~ (member_a @ D @ A)) & ! [D:a]: ((C @ D) | ~ (member_a @ D @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 14.28/4.23 thf(73,axiom,((! [A:int,B:int]: (((sup_sup_int @ A @ B) = B) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_sup__absorb2)). 14.28/4.23 thf(459,plain,((! [A:int,B:int]: (((sup_sup_int @ A @ B) = B) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 14.28/4.23 thf(193,axiom,((! [A:set_a,B:set_a,C:set_a]: ((sup_sup_set_a @ A @ (sup_sup_set_a @ B @ C)) = (sup_sup_set_a @ B @ (sup_sup_set_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_sup_Oleft__commute)). 14.28/4.23 thf(822,plain,((! [A:set_a,B:set_a,C:set_a]: ((sup_sup_set_a @ A @ (sup_sup_set_a @ B @ C)) = (sup_sup_set_a @ B @ (sup_sup_set_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 14.28/4.23 thf(203,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (sup_sup_int @ A @ B) @ C) = ((ord_less_eq_int @ B @ C) & (ord_less_eq_int @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_sup_Obounded__iff)). 14.28/4.23 thf(850,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (sup_sup_int @ A @ B) @ C) = ((ord_less_eq_int @ B @ C) & (ord_less_eq_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 14.28/4.23 thf(149,axiom,((! [A:int,B:int,C:int,D:int]: ((A = (sup_sup_int @ B @ C)) => ((sup_sup_int @ D @ A) = (sup_sup_int @ B @ (sup_sup_int @ D @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_boolean__algebra__cancel_Osup2)). 14.28/4.23 thf(691,plain,((! [A:int,B:int,C:int,D:int]: ((A = (sup_sup_int @ B @ C)) => ((sup_sup_int @ D @ A) = (sup_sup_int @ B @ (sup_sup_int @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 14.28/4.23 thf(67,axiom,((bot_bot_set_a = (collect_a @ (^ [A:a]: (($false)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_empty__def)). 14.28/4.23 thf(442,plain,((bot_bot_set_a = (collect_a @ (^ [A:a]: (($false)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 14.28/4.23 thf(210,axiom,((! [A:(int > (int > int)),B:int,C:int]: (((! [D:int,E:int]: (ord_less_eq_int @ E @ (A @ D @ E))) => ((! [D:int,E:int,F:int]: ((ord_less_eq_int @ E @ D) => ((ord_less_eq_int @ F @ D) => (ord_less_eq_int @ (A @ E @ F) @ D)))) => ((sup_sup_int @ B @ C) = (A @ B @ C)))) <= (! [D:int,E:int]: (ord_less_eq_int @ D @ (A @ D @ E)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_sup__unique)). 14.28/4.23 thf(871,plain,((! [A:(int > (int > int)),B:int,C:int]: (((! [D:int,E:int]: (ord_less_eq_int @ E @ (A @ D @ E))) => ((! [D:int,E:int,F:int]: ((ord_less_eq_int @ E @ D) => ((ord_less_eq_int @ F @ D) => (ord_less_eq_int @ (A @ E @ F) @ D)))) => ((sup_sup_int @ B @ C) = (A @ B @ C)))) | ~ (! [D:int,E:int]: (ord_less_eq_int @ D @ (A @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])). 14.28/4.23 thf(85,axiom,((insert_a = (^ [A:a,B:set_a]: (collect_a @ (^ [C:a]: ((C = A) | (member_a @ C @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_insert__compr)). 14.28/4.23 thf(501,plain,(((insert_a) = (^ [A:a,B:set_a]: (collect_a @ (^ [C:a]: ((C = A) | (member_a @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 14.28/4.23 thf(225,axiom,((binary1721989714Tree_a @ h @ (binary717961607le_T_a @ t1 @ x @ t2))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_s)). 14.28/4.23 thf(935,plain,((binary1721989714Tree_a @ (h) @ (binary717961607le_T_a @ t1 @ x @ t2))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])). 14.28/4.23 thf(221,axiom,((! [A:binary1439146945Tree_a]: ((~ (! [B:binary1439146945Tree_a,C:a,D:binary1439146945Tree_a]: (A != (binary717961607le_T_a @ B @ C @ D)))) <= (A != binary476621312_Tip_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_Tree_Oexhaust)). 14.28/4.23 thf(923,plain,((! [A:binary1439146945Tree_a]: (~ (! [B:binary1439146945Tree_a,C:a,D:binary1439146945Tree_a]: ~ (A = (binary717961607le_T_a @ B @ C @ D))) | (A = binary476621312_Tip_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 14.28/4.23 thf(100,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (sup_sup_int @ A @ B) @ C) = ((ord_less_eq_int @ A @ C) & (ord_less_eq_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_le__sup__iff)). 14.28/4.23 thf(543,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (sup_sup_int @ A @ B) @ C) = ((ord_less_eq_int @ A @ C) & (ord_less_eq_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 14.28/4.23 thf(133,axiom,((! [A:a]: ((collect_a @ ((=) @ a @ A)) = (insert_a @ A @ bot_bot_set_a)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_singleton__conv2)). 14.28/4.23 thf(639,plain,((! [A:a]: ((collect_a @ ((=) @ a @ A)) = (insert_a @ A @ bot_bot_set_a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 14.28/4.23 thf(170,axiom,((! [A:set_a,B:set_a]: ((sup_sup_set_a @ A @ (sup_sup_set_a @ A @ B)) = (sup_sup_set_a @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_Un__left__absorb)). 14.28/4.23 thf(755,plain,((! [A:set_a,B:set_a]: ((sup_sup_set_a @ A @ (sup_sup_set_a @ A @ B)) = (sup_sup_set_a @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 14.28/4.23 thf(117,axiom,((sup_sup_set_a = (^ [A:set_a,B:set_a]: (sup_sup_set_a @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_Un__commute)). 14.28/4.23 thf(592,plain,(((sup_sup_set_a) = (^ [A:set_a,B:set_a]: (sup_sup_set_a @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 14.28/4.23 thf(71,axiom,((! [A:set_a,B:set_a,C:set_a,D:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ C @ D) => (ord_less_eq_set_a @ (sup_sup_set_a @ A @ C) @ (sup_sup_set_a @ B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_Un__mono)). 14.28/4.23 thf(454,plain,((! [A:set_a,B:set_a,C:set_a,D:set_a]: ((ord_less_eq_set_a @ A @ B) => ((ord_less_eq_set_a @ C @ D) => (ord_less_eq_set_a @ (sup_sup_set_a @ A @ C) @ (sup_sup_set_a @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 14.28/4.23 thf(240,axiom,(((binary1217730267_wrm_a @ h @ (binary717961607le_T_a @ t1 @ x @ t2)) = (binary717961607le_T_a @ t1 @ x @ (binary1217730267_wrm_a @ h @ t2)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_wrm__res)). 14.28/4.23 thf(1014,plain,(((binary1217730267_wrm_a @ (h) @ (binary717961607le_T_a @ t1 @ x @ t2)) = (binary717961607le_T_a @ t1 @ x @ (binary1217730267_wrm_a @ (h) @ t2)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 14.28/4.23 thf(246,axiom,((! [A:(int > $o),B:(int > $o),C:(int > $o),D:(int > $o)]: ((? [E:int]: ! [F:int]: ((ord_less_int @ F @ E) => ((A @ F) = (B @ F)))) => ((? [E:int]: ! [F:int]: (((C @ F) = (D @ F)) <= (ord_less_int @ F @ E))) => (? [E:int]: ! [F:int]: ((((A @ F) & (C @ F)) = ((D @ F) & (B @ F))) <= (ord_less_int @ F @ E))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_minf_I1_J)). 14.28/4.23 thf(1037,plain,((! [A:(int > $o),B:(int > $o),C:(int > $o),D:(int > $o)]: ((? [E:int]: ! [F:int]: ((ord_less_int @ F @ E) => ((A @ F) = (B @ F)))) => ((? [E:int]: ! [F:int]: (((C @ F) = (D @ F)) | ~ (ord_less_int @ F @ E))) => (? [E:int]: ! [F:int]: ((((A @ F) & (C @ F)) = ((D @ F) & (B @ F))) | ~ (ord_less_int @ F @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])). 14.28/4.23 thf(177,axiom,((! [A:int,B:int,C:int]: ((sup_sup_int @ A @ (sup_sup_int @ B @ C)) = (sup_sup_int @ B @ (sup_sup_int @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_sup__left__commute)). 14.28/4.23 thf(775,plain,((! [A:int,B:int,C:int]: ((sup_sup_int @ A @ (sup_sup_int @ B @ C)) = (sup_sup_int @ B @ (sup_sup_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 14.28/4.23 thf(105,axiom,((! [A:a,B:a,C:set_a]: ((member_a @ A @ (insert_a @ B @ C)) = ((A = B) | (member_a @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_insert__iff)). 14.28/4.23 thf(560,plain,((! [A:a,B:a,C:set_a]: ((member_a @ A @ (insert_a @ B @ C)) = ((A = B) | (member_a @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 14.28/4.23 thf(1091,plain,(($false)),inference(e,[status(thm)],[1024,365,760,347,941,481,645,892,408,523,683,308,440,597,861,741,1073,715,472,709,885,651,841,417,389,724,917,802,853,881,289,1013,770,475,321,623,514,937,574,353,866,396,660,411,265,312,292,380,512,270,546,810,534,1047,798,746,825,778,302,297,630,429,275,729,260,349,879,329,665,583,889,493,1079,551,285,847,566,484,615,403,356,420,1082,933,537,642,1016,679,706,393,985,738,654,721,569,503,1060,1050,457,343,792,1086,633,805,657,1054,398,558,674,586,718,618,856,444,375,601,423,732,772,577,579,281,259,391,936,787,1058,335,919,540,764,900,831,784,362,318,599,377,990,509,434,758,594,626,1022,668,462,345,858,700,520,983,636,278,608,563,1000,267,431,922,1076,1034,490,426,589,795,927,749,939,836,531,944,663,548,648,487,525,712,1070,414,954,263,310,1053,338,808,359,744,703,864,727,386,571,612,497,465,450,671,581,1010,688,903,368,844,813,517,946,351,401,781,929,478,272,383,800,300,620,752,447,315,833,818,405,790,603,735,305,341,506,437,767,828,696,283,839,987,332,1019,528,459,822,850,691,442,871,501,935,923,543,639,755,592,454,1014,1037,775,560])). 14.28/4.23 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p 14.28/4.23 % [INFO] Killing All external provers ... 14.59/4.26 EOF