0.00/0.00 % Leo-III: Strategy 1 (for '60') 39.99/14.69 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 39.99/14.69 % [INFO] Parsing done (328ms). 39.99/14.69 % [INFO] Running in sequential loop mode. 39.99/14.69 % [CONFIG] Using configuration: timeout(60) with strategy 39.99/14.69 % [INFO] eprover registered as external prover. 39.99/14.69 % [INFO] cvc4 registered as external prover. 39.99/14.69 % [INFO] Parsing finished. Scanning for conjecture ... 39.99/14.69 % [INFO] Found a conjecture and 356 axioms. Running axiom selection ... 39.99/14.69 % [INFO] Axiom selection finished. Selected 180 axioms (removed 176 axioms). 39.99/14.69 % [INFO] Problem is higher-order (TPTP THF). 39.99/14.69 % [INFO] Type checking passed. Searching for refutation ... 39.99/14.69 % External prover 'cvc4' found a proof! 39.99/14.69 % [INFO] Killing All external provers ... 39.99/14.69 % Time passed: 10190ms (effective reasoning time: 9389ms) 39.99/14.69 % Solved by strategy 39.99/14.69 % Axioms used in derivation (180): fact_305_case__prodE2, fact_104_Collect__conv__if2, fact_65_Set_Oset__insert, fact_86_singleton__inject, fact_61_insert__absorb, fact_92_doubleton__eq__iff, fact_71_insertI1, fact_35_Collect__empty__eq, fact_26_empty__iff, fact_1_weaken__post, fact_47_emptyE, fact_309_cond__case__prod__eta, fact_213_Set_Ois__empty__def, fact_257_case__prodI2, fact_212_thoare_OWhile, fact_290_case__prodE, fact_339_execn_OWhileTrue, fact_28_empty__iff, fact_191_wf__irrefl, fact_343_termi_OSemi, fact_157_Pair__inject, fact_164_old_Oprod_Oinducts, fact_209_bot__empty__eq2, fact_73_insertI1, fact_151_prod__cases, fact_25_hoare_OCall, fact_200_wf__eq__minimal, fact_307_case__prod__eta, fact_91_insert__not__empty, fact_88_singleton__inject, fact_288_case__prodD, fact_80_insert__Collect, fact_14_exec_Ointros_I7_J, fact_216_com_Oinject_I4_J, fact_16_insertCI, fact_226_pred__equals__eq2, fact_110_mem__Collect__eq, fact_287_case__prodD, fact_147_surj__pair, fact_107_Collect__conv__if, fact_112_mem__Collect__eq, fact_291_case__prodE, fact_94_doubleton__eq__iff, fact_340_execn_OWhileFalse, fact_242_wf__termi, fact_133_prod_Oinject, fact_286_case__prodD, fact_193_wf__not__sym, fact_32_empty__Collect__eq, fact_100_singletonD, fact_132_prod_Oinject, fact_24_insert__absorb2, fact_170_is__singleton__def, fact_55_insert__commute, fact_74_insertE, fact_12_singletonI, fact_292_case__prodE, fact_3_PHoareTotal__Mirabelle__ynemugpbor_Ostrengthen__pre, fact_156_Pair__inject, fact_155_Pair__inject, fact_21_insert__iff, fact_2_thoare_OConseq, fact_299_total__onI, fact_253_case__prodI, fact_64_insert__ident, fact_115_Collect__mem__eq, fact_250_case__prod__conv, fact_7_singleton__conv2, fact_105_Collect__conv__if, fact_40_ex__in__conv, fact_220_termi_OWhileFalse, fact_345_execn_Ointros_I2_J, fact_131_prod_Oinject, fact_204_prod__cases3, fact_217_com_Odistinct_I25_J, fact_344_com_Oinject_I2_J, fact_18_insertCI, fact_50_mk__disjoint__insert, fact_85_insert__compr, fact_195_wf__not__refl, fact_6_singleton__conv, fact_98_singletonD, fact_82_insert__Collect, fact_116_Collect__cong, fact_95_singleton__iff, fact_34_empty__Collect__eq, fact_144_is__singletonI_H, fact_44_equals0D, fact_141_is__singleton__the__elem, fact_206_bot__empty__eq2, fact_148_surj__pair, fact_109_wf__empty, fact_321_split__cong, fact_153_prod__cases, fact_328_internal__case__prod__def, fact_348_exec_OSemi, fact_256_case__prodI2, fact_58_insert__eq__iff, fact_41_equals0I, fact_334_termi__while__lemma, fact_10_singletonI, fact_326_aboveS__def, fact_178_wfE__min, fact_252_case__prodI, fact_76_insertE, fact_341_exec__iff__execn, fact_160_old_Oprod_Oexhaust, fact_152_prod__cases, fact_225_pred__equals__eq2, fact_254_case__prodI, fact_29_all__not__in__conv, fact_19_insert__iff, fact_53_insert__commute, fact_118_Collect__cong, fact_202_wf__induct__rule, fact_46_equals0D, fact_15_thoare_OCall, fact_346_com_Odistinct_I13_J, fact_265_prod_Ocase__distrib, fact_128_old_Oprod_Oinject, conj_1, fact_135_is__singletonI, fact_13_termi_Ointros_I7_J, fact_337_while__rule, fact_0_thoare_OAsm, fact_22_insert__absorb2, fact_31_all__not__in__conv, fact_68_insertI2, fact_338_while__lemma, fact_101_hoare_OAsm, fact_267_prod_Odisc__eq__case, fact_248_split__part, fact_56_insert__eq__iff, fact_333_termi__while, fact_49_emptyE, fact_207_bot__empty__eq2, fact_161_old_Oprod_Oexhaust, fact_205_prod__induct3, fact_102_Collect__conv__if2, fact_173_wf__def, fact_269_old_Oprod_Ocase, fact_59_insert__absorb, fact_187_wf__asym, fact_221_termi_OWhileTrue, fact_89_insert__not__empty, fact_119_wfE__min_H, fact_189_wf__induct, fact_233_total__on__singleton, fact_52_mk__disjoint__insert, fact_83_insert__compr, fact_159_old_Oprod_Oexhaust, fact_183_wfI__min, fact_67_Set_Oset__insert, fact_302_total__on__empty, fact_227_pred__equals__eq2, fact_219_exec_OWhileTrue, fact_43_equals0I, fact_185_wfUNIVI, fact_37_Collect__empty__eq, fact_210_wf__measure, fact_347_com_Odistinct_I15_J, fact_97_singleton__iff, fact_129_old_Oprod_Oinject, fact_218_exec_OWhileFalse, fact_127_old_Oprod_Oinject, fact_335_execn_Ointros_I7_J, conj_0, fact_258_case__prodI2, fact_38_ex__in__conv, fact_294_total__on__def, fact_62_insert__ident, fact_4_singleton__conv, fact_165_old_Oprod_Oinducts, fact_124_the__elem__eq, fact_163_old_Oprod_Oinducts, fact_9_singleton__conv2, fact_113_Collect__mem__eq, fact_149_surj__pair, fact_70_insertI2, fact_167_is__singletonE 39.99/14.69 % No. of inferences in proof: 414 39.99/14.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10190 ms resp. 9389 ms w/o parsing 39.99/14.69 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 39.99/14.69 thf(set_Pr1702239303tate_o_type, type, set_Pr1702239303tate_o: $tType). 39.99/14.69 thf(produc1307154919tate_o_type, type, produc1307154919tate_o: $tType). 39.99/14.69 thf(set_Pr1590995257tate_o_type, type, set_Pr1590995257tate_o: $tType). 39.99/14.69 thf(set_Pr778812871_state_type, type, set_Pr778812871_state: $tType). 39.99/14.69 thf(produc696469763tate_o_type, type, produc696469763tate_o: $tType). 39.99/14.69 thf(set_Pr1490359111at_nat_type, type, set_Pr1490359111at_nat: $tType). 39.99/14.69 thf(produc1390548711_state_type, type, produc1390548711_state: $tType). 39.99/14.69 thf(produc842455143at_nat_type, type, produc842455143at_nat: $tType). 39.99/14.69 thf(set_Pr1740974983tate_o_type, type, set_Pr1740974983tate_o: $tType). 39.99/14.69 thf(produc204914599tate_o_type, type, produc204914599tate_o: $tType). 39.99/14.69 thf(set_Pr795498619_state_type, type, set_Pr795498619_state: $tType). 39.99/14.69 thf(set_Pr1986765409at_nat_type, type, set_Pr1986765409at_nat: $tType). 39.99/14.69 thf(produc1115495963_state_type, type, produc1115495963_state: $tType). 39.99/14.69 thf(product_prod_nat_nat_type, type, product_prod_nat_nat: $tType). 39.99/14.69 thf(set_state_type, type, set_state: $tType). 39.99/14.69 thf(set_nat_type, type, set_nat: $tType). 39.99/14.69 thf(state_type, type, state: $tType). 39.99/14.69 thf(com_type, type, com: $tType). 39.99/14.69 thf(nat_type, type, nat: $tType). 39.99/14.69 thf(a_type, type, a: $tType). 39.99/14.69 thf(suc_type, type, suc: (nat > nat)). 39.99/14.69 thf(order_aboveS_state_type, type, order_aboveS_state: (set_Pr795498619_state > (state > set_state))). 39.99/14.69 thf(bot_bo2130564770te_o_o_type, type, bot_bo2130564770te_o_o: ((a > (state > $o)) > (produc204914599tate_o > $o))). 39.99/14.69 thf(bot_bo935656620te_o_o_type, type, bot_bo935656620te_o_o: (com > ((a > (state > $o)) > $o))). 39.99/14.69 thf(bot_bo51534648tate_o_type, type, bot_bo51534648tate_o: (state > (state > $o))). 39.99/14.69 thf(bot_bot_set_state_type, type, bot_bot_set_state: set_state). 39.99/14.69 thf(bot_bo170732493tate_o_type, type, bot_bo170732493tate_o: set_Pr1590995257tate_o). 39.99/14.69 thf(bot_bo1692783091tate_o_type, type, bot_bo1692783091tate_o: set_Pr1740974983tate_o). 39.99/14.69 thf(bot_bo1625160935_state_type, type, bot_bo1625160935_state: set_Pr795498619_state). 39.99/14.69 thf(pHoare382919414oare_a_type, type, pHoare382919414oare_a: (set_Pr1590995257tate_o > ((a > (state > $o)) > (com > ((a > (state > $o)) > $o))))). 39.99/14.69 thf(hoare_a_type, type, hoare_a: (set_Pr1590995257tate_o > ((a > (state > $o)) > (com > ((a > (state > $o)) > $o))))). 39.99/14.69 thf(body_type, type, body: com). 39.99/14.69 thf(call_type, type, call: com). 39.99/14.69 thf(semi_type, type, semi: (com > (com > com))). 39.99/14.69 thf(while_type, type, while: ((state > $o) > (com > com))). 39.99/14.69 thf(exec_type, type, exec: (state > (com > (state > $o)))). 39.99/14.69 thf(execn_type, type, execn: (state > (com > (nat > (state > $o))))). 39.99/14.69 thf(termi_type, type, termi: (com > (state > $o))). 39.99/14.69 thf(produc33908149tate_o_type, type, produc33908149tate_o: ((a > (state > $o)) > (produc204914599tate_o > produc696469763tate_o))). 39.99/14.69 thf(produc1948644831tate_o_type, type, produc1948644831tate_o: (com > ((a > (state > $o)) > produc204914599tate_o))). 39.99/14.69 thf(produc64584659_state_type, type, produc64584659_state: (state > (state > produc1115495963_state))). 39.99/14.69 thf(produc938968666tate_o_type, type, produc938968666tate_o: ((state > (state > $o)) > (produc1115495963_state > $o))). 39.99/14.69 thf(produc1271576886te_o_o_type, type, produc1271576886te_o_o: (((a > (state > $o)) > (produc204914599tate_o > $o)) > (produc696469763tate_o > $o))). 39.99/14.69 thf(produc281270436te_o_o_type, type, produc281270436te_o_o: ((com > ((a > (state > $o)) > $o)) > (produc204914599tate_o > $o))). 39.99/14.69 thf(produc789892016tate_o_type, type, produc789892016tate_o: ((state > (state > $o)) > (produc1115495963_state > $o))). 39.99/14.69 thf(total_on_state_type, type, total_on_state: (set_state > (set_Pr795498619_state > $o))). 39.99/14.69 thf(total_795385983tate_o_type, type, total_795385983tate_o: (set_Pr1590995257tate_o > (set_Pr1702239303tate_o > $o))). 39.99/14.69 thf(collect_state_type, type, collect_state: ((state > $o) > set_state)). 39.99/14.69 thf(collec1499596504tate_o_type, type, collec1499596504tate_o: ((produc696469763tate_o > $o) > set_Pr1590995257tate_o)). 39.99/14.69 thf(collec496201222_state_type, type, collec496201222_state: ((produc1115495963_state > $o) > set_Pr795498619_state)). 39.99/14.69 thf(insert_state_type, type, insert_state: (state > (set_state > set_state))). 39.99/14.69 thf(insert2053719859tate_o_type, type, insert2053719859tate_o: (produc696469763tate_o > (set_Pr1590995257tate_o > set_Pr1590995257tate_o))). 39.99/14.69 thf(insert311944171_state_type, type, insert311944171_state: (produc1115495963_state > (set_Pr795498619_state > set_Pr795498619_state))). 39.99/14.69 thf(is_emp807847857tate_o_type, type, is_emp807847857tate_o: (set_Pr1590995257tate_o > $o)). 39.99/14.69 thf(is_sin1547905295tate_o_type, type, is_sin1547905295tate_o: (set_Pr1590995257tate_o > $o)). 39.99/14.69 thf(the_el1569055182tate_o_type, type, the_el1569055182tate_o: (set_Pr1590995257tate_o > produc696469763tate_o)). 39.99/14.69 thf(measure_state_type, type, measure_state: ((state > nat) > set_Pr795498619_state)). 39.99/14.69 thf(wf_state_type, type, wf_state: (set_Pr795498619_state > $o)). 39.99/14.69 thf(member_state_type, type, member_state: (state > (set_state > $o))). 39.99/14.69 thf(member1838112666tate_o_type, type, member1838112666tate_o: (produc696469763tate_o > (set_Pr1590995257tate_o > $o))). 39.99/14.69 thf(member221067728tate_o_type, type, member221067728tate_o: (produc204914599tate_o > (set_Pr1740974983tate_o > $o))). 39.99/14.69 thf(member1389040324_state_type, type, member1389040324_state: (produc1115495963_state > (set_Pr795498619_state > $o))). 39.99/14.69 thf(pa_type, type, pa: (a > (state > $o))). 39.99/14.69 thf(qa_type, type, qa: (a > (state > $o))). 39.99/14.69 thf(r_type, type, r: set_Pr795498619_state). 39.99/14.69 thf(x_type, type, x: state). 39.99/14.69 thf(sk1_type, type, sk1: $o). 39.99/14.69 thf(sk2_type, type, sk2: state). 39.99/14.69 thf(sk3_type, type, sk3: state). 39.99/14.69 thf(sk4_type, type, sk4: a). 39.99/14.69 thf(sk5_type, type, sk5: a). 39.99/14.69 thf(sk6_type, type, sk6: state). 39.99/14.69 thf(63,axiom,((is_sin1547905295tate_o = (^ [A:set_Pr1590995257tate_o]: ? [B:produc696469763tate_o]: (A = (insert2053719859tate_o @ B @ bot_bo170732493tate_o))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_is__singleton__def)). 39.99/14.69 thf(408,plain,(((is_sin1547905295tate_o) = (^ [A:set_Pr1590995257tate_o]: ? [B:produc696469763tate_o]: (A = (insert2053719859tate_o @ B @ bot_bo170732493tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 39.99/14.69 thf(409,plain,(((is_sin1547905295tate_o) = (^ [A:set_Pr1590995257tate_o]: ? [B:produc696469763tate_o]: (A = (insert2053719859tate_o @ B @ bot_bo170732493tate_o))))),inference(lifteq,[status(thm)],[408])). 39.99/14.69 thf(128,axiom,((! [A:state,B:(state > $o),C:com,D:nat,E:state,F:(state > $o)]: ((((! [G:state,H:state]: ((((execn @ G @ C @ D @ H) => (F @ H)) <= (B @ G)) <= (F @ G))) => (~ (B @ E) & (F @ E))) <= (F @ A)) <= (execn @ A @ (while @ B @ C) @ D @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_while__rule)). 39.99/14.69 thf(645,plain,((! [A:state,B:(state > $o),C:com,D:nat,E:state,F:(state > $o)]: (((! [G:state,H:state]: (((execn @ G @ C @ D @ H) => (F @ H)) | ~ (B @ G) | ~ (F @ G))) => (~ (B @ E) & (F @ E))) | ~ (F @ A) | ~ (execn @ A @ (while @ (B) @ C) @ D @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 39.99/14.69 thf(171,axiom,((! [A:(state > $o),B:state,C:com]: ((A @ B) => ((termi @ C @ B) => ((termi @ (while @ A @ C) @ B) <= (! [D:state]: ((termi @ (while @ A @ C) @ D) <= (exec @ B @ C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_termi_OWhileTrue)). 39.99/14.69 thf(809,plain,((! [A:(state > $o),B:state,C:com]: ((A @ B) => ((termi @ C @ B) => ((termi @ (while @ (A) @ C) @ B) | ~ (! [D:state]: ((termi @ (while @ (A) @ C) @ D) | ~ (exec @ B @ C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 39.99/14.69 thf(122,axiom,((! [A:($o > $o),B:(state > (state > $o)),C:produc1115495963_state]: ((A @ (produc789892016tate_o @ B @ C)) = (produc789892016tate_o @ (^ [D:state,E:state]: (A @ (B @ D @ E))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_prod_Ocase__distrib)). 39.99/14.69 thf(619,plain,((! [A:($o > $o),B:(state > (state > $o)),C:produc1115495963_state]: ((A @ (produc789892016tate_o @ (B) @ C)) = (produc789892016tate_o @ (^ [D:state,E:state]: (A @ (B @ D @ E))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 39.99/14.69 thf(622,plain,((! [A:(state > (state > $o)),B:produc1115495963_state]: ($false = (produc789892016tate_o @ (^ [C:state,D:state]: ($false)) @ B)))),inference(instance,[status(thm)],[619])). 39.99/14.69 thf(623,plain,((! [A:produc1115495963_state]: ~ (produc789892016tate_o @ (^ [B:state,C:state]: ($false)) @ A))),inference(simp,[status(thm)],[622])). 39.99/14.69 thf(628,plain,((~ (? [A:produc1115495963_state]: (produc789892016tate_o @ (^ [B:state,C:state]: ($false)) @ A)))),inference(miniscope,[status(thm)],[623])). 39.99/14.69 thf(629,plain,(! [A:produc1115495963_state] : ((~ (produc789892016tate_o @ (^ [B:state,C:state]: ($false)) @ A)))),inference(cnf,[status(esa)],[628])). 39.99/14.69 thf(78,axiom,((! [A:set_state,B:set_Pr795498619_state]: ((! [C:state,D:state]: (((member_state @ D @ A) => ((C != D) => ((member1389040324_state @ (produc64584659_state @ C @ D) @ B) | (member1389040324_state @ (produc64584659_state @ D @ C) @ B)))) <= (member_state @ C @ A))) => (total_on_state @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_total__onI)). 39.99/14.69 thf(468,plain,((! [A:set_state,B:set_Pr795498619_state]: ((! [C:state,D:state]: (((member_state @ D @ A) => ((~ (C = D)) => ((member1389040324_state @ (produc64584659_state @ C @ D) @ B) | (member1389040324_state @ (produc64584659_state @ D @ C) @ B)))) | ~ (member_state @ C @ A))) => (total_on_state @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 39.99/14.69 thf(15,axiom,((! [A:produc1115495963_state,B:set_Pr795498619_state]: ((member1389040324_state @ A @ B) => (? [C:set_Pr795498619_state]: ((B = (insert311944171_state @ A @ C)) & ~ (member1389040324_state @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_mk__disjoint__insert)). 39.99/14.69 thf(234,plain,((! [A:produc1115495963_state,B:set_Pr795498619_state]: ((member1389040324_state @ A @ B) => (? [C:set_Pr795498619_state]: ((B = (insert311944171_state @ A @ C)) & ~ (member1389040324_state @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 39.99/14.69 thf(103,axiom,((! [A:(produc1115495963_state > $o),B:produc1115495963_state]: ((A @ B) <= (! [C:state,D:state]: (A @ (produc64584659_state @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_prod__cases)). 39.99/14.69 thf(555,plain,((! [A:(produc1115495963_state > $o),B:produc1115495963_state]: ((A @ B) | ~ (! [C:state,D:state]: (A @ (produc64584659_state @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 39.99/14.69 thf(44,axiom,((! [A:set_Pr1590995257tate_o,B:set_Pr1590995257tate_o]: (((^ [C:(a > (state > $o)),D:produc204914599tate_o]: (member1838112666tate_o @ (produc33908149tate_o @ C @ D) @ A)) = (^ [C:(a > (state > $o)),D:produc204914599tate_o]: (member1838112666tate_o @ (produc33908149tate_o @ C @ D) @ B))) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_pred__equals__eq2)). 39.99/14.69 thf(333,plain,((! [A:set_Pr1590995257tate_o,B:set_Pr1590995257tate_o]: (((^ [C:(a > (state > $o)),D:produc204914599tate_o]: (member1838112666tate_o @ (produc33908149tate_o @ C @ D) @ A)) = (^ [C:(a > (state > $o)),D:produc204914599tate_o]: (member1838112666tate_o @ (produc33908149tate_o @ C @ D) @ B))) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 39.99/14.69 thf(19,axiom,((! [A:(produc696469763tate_o > $o)]: ((bot_bo170732493tate_o = (collec1499596504tate_o @ A)) = (! [B:produc696469763tate_o]: ~ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_empty__Collect__eq)). 39.99/14.69 thf(249,plain,((! [A:(produc696469763tate_o > $o)]: ((bot_bo170732493tate_o = (collec1499596504tate_o @ (A))) = (! [B:produc696469763tate_o]: ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 39.99/14.69 thf(80,axiom,((! [A:com,B:com,C:com,D:com]: (((semi @ A @ B) = (semi @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_com_Oinject_I2_J)). 39.99/14.69 thf(481,plain,((! [A:com,B:com,C:com,D:com]: (((semi @ A @ B) = (semi @ C @ D)) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 39.99/14.69 thf(50,axiom,((! [A:produc696469763tate_o,B:set_Pr1590995257tate_o,C:produc696469763tate_o]: (((~ (member1838112666tate_o @ A @ B)) => (A = C)) => (member1838112666tate_o @ A @ (insert2053719859tate_o @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_insertCI)). 39.99/14.69 thf(352,plain,((! [A:produc696469763tate_o,B:set_Pr1590995257tate_o,C:produc696469763tate_o]: (((~ (member1838112666tate_o @ A @ B)) => (A = C)) => (member1838112666tate_o @ A @ (insert2053719859tate_o @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 39.99/14.69 thf(137,axiom,((is_emp807847857tate_o = (^ [A:set_Pr1590995257tate_o]: (A = bot_bo170732493tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_Set_Ois__empty__def)). 39.99/14.69 thf(683,plain,(((is_emp807847857tate_o) = (^ [A:set_Pr1590995257tate_o]: (A = bot_bo170732493tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 39.99/14.69 thf(37,axiom,((! [A:produc1115495963_state,B:produc1115495963_state,C:set_Pr795498619_state]: ((member1389040324_state @ A @ (insert311944171_state @ B @ C)) = ((A = B) | (member1389040324_state @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_insert__iff)). 39.99/14.69 thf(308,plain,((! [A:produc1115495963_state,B:produc1115495963_state,C:set_Pr795498619_state]: ((member1389040324_state @ A @ (insert311944171_state @ B @ C)) = ((A = B) | (member1389040324_state @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 39.99/14.69 thf(57,axiom,((! [A:produc696469763tate_o,B:(produc696469763tate_o > $o)]: ((member1838112666tate_o @ A @ (collec1499596504tate_o @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_mem__Collect__eq)). 39.99/14.69 thf(379,plain,((! [A:produc696469763tate_o,B:(produc696469763tate_o > $o)]: ((member1838112666tate_o @ A @ (collec1499596504tate_o @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 39.99/14.69 thf(88,axiom,((! [A:(state > nat)]: (wf_state @ (measure_state @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_wf__measure)). 39.99/14.69 thf(510,plain,((! [A:(state > nat)]: (wf_state @ (measure_state @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 39.99/14.69 thf(511,plain,(! [A:(state > nat)] : ((wf_state @ (measure_state @ (A))))),inference(cnf,[status(esa)],[510])). 39.99/14.69 thf(135,axiom,((! [A:produc696469763tate_o,B:set_Pr1590995257tate_o]: ((insert2053719859tate_o @ A @ (insert2053719859tate_o @ A @ B)) = (insert2053719859tate_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_insert__absorb2)). 39.99/14.69 thf(677,plain,((! [A:produc696469763tate_o,B:set_Pr1590995257tate_o]: ((insert2053719859tate_o @ A @ (insert2053719859tate_o @ A @ B)) = (insert2053719859tate_o @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 39.99/14.69 thf(92,axiom,((insert311944171_state = (^ [A:produc1115495963_state,B:set_Pr795498619_state]: (collec496201222_state @ (^ [C:produc1115495963_state]: ((C = A) | (member1389040324_state @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_insert__compr)). 39.99/14.69 thf(522,plain,(((insert311944171_state) = (^ [A:produc1115495963_state,B:set_Pr795498619_state]: (collec496201222_state @ (^ [C:produc1115495963_state]: ((C = A) | (member1389040324_state @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 39.99/14.69 thf(523,plain,(((insert311944171_state) = (^ [A:produc1115495963_state,B:set_Pr795498619_state]: (collec496201222_state @ (^ [C:produc1115495963_state]: ((C = A) | (member1389040324_state @ C @ B))))))),inference(lifteq,[status(thm)],[522])). 39.99/14.69 thf(112,axiom,((! [A:set_Pr795498619_state]: ((! [B:state,C:set_state]: ((member_state @ B @ C) => (? [D:state]: ((member_state @ D @ C) & ! [E:state]: ((~ (member_state @ E @ C)) <= (member1389040324_state @ (produc64584659_state @ E @ D) @ A)))))) => (wf_state @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_wfI__min)). 39.99/14.69 thf(582,plain,((! [A:set_Pr795498619_state]: ((! [B:state,C:set_state]: ((member_state @ B @ C) => (? [D:state]: ((member_state @ D @ C) & ! [E:state]: (~ (member_state @ E @ C) | ~ (member1389040324_state @ (produc64584659_state @ E @ D) @ A)))))) => (wf_state @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 39.99/14.69 thf(96,axiom,((wf_state = (^ [A:set_Pr795498619_state]: ! [B:(state > $o)]: ((! [C:state]: ((B @ C) <= (! [D:state]: ((member1389040324_state @ (produc64584659_state @ D @ C) @ A) => (B @ D))))) => (! [C:state]: (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_wf__def)). 39.99/14.69 thf(533,plain,(((wf_state) = (^ [A:set_Pr795498619_state]: ! [B:(state > $o)]: ((! [C:state]: ((B @ C) | ~ (! [D:state]: ((member1389040324_state @ (produc64584659_state @ D @ C) @ A) => (B @ D))))) => (! [C:state]: (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 39.99/14.69 thf(168,axiom,((! [A:(state > $o),B:com]: (wf_state @ (collec496201222_state @ (produc789892016tate_o @ (^ [C:state,D:state]: ((exec @ D @ B @ C) & (A @ D) & (termi @ (while @ A @ B) @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_wf__termi)). 39.99/14.69 thf(797,plain,((! [A:(state > $o),B:com]: (wf_state @ (collec496201222_state @ (produc789892016tate_o @ (^ [C:state,D:state]: ((exec @ D @ B @ C) & (A @ D) & (termi @ (while @ A @ B) @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 39.99/14.69 thf(1,conjecture,((! [A:state,B:state]: (! [C:a]: (~ (pa @ C @ A) | (A != x) | (qa @ C @ B)) | ~ (exec @ A @ body @ B)) & ! [A:a,B:state]: (~ (pa @ A @ B) | (termi @ body @ B) | (B != x)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2)). 39.99/14.69 thf(2,negated_conjecture,((~ (! [A:state,B:state]: (! [C:a]: (~ (pa @ C @ A) | (A != x) | (qa @ C @ B)) | ~ (exec @ A @ body @ B)) & ! [A:a,B:state]: (~ (pa @ A @ B) | (termi @ body @ B) | (B != x))))),inference(neg_conjecture,[status(cth)],[1])). 39.99/14.69 thf(183,plain,((~ (! [A:state,B:state]: (! [C:a]: (~ (pa @ C @ A) | ~ (A = x) | (qa @ C @ B)) | ~ (exec @ A @ body @ B)) & ! [A:a,B:state]: (~ (pa @ A @ B) | (termi @ body @ B) | ~ (B = x))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 39.99/14.69 thf(185,plain,(sk1 | (~ (termi @ body @ sk6))),inference(cnf,[status(esa)],[183])). 39.99/14.69 thf(145,axiom,((produc938968666tate_o = produc789892016tate_o)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_internal__case__prod__def)). 39.99/14.69 thf(709,plain,(((produc938968666tate_o) = (produc789892016tate_o))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 39.99/14.69 thf(65,axiom,((! [A:set_Pr795498619_state]: ((collec496201222_state @ (^ [B:produc1115495963_state]: (member1389040324_state @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_Collect__mem__eq)). 39.99/14.69 thf(417,plain,((! [A:set_Pr795498619_state]: ((collec496201222_state @ (^ [B:produc1115495963_state]: (member1389040324_state @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 39.99/14.69 thf(60,axiom,((! [A:(produc1115495963_state > $o)]: (((collec496201222_state @ A) = bot_bo1625160935_state) = (! [B:produc1115495963_state]: ~ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_Collect__empty__eq)). 39.99/14.69 thf(389,plain,((! [A:(produc1115495963_state > $o)]: (((collec496201222_state @ (A)) = bot_bo1625160935_state) = (! [B:produc1115495963_state]: ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 39.99/14.69 thf(108,axiom,((! [A:((a > (state > $o)) > (produc204914599tate_o > $o)),B:(a > (state > $o)),C:produc204914599tate_o]: ((produc1271576886te_o_o @ A @ (produc33908149tate_o @ B @ C)) => (A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_case__prodD)). 39.99/14.69 thf(570,plain,((! [A:((a > (state > $o)) > (produc204914599tate_o > $o)),B:(a > (state > $o)),C:produc204914599tate_o]: ((produc1271576886te_o_o @ (A) @ (produc33908149tate_o @ (B) @ C)) => (A @ (B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 39.99/14.69 thf(184,plain,((pa @ sk4 @ sk2) | ~ (sk1)),inference(cnf,[status(esa)],[183])). 39.99/14.69 thf(51,axiom,((! [A:produc1115495963_state,B:produc1115495963_state,C:set_Pr795498619_state]: ((insert311944171_state @ A @ (insert311944171_state @ B @ C)) = (insert311944171_state @ B @ (insert311944171_state @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_insert__commute)). 39.99/14.69 thf(357,plain,((! [A:produc1115495963_state,B:produc1115495963_state,C:set_Pr795498619_state]: ((insert311944171_state @ A @ (insert311944171_state @ B @ C)) = (insert311944171_state @ B @ (insert311944171_state @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 39.99/14.69 thf(4,axiom,((! [A:produc696469763tate_o,B:set_Pr1590995257tate_o]: (member1838112666tate_o @ A @ (insert2053719859tate_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_insertI1)). 39.99/14.69 thf(195,plain,((! [A:produc696469763tate_o,B:set_Pr1590995257tate_o]: (member1838112666tate_o @ A @ (insert2053719859tate_o @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 39.99/14.69 thf(196,plain,(! [B:set_Pr1590995257tate_o,A:produc696469763tate_o] : ((member1838112666tate_o @ A @ (insert2053719859tate_o @ A @ B)))),inference(cnf,[status(esa)],[195])). 39.99/14.69 thf(100,axiom,((! [A:com,B:(a > (state > $o)),C:com,D:(a > (state > $o))]: (((produc1948644831tate_o @ A @ B) = (produc1948644831tate_o @ C @ D)) => (~ ((B != D) <= (A = C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_Pair__inject)). 39.99/14.69 thf(542,plain,((! [A:com,B:(a > (state > $o)),C:com,D:(a > (state > $o))]: (((produc1948644831tate_o @ A @ (B)) = (produc1948644831tate_o @ C @ (D))) => (~ (~ ((B) = (D)) | ~ (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 39.99/14.69 thf(173,axiom,((! [A:(state > $o),B:com,C:(nat > state),D:nat]: ((termi @ (while @ A @ B) @ (C @ D)) => ((! [E:nat]: (exec @ (C @ E) @ B @ (C @ (suc @ E)))) => (? [E:nat]: ~ (A @ (C @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_termi__while)). 39.99/14.69 thf(817,plain,((! [A:(state > $o),B:com,C:(nat > state),D:nat]: ((termi @ (while @ (A) @ B) @ (C @ D)) => ((! [E:nat]: (exec @ (C @ E) @ B @ (C @ (suc @ E)))) => (? [E:nat]: ~ (A @ (C @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 39.99/14.69 thf(180,axiom,((! [A:(state > $o),B:state,C:com]: ((~ (A @ B)) => (exec @ B @ (while @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_exec_OWhileFalse)). 39.99/14.69 thf(853,plain,((! [A:(state > $o),B:state,C:com]: ((~ (A @ B)) => (exec @ B @ (while @ (A) @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 39.99/14.69 thf(189,plain,((exec @ sk2 @ body @ sk3) | ~ (sk1)),inference(cnf,[status(esa)],[183])). 39.99/14.69 thf(119,axiom,((! [A:set_Pr795498619_state,B:set_state]: ((wf_state @ A) => ((~ (! [C:state]: ((member_state @ C @ B) => (~ (! [D:state]: ((member1389040324_state @ (produc64584659_state @ D @ C) @ A) => (~ (member_state @ D @ B)))))))) <= (B != bot_bot_set_state))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_wfE__min_H)). 39.99/14.69 thf(606,plain,((! [A:set_Pr795498619_state,B:set_state]: ((wf_state @ A) => (~ (! [C:state]: ((member_state @ C @ B) => (~ (! [D:state]: ((member1389040324_state @ (produc64584659_state @ D @ C) @ A) => (~ (member_state @ D @ B))))))) | (B = bot_bot_set_state))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 39.99/14.69 thf(186,plain,(sk1 | (sk6 = x)),inference(cnf,[status(esa)],[183])). 39.99/14.69 thf(192,plain,((sk6 = x) | sk1),inference(lifteq,[status(thm)],[186])). 39.99/14.69 thf(190,plain,(sk1 | (pa @ sk5 @ sk6)),inference(cnf,[status(esa)],[183])). 39.99/14.69 thf(880,plain,(sk1 | (pa @ sk5 @ x) | (sk6 != sk6)),inference(paramod_ordered,[status(thm)],[192,190])). 39.99/14.69 thf(881,plain,(sk1 | (pa @ sk5 @ x)),inference(pattern_uni,[status(thm)],[880:[]])). 39.99/14.69 thf(10,axiom,((! [A:produc1115495963_state,B:set_Pr795498619_state,C:produc1115495963_state]: (((A = C) <= (~ (member1389040324_state @ A @ B))) => (member1389040324_state @ A @ (insert311944171_state @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_insertCI)). 39.99/14.69 thf(216,plain,((! [A:produc1115495963_state,B:set_Pr795498619_state,C:produc1115495963_state]: (((A = C) | (member1389040324_state @ A @ B)) => (member1389040324_state @ A @ (insert311944171_state @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 39.99/14.69 thf(165,axiom,((! [A:set_Pr1590995257tate_o,B:(a > (state > $o)),C:com,D:(a > (state > $o)),E:(a > (state > $o))]: ((pHoare382919414oare_a @ A @ B @ C @ D) => ((pHoare382919414oare_a @ A @ B @ C @ E) <= (! [F:a,G:state]: ((E @ F @ G) <= (D @ F @ G))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_weaken__post)). 39.99/14.69 thf(789,plain,((! [A:set_Pr1590995257tate_o,B:(a > (state > $o)),C:com,D:(a > (state > $o)),E:(a > (state > $o))]: ((pHoare382919414oare_a @ A @ (B) @ C @ (D)) => ((pHoare382919414oare_a @ A @ (B) @ C @ (E)) | ~ (! [F:a,G:state]: ((E @ F @ G) | ~ (D @ F @ G))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 39.99/14.69 thf(115,axiom,((! [A:(state > $o),B:com]: ((while @ A @ B) != call))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_com_Odistinct_I25_J)). 39.99/14.69 thf(591,plain,((! [A:(state > $o),B:com]: ~ ((while @ (A) @ B) = call))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 39.99/14.69 thf(40,axiom,((! [A:produc1115495963_state,B:produc1115495963_state,C:produc1115495963_state,D:produc1115495963_state]: (((insert311944171_state @ A @ (insert311944171_state @ B @ bot_bo1625160935_state)) = (insert311944171_state @ C @ (insert311944171_state @ D @ bot_bo1625160935_state))) = (((A = C) & (B = D)) | ((B = C) & (A = D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_doubleton__eq__iff)). 39.99/14.69 thf(321,plain,((! [A:produc1115495963_state,B:produc1115495963_state,C:produc1115495963_state,D:produc1115495963_state]: (((insert311944171_state @ A @ (insert311944171_state @ B @ bot_bo1625160935_state)) = (insert311944171_state @ C @ (insert311944171_state @ D @ bot_bo1625160935_state))) = (((A = C) & (B = D)) | ((B = C) & (A = D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 39.99/14.69 thf(56,axiom,((! [A:produc1115495963_state]: ((collec496201222_state @ (= @ produc1115495963_state @ A)) = (insert311944171_state @ A @ bot_bo1625160935_state)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_singleton__conv2)). 39.99/14.69 thf(376,plain,((! [A:produc1115495963_state]: ((collec496201222_state @ (= @ produc1115495963_state @ A)) = (insert311944171_state @ A @ bot_bo1625160935_state)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 39.99/14.69 thf(16,axiom,((! [A:produc1115495963_state,B:produc1115495963_state]: ((A = B) <= (member1389040324_state @ A @ (insert311944171_state @ B @ bot_bo1625160935_state))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_singletonD)). 39.99/14.69 thf(238,plain,((! [A:produc1115495963_state,B:produc1115495963_state]: ((A = B) | ~ (member1389040324_state @ A @ (insert311944171_state @ B @ bot_bo1625160935_state))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 39.99/14.69 thf(170,axiom,((! [A:(state > $o),B:state,C:com]: ((termi @ (while @ A @ C) @ B) <= (~ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_termi_OWhileFalse)). 39.99/14.69 thf(806,plain,((! [A:(state > $o),B:state,C:com]: ((termi @ (while @ (A) @ C) @ B) | (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 39.99/14.69 thf(139,axiom,((! [A:$o,B:(state > (state > $o))]: ((produc789892016tate_o @ (^ [C:state,D:state]: ((B @ C @ D) & (A)))) = (^ [C:produc1115495963_state]: ((A) & (produc789892016tate_o @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_split__part)). 39.99/14.69 thf(687,plain,((! [A:$o,B:(state > (state > $o))]: ((produc789892016tate_o @ (^ [C:state,D:state]: ((B @ C @ D) & (A)))) = (^ [C:produc1115495963_state]: ((A) & (produc789892016tate_o @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 39.99/14.69 thf(29,axiom,((! [A:set_Pr1590995257tate_o]: ((collec1499596504tate_o @ (^ [B:produc696469763tate_o]: (member1838112666tate_o @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_Collect__mem__eq)). 39.99/14.69 thf(280,plain,((! [A:set_Pr1590995257tate_o]: ((collec1499596504tate_o @ (^ [B:produc696469763tate_o]: (member1838112666tate_o @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 39.99/14.69 thf(124,axiom,((! [A:(produc1115495963_state > $o)]: ((produc789892016tate_o @ (^ [B:state,C:state]: (A @ (produc64584659_state @ B @ C)))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_case__prod__eta)). 39.99/14.69 thf(634,plain,((! [A:(produc1115495963_state > $o)]: ((produc789892016tate_o @ (^ [B:state,C:state]: (A @ (produc64584659_state @ B @ C)))) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 39.99/14.69 thf(11,axiom,((! [A:set_Pr795498619_state]: ((? [B:produc1115495963_state]: (member1389040324_state @ B @ A)) = (A != bot_bo1625160935_state)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_ex__in__conv)). 39.99/14.69 thf(221,plain,((! [A:set_Pr795498619_state]: ((? [B:produc1115495963_state]: (member1389040324_state @ B @ A)) = (~ (A = bot_bo1625160935_state))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 39.99/14.69 thf(24,axiom,((! [A:set_Pr1590995257tate_o]: ((! [B:produc696469763tate_o]: ~ (member1838112666tate_o @ B @ A)) = (A = bot_bo170732493tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_all__not__in__conv)). 39.99/14.69 thf(265,plain,((! [A:set_Pr1590995257tate_o]: ((! [B:produc696469763tate_o]: ~ (member1838112666tate_o @ B @ A)) = (A = bot_bo170732493tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 39.99/14.69 thf(94,axiom,((! [A:produc696469763tate_o]: (member1838112666tate_o @ A @ (insert2053719859tate_o @ A @ bot_bo170732493tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_singletonI)). 39.99/14.69 thf(527,plain,((! [A:produc696469763tate_o]: (member1838112666tate_o @ A @ (insert2053719859tate_o @ A @ bot_bo170732493tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 39.99/14.69 thf(118,axiom,((! [A:produc1115495963_state,B:(state > (state > $o))]: ((! [C:state,D:state]: ((A = (produc64584659_state @ C @ D)) => (B @ C @ D))) => (produc789892016tate_o @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_case__prodI2)). 39.99/14.69 thf(602,plain,((! [A:produc1115495963_state,B:(state > (state > $o))]: ((! [C:state,D:state]: ((A = (produc64584659_state @ C @ D)) => (B @ C @ D))) => (produc789892016tate_o @ (B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 39.99/14.69 thf(159,axiom,((! [A:(a > (state > $o)),B:produc204914599tate_o,C:(a > (state > $o)),D:produc204914599tate_o]: ((~ ((B != D) <= (A = C))) <= ((produc33908149tate_o @ A @ B) = (produc33908149tate_o @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_Pair__inject)). 39.99/14.69 thf(766,plain,((! [A:(a > (state > $o)),B:produc204914599tate_o,C:(a > (state > $o)),D:produc204914599tate_o]: (~ (~ (B = D) | ~ ((A) = (C))) | ~ ((produc33908149tate_o @ (A) @ B) = (produc33908149tate_o @ (C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 39.99/14.69 thf(89,axiom,((! [A:(produc1115495963_state > $o),B:(produc1115495963_state > $o)]: ((! [C:produc1115495963_state]: ((A @ C) = (B @ C))) => ((collec496201222_state @ A) = (collec496201222_state @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_Collect__cong)). 39.99/14.69 thf(512,plain,((! [A:(produc1115495963_state > $o),B:(produc1115495963_state > $o)]: ((! [C:produc1115495963_state]: ((A @ C) = (B @ C))) => ((collec496201222_state @ (A)) = (collec496201222_state @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 39.99/14.69 thf(95,axiom,((! [A:produc696469763tate_o]: ~ (! [B:(a > (state > $o)),C:produc204914599tate_o]: (A != (produc33908149tate_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_old_Oprod_Oexhaust)). 39.99/14.69 thf(529,plain,((! [A:produc696469763tate_o]: ~ (! [B:(a > (state > $o)),C:produc204914599tate_o]: ~ (A = (produc33908149tate_o @ (B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 39.99/14.69 thf(131,axiom,((! [A:state,B:state,C:state,D:state]: ((~ ((B != D) <= (A = C))) <= ((produc64584659_state @ A @ B) = (produc64584659_state @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_Pair__inject)). 39.99/14.69 thf(661,plain,((! [A:state,B:state,C:state,D:state]: (~ (~ (B = D) | ~ (A = C)) | ~ ((produc64584659_state @ A @ B) = (produc64584659_state @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 39.99/14.69 thf(166,axiom,((! [A:state,B:state]: ((exec @ A @ call @ B) <= (exec @ A @ body @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_exec_Ointros_I7_J)). 39.99/14.69 thf(793,plain,((! [A:state,B:state]: ((exec @ A @ call @ B) | ~ (exec @ A @ body @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 39.99/14.69 thf(157,axiom,((bot_bo2130564770te_o_o = (^ [A:(a > (state > $o)),B:produc204914599tate_o]: (member1838112666tate_o @ (produc33908149tate_o @ A @ B) @ bot_bo170732493tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_bot__empty__eq2)). 39.99/14.69 thf(761,plain,(((bot_bo2130564770te_o_o) = (^ [A:(a > (state > $o)),B:produc204914599tate_o]: (member1838112666tate_o @ (produc33908149tate_o @ A @ B) @ bot_bo170732493tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 39.99/14.69 thf(54,axiom,((! [A:produc1115495963_state]: ~ (member1389040324_state @ A @ bot_bo1625160935_state))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_empty__iff)). 39.99/14.69 thf(366,plain,((! [A:produc1115495963_state]: ~ (member1389040324_state @ A @ bot_bo1625160935_state))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 39.99/14.69 thf(147,axiom,((! [A:com,B:(a > (state > $o)),C:com,D:(a > (state > $o))]: (((produc1948644831tate_o @ A @ B) = (produc1948644831tate_o @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_prod_Oinject)). 39.99/14.69 thf(714,plain,((! [A:com,B:(a > (state > $o)),C:com,D:(a > (state > $o))]: (((produc1948644831tate_o @ A @ (B)) = (produc1948644831tate_o @ C @ (D))) = (((B) = (D)) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 39.99/14.69 thf(176,axiom,((! [A:com,B:state,C:(nat > state),D:nat,E:(state > $o),F:com]: ((termi @ A @ B) => ((? [G:nat]: ~ (E @ (C @ G))) <= (! [G:nat]: (exec @ (C @ G) @ F @ (C @ (suc @ G))) & (A = (while @ E @ F)) & (B = (C @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_termi__while__lemma)). 39.99/14.69 thf(825,plain,((! [A:com,B:state,C:(nat > state),D:nat,E:(state > $o),F:com]: ((termi @ A @ B) => (? [G:nat]: ~ (E @ (C @ G)) | ~ (! [G:nat]: (exec @ (C @ G) @ F @ (C @ (suc @ G))) & (A = (while @ (E) @ F)) & (B = (C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 39.99/14.69 thf(161,axiom,((! [A:state,B:com,C:nat,D:state,E:com,F:state]: ((execn @ A @ B @ C @ D) => ((execn @ D @ E @ C @ F) => (execn @ A @ (semi @ B @ E) @ C @ F))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_execn_Ointros_I2_J)). 39.99/14.69 thf(778,plain,((! [A:state,B:com,C:nat,D:state,E:com,F:state]: ((execn @ A @ B @ C @ D) => ((execn @ D @ E @ C @ F) => (execn @ A @ (semi @ B @ E) @ C @ F))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 39.99/14.69 thf(35,axiom,((! [A:produc1115495963_state]: (member1389040324_state @ A @ (insert311944171_state @ A @ bot_bo1625160935_state)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_singletonI)). 39.99/14.69 thf(302,plain,((! [A:produc1115495963_state]: (member1389040324_state @ A @ (insert311944171_state @ A @ bot_bo1625160935_state)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 39.99/14.69 thf(49,axiom,((! [A:(produc696469763tate_o > $o)]: (((collec1499596504tate_o @ A) = bot_bo170732493tate_o) = (! [B:produc696469763tate_o]: ~ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_Collect__empty__eq)). 39.99/14.69 thf(349,plain,((! [A:(produc696469763tate_o > $o)]: (((collec1499596504tate_o @ (A)) = bot_bo170732493tate_o) = (! [B:produc696469763tate_o]: ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 39.99/14.69 thf(174,axiom,((! [A:(state > $o),B:state,C:com,D:state,E:state]: ((A @ B) => ((exec @ B @ C @ D) => ((exec @ B @ (while @ A @ C) @ E) <= (exec @ D @ (while @ A @ C) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_exec_OWhileTrue)). 39.99/14.69 thf(820,plain,((! [A:(state > $o),B:state,C:com,D:state,E:state]: ((A @ B) => ((exec @ B @ C @ D) => ((exec @ B @ (while @ (A) @ C) @ E) | ~ (exec @ D @ (while @ (A) @ C) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 39.99/14.69 thf(105,axiom,((! [A:produc1115495963_state,B:(produc1115495963_state > $o)]: ((member1389040324_state @ A @ (collec496201222_state @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_mem__Collect__eq)). 39.99/14.69 thf(561,plain,((! [A:produc1115495963_state,B:(produc1115495963_state > $o)]: ((member1389040324_state @ A @ (collec496201222_state @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 39.99/14.69 thf(61,axiom,((! [A:set_Pr1590995257tate_o,B:(a > (state > $o)),C:com,D:(a > (state > $o)),E:(a > (state > $o)),F:(a > (state > $o))]: ((pHoare382919414oare_a @ A @ B @ C @ D) => ((! [G:state,H:state]: ((! [I:a]: ((D @ I @ H) <= (B @ I @ G))) => (! [I:a]: ((F @ I @ H) <= (E @ I @ G)))) & ! [G:state]: ((? [H:a]: (E @ H @ G)) => (? [H:a]: (B @ H @ G)))) => (pHoare382919414oare_a @ A @ E @ C @ F))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_thoare_OConseq)). 39.99/14.69 thf(392,plain,((! [A:set_Pr1590995257tate_o,B:(a > (state > $o)),C:com,D:(a > (state > $o)),E:(a > (state > $o)),F:(a > (state > $o))]: ((pHoare382919414oare_a @ A @ (B) @ C @ (D)) => ((! [G:state,H:state]: ((! [I:a]: ((D @ I @ H) | ~ (B @ I @ G))) => (! [I:a]: ((F @ I @ H) | ~ (E @ I @ G)))) & ! [G:state]: ((? [H:a]: (E @ H @ G)) => (? [H:a]: (B @ H @ G)))) => (pHoare382919414oare_a @ A @ (E) @ C @ (F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 39.99/14.69 thf(68,axiom,((! [A:produc696469763tate_o,B:produc696469763tate_o]: ((member1838112666tate_o @ A @ (insert2053719859tate_o @ B @ bot_bo170732493tate_o)) => (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_singletonD)). 39.99/14.69 thf(424,plain,((! [A:produc696469763tate_o,B:produc696469763tate_o]: ((member1838112666tate_o @ A @ (insert2053719859tate_o @ B @ bot_bo170732493tate_o)) => (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 39.99/14.69 thf(27,axiom,((! [A:produc696469763tate_o,B:set_Pr1590995257tate_o,C:set_Pr1590995257tate_o]: ((~ (member1838112666tate_o @ A @ B)) => ((((insert2053719859tate_o @ A @ B) = (insert2053719859tate_o @ A @ C)) = (B = C)) <= (~ (member1838112666tate_o @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_insert__ident)). 39.99/14.69 thf(275,plain,((! [A:produc696469763tate_o,B:set_Pr1590995257tate_o,C:set_Pr1590995257tate_o]: ((~ (member1838112666tate_o @ A @ B)) => ((((insert2053719859tate_o @ A @ B) = (insert2053719859tate_o @ A @ C)) = (B = C)) | (member1838112666tate_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 39.99/14.69 thf(140,axiom,((! [A:(produc696469763tate_o > $o),B:produc696469763tate_o]: ((! [C:(a > (state > $o)),D:produc204914599tate_o]: (A @ (produc33908149tate_o @ C @ D))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_prod__cases)). 39.99/14.69 thf(693,plain,((! [A:(produc696469763tate_o > $o),B:produc696469763tate_o]: ((! [C:(a > (state > $o)),D:produc204914599tate_o]: (A @ (produc33908149tate_o @ (C) @ D))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 39.99/14.69 thf(20,axiom,((! [A:produc1115495963_state,B:set_Pr795498619_state,C:produc1115495963_state,D:set_Pr795498619_state]: ((~ (member1389040324_state @ A @ B)) => ((~ (member1389040324_state @ C @ D)) => (((insert311944171_state @ A @ B) = (insert311944171_state @ C @ D)) = (((B = D) <= (A = C)) & ((A != C) => (? [E:set_Pr795498619_state]: ((B = (insert311944171_state @ C @ E)) & (D = (insert311944171_state @ A @ E)) & ~ (member1389040324_state @ A @ E) & ~ (member1389040324_state @ C @ E)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_insert__eq__iff)). 39.99/14.69 thf(252,plain,((! [A:produc1115495963_state,B:set_Pr795498619_state,C:produc1115495963_state,D:set_Pr795498619_state]: ((~ (member1389040324_state @ A @ B)) => ((~ (member1389040324_state @ C @ D)) => (((insert311944171_state @ A @ B) = (insert311944171_state @ C @ D)) = (((B = D) | ~ (A = C)) & ((~ (A = C)) => (? [E:set_Pr795498619_state]: ((B = (insert311944171_state @ C @ E)) & (D = (insert311944171_state @ A @ E)) & ~ (member1389040324_state @ A @ E) & ~ (member1389040324_state @ C @ E)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 39.99/14.69 thf(5,axiom,((! [A:set_Pr1590995257tate_o]: ((? [B:produc696469763tate_o]: (member1838112666tate_o @ B @ A)) = (A != bot_bo170732493tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_ex__in__conv)). 39.99/14.69 thf(197,plain,((! [A:set_Pr1590995257tate_o]: ((? [B:produc696469763tate_o]: (member1838112666tate_o @ B @ A)) = (~ (A = bot_bo170732493tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 39.99/14.69 thf(83,axiom,((! [A:produc696469763tate_o,B:set_Pr1590995257tate_o]: ((insert2053719859tate_o @ A @ B) != bot_bo170732493tate_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_insert__not__empty)). 39.99/14.69 thf(493,plain,((! [A:produc696469763tate_o,B:set_Pr1590995257tate_o]: ~ ((insert2053719859tate_o @ A @ B) = bot_bo170732493tate_o))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 39.99/14.69 thf(710,plain,(((produc789892016tate_o) = (produc938968666tate_o))),inference(lifteq,[status(thm)],[709])). 39.99/14.69 thf(74,axiom,((! [A:(produc204914599tate_o > $o),B:produc204914599tate_o]: ((A @ B) <= (! [C:com,D:(a > (state > $o))]: (A @ (produc1948644831tate_o @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_prod__cases)). 39.99/14.69 thf(456,plain,((! [A:(produc204914599tate_o > $o),B:produc204914599tate_o]: ((A @ B) | ~ (! [C:com,D:(a > (state > $o))]: (A @ (produc1948644831tate_o @ C @ (D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 39.99/14.69 thf(41,axiom,((! [A:produc696469763tate_o,B:set_Pr1590995257tate_o]: ((member1838112666tate_o @ A @ B) => (~ (! [C:set_Pr1590995257tate_o]: ((member1838112666tate_o @ A @ C) <= (B = (insert2053719859tate_o @ A @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_Set_Oset__insert)). 39.99/14.69 thf(324,plain,((! [A:produc696469763tate_o,B:set_Pr1590995257tate_o]: ((member1838112666tate_o @ A @ B) => (~ (! [C:set_Pr1590995257tate_o]: ((member1838112666tate_o @ A @ C) | ~ (B = (insert2053719859tate_o @ A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 39.99/14.69 thf(12,axiom,((! [A:produc1115495963_state,B:produc1115495963_state]: (((insert311944171_state @ A @ bot_bo1625160935_state) = (insert311944171_state @ B @ bot_bo1625160935_state)) => (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_singleton__inject)). 39.99/14.69 thf(224,plain,((! [A:produc1115495963_state,B:produc1115495963_state]: (((insert311944171_state @ A @ bot_bo1625160935_state) = (insert311944171_state @ B @ bot_bo1625160935_state)) => (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 39.99/14.69 thf(81,axiom,((! [A:produc696469763tate_o,B:((a > (state > $o)) > (produc204914599tate_o > $o))]: ((! [C:(a > (state > $o)),D:produc204914599tate_o]: ((B @ C @ D) <= (A = (produc33908149tate_o @ C @ D)))) => (produc1271576886te_o_o @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_case__prodI2)). 39.99/14.69 thf(484,plain,((! [A:produc696469763tate_o,B:((a > (state > $o)) > (produc204914599tate_o > $o))]: ((! [C:(a > (state > $o)),D:produc204914599tate_o]: ((B @ (C) @ D) | ~ (A = (produc33908149tate_o @ (C) @ D)))) => (produc1271576886te_o_o @ (B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 39.99/14.69 thf(13,axiom,((! [A:produc696469763tate_o]: ~ (member1838112666tate_o @ A @ bot_bo170732493tate_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_empty__iff)). 39.99/14.69 thf(227,plain,((! [A:produc696469763tate_o]: ~ (member1838112666tate_o @ A @ bot_bo170732493tate_o))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 39.99/14.69 thf(228,plain,((~ (? [A:produc696469763tate_o]: (member1838112666tate_o @ A @ bot_bo170732493tate_o)))),inference(miniscope,[status(thm)],[227])). 39.99/14.69 thf(229,plain,(! [A:produc696469763tate_o] : ((~ (member1838112666tate_o @ A @ bot_bo170732493tate_o)))),inference(cnf,[status(esa)],[228])). 39.99/14.69 thf(178,axiom,((! [A:set_Pr795498619_state,B:(a > (state > $o)),C:(a > (state > $o))]: ((wf_state @ A) => ((pHoare382919414oare_a @ bot_bo170732493tate_o @ B @ call @ C) <= (! [D:state]: (pHoare382919414oare_a @ (insert2053719859tate_o @ (produc33908149tate_o @ (^ [E:a,F:state]: ((member1389040324_state @ (produc64584659_state @ F @ D) @ A) & (B @ E @ F))) @ (produc1948644831tate_o @ call @ C)) @ bot_bo170732493tate_o) @ (^ [E:a,F:state]: ((B @ E @ F) & (F = D))) @ body @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_thoare_OCall)). 39.99/14.69 thf(847,plain,((! [A:set_Pr795498619_state,B:(a > (state > $o)),C:(a > (state > $o))]: ((wf_state @ A) => ((pHoare382919414oare_a @ bot_bo170732493tate_o @ (B) @ call @ (C)) | ~ (! [D:state]: (pHoare382919414oare_a @ (insert2053719859tate_o @ (produc33908149tate_o @ (^ [E:a,F:state]: ((member1389040324_state @ (produc64584659_state @ F @ D) @ A) & (B @ E @ F))) @ (produc1948644831tate_o @ call @ (C))) @ bot_bo170732493tate_o) @ (^ [E:a,F:state]: ((B @ E @ F) & (F = D))) @ body @ (C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 39.99/14.69 thf(177,axiom,((! [A:state]: (((! [B:a,C:state]: ((termi @ body @ C) <= ((pa @ B @ C) & (member1389040324_state @ (produc64584659_state @ C @ A) @ r))) & ! [B:state,C:state]: ((exec @ B @ body @ C) => (! [D:a]: (((member1389040324_state @ (produc64584659_state @ B @ A) @ r) & (pa @ D @ B)) => (qa @ D @ C))))) => (! [B:a,C:state]: ((termi @ body @ C) <= ((pa @ B @ C) & (C = A))) & ! [B:state,C:state]: ((exec @ B @ body @ C) => (! [D:a]: ((qa @ D @ C) <= ((pa @ D @ B) & (B = A))))))) & (pHoare382919414oare_a @ (insert2053719859tate_o @ (produc33908149tate_o @ (^ [B:a,C:state]: ((member1389040324_state @ (produc64584659_state @ C @ A) @ r) & (pa @ B @ C))) @ (produc1948644831tate_o @ call @ qa)) @ bot_bo170732493tate_o) @ (^ [B:a,C:state]: ((pa @ B @ C) & (C = A))) @ body @ qa)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 39.99/14.69 thf(830,plain,((! [A:state]: (((! [B:a,C:state]: ((termi @ body @ C) | ~ ((pa @ B @ C) & (member1389040324_state @ (produc64584659_state @ C @ A) @ r))) & ! [B:state,C:state]: ((exec @ B @ body @ C) => (! [D:a]: (((member1389040324_state @ (produc64584659_state @ B @ A) @ r) & (pa @ D @ B)) => (qa @ D @ C))))) => (! [B:a,C:state]: ((termi @ body @ C) | ~ ((pa @ B @ C) & (C = A))) & ! [B:state,C:state]: ((exec @ B @ body @ C) => (! [D:a]: ((qa @ D @ C) | ~ ((pa @ D @ B) & (B = A))))))) & (pHoare382919414oare_a @ (insert2053719859tate_o @ (produc33908149tate_o @ (^ [B:a,C:state]: ((member1389040324_state @ (produc64584659_state @ C @ A) @ r) & (pa @ B @ C))) @ (produc1948644831tate_o @ call @ (qa))) @ bot_bo170732493tate_o) @ (^ [B:a,C:state]: ((pa @ B @ C) & (C = A))) @ body @ (qa))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 39.99/14.69 thf(150,axiom,((! [A:produc204914599tate_o]: ? [B:com,C:(a > (state > $o))]: (A = (produc1948644831tate_o @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_surj__pair)). 39.99/14.69 thf(725,plain,((! [A:produc204914599tate_o]: ? [B:com,C:(a > (state > $o))]: (A = (produc1948644831tate_o @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 39.99/14.69 thf(66,axiom,((! [A:(state > (state > $o)),B:state,C:state]: ((produc789892016tate_o @ A @ (produc64584659_state @ B @ C)) <= (A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_case__prodI)). 39.99/14.69 thf(420,plain,((! [A:(state > (state > $o)),B:state,C:state]: ((produc789892016tate_o @ (A) @ (produc64584659_state @ B @ C)) | ~ (A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 39.99/14.69 thf(85,axiom,((! [A:set_Pr1590995257tate_o]: ((~ (! [B:produc696469763tate_o]: (A != (insert2053719859tate_o @ B @ bot_bo170732493tate_o)))) <= (is_sin1547905295tate_o @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_is__singletonE)). 39.99/14.69 thf(499,plain,((! [A:set_Pr1590995257tate_o]: (~ (! [B:produc696469763tate_o]: ~ (A = (insert2053719859tate_o @ B @ bot_bo170732493tate_o))) | ~ (is_sin1547905295tate_o @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 39.99/14.69 thf(181,axiom,((exec = (^ [A:state,B:com,C:state]: ? [D:nat]: (execn @ A @ B @ D @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_exec__iff__execn)). 39.99/14.69 thf(856,plain,(((exec) = (^ [A:state,B:com,C:state]: ? [D:nat]: (execn @ A @ B @ D @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 39.99/14.69 thf(857,plain,(((exec) = (^ [A:state,B:com,C:state]: ? [D:nat]: (execn @ A @ B @ D @ C)))),inference(lifteq,[status(thm)],[856])). 39.99/14.69 thf(91,axiom,((! [A:produc1115495963_state]: ? [B:state,C:state]: (A = (produc64584659_state @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_surj__pair)). 39.99/14.69 thf(519,plain,((! [A:produc1115495963_state]: ? [B:state,C:state]: (A = (produc64584659_state @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 39.99/14.69 thf(155,axiom,((! [A:($o > $o),B:(state > (state > $o)),C:produc1115495963_state]: ((~ (! [D:state,E:state]: ((C = (produc64584659_state @ D @ E)) => (~ (A @ (B @ D @ E)))))) <= (A @ (produc789892016tate_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_case__prodE2)). 39.99/14.69 thf(742,plain,((! [A:($o > $o),B:(state > (state > $o)),C:produc1115495963_state]: (~ (! [D:state,E:state]: ((C = (produc64584659_state @ D @ E)) => (~ (A @ (B @ D @ E))))) | ~ (A @ (produc789892016tate_o @ (B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 39.99/14.69 thf(82,axiom,((! [A:set_Pr795498619_state,B:(state > $o),C:state]: (((! [D:state]: ((B @ D) <= (! [E:state]: ((member1389040324_state @ (produc64584659_state @ E @ D) @ A) => (B @ E))))) => (B @ C)) <= (wf_state @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_wf__induct)). 39.99/14.69 thf(488,plain,((! [A:set_Pr795498619_state,B:(state > $o),C:state]: (((! [D:state]: ((B @ D) | ~ (! [E:state]: ((member1389040324_state @ (produc64584659_state @ E @ D) @ A) => (B @ E))))) => (B @ C)) | ~ (wf_state @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 39.99/14.69 thf(46,axiom,((! [A:set_Pr795498619_state]: ((! [B:produc1115495963_state]: ~ (member1389040324_state @ B @ A)) = (A = bot_bo1625160935_state)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_all__not__in__conv)). 39.99/14.69 thf(339,plain,((! [A:set_Pr795498619_state]: ((! [B:produc1115495963_state]: ~ (member1389040324_state @ B @ A)) = (A = bot_bo1625160935_state)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 39.99/14.69 thf(127,axiom,((! [A:set_Pr795498619_state,B:state]: ((~ (member1389040324_state @ (produc64584659_state @ B @ B) @ A)) <= (wf_state @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_wf__not__refl)). 39.99/14.69 thf(642,plain,((! [A:set_Pr795498619_state,B:state]: (~ (member1389040324_state @ (produc64584659_state @ B @ B) @ A) | ~ (wf_state @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 39.99/14.69 thf(125,axiom,((! [A:produc1115495963_state]: (produc789892016tate_o @ (^ [B:state,C:state]: ($true)) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_prod_Odisc__eq__case)). 39.99/14.69 thf(637,plain,((! [A:produc1115495963_state]: (produc789892016tate_o @ (^ [B:state,C:state]: ($true)) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 39.99/14.69 thf(144,axiom,((! [A:state,B:state,C:state,D:state]: (((produc64584659_state @ A @ B) = (produc64584659_state @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_prod_Oinject)). 39.99/14.69 thf(706,plain,((! [A:state,B:state,C:state,D:state]: (((produc64584659_state @ A @ B) = (produc64584659_state @ C @ D)) = ((A = C) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 39.99/14.69 thf(42,axiom,((! [A:produc696469763tate_o,B:set_Pr1590995257tate_o,C:produc696469763tate_o]: ((member1838112666tate_o @ A @ B) => (member1838112666tate_o @ A @ (insert2053719859tate_o @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_insertI2)). 39.99/14.69 thf(328,plain,((! [A:produc696469763tate_o,B:set_Pr1590995257tate_o,C:produc696469763tate_o]: ((member1838112666tate_o @ A @ B) => (member1838112666tate_o @ A @ (insert2053719859tate_o @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 39.99/14.69 thf(21,axiom,((! [A:produc1115495963_state]: ((collec496201222_state @ (^ [B:produc1115495963_state]: (B = A))) = (insert311944171_state @ A @ bot_bo1625160935_state)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_singleton__conv)). 39.99/14.69 thf(256,plain,((! [A:produc1115495963_state]: ((collec496201222_state @ (^ [B:produc1115495963_state]: (B = A))) = (insert311944171_state @ A @ bot_bo1625160935_state)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 39.99/14.69 thf(3,axiom,((insert2053719859tate_o = (^ [A:produc696469763tate_o,B:set_Pr1590995257tate_o]: (collec1499596504tate_o @ (^ [C:produc696469763tate_o]: ((member1838112666tate_o @ C @ B) | (C = A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_insert__compr)). 39.99/14.69 thf(193,plain,(((insert2053719859tate_o) = (^ [A:produc696469763tate_o,B:set_Pr1590995257tate_o]: (collec1499596504tate_o @ (^ [C:produc696469763tate_o]: ((member1838112666tate_o @ C @ B) | (C = A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 39.99/14.69 thf(98,axiom,((! [A:(com > ((a > (state > $o)) > $o)),B:com,C:(a > (state > $o))]: ((A @ B @ C) => (produc281270436te_o_o @ A @ (produc1948644831tate_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_case__prodI)). 39.99/14.69 thf(537,plain,((! [A:(com > ((a > (state > $o)) > $o)),B:com,C:(a > (state > $o))]: ((A @ B @ (C)) => (produc281270436te_o_o @ (A) @ (produc1948644831tate_o @ B @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 39.99/14.69 thf(138,axiom,((bot_bo935656620te_o_o = (^ [A:com,B:(a > (state > $o))]: (member221067728tate_o @ (produc1948644831tate_o @ A @ B) @ bot_bo1692783091tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_bot__empty__eq2)). 39.99/14.69 thf(685,plain,(((bot_bo935656620te_o_o) = (^ [A:com,B:(a > (state > $o))]: (member221067728tate_o @ (produc1948644831tate_o @ A @ B) @ bot_bo1692783091tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 39.99/14.69 thf(686,plain,(((^ [A:com,B:(a > (state > $o))]: (member221067728tate_o @ (produc1948644831tate_o @ A @ B) @ bot_bo1692783091tate_o)) = (bot_bo935656620te_o_o))),inference(lifteq,[status(thm)],[685])). 39.99/14.69 thf(79,axiom,((! [A:set_Pr795498619_state]: ((wf_state @ A) <= (! [B:(state > $o),C:state]: ((! [D:state]: ((B @ D) <= (! [E:state]: ((B @ E) <= (member1389040324_state @ (produc64584659_state @ E @ D) @ A))))) => (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_wfUNIVI)). 39.99/14.69 thf(476,plain,((! [A:set_Pr795498619_state]: ((wf_state @ A) | ~ (! [B:(state > $o),C:state]: ((! [D:state]: ((B @ D) | ~ (! [E:state]: ((B @ E) | ~ (member1389040324_state @ (produc64584659_state @ E @ D) @ A))))) => (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 39.99/14.69 thf(90,axiom,((! [A:set_Pr795498619_state,B:state,C:set_state]: ((wf_state @ A) => ((~ (! [D:state]: ((~ (! [E:state]: ((member1389040324_state @ (produc64584659_state @ E @ D) @ A) => (~ (member_state @ E @ C))))) <= (member_state @ D @ C)))) <= (member_state @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_wfE__min)). 39.99/14.69 thf(515,plain,((! [A:set_Pr795498619_state,B:state,C:set_state]: ((wf_state @ A) => (~ (! [D:state]: (~ (! [E:state]: ((member1389040324_state @ (produc64584659_state @ E @ D) @ A) => (~ (member_state @ E @ C)))) | ~ (member_state @ D @ C))) | ~ (member_state @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 39.99/14.69 thf(149,axiom,((! [A:(state > (state > $o)),B:produc1115495963_state]: ((produc789892016tate_o @ A @ B) => (~ (! [C:state,D:state]: ((~ (A @ C @ D)) <= (B = (produc64584659_state @ C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_case__prodE)). 39.99/14.69 thf(721,plain,((! [A:(state > (state > $o)),B:produc1115495963_state]: ((produc789892016tate_o @ (A) @ B) => (~ (! [C:state,D:state]: (~ (A @ C @ D) | ~ (B = (produc64584659_state @ C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 39.99/14.69 thf(86,axiom,((! [A:(produc696469763tate_o > $o),B:produc696469763tate_o]: ((A @ B) <= (! [C:(a > (state > $o)),D:produc204914599tate_o]: (A @ (produc33908149tate_o @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_old_Oprod_Oinducts)). 39.99/14.69 thf(503,plain,((! [A:(produc696469763tate_o > $o),B:produc696469763tate_o]: ((A @ B) | ~ (! [C:(a > (state > $o)),D:produc204914599tate_o]: (A @ (produc33908149tate_o @ (C) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 39.99/14.69 thf(18,axiom,((! [A:set_Pr1590995257tate_o,B:produc696469763tate_o]: ((A = bot_bo170732493tate_o) => (~ (member1838112666tate_o @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_equals0D)). 39.99/14.69 thf(244,plain,((! [A:set_Pr1590995257tate_o,B:produc696469763tate_o]: ((A = bot_bo170732493tate_o) => (~ (member1838112666tate_o @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 39.99/14.69 thf(38,axiom,((! [A:produc696469763tate_o,B:produc696469763tate_o,C:set_Pr1590995257tate_o]: (((A != B) => (member1838112666tate_o @ A @ C)) <= (member1838112666tate_o @ A @ (insert2053719859tate_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_insertE)). 39.99/14.69 thf(311,plain,((! [A:produc696469763tate_o,B:produc696469763tate_o,C:set_Pr1590995257tate_o]: (((~ (A = B)) => (member1838112666tate_o @ A @ C)) | ~ (member1838112666tate_o @ A @ (insert2053719859tate_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 39.99/14.69 thf(104,axiom,((! [A:set_Pr795498619_state,B:state,C:state]: ((wf_state @ A) => ((member1389040324_state @ (produc64584659_state @ B @ C) @ A) => (~ (member1389040324_state @ (produc64584659_state @ C @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_wf__not__sym)). 39.99/14.69 thf(558,plain,((! [A:set_Pr795498619_state,B:state,C:state]: ((wf_state @ A) => ((member1389040324_state @ (produc64584659_state @ B @ C) @ A) => (~ (member1389040324_state @ (produc64584659_state @ C @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 39.99/14.69 thf(123,axiom,((is_sin1547905295tate_o = (^ [A:set_Pr1590995257tate_o]: (A = (insert2053719859tate_o @ (the_el1569055182tate_o @ A) @ bot_bo170732493tate_o))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_is__singleton__the__elem)). 39.99/14.69 thf(632,plain,(((is_sin1547905295tate_o) = (^ [A:set_Pr1590995257tate_o]: (A = (insert2053719859tate_o @ (the_el1569055182tate_o @ A) @ bot_bo170732493tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 39.99/14.69 thf(633,plain,(((is_sin1547905295tate_o) = (^ [A:set_Pr1590995257tate_o]: (A = (insert2053719859tate_o @ (the_el1569055182tate_o @ A) @ bot_bo170732493tate_o))))),inference(lifteq,[status(thm)],[632])). 39.99/14.69 thf(52,axiom,((! [A:produc1115495963_state,B:set_Pr795498619_state]: (((insert311944171_state @ A @ B) = B) <= (member1389040324_state @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_insert__absorb)). 39.99/14.69 thf(360,plain,((! [A:produc1115495963_state,B:set_Pr795498619_state]: (((insert311944171_state @ A @ B) = B) | ~ (member1389040324_state @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 39.99/14.69 thf(160,axiom,((! [A:set_Pr795498619_state,B:(state > $o),C:state]: ((wf_state @ A) => ((! [D:state]: ((B @ D) <= (! [E:state]: ((B @ E) <= (member1389040324_state @ (produc64584659_state @ E @ D) @ A))))) => (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_wf__induct__rule)). 39.99/14.69 thf(773,plain,((! [A:set_Pr795498619_state,B:(state > $o),C:state]: ((wf_state @ A) => ((! [D:state]: ((B @ D) | ~ (! [E:state]: ((B @ E) | ~ (member1389040324_state @ (produc64584659_state @ E @ D) @ A))))) => (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 39.99/14.69 thf(113,axiom,((! [A:(a > (state > $o)),B:(a > (state > $o))]: (pHoare382919414oare_a @ (insert2053719859tate_o @ (produc33908149tate_o @ A @ (produc1948644831tate_o @ call @ B)) @ bot_bo170732493tate_o) @ A @ call @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_thoare_OAsm)). 39.99/14.69 thf(586,plain,((! [A:(a > (state > $o)),B:(a > (state > $o))]: (pHoare382919414oare_a @ (insert2053719859tate_o @ (produc33908149tate_o @ (A) @ (produc1948644831tate_o @ call @ (B))) @ bot_bo170732493tate_o) @ (A) @ call @ (B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 39.99/14.69 thf(33,axiom,((! [A:set_Pr795498619_state,B:produc1115495963_state]: ((~ (member1389040324_state @ B @ A)) <= (A = bot_bo1625160935_state)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_equals0D)). 39.99/14.69 thf(294,plain,((! [A:set_Pr795498619_state,B:produc1115495963_state]: (~ (member1389040324_state @ B @ A) | ~ (A = bot_bo1625160935_state)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 39.99/14.69 thf(295,plain,((! [A:set_Pr795498619_state]: (~ (? [B:produc1115495963_state]: (member1389040324_state @ B @ A)) | ~ (A = bot_bo1625160935_state)))),inference(miniscope,[status(thm)],[294])). 39.99/14.69 thf(296,plain,(! [B:produc1115495963_state,A:set_Pr795498619_state] : ((~ (member1389040324_state @ B @ A)) | (~ (A = bot_bo1625160935_state)))),inference(cnf,[status(esa)],[295])). 39.99/14.69 thf(297,plain,(! [B:produc1115495963_state,A:set_Pr795498619_state] : ((A != bot_bo1625160935_state) | (~ (member1389040324_state @ B @ A)))),inference(lifteq,[status(thm)],[296])). 39.99/14.69 thf(298,plain,(! [A:produc1115495963_state] : ((~ (member1389040324_state @ A @ bot_bo1625160935_state)))),inference(simp,[status(thm)],[297])). 39.99/14.69 thf(70,axiom,((! [A:state,B:com,C:nat,D:state,E:(state > $o),F:com,G:(state > $o)]: ((execn @ A @ B @ C @ D) => (((G @ D) & ~ (E @ D)) <= ((G @ A) & ! [H:state,I:state]: ((G @ I) <= ((G @ H) & (execn @ H @ F @ C @ I) & (E @ H))) & (B = (while @ E @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_while__lemma)). 39.99/14.69 thf(430,plain,((! [A:state,B:com,C:nat,D:state,E:(state > $o),F:com,G:(state > $o)]: ((execn @ A @ B @ C @ D) => (((G @ D) & ~ (E @ D)) | ~ ((G @ A) & ! [H:state,I:state]: ((G @ I) | ~ ((G @ H) & (execn @ H @ F @ C @ I) & (E @ H))) & (B = (while @ (E) @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 39.99/14.69 thf(28,axiom,((wf_state @ bot_bo1625160935_state)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_wf__empty)). 39.99/14.69 thf(279,plain,((wf_state @ bot_bo1625160935_state)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 39.99/14.69 thf(188,plain,((sk2 = x) | ~ (sk1)),inference(cnf,[status(esa)],[183])). 39.99/14.69 thf(191,plain,((sk2 = x) | ~ (sk1)),inference(lifteq,[status(thm)],[188])). 39.99/14.69 thf(146,axiom,((! [A:produc696469763tate_o,B:produc696469763tate_o,C:set_Pr1590995257tate_o]: ((insert2053719859tate_o @ A @ (insert2053719859tate_o @ B @ C)) = (insert2053719859tate_o @ B @ (insert2053719859tate_o @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_insert__commute)). 39.99/14.69 thf(711,plain,((! [A:produc696469763tate_o,B:produc696469763tate_o,C:set_Pr1590995257tate_o]: ((insert2053719859tate_o @ A @ (insert2053719859tate_o @ B @ C)) = (insert2053719859tate_o @ B @ (insert2053719859tate_o @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 39.99/14.69 thf(111,axiom,((! [A:(state > (state > $o)),B:state,C:state]: ((produc789892016tate_o @ A @ (produc64584659_state @ B @ C)) = (A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_case__prod__conv)). 39.99/14.69 thf(579,plain,((! [A:(state > (state > $o)),B:state,C:state]: ((produc789892016tate_o @ (A) @ (produc64584659_state @ B @ C)) = (A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 39.99/14.69 thf(22,axiom,((! [A:produc1115495963_state,B:set_Pr795498619_state]: ((insert311944171_state @ A @ (insert311944171_state @ A @ B)) = (insert311944171_state @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_insert__absorb2)). 39.99/14.69 thf(259,plain,((! [A:produc1115495963_state,B:set_Pr795498619_state]: ((insert311944171_state @ A @ (insert311944171_state @ A @ B)) = (insert311944171_state @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 39.99/14.69 thf(58,axiom,((! [A:produc696469763tate_o,B:set_Pr1590995257tate_o,C:produc696469763tate_o,D:set_Pr1590995257tate_o]: ((~ (member1838112666tate_o @ A @ B)) => ((((insert2053719859tate_o @ A @ B) = (insert2053719859tate_o @ C @ D)) = (((? [E:set_Pr1590995257tate_o]: ((D = (insert2053719859tate_o @ A @ E)) & ~ (member1838112666tate_o @ A @ E) & ~ (member1838112666tate_o @ C @ E) & (B = (insert2053719859tate_o @ C @ E)))) <= (A != C)) & ((A = C) => (B = D)))) <= (~ (member1838112666tate_o @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_insert__eq__iff)). 39.99/14.69 thf(382,plain,((! [A:produc696469763tate_o,B:set_Pr1590995257tate_o,C:produc696469763tate_o,D:set_Pr1590995257tate_o]: ((~ (member1838112666tate_o @ A @ B)) => ((((insert2053719859tate_o @ A @ B) = (insert2053719859tate_o @ C @ D)) = ((? [E:set_Pr1590995257tate_o]: ((D = (insert2053719859tate_o @ A @ E)) & ~ (member1838112666tate_o @ A @ E) & ~ (member1838112666tate_o @ C @ E) & (B = (insert2053719859tate_o @ C @ E))) | (A = C)) & ((A = C) => (B = D)))) | (member1838112666tate_o @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 39.99/14.69 thf(109,axiom,((! [A:produc204914599tate_o]: ~ (! [B:com,C:(a > (state > $o))]: (A != (produc1948644831tate_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_old_Oprod_Oexhaust)). 39.99/14.69 thf(572,plain,((! [A:produc204914599tate_o]: ~ (! [B:com,C:(a > (state > $o))]: ~ (A = (produc1948644831tate_o @ B @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 39.99/14.69 thf(164,axiom,((! [A:produc696469763tate_o]: (is_sin1547905295tate_o @ (insert2053719859tate_o @ A @ bot_bo170732493tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_is__singletonI)). 39.99/14.69 thf(787,plain,((! [A:produc696469763tate_o]: (is_sin1547905295tate_o @ (insert2053719859tate_o @ A @ bot_bo170732493tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 39.99/14.69 thf(84,axiom,((! [A:set_Pr1702239303tate_o]: (total_795385983tate_o @ bot_bo170732493tate_o @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_total__on__empty)). 39.99/14.69 thf(497,plain,((! [A:set_Pr1702239303tate_o]: (total_795385983tate_o @ bot_bo170732493tate_o @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 39.99/14.69 thf(498,plain,(! [A:set_Pr1702239303tate_o] : ((total_795385983tate_o @ bot_bo170732493tate_o @ A))),inference(cnf,[status(esa)],[497])). 39.99/14.69 thf(133,axiom,((! [A:set_Pr1740974983tate_o,B:set_Pr1740974983tate_o]: (((^ [C:com,D:(a > (state > $o))]: (member221067728tate_o @ (produc1948644831tate_o @ C @ D) @ A)) = (^ [C:com,D:(a > (state > $o))]: (member221067728tate_o @ (produc1948644831tate_o @ C @ D) @ B))) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_pred__equals__eq2)). 39.99/14.69 thf(672,plain,((! [A:set_Pr1740974983tate_o,B:set_Pr1740974983tate_o]: (((^ [C:com,D:(a > (state > $o))]: (member221067728tate_o @ (produc1948644831tate_o @ C @ D) @ A)) = (^ [C:com,D:(a > (state > $o))]: (member221067728tate_o @ (produc1948644831tate_o @ C @ D) @ B))) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 39.99/14.69 thf(187,plain,((~ (qa @ sk4 @ sk3)) | ~ (sk1)),inference(cnf,[status(esa)],[183])). 39.99/14.69 thf(163,axiom,((! [A:com,B:(a > (state > $o)),C:com,D:(a > (state > $o))]: (((produc1948644831tate_o @ A @ B) = (produc1948644831tate_o @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_old_Oprod_Oinject)). 39.99/14.69 thf(784,plain,((! [A:com,B:(a > (state > $o)),C:com,D:(a > (state > $o))]: (((produc1948644831tate_o @ A @ (B)) = (produc1948644831tate_o @ C @ (D))) = (((B) = (D)) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 39.99/14.69 thf(14,axiom,((! [A:produc1115495963_state,B:set_Pr795498619_state]: ((~ (! [C:set_Pr795498619_state]: ((member1389040324_state @ A @ C) <= (B = (insert311944171_state @ A @ C))))) <= (member1389040324_state @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_Set_Oset__insert)). 39.99/14.69 thf(230,plain,((! [A:produc1115495963_state,B:set_Pr795498619_state]: (~ (! [C:set_Pr795498619_state]: ((member1389040324_state @ A @ C) | ~ (B = (insert311944171_state @ A @ C)))) | ~ (member1389040324_state @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 39.99/14.69 thf(107,axiom,((! [A:(produc204914599tate_o > $o),B:produc204914599tate_o]: ((! [C:com,D:(a > (state > $o))]: (A @ (produc1948644831tate_o @ C @ D))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_old_Oprod_Oinducts)). 39.99/14.69 thf(567,plain,((! [A:(produc204914599tate_o > $o),B:produc204914599tate_o]: ((! [C:com,D:(a > (state > $o))]: (A @ (produc1948644831tate_o @ C @ (D)))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 39.99/14.69 thf(153,axiom,((! [A:set_Pr795498619_state,B:state]: ((wf_state @ A) => (~ (member1389040324_state @ (produc64584659_state @ B @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_wf__irrefl)). 39.99/14.69 thf(737,plain,((! [A:set_Pr795498619_state,B:state]: ((wf_state @ A) => (~ (member1389040324_state @ (produc64584659_state @ B @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 39.99/14.69 thf(121,axiom,((! [A:set_Pr795498619_state,B:set_Pr1590995257tate_o,C:(a > (state > $o)),D:(state > $o),E:com]: (((! [F:state]: (pHoare382919414oare_a @ B @ (^ [G:a,H:state]: ((C @ G @ H) & (D @ H) & (F = H))) @ E @ (^ [G:a,H:state]: ((C @ G @ H) & (member1389040324_state @ (produc64584659_state @ H @ F) @ A))))) => (pHoare382919414oare_a @ B @ C @ (while @ D @ E) @ (^ [F:a,G:state]: (~ (D @ G) & (C @ F @ G))))) <= (wf_state @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_thoare_OWhile)). 39.99/14.69 thf(616,plain,((! [A:set_Pr795498619_state,B:set_Pr1590995257tate_o,C:(a > (state > $o)),D:(state > $o),E:com]: (((! [F:state]: (pHoare382919414oare_a @ B @ (^ [G:a,H:state]: ((C @ G @ H) & (D @ H) & (F = H))) @ E @ (^ [G:a,H:state]: ((C @ G @ H) & (member1389040324_state @ (produc64584659_state @ H @ F) @ A))))) => (pHoare382919414oare_a @ B @ (C) @ (while @ (D) @ E) @ (^ [F:a,G:state]: (~ (D @ G) & (C @ F @ G))))) | ~ (wf_state @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 39.99/14.69 thf(117,axiom,((! [A:state,B:state,C:state,D:state]: (((produc64584659_state @ A @ B) = (produc64584659_state @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_old_Oprod_Oinject)). 39.99/14.69 thf(599,plain,((! [A:state,B:state,C:state,D:state]: (((produc64584659_state @ A @ B) = (produc64584659_state @ C @ D)) = ((A = C) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 39.99/14.69 thf(26,axiom,((! [A:set_Pr1590995257tate_o]: ((A = bot_bo170732493tate_o) <= (! [B:produc696469763tate_o]: ~ (member1838112666tate_o @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_equals0I)). 39.99/14.69 thf(271,plain,((! [A:set_Pr1590995257tate_o]: ((A = bot_bo170732493tate_o) | ~ (! [B:produc696469763tate_o]: ~ (member1838112666tate_o @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 39.99/14.69 thf(7,axiom,((! [A:state]: (total_on_state @ (insert_state @ A @ bot_bot_set_state) @ (insert311944171_state @ (produc64584659_state @ A @ A) @ bot_bo1625160935_state)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_total__on__singleton)). 39.99/14.69 thf(208,plain,((! [A:state]: (total_on_state @ (insert_state @ A @ bot_bot_set_state) @ (insert311944171_state @ (produc64584659_state @ A @ A) @ bot_bo1625160935_state)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 39.99/14.69 thf(97,axiom,((! [A:((a > (state > $o)) > (produc204914599tate_o > $o)),B:(a > (state > $o)),C:produc204914599tate_o]: ((A @ B @ C) => (produc1271576886te_o_o @ A @ (produc33908149tate_o @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_case__prodI)). 39.99/14.69 thf(535,plain,((! [A:((a > (state > $o)) > (produc204914599tate_o > $o)),B:(a > (state > $o)),C:produc204914599tate_o]: ((A @ (B) @ C) => (produc1271576886te_o_o @ (A) @ (produc33908149tate_o @ (B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 39.99/14.69 thf(142,axiom,((! [A:(produc1115495963_state > $o),B:produc1115495963_state]: ((A @ B) <= (! [C:state,D:state]: (A @ (produc64584659_state @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_old_Oprod_Oinducts)). 39.99/14.69 thf(700,plain,((! [A:(produc1115495963_state > $o),B:produc1115495963_state]: ((A @ B) | ~ (! [C:state,D:state]: (A @ (produc64584659_state @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 39.99/14.69 thf(132,axiom,((! [A:(com > ((a > (state > $o)) > $o)),B:produc204914599tate_o]: ((produc281270436te_o_o @ A @ B) => (~ (! [C:com,D:(a > (state > $o))]: ((B = (produc1948644831tate_o @ C @ D)) => (~ (A @ C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_case__prodE)). 39.99/14.69 thf(668,plain,((! [A:(com > ((a > (state > $o)) > $o)),B:produc204914599tate_o]: ((produc281270436te_o_o @ (A) @ B) => (~ (! [C:com,D:(a > (state > $o))]: ((B = (produc1948644831tate_o @ C @ (D))) => (~ (A @ C @ (D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 39.99/14.69 thf(76,axiom,((! [A:set_Pr795498619_state,B:state,C:state]: (((~ (member1389040324_state @ (produc64584659_state @ C @ B) @ A)) <= (member1389040324_state @ (produc64584659_state @ B @ C) @ A)) <= (wf_state @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_wf__asym)). 39.99/14.69 thf(462,plain,((! [A:set_Pr795498619_state,B:state,C:state]: (~ (member1389040324_state @ (produc64584659_state @ C @ B) @ A) | ~ (member1389040324_state @ (produc64584659_state @ B @ C) @ A) | ~ (wf_state @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 39.99/14.69 thf(182,axiom,((! [A:(a > (state > $o)),B:(a > (state > $o))]: ((hoare_a @ (insert2053719859tate_o @ (produc33908149tate_o @ A @ (produc1948644831tate_o @ call @ B)) @ bot_bo170732493tate_o) @ A @ body @ B) => (hoare_a @ bot_bo170732493tate_o @ A @ call @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_hoare_OCall)). 39.99/14.69 thf(858,plain,((! [A:(a > (state > $o)),B:(a > (state > $o))]: ((hoare_a @ (insert2053719859tate_o @ (produc33908149tate_o @ (A) @ (produc1948644831tate_o @ call @ (B))) @ bot_bo170732493tate_o) @ (A) @ body @ (B)) => (hoare_a @ bot_bo170732493tate_o @ (A) @ call @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 39.99/14.69 thf(102,axiom,((! [A:produc696469763tate_o]: ((collec1499596504tate_o @ (^ [B:produc696469763tate_o]: (B = A))) = (insert2053719859tate_o @ A @ bot_bo170732493tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_singleton__conv)). 39.99/14.69 thf(552,plain,((! [A:produc696469763tate_o]: ((collec1499596504tate_o @ (^ [B:produc696469763tate_o]: (B = A))) = (insert2053719859tate_o @ A @ bot_bo170732493tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 39.99/14.69 thf(169,axiom,((! [A:state]: ((member1389040324_state @ (produc64584659_state @ A @ x) @ r) => (! [B:state,C:state]: ((! [D:a]: (((pa @ D @ B) & (B = A)) => (qa @ D @ C))) <= (exec @ B @ body @ C)) & ! [B:a,C:state]: (((C = A) & (pa @ B @ C)) => (termi @ body @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)). 39.99/14.69 thf(799,plain,((! [A:state]: ((member1389040324_state @ (produc64584659_state @ A @ x) @ r) => (! [B:state,C:state]: (! [D:a]: (((pa @ D @ B) & (B = A)) => (qa @ D @ C)) | ~ (exec @ B @ body @ C)) & ! [B:a,C:state]: (((C = A) & (pa @ B @ C)) => (termi @ body @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 39.99/14.69 thf(9,axiom,((! [A:produc1115495963_state,B:produc1115495963_state,C:set_Pr795498619_state]: (((member1389040324_state @ A @ C) <= (A != B)) <= (member1389040324_state @ A @ (insert311944171_state @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_insertE)). 39.99/14.69 thf(213,plain,((! [A:produc1115495963_state,B:produc1115495963_state,C:set_Pr795498619_state]: ((member1389040324_state @ A @ C) | (A = B) | ~ (member1389040324_state @ A @ (insert311944171_state @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 39.99/14.69 thf(34,axiom,((! [A:produc696469763tate_o,B:set_Pr1590995257tate_o]: (((insert2053719859tate_o @ A @ B) = B) <= (member1838112666tate_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_insert__absorb)). 39.99/14.69 thf(299,plain,((! [A:produc696469763tate_o,B:set_Pr1590995257tate_o]: (((insert2053719859tate_o @ A @ B) = B) | ~ (member1838112666tate_o @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 39.99/14.69 thf(17,axiom,((! [A:produc696469763tate_o,B:produc696469763tate_o,C:set_Pr1590995257tate_o]: ((member1838112666tate_o @ A @ (insert2053719859tate_o @ B @ C)) = ((member1838112666tate_o @ A @ C) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_insert__iff)). 39.99/14.69 thf(241,plain,((! [A:produc696469763tate_o,B:produc696469763tate_o,C:set_Pr1590995257tate_o]: ((member1838112666tate_o @ A @ (insert2053719859tate_o @ B @ C)) = ((member1838112666tate_o @ A @ C) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 39.99/14.69 thf(130,axiom,((! [A:produc696469763tate_o]: ((the_el1569055182tate_o @ (insert2053719859tate_o @ A @ bot_bo170732493tate_o)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_the__elem__eq)). 39.99/14.69 thf(658,plain,((! [A:produc696469763tate_o]: ((the_el1569055182tate_o @ (insert2053719859tate_o @ A @ bot_bo170732493tate_o)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 39.99/14.69 thf(73,axiom,((order_aboveS_state = (^ [A:set_Pr795498619_state,B:state]: (collect_state @ (^ [C:state]: ((member1389040324_state @ (produc64584659_state @ B @ C) @ A) & (C != B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_aboveS__def)). 39.99/14.69 thf(454,plain,(((order_aboveS_state) = (^ [A:set_Pr795498619_state,B:state]: (collect_state @ (^ [C:state]: ((member1389040324_state @ (produc64584659_state @ B @ C) @ A) & ~ (C = B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 39.99/14.69 thf(455,plain,(((order_aboveS_state) = (^ [A:set_Pr795498619_state,B:state]: (collect_state @ (^ [C:state]: ((member1389040324_state @ (produc64584659_state @ B @ C) @ A) & ~ (C = B))))))),inference(lifteq,[status(thm)],[454])). 39.99/14.69 thf(882,plain,(~ (sk1) | (exec @ x @ body @ sk3) | (sk2 != sk2)),inference(paramod_ordered,[status(thm)],[191,189])). 39.99/14.69 thf(883,plain,(~ (sk1) | (exec @ x @ body @ sk3)),inference(pattern_uni,[status(thm)],[882:[]])). 39.99/14.69 thf(134,axiom,((! [A:(com > ((a > (state > $o)) > $o)),B:com,C:(a > (state > $o))]: ((produc281270436te_o_o @ A @ (produc1948644831tate_o @ B @ C)) => (A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_case__prodD)). 39.99/14.69 thf(675,plain,((! [A:(com > ((a > (state > $o)) > $o)),B:com,C:(a > (state > $o))]: ((produc281270436te_o_o @ (A) @ (produc1948644831tate_o @ B @ (C))) => (A @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 39.99/14.69 thf(47,axiom,((! [A:produc1115495963_state,B:set_Pr795498619_state,C:set_Pr795498619_state]: (((~ (member1389040324_state @ A @ C)) => (((insert311944171_state @ A @ B) = (insert311944171_state @ A @ C)) = (B = C))) <= (~ (member1389040324_state @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_insert__ident)). 39.99/14.69 thf(342,plain,((! [A:produc1115495963_state,B:set_Pr795498619_state,C:set_Pr795498619_state]: (((~ (member1389040324_state @ A @ C)) => (((insert311944171_state @ A @ B) = (insert311944171_state @ A @ C)) = (B = C))) | (member1389040324_state @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 39.99/14.69 thf(175,axiom,((! [A:state,B:nat,C:state]: ((execn @ A @ body @ B @ C) => (execn @ A @ call @ (suc @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_execn_Ointros_I7_J)). 39.99/14.69 thf(823,plain,((! [A:state,B:nat,C:state]: ((execn @ A @ body @ B @ C) => (execn @ A @ call @ (suc @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 39.99/14.69 thf(194,plain,(((insert2053719859tate_o) = (^ [A:produc696469763tate_o,B:set_Pr1590995257tate_o]: (collec1499596504tate_o @ (^ [C:produc696469763tate_o]: ((member1838112666tate_o @ C @ B) | (C = A))))))),inference(lifteq,[status(thm)],[193])). 39.99/14.69 thf(167,axiom,((! [A:state]: ((termi @ call @ A) <= (termi @ body @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_termi_Ointros_I7_J)). 39.99/14.69 thf(795,plain,((! [A:state]: ((termi @ call @ A) | ~ (termi @ body @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 39.99/14.69 thf(136,axiom,((! [A:(produc696469763tate_o > $o),B:produc696469763tate_o]: ((A @ B) <= (! [C:(a > (state > $o)),D:com,E:(a > (state > $o))]: (A @ (produc33908149tate_o @ C @ (produc1948644831tate_o @ D @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_prod__induct3)). 39.99/14.69 thf(680,plain,((! [A:(produc696469763tate_o > $o),B:produc696469763tate_o]: ((A @ B) | ~ (! [C:(a > (state > $o)),D:com,E:(a > (state > $o))]: (A @ (produc33908149tate_o @ (C) @ (produc1948644831tate_o @ D @ (E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 39.99/14.69 thf(198,plain,(! [A:set_Pr1590995257tate_o] : (((? [B:produc696469763tate_o]: (member1838112666tate_o @ B @ A)) = (~ (A = bot_bo170732493tate_o))))),inference(cnf,[status(esa)],[197])). 39.99/14.69 thf(199,plain,(! [A:set_Pr1590995257tate_o] : (((? [B:produc696469763tate_o]: (member1838112666tate_o @ B @ A)) = (~ (A = bot_bo170732493tate_o))))),inference(lifteq,[status(thm)],[198])). 39.99/14.69 thf(43,axiom,((! [A:produc1115495963_state,B:set_Pr795498619_state]: (member1389040324_state @ A @ (insert311944171_state @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_insertI1)). 39.99/14.69 thf(331,plain,((! [A:produc1115495963_state,B:set_Pr795498619_state]: (member1389040324_state @ A @ (insert311944171_state @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 39.99/14.69 thf(148,axiom,((! [A:produc696469763tate_o]: ~ (! [B:(a > (state > $o)),C:com,D:(a > (state > $o))]: (A != (produc33908149tate_o @ B @ (produc1948644831tate_o @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_prod__cases3)). 39.99/14.69 thf(717,plain,((! [A:produc696469763tate_o]: ~ (! [B:(a > (state > $o)),C:com,D:(a > (state > $o))]: ~ (A = (produc33908149tate_o @ (B) @ (produc1948644831tate_o @ C @ (D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 39.99/14.69 thf(110,axiom,((! [A:produc696469763tate_o]: ? [B:(a > (state > $o)),C:produc204914599tate_o]: (A = (produc33908149tate_o @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_surj__pair)). 39.99/14.69 thf(576,plain,((! [A:produc696469763tate_o]: ? [B:(a > (state > $o)),C:produc204914599tate_o]: (A = (produc33908149tate_o @ (B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 39.99/14.69 thf(45,axiom,((! [A:produc1115495963_state]: ~ (member1389040324_state @ A @ bot_bo1625160935_state))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_emptyE)). 39.99/14.69 thf(336,plain,((! [A:produc1115495963_state]: ~ (member1389040324_state @ A @ bot_bo1625160935_state))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 39.99/14.69 thf(143,axiom,((! [A:(state > $o),B:state,C:com,D:nat]: ((execn @ B @ (while @ A @ C) @ D @ B) <= (~ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_execn_OWhileFalse)). 39.99/14.69 thf(703,plain,((! [A:(state > $o),B:state,C:com,D:nat]: ((execn @ B @ (while @ (A) @ C) @ D @ B) | (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 39.99/14.69 thf(129,axiom,((bot_bo51534648tate_o = (^ [A:state,B:state]: (member1389040324_state @ (produc64584659_state @ A @ B) @ bot_bo1625160935_state)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_bot__empty__eq2)). 39.99/14.69 thf(656,plain,(((bot_bo51534648tate_o) = (^ [A:state,B:state]: (member1389040324_state @ (produc64584659_state @ A @ B) @ bot_bo1625160935_state)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 39.99/14.69 thf(59,axiom,((! [A:produc696469763tate_o,B:(produc696469763tate_o > $o)]: ((insert2053719859tate_o @ A @ (collec1499596504tate_o @ B)) = (collec1499596504tate_o @ (^ [C:produc696469763tate_o]: ((C != A) => (B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_insert__Collect)). 39.99/14.69 thf(386,plain,((! [A:produc696469763tate_o,B:(produc696469763tate_o > $o)]: ((insert2053719859tate_o @ A @ (collec1499596504tate_o @ (B))) = (collec1499596504tate_o @ (^ [C:produc696469763tate_o]: ((~ (C = A)) => (B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 39.99/14.69 thf(39,axiom,((! [A:(produc1115495963_state > $o),B:produc1115495963_state]: ((((collec496201222_state @ (^ [C:produc1115495963_state]: ((B = C) & (A @ C)))) = bot_bo1625160935_state) <= (~ (A @ B))) & (((collec496201222_state @ (^ [C:produc1115495963_state]: ((B = C) & (A @ C)))) = (insert311944171_state @ B @ bot_bo1625160935_state)) <= (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_Collect__conv__if2)). 39.99/14.69 thf(314,plain,((! [A:(produc1115495963_state > $o),B:produc1115495963_state]: ((((collec496201222_state @ (^ [C:produc1115495963_state]: ((B = C) & (A @ C)))) = bot_bo1625160935_state) | (A @ B)) & (((collec496201222_state @ (^ [C:produc1115495963_state]: ((B = C) & (A @ C)))) = (insert311944171_state @ B @ bot_bo1625160935_state)) | ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 39.99/14.69 thf(71,axiom,((! [A:(a > (state > $o)),B:(a > (state > $o)),C:set_Pr1590995257tate_o,D:com,E:(a > (state > $o))]: ((! [F:a,G:state]: ((A @ F @ G) => (B @ F @ G))) => ((pHoare382919414oare_a @ C @ A @ D @ E) <= (pHoare382919414oare_a @ C @ B @ D @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_PHoareTotal__Mirabelle__ynemugpbor_Ostrengthen__pre)). 39.99/14.69 thf(446,plain,((! [A:(a > (state > $o)),B:(a > (state > $o)),C:set_Pr1590995257tate_o,D:com,E:(a > (state > $o))]: ((! [F:a,G:state]: ((A @ F @ G) => (B @ F @ G))) => ((pHoare382919414oare_a @ C @ (A) @ D @ (E)) | ~ (pHoare382919414oare_a @ C @ (B) @ D @ (E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 39.99/14.69 thf(116,axiom,((! [A:((a > (state > $o)) > (produc204914599tate_o > $o)),B:produc696469763tate_o]: ((produc1271576886te_o_o @ A @ B) => (~ (! [C:(a > (state > $o)),D:produc204914599tate_o]: ((~ (A @ C @ D)) <= (B = (produc33908149tate_o @ C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_case__prodE)). 39.99/14.69 thf(595,plain,((! [A:((a > (state > $o)) > (produc204914599tate_o > $o)),B:produc696469763tate_o]: ((produc1271576886te_o_o @ (A) @ B) => (~ (! [C:(a > (state > $o)),D:produc204914599tate_o]: (~ (A @ (C) @ D) | ~ (B = (produc33908149tate_o @ (C) @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 39.99/14.69 thf(120,axiom,((! [A:produc204914599tate_o,B:(com > ((a > (state > $o)) > $o))]: ((produc281270436te_o_o @ B @ A) <= (! [C:com,D:(a > (state > $o))]: ((B @ C @ D) <= (A = (produc1948644831tate_o @ C @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_case__prodI2)). 39.99/14.69 thf(612,plain,((! [A:produc204914599tate_o,B:(com > ((a > (state > $o)) > $o))]: ((produc281270436te_o_o @ (B) @ A) | ~ (! [C:com,D:(a > (state > $o))]: ((B @ C @ (D)) | ~ (A = (produc1948644831tate_o @ C @ (D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 39.99/14.69 thf(762,plain,(((^ [A:(a > (state > $o)),B:produc204914599tate_o]: (member1838112666tate_o @ (produc33908149tate_o @ A @ B) @ bot_bo170732493tate_o)) = (bot_bo2130564770te_o_o))),inference(lifteq,[status(thm)],[761])). 39.99/14.69 thf(875,plain,(((bot_bo2130564770te_o_o) = (^ [A:(a > (state > $o)),B:produc204914599tate_o]: ($false)))),inference(rewrite,[status(thm)],[762,229])). 39.99/14.69 thf(876,plain,(! [A:(a > (state > $o))] : (((bot_bo2130564770te_o_o @ A) = (^ [B:produc204914599tate_o]: ($false))))),inference(func_ext,[status(esa)],[875])). 39.99/14.69 thf(77,axiom,((! [A:(state > (state > $o)),B:(produc1115495963_state > $o)]: ((! [C:state,D:state]: ((A @ C @ D) = (B @ (produc64584659_state @ C @ D)))) => ((produc789892016tate_o @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_cond__case__prod__eta)). 39.99/14.69 thf(465,plain,((! [A:(state > (state > $o)),B:(produc1115495963_state > $o)]: ((! [C:state,D:state]: ((A @ C @ D) = (B @ (produc64584659_state @ C @ D)))) => ((produc789892016tate_o @ A) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 39.99/14.69 thf(620,plain,((! [A:(state > (state > $o)),B:produc1115495963_state]: ($true = (produc789892016tate_o @ (^ [C:state,D:state]: ($true)) @ B)))),inference(instance,[status(thm)],[619])). 39.99/14.69 thf(621,plain,((! [A:produc1115495963_state]: (produc789892016tate_o @ (^ [B:state,C:state]: ($true)) @ A))),inference(simp,[status(thm)],[620])). 39.99/14.69 thf(627,plain,(! [A:produc1115495963_state] : ((produc789892016tate_o @ (^ [B:state,C:state]: ($true)) @ A))),inference(cnf,[status(esa)],[621])). 39.99/14.69 thf(72,axiom,((! [A:com,B:com]: ((semi @ A @ B) != call))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_com_Odistinct_I15_J)). 39.99/14.69 thf(450,plain,((! [A:com,B:com]: ~ ((semi @ A @ B) = call))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 39.99/14.69 thf(53,axiom,((! [A:produc1115495963_state,B:(produc1115495963_state > $o)]: ((insert311944171_state @ A @ (collec496201222_state @ B)) = (collec496201222_state @ (^ [C:produc1115495963_state]: ((C != A) => (B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_insert__Collect)). 39.99/14.69 thf(363,plain,((! [A:produc1115495963_state,B:(produc1115495963_state > $o)]: ((insert311944171_state @ A @ (collec496201222_state @ (B))) = (collec496201222_state @ (^ [C:produc1115495963_state]: ((~ (C = A)) => (B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 39.99/14.69 thf(99,axiom,((! [A:produc696469763tate_o,B:produc696469763tate_o]: ((A = B) <= ((insert2053719859tate_o @ A @ bot_bo170732493tate_o) = (insert2053719859tate_o @ B @ bot_bo170732493tate_o))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_singleton__inject)). 39.99/14.69 thf(539,plain,((! [A:produc696469763tate_o,B:produc696469763tate_o]: ((A = B) | ~ ((insert2053719859tate_o @ A @ bot_bo170732493tate_o) = (insert2053719859tate_o @ B @ bot_bo170732493tate_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 39.99/14.69 thf(93,axiom,((! [A:produc696469763tate_o]: ((collec1499596504tate_o @ (= @ produc696469763tate_o @ A)) = (insert2053719859tate_o @ A @ bot_bo170732493tate_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_singleton__conv2)). 39.99/14.69 thf(524,plain,((! [A:produc696469763tate_o]: ((collec1499596504tate_o @ (= @ produc696469763tate_o @ A)) = (insert2053719859tate_o @ A @ bot_bo170732493tate_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 39.99/14.69 thf(156,axiom,((! [A:(a > (state > $o)),B:(a > (state > $o))]: (hoare_a @ (insert2053719859tate_o @ (produc33908149tate_o @ A @ (produc1948644831tate_o @ call @ B)) @ bot_bo170732493tate_o) @ A @ call @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_hoare_OAsm)). 39.99/14.69 thf(759,plain,((! [A:(a > (state > $o)),B:(a > (state > $o))]: (hoare_a @ (insert2053719859tate_o @ (produc33908149tate_o @ (A) @ (produc1948644831tate_o @ call @ (B))) @ bot_bo170732493tate_o) @ (A) @ call @ (B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 39.99/14.69 thf(114,axiom,((! [A:(state > $o),B:com,C:(state > $o),D:com]: (((while @ A @ B) = (while @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_com_Oinject_I4_J)). 39.99/14.69 thf(588,plain,((! [A:(state > $o),B:com,C:(state > $o),D:com]: (((while @ (A) @ B) = (while @ (C) @ D)) = ((B = D) & ((A) = (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 39.99/14.69 thf(172,axiom,((! [A:com,B:state,C:com]: (((termi @ (semi @ A @ C) @ B) <= (! [D:state]: ((termi @ C @ D) <= (exec @ B @ A @ D)))) <= (termi @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_termi_OSemi)). 39.99/14.69 thf(813,plain,((! [A:com,B:state,C:com]: ((termi @ (semi @ A @ C) @ B) | ~ (! [D:state]: ((termi @ C @ D) | ~ (exec @ B @ A @ D))) | ~ (termi @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 39.99/14.69 thf(657,plain,(((^ [A:state,B:state]: (member1389040324_state @ (produc64584659_state @ A @ B) @ bot_bo1625160935_state)) = (bot_bo51534648tate_o))),inference(lifteq,[status(thm)],[656])). 39.99/14.69 thf(894,plain,(((bot_bo51534648tate_o) = (^ [A:state,B:state]: ($false)))),inference(rewrite,[status(thm)],[657,298])). 39.99/14.69 thf(896,plain,(! [A:state] : (((bot_bo51534648tate_o @ A) = (^ [B:state]: ($false))))),inference(func_ext,[status(esa)],[894])). 39.99/14.69 thf(36,axiom,((! [A:set_Pr795498619_state]: ((! [B:produc1115495963_state]: ~ (member1389040324_state @ B @ A)) => (A = bot_bo1625160935_state)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_equals0I)). 39.99/14.69 thf(304,plain,((! [A:set_Pr795498619_state]: ((! [B:produc1115495963_state]: ~ (member1389040324_state @ B @ A)) => (A = bot_bo1625160935_state)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 39.99/14.69 thf(162,axiom,((! [A:(a > (state > $o)),B:produc204914599tate_o,C:(a > (state > $o)),D:produc204914599tate_o]: (((produc33908149tate_o @ A @ B) = (produc33908149tate_o @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_old_Oprod_Oinject)). 39.99/14.69 thf(781,plain,((! [A:(a > (state > $o)),B:produc204914599tate_o,C:(a > (state > $o)),D:produc204914599tate_o]: (((produc33908149tate_o @ (A) @ B) = (produc33908149tate_o @ (C) @ D)) = ((B = D) & ((A) = (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 39.99/14.69 thf(32,axiom,((! [A:produc696469763tate_o,B:set_Pr1590995257tate_o]: ((? [C:set_Pr1590995257tate_o]: (~ (member1838112666tate_o @ A @ C) & (B = (insert2053719859tate_o @ A @ C)))) <= (member1838112666tate_o @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_mk__disjoint__insert)). 39.99/14.69 thf(290,plain,((! [A:produc696469763tate_o,B:set_Pr1590995257tate_o]: (? [C:set_Pr1590995257tate_o]: (~ (member1838112666tate_o @ A @ C) & (B = (insert2053719859tate_o @ A @ C))) | ~ (member1838112666tate_o @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 39.99/14.69 thf(158,axiom,((! [A:produc696469763tate_o,B:produc696469763tate_o,C:produc696469763tate_o,D:produc696469763tate_o]: (((insert2053719859tate_o @ A @ (insert2053719859tate_o @ B @ bot_bo170732493tate_o)) = (insert2053719859tate_o @ C @ (insert2053719859tate_o @ D @ bot_bo170732493tate_o))) = (((B = C) & (A = D)) | ((B = D) & (A = C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_doubleton__eq__iff)). 39.99/14.69 thf(763,plain,((! [A:produc696469763tate_o,B:produc696469763tate_o,C:produc696469763tate_o,D:produc696469763tate_o]: (((insert2053719859tate_o @ A @ (insert2053719859tate_o @ B @ bot_bo170732493tate_o)) = (insert2053719859tate_o @ C @ (insert2053719859tate_o @ D @ bot_bo170732493tate_o))) = (((B = C) & (A = D)) | ((B = D) & (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 39.99/14.69 thf(684,plain,(((is_emp807847857tate_o) = (^ [A:set_Pr1590995257tate_o]: (A = bot_bo170732493tate_o)))),inference(lifteq,[status(thm)],[683])). 39.99/14.69 thf(48,axiom,((! [A:produc1115495963_state,B:produc1115495963_state]: ((member1389040324_state @ A @ (insert311944171_state @ B @ bot_bo1625160935_state)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_singleton__iff)). 39.99/14.69 thf(346,plain,((! [A:produc1115495963_state,B:produc1115495963_state]: ((member1389040324_state @ A @ (insert311944171_state @ B @ bot_bo1625160935_state)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 39.99/14.69 thf(101,axiom,((! [A:set_Pr795498619_state,B:set_Pr795498619_state]: (((^ [C:state,D:state]: (member1389040324_state @ (produc64584659_state @ C @ D) @ A)) = (^ [C:state,D:state]: (member1389040324_state @ (produc64584659_state @ C @ D) @ B))) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_pred__equals__eq2)). 39.99/14.69 thf(549,plain,((! [A:set_Pr795498619_state,B:set_Pr795498619_state]: (((^ [C:state,D:state]: (member1389040324_state @ (produc64584659_state @ C @ D) @ A)) = (^ [C:state,D:state]: (member1389040324_state @ (produc64584659_state @ C @ D) @ B))) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 39.99/14.69 thf(31,axiom,((! [A:(produc696469763tate_o > $o),B:(produc696469763tate_o > $o)]: (((collec1499596504tate_o @ A) = (collec1499596504tate_o @ B)) <= (! [C:produc696469763tate_o]: ((A @ C) = (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_Collect__cong)). 39.99/14.69 thf(287,plain,((! [A:(produc696469763tate_o > $o),B:(produc696469763tate_o > $o)]: (((collec1499596504tate_o @ (A)) = (collec1499596504tate_o @ (B))) | ~ (! [C:produc696469763tate_o]: ((A @ C) = (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 39.99/14.69 thf(64,axiom,((! [A:(produc696469763tate_o > $o),B:produc696469763tate_o]: ((((collec1499596504tate_o @ (^ [C:produc696469763tate_o]: ((B = C) & (A @ C)))) = bot_bo170732493tate_o) <= (~ (A @ B))) & (((collec1499596504tate_o @ (^ [C:produc696469763tate_o]: ((B = C) & (A @ C)))) = (insert2053719859tate_o @ B @ bot_bo170732493tate_o)) <= (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_Collect__conv__if2)). 39.99/14.69 thf(410,plain,((! [A:(produc696469763tate_o > $o),B:produc696469763tate_o]: ((((collec1499596504tate_o @ (^ [C:produc696469763tate_o]: ((B = C) & (A @ C)))) = bot_bo170732493tate_o) | (A @ B)) & (((collec1499596504tate_o @ (^ [C:produc696469763tate_o]: ((B = C) & (A @ C)))) = (insert2053719859tate_o @ B @ bot_bo170732493tate_o)) | ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 39.99/14.69 thf(23,axiom,((! [A:produc1115495963_state,B:set_Pr795498619_state,C:produc1115495963_state]: ((member1389040324_state @ A @ (insert311944171_state @ C @ B)) <= (member1389040324_state @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_insertI2)). 39.99/14.69 thf(262,plain,((! [A:produc1115495963_state,B:set_Pr795498619_state,C:produc1115495963_state]: ((member1389040324_state @ A @ (insert311944171_state @ C @ B)) | ~ (member1389040324_state @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 39.99/14.69 thf(67,axiom,((! [A:(state > (state > $o)),B:state,C:state]: ((produc789892016tate_o @ A @ (produc64584659_state @ B @ C)) => (A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_case__prodD)). 39.99/14.69 thf(422,plain,((! [A:(state > (state > $o)),B:state,C:state]: ((produc789892016tate_o @ (A) @ (produc64584659_state @ B @ C)) => (A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 39.99/14.69 thf(866,plain,(sk1 | (~ (termi @ body @ x)) | (sk6 != sk6)),inference(paramod_ordered,[status(thm)],[192,185])). 39.99/14.69 thf(867,plain,(sk1 | (~ (termi @ body @ x))),inference(pattern_uni,[status(thm)],[866:[]])). 39.99/14.69 thf(864,plain,(~ (sk1) | (pa @ sk4 @ x) | (sk2 != sk2)),inference(paramod_ordered,[status(thm)],[191,184])). 39.99/14.69 thf(865,plain,(~ (sk1) | (pa @ sk4 @ x)),inference(pattern_uni,[status(thm)],[864:[]])). 39.99/14.69 thf(152,axiom,((wf_state = (^ [A:set_Pr795498619_state]: ! [B:set_state]: ((? [C:state]: ((member_state @ C @ B) & ! [D:state]: ((member1389040324_state @ (produc64584659_state @ D @ C) @ A) => (~ (member_state @ D @ B))))) <= (? [C:state]: (member_state @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_wf__eq__minimal)). 39.99/14.69 thf(735,plain,(((wf_state) = (^ [A:set_Pr795498619_state]: ! [B:set_state]: (? [C:state]: ((member_state @ C @ B) & ! [D:state]: ((member1389040324_state @ (produc64584659_state @ D @ C) @ A) => (~ (member_state @ D @ B)))) | ~ (? [C:state]: (member_state @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 39.99/14.69 thf(106,axiom,((! [A:produc696469763tate_o,B:produc696469763tate_o]: ((member1838112666tate_o @ A @ (insert2053719859tate_o @ B @ bot_bo170732493tate_o)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_singleton__iff)). 39.99/14.69 thf(564,plain,((! [A:produc696469763tate_o,B:produc696469763tate_o]: ((member1838112666tate_o @ A @ (insert2053719859tate_o @ B @ bot_bo170732493tate_o)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 39.99/14.69 thf(8,axiom,((! [A:(produc1115495963_state > $o)]: ((bot_bo1625160935_state = (collec496201222_state @ A)) = (! [B:produc1115495963_state]: ~ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_empty__Collect__eq)). 39.99/14.69 thf(210,plain,((! [A:(produc1115495963_state > $o)]: ((bot_bo1625160935_state = (collec496201222_state @ (A))) = (! [B:produc1115495963_state]: ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 39.99/14.69 thf(62,axiom,((! [A:produc1115495963_state,B:(state > (state > $o)),C:(state > (state > $o)),D:produc1115495963_state]: ((! [E:state,F:state]: (((produc64584659_state @ E @ F) = A) => ((B @ E @ F) = (C @ E @ F)))) => ((D = A) => ((produc789892016tate_o @ B @ D) = (produc789892016tate_o @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_split__cong)). 39.99/14.69 thf(400,plain,((! [A:produc1115495963_state,B:(state > (state > $o)),C:(state > (state > $o)),D:produc1115495963_state]: ((! [E:state,F:state]: (((produc64584659_state @ E @ F) = A) => ((B @ E @ F) = (C @ E @ F)))) => ((D = A) => ((produc789892016tate_o @ (B) @ D) = (produc789892016tate_o @ (C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 39.99/14.69 thf(141,axiom,((! [A:produc1115495963_state]: ~ (! [B:state,C:state]: (A != (produc64584659_state @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_old_Oprod_Oexhaust)). 39.99/14.69 thf(696,plain,((! [A:produc1115495963_state]: ~ (! [B:state,C:state]: ~ (A = (produc64584659_state @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 39.99/14.69 thf(30,axiom,((! [A:produc1115495963_state,B:set_Pr795498619_state]: ((insert311944171_state @ A @ B) != bot_bo1625160935_state))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_insert__not__empty)). 39.99/14.69 thf(283,plain,((! [A:produc1115495963_state,B:set_Pr795498619_state]: ~ ((insert311944171_state @ A @ B) = bot_bo1625160935_state))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 39.99/14.69 thf(87,axiom,((! [A:com,B:com,C:(state > $o),D:com]: ((semi @ A @ B) != (while @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_com_Odistinct_I13_J)). 39.99/14.69 thf(506,plain,((! [A:com,B:com,C:(state > $o),D:com]: ~ ((semi @ A @ B) = (while @ (C) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 39.99/14.69 thf(25,axiom,((! [A:produc696469763tate_o]: ~ (member1838112666tate_o @ A @ bot_bo170732493tate_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_emptyE)). 39.99/14.69 thf(268,plain,((! [A:produc696469763tate_o]: ~ (member1838112666tate_o @ A @ bot_bo170732493tate_o))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 39.99/14.69 thf(69,axiom,((! [A:(state > (state > $o)),B:state,C:state]: ((produc789892016tate_o @ A @ (produc64584659_state @ B @ C)) = (A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_old_Oprod_Ocase)). 39.99/14.69 thf(427,plain,((! [A:(state > (state > $o)),B:state,C:state]: ((produc789892016tate_o @ (A) @ (produc64584659_state @ B @ C)) = (A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 39.99/14.69 thf(75,axiom,((! [A:(state > $o),B:state,C:com,D:nat,E:state,F:state]: ((((execn @ B @ (while @ A @ C) @ D @ F) <= (execn @ E @ (while @ A @ C) @ D @ F)) <= (execn @ B @ C @ D @ E)) <= (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_execn_OWhileTrue)). 39.99/14.69 thf(459,plain,((! [A:(state > $o),B:state,C:com,D:nat,E:state,F:state]: ((execn @ B @ (while @ (A) @ C) @ D @ F) | ~ (execn @ E @ (while @ (A) @ C) @ D @ F) | ~ (execn @ B @ C @ D @ E) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 39.99/14.69 thf(6,axiom,((! [A:set_Pr1590995257tate_o]: ((A != bot_bo170732493tate_o) => ((is_sin1547905295tate_o @ A) <= (! [B:produc696469763tate_o,C:produc696469763tate_o]: (((member1838112666tate_o @ C @ A) => (B = C)) <= (member1838112666tate_o @ B @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_is__singletonI_H)). 39.99/14.69 thf(200,plain,((! [A:set_Pr1590995257tate_o]: ((~ (A = bot_bo170732493tate_o)) => ((is_sin1547905295tate_o @ A) | ~ (! [B:produc696469763tate_o,C:produc696469763tate_o]: (((member1838112666tate_o @ C @ A) => (B = C)) | ~ (member1838112666tate_o @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 39.99/14.69 thf(179,axiom,((! [A:state,B:com,C:state,D:com,E:state]: ((exec @ A @ B @ C) => ((exec @ C @ D @ E) => (exec @ A @ (semi @ B @ D) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_exec_OSemi)). 39.99/14.69 thf(850,plain,((! [A:state,B:com,C:state,D:com,E:state]: ((exec @ A @ B @ C) => ((exec @ C @ D @ E) => (exec @ A @ (semi @ B @ D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 39.99/14.69 thf(55,axiom,((! [A:(produc1115495963_state > $o),B:produc1115495963_state]: ((((collec496201222_state @ (^ [C:produc1115495963_state]: ((A @ C) & (C = B)))) = (insert311944171_state @ B @ bot_bo1625160935_state)) <= (A @ B)) & (((collec496201222_state @ (^ [C:produc1115495963_state]: ((A @ C) & (C = B)))) = bot_bo1625160935_state) <= (~ (A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_Collect__conv__if)). 39.99/14.69 thf(369,plain,((! [A:(produc1115495963_state > $o),B:produc1115495963_state]: ((((collec496201222_state @ (^ [C:produc1115495963_state]: ((A @ C) & (C = B)))) = (insert311944171_state @ B @ bot_bo1625160935_state)) | ~ (A @ B)) & (((collec496201222_state @ (^ [C:produc1115495963_state]: ((A @ C) & (C = B)))) = bot_bo1625160935_state) | (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 39.99/14.69 thf(151,axiom,((! [A:(produc696469763tate_o > $o),B:produc696469763tate_o]: ((((collec1499596504tate_o @ (^ [C:produc696469763tate_o]: ((A @ C) & (C = B)))) = bot_bo170732493tate_o) <= (~ (A @ B))) & ((A @ B) => ((collec1499596504tate_o @ (^ [C:produc696469763tate_o]: ((C = B) & (A @ C)))) = (insert2053719859tate_o @ B @ bot_bo170732493tate_o)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_Collect__conv__if)). 39.99/14.69 thf(728,plain,((! [A:(produc696469763tate_o > $o),B:produc696469763tate_o]: ((((collec1499596504tate_o @ (^ [C:produc696469763tate_o]: ((A @ C) & (C = B)))) = bot_bo170732493tate_o) | (A @ B)) & ((A @ B) => ((collec1499596504tate_o @ (^ [C:produc696469763tate_o]: ((C = B) & (A @ C)))) = (insert2053719859tate_o @ B @ bot_bo170732493tate_o)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 39.99/14.69 thf(154,axiom,((total_on_state = (^ [A:set_state,B:set_Pr795498619_state]: ! [C:state]: ((! [D:state]: (((C != D) => ((member1389040324_state @ (produc64584659_state @ D @ C) @ B) | (member1389040324_state @ (produc64584659_state @ C @ D) @ B))) <= (member_state @ D @ A))) <= (member_state @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_total__on__def)). 39.99/14.69 thf(740,plain,(((total_on_state) = (^ [A:set_state,B:set_Pr795498619_state]: ! [C:state]: (! [D:state]: (((~ (C = D)) => ((member1389040324_state @ (produc64584659_state @ D @ C) @ B) | (member1389040324_state @ (produc64584659_state @ C @ D) @ B))) | ~ (member_state @ D @ A)) | ~ (member_state @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 39.99/14.69 thf(126,axiom,((! [A:(a > (state > $o)),B:produc204914599tate_o,C:(a > (state > $o)),D:produc204914599tate_o]: (((produc33908149tate_o @ A @ B) = (produc33908149tate_o @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_prod_Oinject)). 39.99/14.69 thf(639,plain,((! [A:(a > (state > $o)),B:produc204914599tate_o,C:(a > (state > $o)),D:produc204914599tate_o]: (((produc33908149tate_o @ (A) @ B) = (produc33908149tate_o @ (C) @ D)) = (((A) = (C)) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 39.99/14.69 thf(1106,plain,($false),inference(cvc4,[status(thm)],[409,645,809,629,468,234,555,333,249,481,352,408,683,308,379,511,677,523,582,533,797,185,709,417,389,570,184,619,357,196,542,817,853,189,606,881,216,789,591,321,376,238,806,687,280,634,221,265,527,602,766,512,529,661,793,761,366,714,825,778,302,349,820,561,392,424,275,192,693,252,197,493,710,456,324,224,484,229,847,522,830,725,420,499,857,519,742,488,339,642,637,706,328,256,193,537,686,476,515,721,503,244,311,558,633,360,773,586,298,430,856,279,191,711,579,259,382,572,787,498,672,187,784,230,567,737,616,599,271,208,535,700,668,462,858,552,799,213,685,299,241,658,455,883,675,342,823,194,795,680,199,331,717,576,336,703,656,386,314,446,595,612,497,876,465,627,450,363,539,524,759,588,813,896,304,632,781,290,510,763,684,346,549,287,410,262,190,183,422,867,865,735,564,210,294,195,400,696,283,506,268,427,459,200,850,369,728,740,227,639,454])). 39.99/14.69 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 39.99/14.69 % [INFO] Killing All external provers ... 39.99/14.69 WARNING: TreeLimitedRun lost 6.42s, total lost is 6.42s 39.99/14.69 FINAL WATCH: 37.8 CPU 10.6 WC 39.99/14.69 Killed 2 orphans 39.99/14.69 Killed 1 orphans 39.99/14.69 Killed 1 orphans 39.99/14.69 EOF