%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP199^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:07:09 AM UTC 2026
% Result : Theorem 135.30s 59.26s
% Output : Refutation 132.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP199^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.19 % Computer : n014.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 20:10:29 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.89/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.41/1.22 % [INFO] Parsing done (430ms).
% 2.41/1.24 % [INFO] Running in sequential loop mode.
% 3.52/1.64 % [INFO] eprover registered as external prover.
% 3.52/1.64 % [INFO] Scanning for conjecture ...
% 3.74/1.80 % [INFO] Found a conjecture (or negated_conjecture) and 356 axioms. Running axiom selection ...
% 4.27/1.95 % [INFO] Axiom selection finished. Selected 246 axioms (removed 110 axioms).
% 5.27/2.21 % [INFO] Problem is higher-order (TPTP THF).
% 5.27/2.23 % [INFO] Type checking passed.
% 5.27/2.24 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 135.30/59.25 % External prover 'e' found a proof!
% 135.30/59.25 % [INFO] Killing All external provers ...
% 135.30/59.25 % Time passed: 58910ms (effective reasoning time: 58002ms)
% 135.30/59.25 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 135.30/59.25 % Axioms used in derivation (246): fact_351_le__sup__iff, fact_345_le__zero__eq, fact_46_sup_Oidem, fact_283_option_Oset__sel, fact_338_inf__left__idem, fact_175_bot__empty__eq, fact_289_double__compl, fact_26_Collect__empty__eq, fact_260_set__empty__eq, fact_288_compl__eq__compl__iff, fact_276_Vagree__sym__rel, fact_129_Uvariation__refl, fact_334_subset__antisym, fact_56_equals0I, fact_17_sup__bot_Oeq__neutr__iff, fact_342_IntI, fact_197_usubstappt__det, fact_277_Vagree__empty, fact_286_Timeso_Osimps_I3_J, fact_239_option_Oexhaust, fact_340_inf__right__idem, fact_349_inf_Obounded__iff, fact_2_Un__insert__left, fact_122_UnI2, fact_300_equal__neg__zero, fact_273_Vagree__def, fact_86_mem__Collect__eq, fact_343_Int__iff, fact_138_singleton__iff, fact_40_sup__left__idem, fact_78_insertE, fact_100_inf__sup__aci_I5_J, fact_131_Uvariation__def, fact_232_in__these__eq, fact_118_ball__Un, fact_317_stateinterpol__right, fact_182_is__singletonI, fact_200_variable_Osize__gen_I2_J, fact_199_usubst__ode, fact_247_Assigno_Oinduct, fact_348_le__inf__iff, fact_306_ComplD, fact_320_Vagree__stateinterpol, fact_285_Vagree__repv, fact_257_elem__set, fact_149_Un__singleton__iff, fact_319_stateinterpol__empty, fact_74_insertI2, fact_204_Set_Ois__empty__def, fact_224_repv__selectlike__self, fact_116_Un__assoc, fact_104_inf__sup__aci_I7_J, fact_106_inf__sup__aci_I8_J, fact_347_compl__le__compl__iff, fact_201_option_Oexpand, fact_58_equals0D, fact_157_set__zero, fact_295_ComplI, fact_272_Vagree__union, fact_236_option_Odistinct_I1_J, fact_64_insert__commute, fact_324_Timeso_Osimps_I1_J, fact_44_sup__idem, fact_297_add_Oinverse__neutral, fact_174_variable_Oexhaust, fact_250_option_Oexhaust__sel, fact_218_repv__def__correct, fact_316_stateinterpol__left, fact_90_sup_Ocommute, fact_162_ball__insert, fact_140_singletonD, fact_193_IH, fact_301_neg__equal__zero, fact_326_stateinterpol__FVT, fact_94_sup_Oassoc, fact_335_inf_Oidem, fact_102_inf__sup__aci_I6_J, fact_294_Compl__iff, fact_110_Un__left__absorb, fact_52_bot__set__def, fact_82_sup_Oleft__commute, fact_305_ComplD, fact_249_Differentialo_Oinduct, fact_114_Un__absorb, fact_230_selectlike__compose, fact_15_sup__eq__bot__iff, fact_323_usubstappt_Osimps_I6_J, fact_128_Uvariation__sym__rel, fact_254_Vagree__repv__self, fact_92_sup__assoc, fact_314_Timeso_Oelims, fact_66_insert__eq__iff, fact_156_variable_Oinject_I1_J, fact_321_stateinterpol__def, fact_22_sup__bot_Oright__neutral, fact_1_Uvariation__empty, fact_136_doubleton__eq__iff, fact_7_Un__empty, fact_270_option_Oset__cases, fact_169_not__union__or, fact_30_empty__iff, fact_72_Set_Oset__insert, fact_206_Uvariation__repv, fact_290_double__compl, fact_275_Vagree__refl, fact_322_usubstappt__times__conv, fact_299_neg__equal__0__iff__equal, fact_172_variable_Odistinct_I1_J, fact_80_sup__left__commute, fact_11_sup__bot__right, fact_219_these__insert__Some, fact_263_selectlike__Vagree, fact_279_option_Osimps_I14_J, fact_341_IntI, fact_62_mk__disjoint__insert, fact_177_Collect__empty__eq__bot, fact_240_option_Oinducts, fact_130_Uvariation__sym, fact_304_double__complement, fact_198_undeft__None, fact_20_sup__bot_Oneutr__eq__iff, fact_4_Un__insert__right, fact_192_l2r, fact_124_UnI1, fact_271_ospec, fact_187_is__singleton__def, fact_336_inf__idem, fact_184_a1, fact_246_Timeso_Oinduct, fact_325_stateinterpol__diff, fact_241_split__option__ex, fact_292_Compl__eq__Compl__iff, fact_54_ex__in__conv, fact_146_Uvariation__trans, fact_120_bex__Un, fact_191_vaflow1, fact_179_is__singleton__the__elem, fact_223_repv__selectlike__other, fact_42_sup_Oleft__idem, fact_331_order__refl, fact_32_insert__absorb2, fact_24_empty__Collect__eq, fact_164_the__elem__eq, fact_312_selectlike__equal__cond, fact_327_nostatediff, fact_34_insert__iff, fact_214_repv__access, fact_108_Un__left__commute, fact_195_variable_Osize__gen_I1_J, fact_302_Uvariation__Vagree, fact_126_UnE, fact_215_these__empty, fact_252_option_Osimps_I15_J, fact_339_inf_Oright__idem, fact_237_option_Osel, fact_227_not__None__eq, fact_132_singleton__inject, fact_154_solves__Vagree__trans, fact_144_Un__empty__left, fact_153__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rr_O_A_092_060forall_062x0_Ax1_Ax2_Ax3_Ax4_Ax5_O_A_I_092_060exists_062v6_O_AUvariation_Av6_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_Av6_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_Av6_J_A_061_A_IUvariation_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_329_coincidence__term__cor, fact_173_variable_Oinduct, fact_9_sup__bot__left, fact_244_ODEo_Oinduct, fact_171_same__ODE__same__sol, fact_328_coincidence__term, fact_346_compl__le__compl__iff, fact_274_Vagree__sym, fact_296_ComplI, fact_311_selectlike__equal__cocond, fact_28_all__not__in__conv, fact_76_insertI1, fact_245_undeft__equiv, fact_258_Vagree__and, fact_281_option_Oset__sel, fact_48_UnCI, fact_267_option_Oset__intros, fact_284_solves__Vagree, fact_332_subsetI, fact_313_stateinterpol__insert, fact_238_option_OdiscI, fact_84_sup__commute, fact_225_option_Oinject, fact_287_compl__eq__compl__iff, fact_265_option_Oset__intros, fact_291_Compl__eq__Compl__iff, fact_264_Aterm__Some, fact_293_Compl__iff, fact_18_sup__bot_Oleft__neutral, fact_155__092_060open_062_092_060forall_062x0_Ax1_Ax2_Ax3_Ax4_Ax5_O_A_I_092_060exists_062v6_O_AUvariation_Av6_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_Av6_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_Av6_J_A_061_A_IUvariation_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_J_092_060close_062, fact_309_selectlike__equal__cocond__corule, fact_98_boolean__algebra__cancel_Osup1, fact_68_insert__absorb, fact_222_repv__selectlike__other__converse, fact_243_combine__options__cases, fact_167_zero__reorient, fact_211_these__not__empty__eq, fact_298_neg__0__equal__iff__equal, fact_159_variable_Oinject_I2_J, fact_203_variable_Osize_I4_J, fact_208_these__empty__eq, fact_310_selectlike__equal__cocond__rule, fact_60_emptyE, fact_318_selectlike__co__selectlike, fact_262_similar__selectlike__mem, fact_307_Timeso_Osimps_I2_J, fact_242_split__option__all, fact_160_union__or, fact_185_is__singletonI_H, fact_194_subdef, fact_308_Timeso__undef, fact_147_singleton__Un__iff, fact_158_set__zero, fact_36_insertCI, fact_112_Un__commute, fact_228_not__Some__eq, fact_134_insert__not__empty, fact_303_double__complement, fact_181_vaflow2, fact_248_Differentialo_Ocases, fact_344_Int__iff, fact_50_singletonI, fact_70_insert__ident, fact_213_repv__self, fact_226_selectlike__self, fact_96_boolean__algebra__cancel_Osup2, fact_196_usubst__term, fact_202_variable_Osize_I3_J, fact_231_option_Ocollapse, fact_229_selectlike__empty, fact_88_Collect__mem__eq, fact_268_option_Oset__cases, fact_168_zero__reorient, fact_166_f2, fact_38_sup_Oright__idem, fact_189_is__singletonE, fact_315_trm_Oinject_I6_J, fact_337_inf_Oleft__idem, fact_0_uv, fact_151_insert__is__Un, fact_352_sup_Obounded__iff, fact_330_Vagree__statediff, fact_255_elem__set, fact_13_bot__eq__sup__iff, fact_333_subsetI, fact_142_Un__empty__right
% 135.30/59.25 % No. of inferences in proof: 828
% 135.30/59.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 58910 ms resp. 58002 ms w/o parsing
% 132.99/59.63 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 132.99/59.63 thf(produc1418842292n_game_type, type, produc1418842292n_game: $tType).
% 132.99/59.63 thf(set_op12188086e_real_type, type, set_op12188086e_real: $tType).
% 132.99/59.63 thf(option_variable_real_type, type, option_variable_real: $tType).
% 132.99/59.63 thf(set_variable_real_type, type, set_variable_real: $tType).
% 132.99/59.63 thf(set_option_variable_type, type, set_option_variable: $tType).
% 132.99/59.63 thf(set_option_trm_type, type, set_option_trm: $tType).
% 132.99/59.63 thf(option_variable_type, type, option_variable: $tType).
% 132.99/59.63 thf(option_trm_type, type, option_trm: $tType).
% 132.99/59.63 thf(denotational_interp_type, type, denotational_interp: $tType).
% 132.99/59.63 thf(set_variable_type, type, set_variable: $tType).
% 132.99/59.63 thf(set_trm_type, type, set_trm: $tType).
% 132.99/59.63 thf(set_real_type, type, set_real: $tType).
% 132.99/59.63 thf(set_nat_type, type, set_nat: $tType).
% 132.99/59.63 thf(variable_type, type, variable: $tType).
% 132.99/59.63 thf(char_type, type, char: $tType).
% 132.99/59.63 thf(trm_type, type, trm: $tType).
% 132.99/59.63 thf(real_type, type, real: $tType).
% 132.99/59.63 thf(nat_type, type, nat: $tType).
% 132.99/59.63 thf(statediff_decl, type, statediff: ((variable > real) > ((variable > real) > set_variable))).
% 132.99/59.63 thf(stateinterpol_decl, type, stateinterpol: ((variable > real) > ((variable > real) > (set_variable > (variable > real))))).
% 132.99/59.63 thf(denota1419872369iation_decl, type, denota1419872369iation: ((variable > real) > ((variable > real) > (set_variable > $o)))).
% 132.99/59.63 thf(denotational_Vagree_decl, type, denotational_Vagree: ((variable > real) > ((variable > real) > (set_variable > $o)))).
% 132.99/59.63 thf(denotational_repv_decl, type, denotational_repv: ((variable > real) > (variable > (real > (variable > real))))).
% 132.99/59.63 thf(denota1778088425es_ODE_decl, type, denota1778088425es_ODE: (denotational_interp > ((real > (variable > real)) > (char > (trm > $o))))).
% 132.99/59.63 thf(denota1863255036rm_sem_decl, type, denota1863255036rm_sem: (denotational_interp > (trm > ((variable > real) > real)))).
% 132.99/59.63 thf(uminus_uminus_real_decl, type, uminus_uminus_real: (real > real)).
% 132.99/59.63 thf(uminus430703407e_real_decl, type, uminus430703407e_real: (set_variable_real > set_variable_real)).
% 132.99/59.63 thf(uminus1851247844riable_decl, type, uminus1851247844riable: (set_variable > set_variable)).
% 132.99/59.63 thf(zero_zero_nat_decl, type, zero_zero_nat: nat).
% 132.99/59.63 thf(zero_zero_real_decl, type, zero_zero_real: real).
% 132.99/59.63 thf(zero_zero_set_nat_decl, type, zero_zero_set_nat: set_nat).
% 132.99/59.63 thf(zero_zero_set_real_decl, type, zero_zero_set_real: set_real).
% 132.99/59.63 thf(if_real_decl, type, if_real: ($o > (real > (real > real)))).
% 132.99/59.63 thf(inf_in1556002680e_real_decl, type, inf_in1556002680e_real: (set_variable_real > (set_variable_real > set_variable_real))).
% 132.99/59.63 thf(inf_inf_set_variable_decl, type, inf_inf_set_variable: (set_variable > (set_variable > set_variable))).
% 132.99/59.63 thf(sup_sup_set_variable_decl, type, sup_sup_set_variable: (set_variable > (set_variable > set_variable))).
% 132.99/59.63 thf(size_size_variable_decl, type, size_size_variable: (variable > nat)).
% 132.99/59.63 thf(none_trm_decl, type, none_trm: option_trm).
% 132.99/59.63 thf(none_variable_decl, type, none_variable: option_variable).
% 132.99/59.63 thf(some_trm_decl, type, some_trm: (trm > option_trm)).
% 132.99/59.63 thf(some_variable_decl, type, some_variable: (variable > option_variable)).
% 132.99/59.63 thf(set_option_trm2_decl, type, set_option_trm2: (option_trm > set_trm)).
% 132.99/59.63 thf(set_option_variable2_decl, type, set_option_variable2: (option_variable > set_variable)).
% 132.99/59.63 thf(the_trm_decl, type, the_trm: (option_trm > trm)).
% 132.99/59.63 thf(the_variable_decl, type, the_variable: (option_variable > variable)).
% 132.99/59.63 thf(these_variable_decl, type, these_variable: (set_option_variable > set_variable)).
% 132.99/59.63 thf(bot_bot_variable_o_decl, type, bot_bot_variable_o: (variable > $o)).
% 132.99/59.63 thf(bot_bot_set_nat_decl, type, bot_bot_set_nat: set_nat).
% 132.99/59.63 thf(bot_bo266290559riable_decl, type, bot_bo266290559riable: set_option_variable).
% 132.99/59.63 thf(bot_bot_set_real_decl, type, bot_bot_set_real: set_real).
% 132.99/59.63 thf(bot_bot_set_variable_decl, type, bot_bot_set_variable: set_variable).
% 132.99/59.63 thf(ord_less_eq_nat_decl, type, ord_less_eq_nat: (nat > (nat > $o))).
% 132.99/59.63 thf(ord_le1113654598e_real_decl, type, ord_le1113654598e_real: (set_variable_real > (set_variable_real > $o))).
% 132.99/59.63 thf(ord_le282106107riable_decl, type, ord_le282106107riable: (set_variable > (set_variable > $o))).
% 132.99/59.63 thf(collect_variable_decl, type, collect_variable: ((variable > $o) > set_variable)).
% 132.99/59.63 thf(insert_nat_decl, type, insert_nat: (nat > (set_nat > set_nat))).
% 132.99/59.63 thf(insert1340772453riable_decl, type, insert1340772453riable: (option_variable > (set_option_variable > set_option_variable))).
% 132.99/59.63 thf(insert_real_decl, type, insert_real: (real > (set_real > set_real))).
% 132.99/59.63 thf(insert_variable_decl, type, insert_variable: (variable > (set_variable > set_variable))).
% 132.99/59.63 thf(is_empty_variable_decl, type, is_empty_variable: (set_variable > $o)).
% 132.99/59.63 thf(is_sin155454833riable_decl, type, is_sin155454833riable: (set_variable > $o)).
% 132.99/59.63 thf(the_elem_variable_decl, type, the_elem_variable: (set_variable > variable)).
% 132.99/59.63 thf(static_FVT_decl, type, static_FVT: (trm > set_variable)).
% 132.99/59.63 thf(static_selectlike_decl, type, static_selectlike: (set_variable_real > ((variable > real) > (set_variable > set_variable_real)))).
% 132.99/59.63 thf(times_decl, type, times: (trm > (trm > trm))).
% 132.99/59.63 thf(dVar_decl, type, dVar: (char > variable)).
% 132.99/59.63 thf(rVar_decl, type, rVar: (char > variable)).
% 132.99/59.63 thf(size_variable_decl, type, size_variable: (variable > nat)).
% 132.99/59.63 thf(uSubst918876924Timeso_decl, type, uSubst918876924Timeso: (option_trm > (option_trm > option_trm))).
% 132.99/59.63 thf(uSubst1599435252djoint_decl, type, uSubst1599435252djoint: (produc1418842292n_game > (denotational_interp > ((variable > real) > denotational_interp)))).
% 132.99/59.63 thf(uSubst516392818stappt_decl, type, uSubst516392818stappt: (produc1418842292n_game > (set_variable > (trm > option_trm)))).
% 132.99/59.63 thf(member_variable_real_decl, type, member_variable_real: ((variable > real) > (set_variable_real > $o))).
% 132.99/59.63 thf(member814448204riable_decl, type, member814448204riable: (option_variable > (set_option_variable > $o))).
% 132.99/59.63 thf(member_trm_decl, type, member_trm: (trm > (set_trm > $o))).
% 132.99/59.63 thf(member_variable_decl, type, member_variable: (variable > (set_variable > $o))).
% 132.99/59.63 thf(f_decl, type, f: (real > (variable > real))).
% 132.99/59.63 thf(i_decl, type, i: denotational_interp).
% 132.99/59.63 thf(u_decl, type, u: set_variable).
% 132.99/59.63 thf(omega_decl, type, omega: (variable > real)).
% 132.99/59.63 thf(sigma_decl, type, sigma: produc1418842292n_game).
% 132.99/59.63 thf(theta_decl, type, theta: trm).
% 132.99/59.63 thf(rr_decl, type, rr: (trm > (denotational_interp > (trm > (denotational_interp > (char > ((real > (variable > real)) > (variable > real)))))))).
% 132.99/59.63 thf(x_decl, type, x: char).
% 132.99/59.63 thf(sk1_decl, type, sk1: ((char > (option_trm > $o)) > char)).
% 132.99/59.63 thf(sk2_decl, type, sk2: ((char > (option_trm > $o)) > trm)).
% 132.99/59.63 thf(sk3_decl, type, sk3: ((char > (option_trm > $o)) > char)).
% 132.99/59.63 thf(sk4_decl, type, sk4: (option_trm > trm)).
% 132.99/59.63 thf(sk5_decl, type, sk5: ((option_trm > $o) > trm)).
% 132.99/59.63 thf(sk6_decl, type, sk6: (option_trm > trm)).
% 132.99/59.63 thf(sk7_decl, type, sk7: ((option_trm > $o) > trm)).
% 132.99/59.63 thf(sk8_decl, type, sk8: ((trm > $o) > (option_trm > trm))).
% 132.99/59.63 thf(sk9_decl, type, sk9: (option_trm > (option_trm > (option_trm > $o)))).
% 132.99/59.63 thf(sk10_decl, type, sk10: (option_trm > (option_trm > (option_trm > trm)))).
% 132.99/59.63 thf(sk11_decl, type, sk11: (option_trm > (option_trm > (option_trm > trm)))).
% 132.99/59.63 thf(sk12_decl, type, sk12: (option_trm > (option_trm > (option_trm > trm)))).
% 132.99/59.63 thf(sk13_decl, type, sk13: ((variable > (option_trm > $o)) > variable)).
% 132.99/59.63 thf(sk14_decl, type, sk14: ((variable > (option_trm > $o)) > trm)).
% 132.99/59.63 thf(sk15_decl, type, sk15: ((variable > (option_trm > $o)) > variable)).
% 132.99/59.63 thf(sk16_decl, type, sk16: ((option_trm > (option_trm > $o)) > trm)).
% 132.99/59.63 thf(sk17_decl, type, sk17: ((option_trm > (option_trm > $o)) > trm)).
% 132.99/59.63 thf(sk18_decl, type, sk18: ((option_trm > (option_trm > $o)) > option_trm)).
% 132.99/59.63 thf(sk19_decl, type, sk19: ((option_trm > (option_trm > $o)) > trm)).
% 132.99/59.63 thf(sk20_decl, type, sk20: (option_trm > (option_trm > ((option_trm > (option_trm > $o)) > $o)))).
% 132.99/59.63 thf(sk21_decl, type, sk21: (option_trm > ((option_trm > (option_trm > $o)) > (option_trm > trm)))).
% 132.99/59.63 thf(sk22_decl, type, sk22: (option_trm > ((option_trm > (option_trm > $o)) > (option_trm > trm)))).
% 132.99/59.63 thf(sk87_decl, type, sk87: (variable > variable)).
% 132.99/59.63 thf(sk89_decl, type, sk89: (variable > variable)).
% 132.99/59.63 thf(sk132_decl, type, sk132: variable).
% 132.99/59.63 thf(sk1_def, definition, sk1 = (^ [A:(char > (option_trm > $o))]: (@+ [B:char]: ~ (! [C:trm]: (A @ B @ (some_trm @ C))))) ).
% 132.99/59.63 thf(sk2_def, definition, sk2 = (^ [A:(char > (option_trm > $o))]: (@+ [B:trm]: ~ (A @ (sk1 @ A) @ (some_trm @ B)))) ).
% 132.99/59.63 thf(sk3_def, definition, sk3 = (^ [A:(char > (option_trm > $o))]: (@+ [B:char]: ~ (A @ B @ none_trm))) ).
% 132.99/59.63 thf(sk4_def, definition, sk4 = (^ [A:option_trm]: (@+ [B:trm]: (A = (some_trm @ B)))) ).
% 132.99/59.63 thf(sk5_def, definition, sk5 = (^ [A:(option_trm > $o)]: (@+ [B:trm]: ~ (A @ (some_trm @ B)))) ).
% 132.99/59.63 thf(sk6_def, definition, sk6 = (^ [A:option_trm]: (@+ [B:trm]: (A = (some_trm @ B)))) ).
% 132.99/59.63 thf(sk7_def, definition, sk7 = (^ [A:(option_trm > $o)]: (@+ [B:trm]: ~ (A @ (some_trm @ B)))) ).
% 132.99/59.63 thf(sk8_def, definition, sk8 = (^ [A:(trm > $o),B:option_trm]: (@+ [C:trm]: ~ ((member_trm @ C @ (set_option_trm2 @ B)) => (A @ C)))) ).
% 132.99/59.63 thf(sk10_def, definition, sk10 = (^ [A:option_trm,B:option_trm,C:option_trm]: (@+ [D:trm]: ~ ((C = (some_trm @ D)) => (! [E:trm]: ((B = (some_trm @ E)) => (~ (A = (some_trm @ (times @ D @ E))))))))) ).
% 132.99/59.63 thf(sk11_def, definition, sk11 = (^ [A:option_trm,B:option_trm,C:option_trm]: (@+ [D:trm]: ~ ((B = (some_trm @ D)) => (~ (A = (some_trm @ (times @ (sk10 @ A @ B @ C) @ D))))))) ).
% 132.99/59.63 thf(sk12_def, definition, sk12 = (^ [A:option_trm,B:option_trm,C:option_trm]: (@+ [D:trm]: (C = (some_trm @ D)))) ).
% 132.99/59.63 thf(sk13_def, definition, sk13 = (^ [A:(variable > (option_trm > $o))]: (@+ [B:variable]: ~ (! [C:trm]: (A @ B @ (some_trm @ C))))) ).
% 132.99/59.63 thf(sk14_def, definition, sk14 = (^ [A:(variable > (option_trm > $o))]: (@+ [B:trm]: ~ (A @ (sk13 @ A) @ (some_trm @ B)))) ).
% 132.99/59.63 thf(sk15_def, definition, sk15 = (^ [A:(variable > (option_trm > $o))]: (@+ [B:variable]: ~ (A @ B @ none_trm))) ).
% 132.99/59.63 thf(sk16_def, definition, sk16 = (^ [A:(option_trm > (option_trm > $o))]: (@+ [B:trm]: ~ (! [C:trm]: (A @ (some_trm @ B) @ (some_trm @ C))))) ).
% 132.99/59.63 thf(sk17_def, definition, sk17 = (^ [A:(option_trm > (option_trm > $o))]: (@+ [B:trm]: ~ (A @ (some_trm @ (sk16 @ A)) @ (some_trm @ B)))) ).
% 132.99/59.63 thf(sk18_def, definition, sk18 = (^ [A:(option_trm > (option_trm > $o))]: (@+ [B:option_trm]: ~ (A @ none_trm @ B))) ).
% 132.99/59.63 thf(sk19_def, definition, sk19 = (^ [A:(option_trm > (option_trm > $o))]: (@+ [B:trm]: ~ (A @ (some_trm @ B) @ none_trm))) ).
% 132.99/59.63 thf(sk21_def, definition, sk21 = (^ [A:option_trm,B:(option_trm > (option_trm > $o)),C:option_trm]: (@+ [D:trm]: (C = (some_trm @ D)))) ).
% 132.99/59.63 thf(sk22_def, definition, sk22 = (^ [A:option_trm,B:(option_trm > (option_trm > $o)),C:option_trm]: (@+ [D:trm]: (A = (some_trm @ D)))) ).
% 132.99/59.63 thf(168,axiom,((! [A:variable,B:set_variable,C:variable]: (((~ (member_variable @ A @ B)) => (A = C)) => (member_variable @ A @ (insert_variable @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_insertCI)).
% 132.99/59.63 thf(809,plain,((! [A:variable,B:set_variable,C:variable]: (((~ (member_variable @ A @ B)) => (A = C)) => (member_variable @ A @ (insert_variable @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])).
% 132.99/59.63 thf(29,axiom,((! [A:option_trm,B:trm]: ((A = (some_trm @ B)) => (A != none_trm)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_option_OdiscI)).
% 132.99/59.63 thf(365,plain,((! [A:option_trm,B:trm]: ((A = (some_trm @ B)) => (~ (A = none_trm))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])).
% 132.99/59.63 thf(22,axiom,((! [A:(variable > (option_trm > $o)),B:variable,C:option_trm]: ((! [D:variable,E:trm]: (A @ D @ (some_trm @ E))) => ((! [D:variable]: (A @ D @ none_trm)) => (A @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_Assigno_Oinduct)).
% 132.99/59.63 thf(347,plain,((! [A:(variable > (option_trm > $o)),B:variable,C:option_trm]: ((! [D:variable,E:trm]: (A @ D @ (some_trm @ E))) => ((! [D:variable]: (A @ D @ none_trm)) => (A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])).
% 132.99/59.63 thf(74,axiom,((! [A:variable,B:option_variable]: ((member_variable @ A @ (set_option_variable2 @ B)) => (B = (some_variable @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_option_Oset__cases)).
% 132.99/59.63 thf(518,plain,((! [A:variable,B:option_variable]: ((member_variable @ A @ (set_option_variable2 @ B)) => (B = (some_variable @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])).
% 132.99/59.63 thf(217,axiom,((! [A:variable,B:set_variable]: ((insert_variable @ A @ B) != bot_bot_set_variable))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_insert__not__empty)).
% 132.99/59.63 thf(962,plain,((! [A:variable,B:set_variable]: ~ ((insert_variable @ A @ B) = bot_bot_set_variable))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])).
% 132.99/59.63 thf(86,axiom,((! [A:(variable > real),B:(variable > real),C:set_variable,D:set_variable_real]: ((denotational_Vagree @ A @ B @ C) => ((member_variable_real @ A @ (static_selectlike @ D @ B @ C)) = (member_variable_real @ A @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_similar__selectlike__mem)).
% 132.99/59.63 thf(555,plain,((! [A:(variable > real),B:(variable > real),C:set_variable,D:set_variable_real]: ((denotational_Vagree @ (A) @ (B) @ C) => ((member_variable_real @ (A) @ (static_selectlike @ D @ (B) @ C)) = (member_variable_real @ (A) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])).
% 132.99/59.63 thf(115,axiom,((! [A:set_variable_real,B:(variable > real),C:set_variable,D:set_variable]: ((static_selectlike @ (static_selectlike @ A @ B @ C) @ B @ D) = (static_selectlike @ A @ B @ (sup_sup_set_variable @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_selectlike__compose)).
% 132.99/59.63 thf(645,plain,((! [A:set_variable_real,B:(variable > real),C:set_variable,D:set_variable]: ((static_selectlike @ (static_selectlike @ A @ (B) @ C) @ (B) @ D) = (static_selectlike @ A @ (B) @ (sup_sup_set_variable @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])).
% 132.99/59.63 thf(194,axiom,((! [A:variable,B:variable,C:set_variable]: ((member_variable @ A @ (insert_variable @ B @ C)) = ((A = B) | (member_variable @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_insert__iff)).
% 132.99/59.63 thf(892,plain,((! [A:variable,B:variable,C:set_variable]: ((member_variable @ A @ (insert_variable @ B @ C)) = ((A = B) | (member_variable @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])).
% 132.99/59.63 thf(111,axiom,((! [A:set_variable]: ((A != bot_bot_set_variable) => ((! [B:variable,C:variable]: ((member_variable @ B @ A) => ((member_variable @ C @ A) => (B = C)))) => (is_sin155454833riable @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_is__singletonI_H)).
% 132.99/59.63 thf(628,plain,((! [A:set_variable]: ((~ (A = bot_bot_set_variable)) => ((! [B:variable,C:variable]: ((member_variable @ B @ A) => ((member_variable @ C @ A) => (B = C)))) => (is_sin155454833riable @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])).
% 132.99/59.63 thf(1,conjecture,((denota1419872369iation @ (f @ zero_zero_real) @ omega @ (sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)) @ u))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 132.99/59.63 thf(2,negated_conjecture,((~ (denota1419872369iation @ (f @ zero_zero_real) @ omega @ (sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)) @ u)))),inference(neg_conjecture,[status(cth)],[1])).
% 132.99/59.63 thf(249,plain,((~ (denota1419872369iation @ (f @ zero_zero_real) @ (omega) @ (sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)) @ u)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 132.99/59.63 thf(61,axiom,((! [A:(variable > real),B:(variable > real),C:set_variable,D:set_variable_real]: ((denotational_Vagree @ A @ B @ C) => ((static_selectlike @ D @ A @ C) = (static_selectlike @ D @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_selectlike__Vagree)).
% 132.99/59.63 thf(481,plain,((! [A:(variable > real),B:(variable > real),C:set_variable,D:set_variable_real]: ((denotational_Vagree @ (A) @ (B) @ C) => ((static_selectlike @ D @ (A) @ C) = (static_selectlike @ D @ (B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])).
% 132.99/59.63 thf(24,axiom,((((!) @ option_trm) = (^ [A:(option_trm > $o)]: ((A @ none_trm) & ! [B:trm]: (A @ (some_trm @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_split__option__all)).
% 132.99/59.63 thf(352,plain,((((!) @ option_trm) = (^ [A:(option_trm > $o)]: ((A @ none_trm) & ! [B:trm]: (A @ (some_trm @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])).
% 132.99/59.63 thf(43,axiom,((! [A:set_variable]: ((uminus1851247844riable @ (uminus1851247844riable @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_double__complement)).
% 132.99/59.63 thf(424,plain,((! [A:set_variable]: ((uminus1851247844riable @ (uminus1851247844riable @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])).
% 132.99/59.63 thf(425,plain,(! [A:set_variable] : (((uminus1851247844riable @ (uminus1851247844riable @ A)) = A))),inference(cnf,[status(esa)],[424])).
% 132.99/59.63 thf(426,plain,(! [A:set_variable] : (((uminus1851247844riable @ (uminus1851247844riable @ A)) = A))),inference(lifteq,[status(thm)],[425])).
% 132.99/59.63 thf(81,axiom,((! [A:set_variable]: ((collect_variable @ (^ [B:variable]: (member_variable @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_Collect__mem__eq)).
% 132.99/59.63 thf(541,plain,((! [A:set_variable]: ((collect_variable @ (^ [B:variable]: (member_variable @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])).
% 132.99/59.63 thf(542,plain,(! [A:set_variable] : (((collect_variable @ (^ [B:variable]: (member_variable @ B @ A))) = A))),inference(cnf,[status(esa)],[541])).
% 132.99/59.63 thf(543,plain,(! [A:set_variable] : (((collect_variable @ (^ [B:variable]: (member_variable @ B @ A))) = A))),inference(lifteq,[status(thm)],[542])).
% 132.99/59.63 thf(1595,plain,(! [B:set_variable,A:set_variable] : (((uminus1851247844riable @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ A)))) = B) | (A != (uminus1851247844riable @ B)))),inference(paramod_ordered,[status(thm)],[543,426])).
% 132.99/59.63 thf(1596,plain,(! [A:set_variable] : (((uminus1851247844riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ (uminus1851247844riable @ A))))) = A))),inference(pattern_uni,[status(thm)],[1595:[bind(A, $thf(uminus1851247844riable @ C)),bind(B, $thf(C))]])).
% 132.99/59.63 thf(1610,plain,(! [A:set_variable] : (((uminus1851247844riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ (uminus1851247844riable @ A))))) = A))),inference(simp,[status(thm)],[1596])).
% 132.99/59.63 thf(88,axiom,((! [A:variable]: (member_variable @ A @ (set_option_variable2 @ (some_variable @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_option_Oset__intros)).
% 132.99/59.63 thf(562,plain,((! [A:variable]: (member_variable @ A @ (set_option_variable2 @ (some_variable @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])).
% 132.99/59.63 thf(563,plain,(! [A:variable] : ((member_variable @ A @ (set_option_variable2 @ (some_variable @ A))))),inference(cnf,[status(esa)],[562])).
% 132.99/59.63 thf(108,axiom,((! [A:variable]: ~ (member_variable @ A @ bot_bot_set_variable))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_emptyE)).
% 132.99/59.63 thf(619,plain,((! [A:variable]: ~ (member_variable @ A @ bot_bot_set_variable))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])).
% 132.99/59.63 thf(620,plain,((~ (? [A:variable]: (member_variable @ A @ bot_bot_set_variable)))),inference(miniscope,[status(thm)],[619])).
% 132.99/59.63 thf(621,plain,(! [A:variable] : ((~ (member_variable @ A @ bot_bot_set_variable)))),inference(cnf,[status(esa)],[620])).
% 132.99/59.63 thf(2290,plain,(! [B:variable,A:variable] : (~ (($true)) | ((member_variable @ A @ (set_option_variable2 @ (some_variable @ A))) != (member_variable @ B @ bot_bot_set_variable)))),inference(paramod_ordered,[status(thm)],[563,621])).
% 132.99/59.63 thf(2291,plain,(! [B:variable,A:variable] : (((member_variable @ A @ (set_option_variable2 @ (some_variable @ A))) != (member_variable @ B @ bot_bot_set_variable)))),inference(simp,[status(thm)],[2290])).
% 132.99/59.63 thf(2307,plain,(! [B:variable,A:variable] : ((A != B) | ((set_option_variable2 @ (some_variable @ A)) != bot_bot_set_variable))),inference(simp,[status(thm)],[2291])).
% 132.99/59.63 thf(2318,plain,(! [A:variable] : (((set_option_variable2 @ (some_variable @ A)) != bot_bot_set_variable))),inference(simp,[status(thm)],[2307])).
% 132.99/59.63 thf(4819,plain,(! [B:variable,A:set_variable] : (((uminus1851247844riable @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (uminus1851247844riable @ A))))) != bot_bot_set_variable) | (A != (set_option_variable2 @ (some_variable @ B))))),inference(paramod_ordered,[status(thm)],[1610,2318])).
% 132.99/59.63 thf(4820,plain,(! [A:variable] : (((uminus1851247844riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ A))))))) != bot_bot_set_variable))),inference(pattern_uni,[status(thm)],[4819:[bind(A, $thf(set_option_variable2 @ (some_variable @ D))),bind(B, $thf(D))]])).
% 132.99/59.63 thf(4866,plain,(! [A:variable] : (((uminus1851247844riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ A))))))) != bot_bot_set_variable))),inference(simp,[status(thm)],[4820])).
% 132.99/59.63 thf(4892,plain,(! [B:variable,A:set_variable] : ((A != bot_bot_set_variable) | ((uminus1851247844riable @ (uminus1851247844riable @ A)) != (uminus1851247844riable @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ B)))))))))),inference(paramod_ordered,[status(thm)],[426,4866])).
% 132.99/59.63 thf(4917,plain,(! [A:variable] : (((collect_variable @ (^ [B:variable]: (member_variable @ B @ (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ A)))))) != (uminus1851247844riable @ bot_bot_set_variable)))),inference(simp,[status(thm)],[4892])).
% 132.99/59.63 thf(4931,plain,(! [A:variable] : (((collect_variable @ (^ [B:variable]: (member_variable @ B @ (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ A)))))) != (uminus1851247844riable @ bot_bot_set_variable)))),inference(simp,[status(thm)],[4917])).
% 132.99/59.63 thf(95,axiom,((zero_zero_set_nat = (insert_nat @ zero_zero_nat @ bot_bot_set_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_set__zero)).
% 132.99/59.63 thf(582,plain,((zero_zero_set_nat = (insert_nat @ zero_zero_nat @ bot_bot_set_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])).
% 132.99/59.63 thf(232,axiom,((! [A:set_variable]: ((sup_sup_set_variable @ bot_bot_set_variable @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_sup__bot__left)).
% 132.99/59.63 thf(1005,plain,((! [A:set_variable]: ((sup_sup_set_variable @ bot_bot_set_variable @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])).
% 132.99/59.63 thf(127,axiom,((! [A:(variable > real),B:(variable > real),C:set_variable,D:set_variable]: (((denotational_Vagree @ A @ B @ C) & (denotational_Vagree @ A @ B @ D)) = (denotational_Vagree @ A @ B @ (sup_sup_set_variable @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_Vagree__and)).
% 132.99/59.63 thf(683,plain,((! [A:(variable > real),B:(variable > real),C:set_variable,D:set_variable]: (((denotational_Vagree @ (A) @ (B) @ C) & (denotational_Vagree @ (A) @ (B) @ D)) = (denotational_Vagree @ (A) @ (B) @ (sup_sup_set_variable @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])).
% 132.99/59.63 thf(143,axiom,((! [A:(real > (variable > real)),B:char,C:denotational_interp,D:trm,E:denotational_interp,F:trm]: (((denota1419872369iation @ (rr @ F @ E @ D @ C @ B @ A) @ (A @ zero_zero_real) @ (insert_variable @ (rVar @ B) @ (insert_variable @ (dVar @ B) @ bot_bot_set_variable))) & ((denota1863255036rm_sem @ C @ D @ (rr @ F @ E @ D @ C @ B @ A)) != (denota1863255036rm_sem @ E @ F @ (rr @ F @ E @ D @ C @ B @ A)))) | ((denota1778088425es_ODE @ C @ A @ B @ D) = (denota1778088425es_ODE @ E @ A @ B @ F))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_f2)).
% 132.99/59.63 thf(730,plain,((! [A:(real > (variable > real)),B:char,C:denotational_interp,D:trm,E:denotational_interp,F:trm]: (((denota1419872369iation @ (rr @ F @ E @ D @ C @ B @ A) @ (A @ zero_zero_real) @ (insert_variable @ (rVar @ B) @ (insert_variable @ (dVar @ B) @ bot_bot_set_variable))) & ~ ((denota1863255036rm_sem @ C @ D @ (rr @ F @ E @ D @ C @ B @ A)) = (denota1863255036rm_sem @ E @ F @ (rr @ F @ E @ D @ C @ B @ A)))) | ((denota1778088425es_ODE @ C @ (A) @ B @ D) = (denota1778088425es_ODE @ E @ (A) @ B @ F))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])).
% 132.99/59.63 thf(137,axiom,((sup_sup_set_variable = (^ [A:set_variable,B:set_variable]: (sup_sup_set_variable @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_sup_Ocommute)).
% 132.99/59.63 thf(713,plain,(((sup_sup_set_variable) = (^ [A:set_variable,B:set_variable]: (sup_sup_set_variable @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])).
% 132.99/59.63 thf(714,plain,(((sup_sup_set_variable) = (^ [A:set_variable,B:set_variable]: (sup_sup_set_variable @ B @ A)))),inference(lifteq,[status(thm)],[713])).
% 132.99/59.63 thf(1068,plain,(! [A:set_variable] : (((sup_sup_set_variable @ A) = (^ [B:set_variable]: (sup_sup_set_variable @ B @ A))))),inference(func_ext,[status(esa)],[714])).
% 132.99/59.63 thf(146,axiom,((! [A:set_variable,B:set_variable,C:set_variable]: ((sup_sup_set_variable @ (sup_sup_set_variable @ A @ B) @ C) = (sup_sup_set_variable @ A @ (sup_sup_set_variable @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_sup_Oassoc)).
% 132.99/59.63 thf(741,plain,((! [A:set_variable,B:set_variable,C:set_variable]: ((sup_sup_set_variable @ (sup_sup_set_variable @ A @ B) @ C) = (sup_sup_set_variable @ A @ (sup_sup_set_variable @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])).
% 132.99/59.63 thf(188,axiom,((! [A:real]: ((zero_zero_real = (uminus_uminus_real @ A)) = (zero_zero_real = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_neg__0__equal__iff__equal)).
% 132.99/59.63 thf(873,plain,((! [A:real]: ((zero_zero_real = (uminus_uminus_real @ A)) = (zero_zero_real = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])).
% 132.99/59.63 thf(48,axiom,((denotational_repv = (^ [A:(variable > real),B:variable,C:real,D:variable]: (if_real @ (B = D) @ C @ (A @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_repv__def__correct)).
% 132.99/59.63 thf(439,plain,(((denotational_repv) = (^ [A:(variable > real),B:variable,C:real,D:variable]: (if_real @ (B = D) @ C @ (A @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])).
% 132.99/59.63 thf(440,plain,(((denotational_repv) = (^ [A:(variable > real),B:variable,C:real,D:variable]: (if_real @ (B = D) @ C @ (A @ D))))),inference(lifteq,[status(thm)],[439])).
% 132.99/59.63 thf(100,axiom,((denota1419872369iation = (^ [A:(variable > real),B:(variable > real)]: (denota1419872369iation @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_Uvariation__sym)).
% 132.99/59.63 thf(597,plain,(((denota1419872369iation) = (^ [A:(variable > real),B:(variable > real)]: (denota1419872369iation @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])).
% 132.99/59.63 thf(244,axiom,((! [A:(real > (variable > real)),B:char,C:denotational_interp,D:trm,E:denotational_interp,F:trm]: ((! [G:(variable > real)]: ((denota1419872369iation @ G @ (A @ zero_zero_real) @ (insert_variable @ (rVar @ B) @ (insert_variable @ (dVar @ B) @ bot_bot_set_variable))) => ((denota1863255036rm_sem @ C @ D @ G) = (denota1863255036rm_sem @ E @ F @ G)))) => ((denota1778088425es_ODE @ C @ A @ B @ D) = (denota1778088425es_ODE @ E @ A @ B @ F))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_same__ODE__same__sol)).
% 132.99/59.63 thf(1041,plain,((! [A:(real > (variable > real)),B:char,C:denotational_interp,D:trm,E:denotational_interp,F:trm]: ((! [G:(variable > real)]: ((denota1419872369iation @ (G) @ (A @ zero_zero_real) @ (insert_variable @ (rVar @ B) @ (insert_variable @ (dVar @ B) @ bot_bot_set_variable))) => ((denota1863255036rm_sem @ C @ D @ (G)) = (denota1863255036rm_sem @ E @ F @ (G))))) => ((denota1778088425es_ODE @ C @ (A) @ B @ D) = (denota1778088425es_ODE @ E @ (A) @ B @ F))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])).
% 132.99/59.63 thf(184,axiom,((! [A:(variable > real),B:variable,C:real,D:set_variable_real]: ((member_variable_real @ (denotational_repv @ A @ B @ C) @ (static_selectlike @ D @ A @ (insert_variable @ B @ bot_bot_set_variable))) = ((C = (A @ B)) & (member_variable_real @ A @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_repv__selectlike__self)).
% 132.99/59.63 thf(861,plain,((! [A:(variable > real),B:variable,C:real,D:set_variable_real]: ((member_variable_real @ (denotational_repv @ A @ B @ C) @ (static_selectlike @ D @ (A) @ (insert_variable @ B @ bot_bot_set_variable))) = ((C = (A @ B)) & (member_variable_real @ (A) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])).
% 132.99/59.63 thf(145,axiom,((is_sin155454833riable = (^ [A:set_variable]: ? [B:variable]: (A = (insert_variable @ B @ bot_bot_set_variable))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_is__singleton__def)).
% 132.99/59.63 thf(739,plain,(((is_sin155454833riable) = (^ [A:set_variable]: ? [B:variable]: (A = (insert_variable @ B @ bot_bot_set_variable))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])).
% 132.99/59.63 thf(740,plain,(((is_sin155454833riable) = (^ [A:set_variable]: ? [B:variable]: (A = (insert_variable @ B @ bot_bot_set_variable))))),inference(lifteq,[status(thm)],[739])).
% 132.99/59.63 thf(159,axiom,((! [A:variable]: ((set_option_variable2 @ (some_variable @ A)) = (insert_variable @ A @ bot_bot_set_variable)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_option_Osimps_I15_J)).
% 132.99/59.63 thf(782,plain,((! [A:variable]: ((set_option_variable2 @ (some_variable @ A)) = (insert_variable @ A @ bot_bot_set_variable)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])).
% 132.99/59.63 thf(783,plain,(! [A:variable] : (((set_option_variable2 @ (some_variable @ A)) = (insert_variable @ A @ bot_bot_set_variable)))),inference(cnf,[status(esa)],[782])).
% 132.99/59.63 thf(784,plain,(! [A:variable] : (((insert_variable @ A @ bot_bot_set_variable) = (set_option_variable2 @ (some_variable @ A))))),inference(lifteq,[status(thm)],[783])).
% 132.99/59.63 thf(3848,plain,(((is_sin155454833riable) = (^ [A:set_variable]: ? [B:variable]: (A = (set_option_variable2 @ (some_variable @ B)))))),inference(rewrite,[status(thm)],[740,784])).
% 132.99/59.63 thf(963,plain,((~ (? [A:variable,B:set_variable]: ((insert_variable @ A @ B) = bot_bot_set_variable)))),inference(miniscope,[status(thm)],[962])).
% 132.99/59.63 thf(964,plain,(! [B:set_variable,A:variable] : ((~ ((insert_variable @ A @ B) = bot_bot_set_variable)))),inference(cnf,[status(esa)],[963])).
% 132.99/59.63 thf(965,plain,(! [B:set_variable,A:variable] : (((insert_variable @ A @ B) != bot_bot_set_variable))),inference(lifteq,[status(thm)],[964])).
% 132.99/59.63 thf(1590,plain,(! [C:set_variable,B:variable,A:set_variable] : (((collect_variable @ (^ [D:variable]: (member_variable @ D @ A))) != bot_bot_set_variable) | (A != (insert_variable @ B @ C)))),inference(paramod_ordered,[status(thm)],[543,965])).
% 132.99/59.63 thf(1591,plain,(! [B:set_variable,A:variable] : (((collect_variable @ (^ [C:variable]: (member_variable @ C @ (insert_variable @ A @ B)))) != bot_bot_set_variable))),inference(pattern_uni,[status(thm)],[1590:[bind(A, $thf(insert_variable @ D @ E)),bind(B, $thf(D)),bind(C, $thf(E))]])).
% 132.99/59.63 thf(1608,plain,(! [B:set_variable,A:variable] : (((collect_variable @ (^ [C:variable]: (member_variable @ C @ (insert_variable @ A @ B)))) != bot_bot_set_variable))),inference(simp,[status(thm)],[1591])).
% 132.99/59.63 thf(32,axiom,((! [A:option_trm,B:(option_trm > (option_trm > $o)),C:option_trm]: (((A = none_trm) => (B @ A @ C)) => (((C = none_trm) => (B @ A @ C)) => ((! [D:trm,E:trm]: ((A = (some_trm @ D)) => ((C = (some_trm @ E)) => (B @ A @ C)))) => (B @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_combine__options__cases)).
% 132.99/59.63 thf(376,plain,((! [A:option_trm,B:(option_trm > (option_trm > $o)),C:option_trm]: (((A = none_trm) => (B @ A @ C)) => (((C = none_trm) => (B @ A @ C)) => ((! [D:trm,E:trm]: ((A = (some_trm @ D)) => ((C = (some_trm @ E)) => (B @ A @ C)))) => (B @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])).
% 132.99/59.63 thf(377,plain,((! [A:option_trm,B:(option_trm > (option_trm > $o)),C:option_trm]: (((A = none_trm) => (B @ A @ C)) => (((C = none_trm) => (B @ A @ C)) => (((? [D:trm]: (A = (some_trm @ D))) => ((? [D:trm]: (C = (some_trm @ D))) => (B @ A @ C))) => (B @ A @ C)))))),inference(miniscope,[status(thm)],[376])).
% 132.99/59.63 thf(378,plain,(! [C:option_trm,B:(option_trm > (option_trm > $o)),A:option_trm] : ((((A = none_trm) | (sk20 @ C @ A @ B)) & (~ (B @ A @ C) | (sk20 @ C @ A @ B)) & (~ (sk20 @ C @ A @ B) | (C = none_trm) | (A = (some_trm @ (sk21 @ C @ (B) @ A))) | (B @ A @ C)) & (~ (sk20 @ C @ A @ B) | (C = none_trm) | (C = (some_trm @ (sk22 @ C @ (B) @ A))) | (B @ A @ C)) & (~ (sk20 @ C @ A @ B) | (C = none_trm) | ~ (B @ A @ C) | (B @ A @ C)) & (~ (sk20 @ C @ A @ B) | ~ (B @ A @ C) | (A = (some_trm @ (sk21 @ C @ (B) @ A))) | (B @ A @ C)) & (~ (sk20 @ C @ A @ B) | ~ (B @ A @ C) | (C = (some_trm @ (sk22 @ C @ (B) @ A))) | (B @ A @ C)) & (~ (sk20 @ C @ A @ B) | ~ (B @ A @ C) | ~ (B @ A @ C) | (B @ A @ C))))),inference(cnf,[status(esa)],[377])).
% 132.99/59.63 thf(384,plain,(! [C:option_trm,B:(option_trm > (option_trm > $o)),A:option_trm] : ((~ (B @ A @ C)) | (sk20 @ C @ A @ B))),inference(cnfConj,[status(thm)],[378])).
% 132.99/59.63 thf(68,axiom,((! [A:option_variable]: ((A != none_variable) => (member_variable @ (the_variable @ A) @ (set_option_variable2 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_option_Oset__sel)).
% 132.99/59.63 thf(500,plain,((! [A:option_variable]: ((~ (A = none_variable)) => (member_variable @ (the_variable @ A) @ (set_option_variable2 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])).
% 132.99/59.63 thf(138,axiom,((! [A:set_variable,B:set_variable,C:set_variable]: ((sup_sup_set_variable @ (sup_sup_set_variable @ A @ B) @ C) = (sup_sup_set_variable @ A @ (sup_sup_set_variable @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_sup__assoc)).
% 132.99/59.63 thf(715,plain,((! [A:set_variable,B:set_variable,C:set_variable]: ((sup_sup_set_variable @ (sup_sup_set_variable @ A @ B) @ C) = (sup_sup_set_variable @ A @ (sup_sup_set_variable @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])).
% 132.99/59.63 thf(212,axiom,(((these_variable @ bot_bo266290559riable) = bot_bot_set_variable)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_these__empty)).
% 132.99/59.63 thf(945,plain,(((these_variable @ bot_bo266290559riable) = bot_bot_set_variable)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])).
% 132.99/59.63 thf(21,axiom,((! [A:option_trm,B:option_trm,C:option_trm]: (((uSubst918876924Timeso @ A @ B) = C) => ((! [D:trm]: ((A = (some_trm @ D)) => (! [E:trm]: ((B = (some_trm @ E)) => (C != (some_trm @ (times @ D @ E))))))) => (((A = none_trm) => (C != none_trm)) => (~ ((? [D:trm]: (A = (some_trm @ D))) => ((B = none_trm) => (C != none_trm))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_Timeso_Oelims)).
% 132.99/59.63 thf(318,plain,((! [A:option_trm,B:option_trm,C:option_trm]: (((uSubst918876924Timeso @ A @ B) = C) => ((! [D:trm]: ((A = (some_trm @ D)) => (! [E:trm]: ((B = (some_trm @ E)) => (~ (C = (some_trm @ (times @ D @ E)))))))) => (((A = none_trm) => (~ (C = none_trm))) => (~ ((? [D:trm]: (A = (some_trm @ D))) => ((B = none_trm) => (~ (C = none_trm)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])).
% 132.99/59.63 thf(319,plain,(! [C:option_trm,B:option_trm,A:option_trm] : (((~ ((uSubst918876924Timeso @ A @ B) = C) | (A = (some_trm @ (sk10 @ C @ B @ A))) | (sk9 @ A @ C @ B)) & (~ ((uSubst918876924Timeso @ A @ B) = C) | (B = (some_trm @ (sk11 @ C @ B @ A))) | (sk9 @ A @ C @ B)) & (~ ((uSubst918876924Timeso @ A @ B) = C) | (C = (some_trm @ (times @ (sk10 @ C @ B @ A) @ (sk11 @ C @ B @ A)))) | (sk9 @ A @ C @ B)) & (~ ((uSubst918876924Timeso @ A @ B) = C) | ~ (sk9 @ A @ C @ B) | (A = none_trm) | (A = (some_trm @ (sk12 @ C @ B @ A)))) & (~ ((uSubst918876924Timeso @ A @ B) = C) | ~ (sk9 @ A @ C @ B) | (A = none_trm) | (B = none_trm)) & (~ ((uSubst918876924Timeso @ A @ B) = C) | ~ (sk9 @ A @ C @ B) | (A = none_trm) | (C = none_trm)) & (~ ((uSubst918876924Timeso @ A @ B) = C) | ~ (sk9 @ A @ C @ B) | (C = none_trm) | (A = (some_trm @ (sk12 @ C @ B @ A)))) & (~ ((uSubst918876924Timeso @ A @ B) = C) | ~ (sk9 @ A @ C @ B) | (C = none_trm) | (B = none_trm)) & (~ ((uSubst918876924Timeso @ A @ B) = C) | ~ (sk9 @ A @ C @ B) | (C = none_trm) | (C = none_trm))))),inference(cnf,[status(esa)],[318])).
% 132.99/59.63 thf(323,plain,(! [C:option_trm,B:option_trm,A:option_trm] : ((~ ((uSubst918876924Timeso @ A @ B) = C)) | (A = (some_trm @ (sk10 @ C @ B @ A))) | (sk9 @ A @ C @ B))),inference(cnfConj,[status(thm)],[319])).
% 132.99/59.63 thf(339,plain,(! [C:option_trm,B:option_trm,A:option_trm] : (((uSubst918876924Timeso @ A @ B) != C) | ((some_trm @ (sk10 @ C @ B @ A)) = A) | (sk9 @ A @ C @ B))),inference(lifteq,[status(thm)],[323])).
% 132.99/59.63 thf(340,plain,(! [B:option_trm,A:option_trm] : (((some_trm @ (sk10 @ (uSubst918876924Timeso @ A @ B) @ B @ A)) = A) | (sk9 @ A @ (uSubst918876924Timeso @ A @ B) @ B))),inference(simp,[status(thm)],[339])).
% 132.99/59.63 thf(80,axiom,((! [A:variable,B:set_variable,C:set_variable]: ((member_variable @ A @ (inf_inf_set_variable @ B @ C)) = ((member_variable @ A @ B) & (member_variable @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_Int__iff)).
% 132.99/59.63 thf(538,plain,((! [A:variable,B:set_variable,C:set_variable]: ((member_variable @ A @ (inf_inf_set_variable @ B @ C)) = ((member_variable @ A @ B) & (member_variable @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])).
% 132.99/59.63 thf(207,axiom,((! [A:variable]: (is_sin155454833riable @ (insert_variable @ A @ bot_bot_set_variable)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_is__singletonI)).
% 132.99/59.63 thf(930,plain,((! [A:variable]: (is_sin155454833riable @ (insert_variable @ A @ bot_bot_set_variable)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])).
% 132.99/59.63 thf(4944,plain,(! [B:variable,A:set_variable] : ((A != (uminus1851247844riable @ bot_bot_set_variable)) | ((collect_variable @ (^ [C:variable]: (member_variable @ C @ A))) != (collect_variable @ (^ [C:variable]: (member_variable @ C @ (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ B))))))))),inference(paramod_ordered,[status(thm)],[543,4931])).
% 132.99/59.63 thf(4945,plain,(! [A:variable] : (((uminus1851247844riable @ (set_option_variable2 @ (some_variable @ A))) != (uminus1851247844riable @ bot_bot_set_variable)))),inference(pattern_uni,[status(thm)],[4944:[bind(A, $thf(uminus1851247844riable @ (set_option_variable2 @ (some_variable @ E)))),bind(B, $thf(E))]])).
% 132.99/59.63 thf(4956,plain,(! [A:variable] : (((uminus1851247844riable @ (set_option_variable2 @ (some_variable @ A))) != (uminus1851247844riable @ bot_bot_set_variable)))),inference(simp,[status(thm)],[4945])).
% 132.99/59.63 thf(5032,plain,(! [B:variable,A:set_variable] : ((A != (uminus1851247844riable @ bot_bot_set_variable)) | ((uminus1851247844riable @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (uminus1851247844riable @ A))))) != (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ B)))))),inference(paramod_ordered,[status(thm)],[1610,4956])).
% 132.99/59.63 thf(5042,plain,(! [A:variable] : (((collect_variable @ (^ [B:variable]: (member_variable @ B @ (uminus1851247844riable @ (uminus1851247844riable @ bot_bot_set_variable))))) != (set_option_variable2 @ (some_variable @ A))))),inference(simp,[status(thm)],[5032])).
% 132.99/59.63 thf(5048,plain,(! [A:variable] : (((collect_variable @ (^ [B:variable]: (member_variable @ B @ (uminus1851247844riable @ (uminus1851247844riable @ bot_bot_set_variable))))) != (set_option_variable2 @ (some_variable @ A))))),inference(simp,[status(thm)],[5042])).
% 132.99/59.63 thf(5096,plain,(! [A:variable] : (((collect_variable @ (^ [B:variable]: (member_variable @ B @ bot_bot_set_variable))) != (set_option_variable2 @ (some_variable @ A))))),inference(rewrite,[status(thm)],[5048,426])).
% 132.99/59.63 thf(5107,plain,(! [B:variable,A:set_variable] : (((collect_variable @ (^ [C:variable]: (member_variable @ C @ A))) != (collect_variable @ (^ [C:variable]: (member_variable @ C @ bot_bot_set_variable)))) | (A != (set_option_variable2 @ (some_variable @ B))))),inference(paramod_ordered,[status(thm)],[543,5096])).
% 132.99/59.63 thf(5108,plain,(! [A:variable] : (((collect_variable @ (^ [B:variable]: (member_variable @ B @ (set_option_variable2 @ (some_variable @ A))))) != (collect_variable @ (^ [B:variable]: (member_variable @ B @ bot_bot_set_variable)))))),inference(pattern_uni,[status(thm)],[5107:[bind(A, $thf(set_option_variable2 @ (some_variable @ D))),bind(B, $thf(D))]])).
% 132.99/59.63 thf(5112,plain,(! [A:variable] : (((collect_variable @ (^ [B:variable]: (member_variable @ B @ (set_option_variable2 @ (some_variable @ A))))) != (collect_variable @ (^ [B:variable]: (member_variable @ B @ bot_bot_set_variable)))))),inference(simp,[status(thm)],[5108])).
% 132.99/59.63 thf(5146,plain,(! [A:variable] : (((collect_variable @ (^ [B:variable]: (member_variable @ B @ (set_option_variable2 @ (some_variable @ A))))) != (collect_variable @ (^ [B:variable]: (($false))))))),inference(rewrite,[status(thm)],[5112,621])).
% 132.99/59.63 thf(58,axiom,((! [A:set_variable,B:set_variable]: (((uminus1851247844riable @ A) = (uminus1851247844riable @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_compl__eq__compl__iff)).
% 132.99/59.63 thf(472,plain,((! [A:set_variable,B:set_variable]: (((uminus1851247844riable @ A) = (uminus1851247844riable @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])).
% 132.99/59.63 thf(173,axiom,((! [A:real]: ((zero_zero_real = A) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_zero__reorient)).
% 132.99/59.63 thf(827,plain,((! [A:real]: ((zero_zero_real = A) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])).
% 132.99/59.63 thf(828,plain,(! [A:real] : (((zero_zero_real = A) = (A = zero_zero_real)))),inference(cnf,[status(esa)],[827])).
% 132.99/59.63 thf(829,plain,(! [A:real] : (((zero_zero_real = A) = (A = zero_zero_real)))),inference(lifteq,[status(thm)],[828])).
% 132.99/59.63 thf(196,axiom,((! [A:produc1418842292n_game,B:char,C:trm,D:denotational_interp,E:(real > (variable > real))]: (((uSubst516392818stappt @ A @ (insert_variable @ (rVar @ B) @ (insert_variable @ (dVar @ B) @ bot_bot_set_variable)) @ C) != none_trm) => ((denota1778088425es_ODE @ D @ E @ B @ (the_trm @ (uSubst516392818stappt @ A @ (insert_variable @ (rVar @ B) @ (insert_variable @ (dVar @ B) @ bot_bot_set_variable)) @ C))) = (denota1778088425es_ODE @ (uSubst1599435252djoint @ A @ D @ (E @ zero_zero_real)) @ E @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_usubst__ode)).
% 132.99/59.63 thf(898,plain,((! [A:produc1418842292n_game,B:char,C:trm,D:denotational_interp,E:(real > (variable > real))]: ((~ ((uSubst516392818stappt @ A @ (insert_variable @ (rVar @ B) @ (insert_variable @ (dVar @ B) @ bot_bot_set_variable)) @ C) = none_trm)) => ((denota1778088425es_ODE @ D @ (E) @ B @ (the_trm @ (uSubst516392818stappt @ A @ (insert_variable @ (rVar @ B) @ (insert_variable @ (dVar @ B) @ bot_bot_set_variable)) @ C))) = (denota1778088425es_ODE @ (uSubst1599435252djoint @ A @ D @ (E @ zero_zero_real)) @ (E) @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])).
% 132.99/59.63 thf(231,axiom,((! [A:(variable > real),B:(variable > real),C:set_variable,D:trm,E:denotational_interp]: ((denota1419872369iation @ A @ B @ C) => (((inf_inf_set_variable @ (static_FVT @ D) @ C) = bot_bot_set_variable) => ((denota1863255036rm_sem @ E @ D @ A) = (denota1863255036rm_sem @ E @ D @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_coincidence__term__cor)).
% 132.99/59.63 thf(1001,plain,((! [A:(variable > real),B:(variable > real),C:set_variable,D:trm,E:denotational_interp]: ((denota1419872369iation @ (A) @ (B) @ C) => (((inf_inf_set_variable @ (static_FVT @ D) @ C) = bot_bot_set_variable) => ((denota1863255036rm_sem @ E @ D @ (A)) = (denota1863255036rm_sem @ E @ D @ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])).
% 132.99/59.63 thf(2326,plain,(! [B:variable,A:set_variable] : (((collect_variable @ (^ [C:variable]: (member_variable @ C @ A))) != bot_bot_set_variable) | (A != (set_option_variable2 @ (some_variable @ B))))),inference(paramod_ordered,[status(thm)],[543,2318])).
% 132.99/59.63 thf(2327,plain,(! [A:variable] : (((collect_variable @ (^ [B:variable]: (member_variable @ B @ (set_option_variable2 @ (some_variable @ A))))) != bot_bot_set_variable))),inference(pattern_uni,[status(thm)],[2326:[bind(A, $thf(set_option_variable2 @ (some_variable @ D))),bind(B, $thf(D))]])).
% 132.99/59.63 thf(2329,plain,(! [A:variable] : (((collect_variable @ (^ [B:variable]: (member_variable @ B @ (set_option_variable2 @ (some_variable @ A))))) != bot_bot_set_variable))),inference(simp,[status(thm)],[2327])).
% 132.99/59.63 thf(2484,plain,(! [B:variable,A:set_variable] : (((collect_variable @ (^ [C:variable]: (member_variable @ C @ (collect_variable @ (^ [D:variable]: (member_variable @ D @ A)))))) != bot_bot_set_variable) | (A != (set_option_variable2 @ (some_variable @ B))))),inference(paramod_ordered,[status(thm)],[543,2329])).
% 132.99/59.63 thf(2485,plain,(! [A:variable] : (((collect_variable @ (^ [B:variable]: (member_variable @ B @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (set_option_variable2 @ (some_variable @ A)))))))) != bot_bot_set_variable))),inference(pattern_uni,[status(thm)],[2484:[bind(A, $thf(set_option_variable2 @ (some_variable @ D))),bind(B, $thf(D))]])).
% 132.99/59.63 thf(2491,plain,(! [A:variable] : (((collect_variable @ (^ [B:variable]: (member_variable @ B @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (set_option_variable2 @ (some_variable @ A)))))))) != bot_bot_set_variable))),inference(simp,[status(thm)],[2485])).
% 132.99/59.63 thf(47,axiom,((! [A:set_variable]: ((inf_inf_set_variable @ A @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_inf__idem)).
% 132.99/59.63 thf(436,plain,((! [A:set_variable]: ((inf_inf_set_variable @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])).
% 132.99/59.63 thf(4817,plain,(! [B:set_variable,A:set_variable] : (((uminus1851247844riable @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ A)))) = B) | ((uminus1851247844riable @ (uminus1851247844riable @ A)) != (uminus1851247844riable @ B)))),inference(paramod_ordered,[status(thm)],[426,1610])).
% 132.99/59.63 thf(4818,plain,(! [A:set_variable] : (((uminus1851247844riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ A)))) = (uminus1851247844riable @ A)))),inference(pattern_uni,[status(thm)],[4817:[bind(A, $thf(C)),bind(B, $thf(uminus1851247844riable @ C))]])).
% 132.99/59.63 thf(4864,plain,(! [A:set_variable] : (((uminus1851247844riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ A)))) = (uminus1851247844riable @ A)))),inference(simp,[status(thm)],[4818])).
% 132.99/59.63 thf(6674,plain,(! [B:variable,A:set_variable] : (((uminus1851247844riable @ A) != (uminus1851247844riable @ bot_bot_set_variable)) | ((uminus1851247844riable @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ A)))) != (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ B)))))),inference(paramod_ordered,[status(thm)],[4864,4956])).
% 132.99/59.63 thf(6745,plain,(! [B:variable,A:set_variable] : ((A != bot_bot_set_variable) | ((uminus1851247844riable @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ A)))) != (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ B)))))),inference(simp,[status(thm)],[6674])).
% 132.99/59.63 thf(6762,plain,(! [A:variable] : (((uminus1851247844riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ bot_bot_set_variable)))) != (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ A)))))),inference(simp,[status(thm)],[6745])).
% 132.99/59.63 thf(6774,plain,(! [A:variable] : (((uminus1851247844riable @ (collect_variable @ (^ [B:variable]: (($false))))) != (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ A)))))),inference(rewrite,[status(thm)],[6762,621])).
% 132.99/59.63 thf(6781,plain,(! [B:variable,A:set_variable] : ((A != (uminus1851247844riable @ (collect_variable @ (^ [C:variable]: (($false)))))) | ((uminus1851247844riable @ (uminus1851247844riable @ A)) != (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ B)))))),inference(paramod_ordered,[status(thm)],[426,6774])).
% 132.99/59.63 thf(6814,plain,(! [A:variable] : (((uminus1851247844riable @ (uminus1851247844riable @ (collect_variable @ (^ [B:variable]: (($false)))))) != (set_option_variable2 @ (some_variable @ A))))),inference(simp,[status(thm)],[6781])).
% 132.99/59.63 thf(6849,plain,(! [A:variable] : (((uminus1851247844riable @ (uminus1851247844riable @ (collect_variable @ (^ [B:variable]: (($false)))))) != (set_option_variable2 @ (some_variable @ A))))),inference(simp,[status(thm)],[6814])).
% 132.99/59.63 thf(6872,plain,(! [A:variable] : (((collect_variable @ (^ [B:variable]: (($false)))) != (set_option_variable2 @ (some_variable @ A))))),inference(rewrite,[status(thm)],[6849,426])).
% 132.99/59.63 thf(220,axiom,((! [A:set_variable,B:variable,C:set_variable]: ((sup_sup_set_variable @ A @ (insert_variable @ B @ C)) = (insert_variable @ B @ (sup_sup_set_variable @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_Un__insert__right)).
% 132.99/59.63 thf(973,plain,((! [A:set_variable,B:variable,C:set_variable]: ((sup_sup_set_variable @ A @ (insert_variable @ B @ C)) = (insert_variable @ B @ (sup_sup_set_variable @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])).
% 132.99/59.63 thf(192,axiom,((! [A:char,B:char]: ((rVar @ A) != (dVar @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_variable_Odistinct_I1_J)).
% 132.99/59.63 thf(885,plain,((! [A:char,B:char]: ~ ((rVar @ A) = (dVar @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])).
% 132.99/59.63 thf(117,axiom,((! [A:(variable > real),B:(variable > real),C:set_variable,D:(variable > real),E:set_variable]: ((denota1419872369iation @ A @ B @ C) => ((denota1419872369iation @ B @ D @ E) => (denota1419872369iation @ A @ D @ (sup_sup_set_variable @ C @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_Uvariation__trans)).
% 132.99/59.63 thf(651,plain,((! [A:(variable > real),B:(variable > real),C:set_variable,D:(variable > real),E:set_variable]: ((denota1419872369iation @ (A) @ (B) @ C) => ((denota1419872369iation @ (B) @ (D) @ E) => (denota1419872369iation @ (A) @ (D) @ (sup_sup_set_variable @ C @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])).
% 132.99/59.63 thf(5,axiom,((((?) @ option_trm) = (^ [A:(option_trm > $o)]: ((A @ none_trm) | ? [B:trm]: (A @ (some_trm @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_split__option__ex)).
% 132.99/59.63 thf(256,plain,((((?) @ option_trm) = (^ [A:(option_trm > $o)]: ((A @ none_trm) | ? [B:trm]: (A @ (some_trm @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 132.99/59.63 thf(257,plain,(((^ [A:(option_trm > $o)]: ((A @ none_trm) | ? [B:trm]: (A @ (some_trm @ B)))) = ((?) @ option_trm))),inference(lifteq,[status(thm)],[256])).
% 132.99/59.63 thf(141,axiom,((! [A:set_variable_real,B:(variable > real)]: ((static_selectlike @ A @ B @ bot_bot_set_variable) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_selectlike__empty)).
% 132.99/59.63 thf(724,plain,((! [A:set_variable_real,B:(variable > real)]: ((static_selectlike @ A @ (B) @ bot_bot_set_variable) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])).
% 132.99/59.63 thf(147,axiom,(((set_option_variable2 @ none_variable) = bot_bot_set_variable)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_option_Osimps_I14_J)).
% 132.99/59.63 thf(744,plain,(((set_option_variable2 @ none_variable) = bot_bot_set_variable)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])).
% 132.99/59.63 thf(745,plain,(((set_option_variable2 @ none_variable) = bot_bot_set_variable)),inference(lifteq,[status(thm)],[744])).
% 132.99/59.63 thf(2324,plain,(! [A:variable] : ((bot_bot_set_variable != bot_bot_set_variable) | ((set_option_variable2 @ (some_variable @ A)) != (set_option_variable2 @ none_variable)))),inference(paramod_ordered,[status(thm)],[745,2318])).
% 132.99/59.63 thf(2325,plain,(! [A:variable] : (((set_option_variable2 @ (some_variable @ A)) != (set_option_variable2 @ none_variable)))),inference(simp,[status(thm)],[2324])).
% 132.99/59.63 thf(2328,plain,(! [A:variable] : (((some_variable @ A) != none_variable))),inference(simp,[status(thm)],[2325])).
% 132.99/59.63 thf(91,axiom,((! [A:variable,B:set_variable]: ((member_variable @ A @ (uminus1851247844riable @ B)) = (~ (member_variable @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_Compl__iff)).
% 132.99/59.63 thf(570,plain,((! [A:variable,B:set_variable]: ((member_variable @ A @ (uminus1851247844riable @ B)) = (~ (member_variable @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])).
% 132.99/59.63 thf(160,axiom,((! [A:(variable > real),B:(variable > real)]: ((stateinterpol @ A @ B @ bot_bot_set_variable) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_stateinterpol__empty)).
% 132.99/59.63 thf(785,plain,((! [A:(variable > real),B:(variable > real)]: ((stateinterpol @ A @ B @ bot_bot_set_variable) = (B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])).
% 132.99/59.63 thf(30,axiom,((! [A:(option_trm > (option_trm > $o)),B:option_trm,C:option_trm]: ((! [D:trm,E:trm]: (A @ (some_trm @ D) @ (some_trm @ E))) => ((! [D:option_trm]: (A @ none_trm @ D)) => ((! [D:trm]: (A @ (some_trm @ D) @ none_trm)) => (A @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_Timeso_Oinduct)).
% 132.99/59.63 thf(370,plain,((! [A:(option_trm > (option_trm > $o)),B:option_trm,C:option_trm]: ((! [D:trm,E:trm]: (A @ (some_trm @ D) @ (some_trm @ E))) => ((! [D:option_trm]: (A @ none_trm @ D)) => ((! [D:trm]: (A @ (some_trm @ D) @ none_trm)) => (A @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])).
% 132.99/59.63 thf(371,plain,((! [A:(option_trm > (option_trm > $o))]: ((! [B:trm,C:trm]: (A @ (some_trm @ B) @ (some_trm @ C))) => ((! [B:option_trm]: (A @ none_trm @ B)) => ((! [B:trm]: (A @ (some_trm @ B) @ none_trm)) => (! [B:option_trm,C:option_trm]: (A @ B @ C))))))),inference(miniscope,[status(thm)],[370])).
% 132.99/59.63 thf(372,plain,(! [C:option_trm,B:option_trm,A:(option_trm > (option_trm > $o))] : ((~ (A @ (some_trm @ (sk16 @ (A))) @ (some_trm @ (sk17 @ (A))))) | (~ (A @ none_trm @ (sk18 @ (A)))) | (~ (A @ (some_trm @ (sk19 @ (A))) @ none_trm)) | (A @ B @ C))),inference(cnf,[status(esa)],[371])).
% 132.99/59.63 thf(326,plain,(! [C:option_trm,B:option_trm,A:option_trm] : ((~ ((uSubst918876924Timeso @ A @ B) = C)) | (~ (sk9 @ A @ C @ B)) | (A = none_trm) | (B = none_trm))),inference(cnfConj,[status(thm)],[319])).
% 132.99/59.63 thf(343,plain,(! [C:option_trm,B:option_trm,A:option_trm] : (((uSubst918876924Timeso @ A @ B) != C) | (A = none_trm) | (B = none_trm) | (~ (sk9 @ A @ C @ B)))),inference(lifteq,[status(thm)],[326])).
% 132.99/59.63 thf(344,plain,(! [B:option_trm,A:option_trm] : ((A = none_trm) | (B = none_trm) | (~ (sk9 @ A @ (uSubst918876924Timeso @ A @ B) @ B)))),inference(simp,[status(thm)],[343])).
% 132.99/59.63 thf(26,axiom,((! [A:trm]: (member_trm @ A @ (set_option_trm2 @ (some_trm @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_option_Oset__intros)).
% 132.99/59.63 thf(357,plain,((! [A:trm]: (member_trm @ A @ (set_option_trm2 @ (some_trm @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])).
% 132.99/59.63 thf(358,plain,(! [A:trm] : ((member_trm @ A @ (set_option_trm2 @ (some_trm @ A))))),inference(cnf,[status(esa)],[357])).
% 132.99/59.63 thf(13,axiom,((! [A:trm,B:option_trm]: ((member_trm @ A @ (set_option_trm2 @ B)) => (B = (some_trm @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_option_Oset__cases)).
% 132.99/59.63 thf(284,plain,((! [A:trm,B:option_trm]: ((member_trm @ A @ (set_option_trm2 @ B)) => (B = (some_trm @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])).
% 132.99/59.63 thf(285,plain,(! [B:option_trm,A:trm] : ((~ (member_trm @ A @ (set_option_trm2 @ B))) | (B = (some_trm @ A)))),inference(cnf,[status(esa)],[284])).
% 132.99/59.63 thf(286,plain,(! [B:option_trm,A:trm] : ((B = (some_trm @ A)) | (~ (member_trm @ A @ (set_option_trm2 @ B))))),inference(lifteq,[status(thm)],[285])).
% 132.99/59.63 thf(366,plain,((! [A:option_trm]: ((? [B:trm]: (A = (some_trm @ B))) => (~ (A = none_trm))))),inference(miniscope,[status(thm)],[365])).
% 132.99/59.63 thf(367,plain,(! [B:trm,A:option_trm] : ((~ (A = (some_trm @ B))) | (~ (A = none_trm)))),inference(cnf,[status(esa)],[366])).
% 132.99/59.63 thf(368,plain,(! [B:trm,A:option_trm] : ((A != (some_trm @ B)) | (A != none_trm))),inference(lifteq,[status(thm)],[367])).
% 132.99/59.63 thf(369,plain,(! [A:trm] : (((some_trm @ A) != none_trm))),inference(simp,[status(thm)],[368])).
% 132.99/59.63 thf(2420,plain,(! [C:trm,B:option_trm,A:trm] : ((~ (member_trm @ A @ (set_option_trm2 @ B))) | (B != none_trm) | ((some_trm @ A) != (some_trm @ C)))),inference(paramod_ordered,[status(thm)],[286,369])).
% 132.99/59.63 thf(2421,plain,(! [B:option_trm,A:trm] : ((~ (member_trm @ A @ (set_option_trm2 @ B))) | (B != none_trm))),inference(pattern_uni,[status(thm)],[2420:[bind(A, $thf(A)),bind(B, $thf(B)),bind(C, $thf(A))]])).
% 132.99/59.63 thf(2444,plain,(! [A:trm] : ((~ (member_trm @ A @ (set_option_trm2 @ none_trm))))),inference(simp,[status(thm)],[2421])).
% 132.99/59.63 thf(2455,plain,(! [B:trm,A:trm] : (~ (($true)) | ((member_trm @ A @ (set_option_trm2 @ (some_trm @ A))) != (member_trm @ B @ (set_option_trm2 @ none_trm))))),inference(paramod_ordered,[status(thm)],[358,2444])).
% 132.99/59.63 thf(2456,plain,(! [B:trm,A:trm] : (((member_trm @ A @ (set_option_trm2 @ (some_trm @ A))) != (member_trm @ B @ (set_option_trm2 @ none_trm))))),inference(simp,[status(thm)],[2455])).
% 132.99/59.63 thf(2461,plain,(! [B:trm,A:trm] : ((A != B) | ((set_option_trm2 @ (some_trm @ A)) != (set_option_trm2 @ none_trm)))),inference(simp,[status(thm)],[2456])).
% 132.99/59.63 thf(2466,plain,(! [A:trm] : (((set_option_trm2 @ (some_trm @ A)) != (set_option_trm2 @ none_trm)))),inference(simp,[status(thm)],[2461])).
% 132.99/59.63 thf(53,axiom,((! [A:set_variable,B:set_variable]: ((inf_inf_set_variable @ A @ (inf_inf_set_variable @ A @ B)) = (inf_inf_set_variable @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_inf__left__idem)).
% 132.99/59.63 thf(460,plain,((! [A:set_variable,B:set_variable]: ((inf_inf_set_variable @ A @ (inf_inf_set_variable @ A @ B)) = (inf_inf_set_variable @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])).
% 132.99/59.63 thf(54,axiom,((denotational_Vagree = (^ [A:(variable > real),B:(variable > real),C:set_variable]: ! [D:variable]: ((member_variable @ D @ C) => ((A @ D) = (B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_Vagree__def)).
% 132.99/59.63 thf(463,plain,(((denotational_Vagree) = (^ [A:(variable > real),B:(variable > real),C:set_variable]: ! [D:variable]: ((member_variable @ D @ C) => ((A @ D) = (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])).
% 132.99/59.63 thf(464,plain,(((denotational_Vagree) = (^ [A:(variable > real),B:(variable > real),C:set_variable]: ! [D:variable]: ((member_variable @ D @ C) => ((A @ D) = (B @ D)))))),inference(lifteq,[status(thm)],[463])).
% 132.99/59.63 thf(55,axiom,((denotational_Vagree = (^ [A:(variable > real),B:(variable > real)]: (denotational_Vagree @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_Vagree__sym)).
% 132.99/59.63 thf(465,plain,(((denotational_Vagree) = (^ [A:(variable > real),B:(variable > real)]: (denotational_Vagree @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])).
% 132.99/59.63 thf(466,plain,(((denotational_Vagree) = (^ [A:(variable > real),B:(variable > real)]: (denotational_Vagree @ B @ A)))),inference(lifteq,[status(thm)],[465])).
% 132.99/59.63 thf(1329,plain,(((^ [A:(variable > real),B:(variable > real),C:set_variable]: ! [D:variable]: ((member_variable @ D @ C) => ((A @ D) = (B @ D)))) = (^ [A:(variable > real),B:(variable > real)]: (denotational_Vagree @ B @ A))) | ((denotational_Vagree) != (denotational_Vagree))),inference(paramod_ordered,[status(thm)],[464,466])).
% 132.99/59.63 thf(1330,plain,(((^ [A:(variable > real),B:(variable > real),C:set_variable]: ! [D:variable]: ((member_variable @ D @ C) => ((A @ D) = (B @ D)))) = (^ [A:(variable > real),B:(variable > real)]: (denotational_Vagree @ B @ A)))),inference(pattern_uni,[status(thm)],[1329:[]])).
% 132.99/59.63 thf(202,axiom,((! [A:variable,B:set_variable,C:set_variable]: ((member_variable @ A @ B) => (member_variable @ A @ (sup_sup_set_variable @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_UnI2)).
% 132.99/59.63 thf(917,plain,((! [A:variable,B:set_variable,C:set_variable]: ((member_variable @ A @ B) => (member_variable @ A @ (sup_sup_set_variable @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])).
% 132.99/59.63 thf(133,axiom,((! [A:(variable > real),B:set_variable]: (denota1419872369iation @ A @ A @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_Uvariation__refl)).
% 132.99/59.63 thf(702,plain,((! [A:(variable > real),B:set_variable]: (denota1419872369iation @ (A) @ (A) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])).
% 132.99/59.63 thf(931,plain,(! [A:variable] : ((is_sin155454833riable @ (insert_variable @ A @ bot_bot_set_variable)))),inference(cnf,[status(esa)],[930])).
% 132.99/59.63 thf(1597,plain,(! [B:variable,A:set_variable] : ((is_sin155454833riable @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ A)))) | (A != (insert_variable @ B @ bot_bot_set_variable)))),inference(paramod_ordered,[status(thm)],[543,931])).
% 132.99/59.63 thf(1598,plain,(! [A:variable] : ((is_sin155454833riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ (insert_variable @ A @ bot_bot_set_variable))))))),inference(pattern_uni,[status(thm)],[1597:[bind(A, $thf(insert_variable @ C @ bot_bot_set_variable)),bind(B, $thf(C))]])).
% 132.99/59.63 thf(1611,plain,(! [A:variable] : ((is_sin155454833riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ (insert_variable @ A @ bot_bot_set_variable))))))),inference(simp,[status(thm)],[1598])).
% 132.99/59.63 thf(2070,plain,(! [B:variable,A:set_variable] : ((is_sin155454833riable @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ A)))) | (A != (collect_variable @ (^ [C:variable]: (member_variable @ C @ (insert_variable @ B @ bot_bot_set_variable))))))),inference(paramod_ordered,[status(thm)],[543,1611])).
% 132.99/59.63 thf(2071,plain,(! [A:variable] : ((is_sin155454833riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (insert_variable @ A @ bot_bot_set_variable)))))))))),inference(pattern_uni,[status(thm)],[2070:[bind(A, $thf(collect_variable @ (^ [C:variable]: (member_variable @ C @ (insert_variable @ B @ bot_bot_set_variable))))),bind(B, $thf(B))]])).
% 132.99/59.63 thf(2092,plain,(! [A:variable] : ((is_sin155454833riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (insert_variable @ A @ bot_bot_set_variable)))))))))),inference(simp,[status(thm)],[2071])).
% 132.99/59.63 thf(3845,plain,(! [A:variable] : ((is_sin155454833riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (set_option_variable2 @ (some_variable @ A))))))))))),inference(rewrite,[status(thm)],[2092,784])).
% 132.99/59.63 thf(229,axiom,((bot_bot_set_variable = (collect_variable @ bot_bot_variable_o))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_bot__set__def)).
% 132.99/59.63 thf(997,plain,((bot_bot_set_variable = (collect_variable @ (bot_bot_variable_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])).
% 132.99/59.63 thf(998,plain,(((collect_variable @ (bot_bot_variable_o)) = bot_bot_set_variable)),inference(lifteq,[status(thm)],[997])).
% 132.99/59.63 thf(150,axiom,((bot_bot_variable_o = (^ [A:variable]: (member_variable @ A @ bot_bot_set_variable)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_bot__empty__eq)).
% 132.99/59.63 thf(752,plain,(((bot_bot_variable_o) = (^ [A:variable]: (member_variable @ A @ bot_bot_set_variable)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])).
% 132.99/59.63 thf(753,plain,(((^ [A:variable]: (member_variable @ A @ bot_bot_set_variable)) = (bot_bot_variable_o))),inference(lifteq,[status(thm)],[752])).
% 132.99/59.63 thf(1086,plain,(((bot_bot_variable_o) = (^ [A:variable]: (($false))))),inference(rewrite,[status(thm)],[753,621])).
% 132.99/59.63 thf(1242,plain,(((collect_variable @ (^ [A:variable]: (($false)))) = bot_bot_set_variable)),inference(rewrite,[status(thm)],[998,1086])).
% 132.99/59.63 thf(2479,plain,(! [A:variable] : ((bot_bot_set_variable != bot_bot_set_variable) | ((collect_variable @ (^ [B:variable]: (member_variable @ B @ (set_option_variable2 @ (some_variable @ A))))) != (collect_variable @ (^ [B:variable]: (($false))))))),inference(paramod_ordered,[status(thm)],[1242,2329])).
% 132.99/59.63 thf(2480,plain,(! [A:variable] : (((collect_variable @ (^ [B:variable]: (member_variable @ B @ (set_option_variable2 @ (some_variable @ A))))) != (collect_variable @ (^ [B:variable]: (($false))))))),inference(simp,[status(thm)],[2479])).
% 132.99/59.63 thf(2488,plain,(! [A:variable] : (((^ [B:variable]: (member_variable @ B @ (set_option_variable2 @ (some_variable @ A)))) != (^ [B:variable]: (($false)))))),inference(simp,[status(thm)],[2480])).
% 132.99/59.63 thf(87,axiom,((! [A:set_variable,B:set_variable]: ((inf_inf_set_variable @ A @ (inf_inf_set_variable @ A @ B)) = (inf_inf_set_variable @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_inf_Oleft__idem)).
% 132.99/59.63 thf(559,plain,((! [A:set_variable,B:set_variable]: ((inf_inf_set_variable @ A @ (inf_inf_set_variable @ A @ B)) = (inf_inf_set_variable @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])).
% 132.99/59.63 thf(183,axiom,((denota1419872369iation @ (f @ zero_zero_real) @ omega @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_uv)).
% 132.99/59.63 thf(860,plain,((denota1419872369iation @ (f @ zero_zero_real) @ (omega) @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])).
% 132.99/59.63 thf(2576,plain,(~ (($true)) | ((denota1419872369iation @ (f @ zero_zero_real) @ (omega) @ (sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)) @ u)) != (denota1419872369iation @ (f @ zero_zero_real) @ (omega) @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)))))),inference(paramod_ordered,[status(thm)],[860,249])).
% 132.99/59.63 thf(2577,plain,(((denota1419872369iation @ (f @ zero_zero_real) @ (omega) @ (sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)) @ u)) != (denota1419872369iation @ (f @ zero_zero_real) @ (omega) @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)))))),inference(simp,[status(thm)],[2576])).
% 132.99/59.63 thf(2600,plain,(((f @ zero_zero_real) != (f @ zero_zero_real)) | ((omega) != (omega)) | ((sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)) @ u) != (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable))))),inference(simp,[status(thm)],[2577])).
% 132.99/59.63 thf(2605,plain,(((sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)) @ u) != (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable))))),inference(simp,[status(thm)],[2600])).
% 132.99/59.63 thf(3840,plain,(((sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (set_option_variable2 @ (some_variable @ (dVar @ x)))) @ u) != (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (set_option_variable2 @ (some_variable @ (dVar @ x))))))),inference(rewrite,[status(thm)],[2605,784])).
% 132.99/59.63 thf(1087,plain,(! [A:variable] : ((~ (bot_bot_variable_o @ A)))),inference(func_ext,[status(esa)],[1086])).
% 132.99/59.63 thf(42,axiom,((! [A:option_trm]: ((A != none_trm) => (member_trm @ (the_trm @ A) @ (set_option_trm2 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_option_Oset__sel)).
% 132.99/59.63 thf(421,plain,((! [A:option_trm]: ((~ (A = none_trm)) => (member_trm @ (the_trm @ A) @ (set_option_trm2 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])).
% 132.99/59.63 thf(14,axiom,((! [A:set_variable_real]: ((uminus430703407e_real @ (uminus430703407e_real @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_double__complement)).
% 132.99/59.63 thf(287,plain,((! [A:set_variable_real]: ((uminus430703407e_real @ (uminus430703407e_real @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])).
% 132.99/59.63 thf(288,plain,(! [A:set_variable_real] : (((uminus430703407e_real @ (uminus430703407e_real @ A)) = A))),inference(cnf,[status(esa)],[287])).
% 132.99/59.63 thf(289,plain,(! [A:set_variable_real] : (((uminus430703407e_real @ (uminus430703407e_real @ A)) = A))),inference(lifteq,[status(thm)],[288])).
% 132.99/59.63 thf(7,axiom,((! [A:set_variable_real,B:set_variable_real]: (((uminus430703407e_real @ A) = (uminus430703407e_real @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_Compl__eq__Compl__iff)).
% 132.99/59.63 thf(261,plain,((! [A:set_variable_real,B:set_variable_real]: (((uminus430703407e_real @ A) = (uminus430703407e_real @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 132.99/59.63 thf(170,axiom,((! [A:set_variable]: ((sup_sup_set_variable @ A @ bot_bot_set_variable) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_Un__empty__right)).
% 132.99/59.63 thf(817,plain,((! [A:set_variable]: ((sup_sup_set_variable @ A @ bot_bot_set_variable) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])).
% 132.99/59.63 thf(197,axiom,((! [A:(real > (variable > real)),B:(variable > real),C:set_variable,D:denotational_interp,E:char,F:trm,G:real]: ((denota1419872369iation @ (A @ zero_zero_real) @ B @ C) => ((denota1778088425es_ODE @ D @ A @ E @ F) => (denota1419872369iation @ (A @ G) @ B @ (sup_sup_set_variable @ C @ (insert_variable @ (rVar @ E) @ (insert_variable @ (dVar @ E) @ bot_bot_set_variable)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_solves__Vagree__trans)).
% 132.99/59.63 thf(902,plain,((! [A:(real > (variable > real)),B:(variable > real),C:set_variable,D:denotational_interp,E:char,F:trm,G:real]: ((denota1419872369iation @ (A @ zero_zero_real) @ (B) @ C) => ((denota1778088425es_ODE @ D @ (A) @ E @ F) => (denota1419872369iation @ (A @ G) @ (B) @ (sup_sup_set_variable @ C @ (insert_variable @ (rVar @ E) @ (insert_variable @ (dVar @ E) @ bot_bot_set_variable)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])).
% 132.99/59.63 thf(59,axiom,((! [A:set_variable,B:set_variable]: ((ord_le282106107riable @ A @ B) => ((ord_le282106107riable @ B @ A) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_subset__antisym)).
% 132.99/59.63 thf(475,plain,((! [A:set_variable,B:set_variable]: ((ord_le282106107riable @ A @ B) => ((ord_le282106107riable @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])).
% 132.99/59.63 thf(65,axiom,((! [A:(variable > real),B:set_variable]: (denotational_Vagree @ A @ A @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_Vagree__refl)).
% 132.99/59.63 thf(492,plain,((! [A:(variable > real),B:set_variable]: (denotational_Vagree @ (A) @ (A) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])).
% 132.99/59.63 thf(152,axiom,((! [A:set_variable,B:set_variable]: ((sup_sup_set_variable @ A @ (sup_sup_set_variable @ A @ B)) = (sup_sup_set_variable @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_Un__left__absorb)).
% 132.99/59.63 thf(756,plain,((! [A:set_variable,B:set_variable]: ((sup_sup_set_variable @ A @ (sup_sup_set_variable @ A @ B)) = (sup_sup_set_variable @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])).
% 132.99/59.63 thf(4,axiom,((! [A:(char > (option_trm > $o)),B:char,C:option_trm]: ((! [D:char,E:trm]: (A @ D @ (some_trm @ E))) => ((! [D:char]: (A @ D @ none_trm)) => (A @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_ODEo_Oinduct)).
% 132.99/59.63 thf(253,plain,((! [A:(char > (option_trm > $o)),B:char,C:option_trm]: ((! [D:char,E:trm]: (A @ D @ (some_trm @ E))) => ((! [D:char]: (A @ D @ none_trm)) => (A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 132.99/59.63 thf(62,axiom,((! [A:option_trm]: ((uSubst918876924Timeso @ none_trm @ A) = none_trm))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_Timeso_Osimps_I2_J)).
% 132.99/59.63 thf(485,plain,((! [A:option_trm]: ((uSubst918876924Timeso @ none_trm @ A) = none_trm))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])).
% 132.99/59.63 thf(73,axiom,((! [A:variable,B:set_variable,C:(variable > real),D:(variable > real)]: ((~ (member_variable @ A @ B)) => ((stateinterpol @ C @ D @ B @ A) = (D @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_stateinterpol__right)).
% 132.99/59.63 thf(514,plain,((! [A:variable,B:set_variable,C:(variable > real),D:(variable > real)]: ((~ (member_variable @ A @ B)) => ((stateinterpol @ (C) @ (D) @ B @ A) = (D @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])).
% 132.99/59.63 thf(3843,plain,(! [A:variable] : ((is_sin155454833riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ (set_option_variable2 @ (some_variable @ A)))))))),inference(rewrite,[status(thm)],[1611,784])).
% 132.99/59.63 thf(4827,plain,(! [B:variable,A:set_variable] : ((is_sin155454833riable @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (uminus1851247844riable @ (collect_variable @ (^ [D:variable]: (member_variable @ D @ (uminus1851247844riable @ A))))))))) | (A != (set_option_variable2 @ (some_variable @ B))))),inference(paramod_ordered,[status(thm)],[1610,3843])).
% 132.99/59.63 thf(4828,plain,(! [A:variable] : ((is_sin155454833riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ (uminus1851247844riable @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ A))))))))))))),inference(pattern_uni,[status(thm)],[4827:[bind(A, $thf(set_option_variable2 @ (some_variable @ D))),bind(B, $thf(D))]])).
% 132.99/59.63 thf(4871,plain,(! [A:variable] : ((is_sin155454833riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ (uminus1851247844riable @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ A))))))))))))),inference(simp,[status(thm)],[4828])).
% 132.99/59.63 thf(167,axiom,((! [A:set_variable,B:set_variable]: ((sup_sup_set_variable @ A @ (sup_sup_set_variable @ A @ B)) = (sup_sup_set_variable @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_sup__left__idem)).
% 132.99/59.63 thf(806,plain,((! [A:set_variable,B:set_variable]: ((sup_sup_set_variable @ A @ (sup_sup_set_variable @ A @ B)) = (sup_sup_set_variable @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])).
% 132.99/59.63 thf(198,axiom,((! [A:set_variable,B:set_variable]: ((bot_bot_set_variable = (sup_sup_set_variable @ A @ B)) = ((A = bot_bot_set_variable) & (B = bot_bot_set_variable))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_bot__eq__sup__iff)).
% 132.99/59.63 thf(905,plain,((! [A:set_variable,B:set_variable]: ((bot_bot_set_variable = (sup_sup_set_variable @ A @ B)) = ((A = bot_bot_set_variable) & (B = bot_bot_set_variable))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])).
% 132.99/59.63 thf(353,plain,(((^ [A:(option_trm > $o)]: ((A @ none_trm) & ! [B:trm]: (A @ (some_trm @ B)))) = ((!) @ option_trm))),inference(lifteq,[status(thm)],[352])).
% 132.99/59.63 thf(218,axiom,((! [A:variable,B:set_variable,C:set_variable]: (((~ (member_variable @ A @ B)) => (member_variable @ A @ C)) => (member_variable @ A @ (sup_sup_set_variable @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_UnCI)).
% 132.99/59.63 thf(966,plain,((! [A:variable,B:set_variable,C:set_variable]: (((~ (member_variable @ A @ B)) => (member_variable @ A @ C)) => (member_variable @ A @ (sup_sup_set_variable @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])).
% 132.99/59.63 thf(11,axiom,((! [A:option_trm]: ((! [B:trm]: (A != (some_trm @ B))) => (A = none_trm)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_Differentialo_Ocases)).
% 132.99/59.63 thf(277,plain,((! [A:option_trm]: ((! [B:trm]: ~ (A = (some_trm @ B))) => (A = none_trm)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])).
% 132.99/59.63 thf(278,plain,((! [A:option_trm]: ((~ (? [B:trm]: (A = (some_trm @ B)))) => (A = none_trm)))),inference(miniscope,[status(thm)],[277])).
% 132.99/59.63 thf(279,plain,(! [A:option_trm] : ((A = (some_trm @ (sk6 @ A))) | (A = none_trm))),inference(cnf,[status(esa)],[278])).
% 132.99/59.63 thf(280,plain,(! [A:option_trm] : (((some_trm @ (sk6 @ A)) = A) | (A = none_trm))),inference(lifteq,[status(thm)],[279])).
% 132.99/59.63 thf(157,axiom,((! [A:(variable > $o),B:variable]: ((! [C:char]: (A @ (rVar @ C))) => ((! [C:char]: (A @ (dVar @ C))) => (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_variable_Oinduct)).
% 132.99/59.63 thf(774,plain,((! [A:(variable > $o),B:variable]: ((! [C:char]: (A @ (rVar @ C))) => ((! [C:char]: (A @ (dVar @ C))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])).
% 132.99/59.63 thf(34,axiom,((! [A:set_variable_real,B:set_variable_real]: ((ord_le1113654598e_real @ (uminus430703407e_real @ A) @ (uminus430703407e_real @ B)) = (ord_le1113654598e_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_compl__le__compl__iff)).
% 132.99/59.63 thf(396,plain,((! [A:set_variable_real,B:set_variable_real]: ((ord_le1113654598e_real @ (uminus430703407e_real @ A) @ (uminus430703407e_real @ B)) = (ord_le1113654598e_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])).
% 132.99/59.63 thf(120,axiom,((! [A:set_variable,B:set_variable,C:set_variable,D:set_variable]: ((A = (sup_sup_set_variable @ B @ C)) => ((sup_sup_set_variable @ A @ D) = (sup_sup_set_variable @ B @ (sup_sup_set_variable @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_boolean__algebra__cancel_Osup1)).
% 132.99/59.63 thf(660,plain,((! [A:set_variable,B:set_variable,C:set_variable,D:set_variable]: ((A = (sup_sup_set_variable @ B @ C)) => ((sup_sup_set_variable @ A @ D) = (sup_sup_set_variable @ B @ (sup_sup_set_variable @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])).
% 132.99/59.63 thf(16,axiom,((! [A:trm]: ((uSubst918876924Timeso @ (some_trm @ A) @ none_trm) = none_trm))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_Timeso_Osimps_I3_J)).
% 132.99/59.63 thf(293,plain,((! [A:trm]: ((uSubst918876924Timeso @ (some_trm @ A) @ none_trm) = none_trm))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])).
% 132.99/59.63 thf(215,axiom,((! [A:variable]: ((the_elem_variable @ (insert_variable @ A @ bot_bot_set_variable)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_the__elem__eq)).
% 132.99/59.63 thf(956,plain,((! [A:variable]: ((the_elem_variable @ (insert_variable @ A @ bot_bot_set_variable)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])).
% 132.99/59.63 thf(39,axiom,((! [A:set_variable,B:set_variable,C:set_variable]: ((ord_le282106107riable @ A @ (inf_inf_set_variable @ B @ C)) = ((ord_le282106107riable @ A @ B) & (ord_le282106107riable @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_inf_Obounded__iff)).
% 132.99/59.63 thf(411,plain,((! [A:set_variable,B:set_variable,C:set_variable]: ((ord_le282106107riable @ A @ (inf_inf_set_variable @ B @ C)) = ((ord_le282106107riable @ A @ B) & (ord_le282106107riable @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])).
% 132.99/59.63 thf(226,axiom,((! [A:set_variable]: ((is_sin155454833riable @ A) => (~ (! [B:variable]: (A != (insert_variable @ B @ bot_bot_set_variable))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_is__singletonE)).
% 132.99/59.63 thf(988,plain,((! [A:set_variable]: ((is_sin155454833riable @ A) => (~ (! [B:variable]: ~ (A = (insert_variable @ B @ bot_bot_set_variable))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])).
% 132.99/59.63 thf(203,axiom,((is_empty_variable = (^ [A:set_variable]: (A = bot_bot_set_variable)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_Set_Ois__empty__def)).
% 132.99/59.63 thf(920,plain,(((is_empty_variable) = (^ [A:set_variable]: (A = bot_bot_set_variable)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])).
% 132.99/59.63 thf(125,axiom,((denota1419872369iation = (^ [A:(variable > real),B:(variable > real),C:set_variable]: ! [D:variable]: ((~ (member_variable @ D @ C)) => ((A @ D) = (B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_Uvariation__def)).
% 132.99/59.63 thf(678,plain,(((denota1419872369iation) = (^ [A:(variable > real),B:(variable > real),C:set_variable]: ! [D:variable]: ((~ (member_variable @ D @ C)) => ((A @ D) = (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])).
% 132.99/59.63 thf(9,axiom,((! [A:option_trm]: ((A != none_trm) => (~ (! [B:trm]: (A != (some_trm @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_option_Oexhaust)).
% 132.99/59.63 thf(267,plain,((! [A:option_trm]: ((~ (A = none_trm)) => (~ (! [B:trm]: ~ (A = (some_trm @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])).
% 132.99/59.63 thf(268,plain,((! [A:option_trm]: ((~ (A = none_trm)) => (~ (~ (? [B:trm]: (A = (some_trm @ B)))))))),inference(miniscope,[status(thm)],[267])).
% 132.99/59.63 thf(269,plain,(! [A:option_trm] : ((A = none_trm) | (A = (some_trm @ (sk4 @ A))))),inference(cnf,[status(esa)],[268])).
% 132.99/59.63 thf(270,plain,(! [A:option_trm] : ((A = none_trm) | ((some_trm @ (sk4 @ A)) = A))),inference(lifteq,[status(thm)],[269])).
% 132.99/59.63 thf(3846,plain,(! [A:variable] : ((is_sin155454833riable @ (set_option_variable2 @ (some_variable @ A))))),inference(rewrite,[status(thm)],[931,784])).
% 132.99/59.63 thf(4790,plain,(! [B:variable,A:set_variable] : ((is_sin155454833riable @ (uminus1851247844riable @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (uminus1851247844riable @ A)))))) | (A != (set_option_variable2 @ (some_variable @ B))))),inference(paramod_ordered,[status(thm)],[1610,3846])).
% 132.99/59.63 thf(4791,plain,(! [A:variable] : ((is_sin155454833riable @ (uminus1851247844riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ A)))))))))),inference(pattern_uni,[status(thm)],[4790:[bind(A, $thf(set_option_variable2 @ (some_variable @ D))),bind(B, $thf(D))]])).
% 132.99/59.63 thf(4888,plain,(! [A:variable] : ((is_sin155454833riable @ (uminus1851247844riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ A)))))))))),inference(simp,[status(thm)],[4791])).
% 132.99/59.63 thf(163,axiom,((sup_sup_set_variable = (^ [A:set_variable,B:set_variable]: (sup_sup_set_variable @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_Un__commute)).
% 132.99/59.63 thf(793,plain,(((sup_sup_set_variable) = (^ [A:set_variable,B:set_variable]: (sup_sup_set_variable @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])).
% 132.99/59.63 thf(205,axiom,((! [A:(variable > real),B:(variable > real),C:set_variable,D:variable]: (denotational_Vagree @ (stateinterpol @ A @ B @ C) @ (stateinterpol @ A @ B @ (insert_variable @ D @ C)) @ (uminus1851247844riable @ (insert_variable @ D @ bot_bot_set_variable))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_stateinterpol__insert)).
% 132.99/59.63 thf(925,plain,((! [A:(variable > real),B:(variable > real),C:set_variable,D:variable]: (denotational_Vagree @ (stateinterpol @ A @ B @ C) @ (stateinterpol @ A @ B @ (insert_variable @ D @ C)) @ (uminus1851247844riable @ (insert_variable @ D @ bot_bot_set_variable))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])).
% 132.99/59.63 thf(1331,plain,(((^ [A:(variable > real),B:(variable > real),C:set_variable]: ! [D:variable]: ((member_variable @ D @ C) => ((A @ D) = (B @ D)))) = (denotational_Vagree)) | ((denotational_Vagree) != (^ [A:(variable > real),B:(variable > real)]: (denotational_Vagree @ B @ A)))),inference(paramod_ordered,[status(thm)],[464,466])).
% 132.99/59.63 thf(1336,plain,(((^ [A:(variable > real),B:(variable > real),C:set_variable]: ! [D:variable]: ((member_variable @ D @ C) => ((A @ D) = (B @ D)))) = (denotational_Vagree)) | ((^ [A:(variable > real),B:(variable > real),C:set_variable]: (A)) != (^ [A:(variable > real),B:(variable > real),C:set_variable]: (B))) | ((^ [A:(variable > real),B:(variable > real),C:set_variable]: (B)) != (^ [A:(variable > real),B:(variable > real),C:set_variable]: (A))) | ((^ [A:(variable > real),B:(variable > real),C:set_variable]: (C)) != (^ [A:(variable > real),B:(variable > real),C:set_variable]: (C)))),inference(simp,[status(thm)],[1331])).
% 132.99/59.63 thf(1338,plain,(((^ [A:(variable > real),B:(variable > real),C:set_variable]: ! [D:variable]: ((member_variable @ D @ C) => ((A @ D) = (B @ D)))) = (denotational_Vagree)) | ((^ [A:(variable > real),B:(variable > real),C:set_variable]: (A)) != (^ [A:(variable > real),B:(variable > real),C:set_variable]: (B)))),inference(simp,[status(thm)],[1336])).
% 132.99/59.63 thf(79,axiom,((! [A:set_variable_real,B:set_variable_real]: ((! [C:(variable > real)]: ((member_variable_real @ C @ A) => (member_variable_real @ C @ B))) => (ord_le1113654598e_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_subsetI)).
% 132.99/59.63 thf(534,plain,((! [A:set_variable_real,B:set_variable_real]: ((! [C:(variable > real)]: ((member_variable_real @ (C) @ A) => (member_variable_real @ (C) @ B))) => (ord_le1113654598e_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])).
% 132.99/59.63 thf(72,axiom,((! [A:variable,B:set_variable]: ((member_variable @ A @ (uminus1851247844riable @ B)) => (~ (member_variable @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_ComplD)).
% 132.99/59.63 thf(512,plain,((! [A:variable,B:set_variable]: ((member_variable @ A @ (uminus1851247844riable @ B)) => (~ (member_variable @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])).
% 132.99/59.63 thf(245,axiom,((! [A:set_variable,B:set_variable,C:set_variable]: ((ord_le282106107riable @ (sup_sup_set_variable @ A @ B) @ C) = ((ord_le282106107riable @ A @ C) & (ord_le282106107riable @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_le__sup__iff)).
% 132.99/59.63 thf(1047,plain,((! [A:set_variable,B:set_variable,C:set_variable]: ((ord_le282106107riable @ (sup_sup_set_variable @ A @ B) @ C) = ((ord_le282106107riable @ A @ C) & (ord_le282106107riable @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])).
% 132.99/59.63 thf(165,axiom,((! [A:set_variable,B:variable]: ((A = bot_bot_set_variable) => (~ (member_variable @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_equals0D)).
% 132.99/59.63 thf(798,plain,((! [A:set_variable,B:variable]: ((A = bot_bot_set_variable) => (~ (member_variable @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])).
% 132.99/59.63 thf(148,axiom,((! [A:option_variable]: (((set_option_variable2 @ A) = bot_bot_set_variable) = (A = none_variable)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_set__empty__eq)).
% 132.99/59.63 thf(746,plain,((! [A:option_variable]: (((set_option_variable2 @ A) = bot_bot_set_variable) = (A = none_variable)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])).
% 132.99/59.63 thf(18,axiom,((! [A:option_trm,B:(trm > $o),C:trm]: ((! [D:trm]: ((member_trm @ D @ (set_option_trm2 @ A)) => (B @ D))) => ((A = (some_trm @ C)) => (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_ospec)).
% 132.99/59.63 thf(302,plain,((! [A:option_trm,B:(trm > $o),C:trm]: ((! [D:trm]: ((member_trm @ D @ (set_option_trm2 @ A)) => (B @ D))) => ((A = (some_trm @ C)) => (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])).
% 132.99/59.63 thf(598,plain,(((denota1419872369iation) = (^ [A:(variable > real),B:(variable > real)]: (denota1419872369iation @ B @ A)))),inference(lifteq,[status(thm)],[597])).
% 132.99/59.63 thf(171,axiom,((is_sin155454833riable = (^ [A:set_variable]: (A = (insert_variable @ (the_elem_variable @ A) @ bot_bot_set_variable))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_is__singleton__the__elem)).
% 132.99/59.63 thf(820,plain,(((is_sin155454833riable) = (^ [A:set_variable]: (A = (insert_variable @ (the_elem_variable @ A) @ bot_bot_set_variable))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])).
% 132.99/59.63 thf(130,axiom,((! [A:set_variable,B:set_variable,C:set_variable]: ((sup_sup_set_variable @ A @ (sup_sup_set_variable @ B @ C)) = (sup_sup_set_variable @ B @ (sup_sup_set_variable @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_Un__left__commute)).
% 132.99/59.63 thf(693,plain,((! [A:set_variable,B:set_variable,C:set_variable]: ((sup_sup_set_variable @ A @ (sup_sup_set_variable @ B @ C)) = (sup_sup_set_variable @ B @ (sup_sup_set_variable @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])).
% 132.99/59.63 thf(161,axiom,((insert_variable = (^ [A:variable]: (sup_sup_set_variable @ (insert_variable @ A @ bot_bot_set_variable))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_insert__is__Un)).
% 132.99/59.63 thf(788,plain,(((insert_variable) = (^ [A:variable]: (sup_sup_set_variable @ (insert_variable @ A @ bot_bot_set_variable))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])).
% 132.99/59.63 thf(169,axiom,((! [A:variable,B:set_variable]: (member_variable @ A @ (insert_variable @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_insertI1)).
% 132.99/59.63 thf(815,plain,((! [A:variable,B:set_variable]: (member_variable @ A @ (insert_variable @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])).
% 132.99/59.63 thf(142,axiom,((! [A:set_variable]: ((sup_sup_set_variable @ A @ bot_bot_set_variable) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_sup__bot__right)).
% 132.99/59.63 thf(727,plain,((! [A:set_variable]: ((sup_sup_set_variable @ A @ bot_bot_set_variable) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])).
% 132.99/59.63 thf(728,plain,(! [A:set_variable] : (((sup_sup_set_variable @ A @ bot_bot_set_variable) = A))),inference(cnf,[status(esa)],[727])).
% 132.99/59.63 thf(729,plain,(! [A:set_variable] : (((sup_sup_set_variable @ A @ bot_bot_set_variable) = A))),inference(lifteq,[status(thm)],[728])).
% 132.99/59.63 thf(6,axiom,((! [A:option_trm]: ((! [B:trm]: (A != (some_trm @ B))) = (A = none_trm)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_not__Some__eq)).
% 132.99/59.63 thf(258,plain,((! [A:option_trm]: ((! [B:trm]: ~ (A = (some_trm @ B))) = (A = none_trm)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 132.99/59.63 thf(259,plain,(! [A:option_trm] : (((! [B:trm]: ~ (A = (some_trm @ B))) = (A = none_trm)))),inference(cnf,[status(esa)],[258])).
% 132.99/59.63 thf(260,plain,(! [A:option_trm] : (((! [B:trm]: ~ (A = (some_trm @ B))) = (A = none_trm)))),inference(lifteq,[status(thm)],[259])).
% 132.99/59.63 thf(348,plain,((! [A:(variable > (option_trm > $o))]: ((! [B:variable,C:trm]: (A @ B @ (some_trm @ C))) => ((! [B:variable]: (A @ B @ none_trm)) => (! [B:variable,C:option_trm]: (A @ B @ C)))))),inference(miniscope,[status(thm)],[347])).
% 132.99/59.63 thf(349,plain,(! [C:option_trm,B:variable,A:(variable > (option_trm > $o))] : ((~ (A @ (sk13 @ (A)) @ (some_trm @ (sk14 @ (A))))) | (~ (A @ (sk15 @ (A)) @ none_trm)) | (A @ B @ C))),inference(cnf,[status(esa)],[348])).
% 132.99/59.63 thf(56,axiom,((denotational_repv = (^ [A:(variable > real),B:variable,C:real,D:variable]: (if_real @ (B = D) @ C @ (A @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_repv__access)).
% 132.99/59.63 thf(467,plain,(((denotational_repv) = (^ [A:(variable > real),B:variable,C:real,D:variable]: (if_real @ (B = D) @ C @ (A @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])).
% 132.99/59.63 thf(1351,plain,(((^ [A:(variable > real),B:(variable > real)]: (denotational_Vagree @ B @ A)) = (^ [A:(variable > real),B:(variable > real),C:set_variable]: ! [D:variable]: ((member_variable @ D @ C) => ((A @ D) = (B @ D))))) | ((denotational_Vagree) != (^ [A:(variable > real),B:(variable > real)]: (denotational_Vagree @ B @ A)))),inference(paramod_ordered,[status(thm)],[466,1330])).
% 132.99/59.63 thf(1363,plain,(((^ [A:(variable > real),B:(variable > real)]: (denotational_Vagree @ B @ A)) = (^ [A:(variable > real),B:(variable > real),C:set_variable]: ! [D:variable]: ((member_variable @ D @ C) => ((A @ D) = (B @ D))))) | ((^ [A:(variable > real),B:(variable > real),C:set_variable]: (A)) != (^ [A:(variable > real),B:(variable > real),C:set_variable]: (B))) | ((^ [A:(variable > real),B:(variable > real),C:set_variable]: (B)) != (^ [A:(variable > real),B:(variable > real),C:set_variable]: (A))) | ((^ [A:(variable > real),B:(variable > real),C:set_variable]: (C)) != (^ [A:(variable > real),B:(variable > real),C:set_variable]: (C)))),inference(simp,[status(thm)],[1351])).
% 132.99/59.63 thf(1365,plain,(((^ [A:(variable > real),B:(variable > real)]: (denotational_Vagree @ B @ A)) = (^ [A:(variable > real),B:(variable > real),C:set_variable]: ! [D:variable]: ((member_variable @ D @ C) => ((A @ D) = (B @ D))))) | ((^ [A:(variable > real),B:(variable > real),C:set_variable]: (A)) != (^ [A:(variable > real),B:(variable > real),C:set_variable]: (B)))),inference(simp,[status(thm)],[1363])).
% 132.99/59.63 thf(110,axiom,((! [A:set_variable,B:set_variable]: (((sup_sup_set_variable @ A @ B) = bot_bot_set_variable) = ((A = bot_bot_set_variable) & (B = bot_bot_set_variable))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_sup__eq__bot__iff)).
% 132.99/59.63 thf(625,plain,((! [A:set_variable,B:set_variable]: (((sup_sup_set_variable @ A @ B) = bot_bot_set_variable) = ((A = bot_bot_set_variable) & (B = bot_bot_set_variable))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])).
% 132.99/59.63 thf(190,axiom,((! [A:set_option_variable]: (((these_variable @ A) != bot_bot_set_variable) = ((A != bot_bo266290559riable) & (A != (insert1340772453riable @ none_variable @ bot_bo266290559riable)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_these__not__empty__eq)).
% 132.99/59.63 thf(879,plain,((! [A:set_option_variable]: ((~ ((these_variable @ A) = bot_bot_set_variable)) = (~ (A = bot_bo266290559riable) & ~ (A = (insert1340772453riable @ none_variable @ bot_bo266290559riable)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])).
% 132.99/59.63 thf(121,axiom,((! [A:variable,B:set_variable,C:set_variable]: ((sup_sup_set_variable @ (insert_variable @ A @ B) @ C) = (insert_variable @ A @ (sup_sup_set_variable @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_Un__insert__left)).
% 132.99/59.63 thf(665,plain,((! [A:variable,B:set_variable,C:set_variable]: ((sup_sup_set_variable @ (insert_variable @ A @ B) @ C) = (insert_variable @ A @ (sup_sup_set_variable @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])).
% 132.99/59.63 thf(193,axiom,((! [A:set_variable,B:set_variable]: ((sup_sup_set_variable @ A @ (sup_sup_set_variable @ A @ B)) = (sup_sup_set_variable @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_sup_Oleft__idem)).
% 132.99/59.63 thf(889,plain,((! [A:set_variable,B:set_variable]: ((sup_sup_set_variable @ A @ (sup_sup_set_variable @ A @ B)) = (sup_sup_set_variable @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])).
% 132.99/59.63 thf(493,plain,(! [B:set_variable,A:(variable > real)] : ((denotational_Vagree @ (A) @ (A) @ B))),inference(cnf,[status(esa)],[492])).
% 132.99/59.63 thf(136,axiom,((! [A:(variable > real),B:(variable > real),C:set_variable]: ((denota1419872369iation @ A @ B @ (uminus1851247844riable @ C)) = (denotational_Vagree @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_Uvariation__Vagree)).
% 132.99/59.63 thf(710,plain,((! [A:(variable > real),B:(variable > real),C:set_variable]: ((denota1419872369iation @ (A) @ (B) @ (uminus1851247844riable @ C)) = (denotational_Vagree @ (A) @ (B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])).
% 132.99/59.63 thf(178,axiom,((! [A:set_variable,B:set_variable]: ((bot_bot_set_variable = (sup_sup_set_variable @ A @ B)) = ((A = bot_bot_set_variable) & (B = bot_bot_set_variable))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_sup__bot_Oneutr__eq__iff)).
% 132.99/59.63 thf(842,plain,((! [A:set_variable,B:set_variable]: ((bot_bot_set_variable = (sup_sup_set_variable @ A @ B)) = ((A = bot_bot_set_variable) & (B = bot_bot_set_variable))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])).
% 132.99/59.63 thf(241,axiom,((! [A:variable,B:variable]: ((member_variable @ A @ (insert_variable @ B @ bot_bot_set_variable)) => (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_singletonD)).
% 132.99/59.63 thf(1032,plain,((! [A:variable,B:variable]: ((member_variable @ A @ (insert_variable @ B @ bot_bot_set_variable)) => (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])).
% 132.99/59.63 thf(3,axiom,((! [A:option_trm]: ((A != none_trm) = (? [B:trm]: (A = (some_trm @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_undeft__equiv)).
% 132.99/59.63 thf(250,plain,((! [A:option_trm]: ((~ (A = none_trm)) = (? [B:trm]: (A = (some_trm @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 132.99/59.63 thf(251,plain,(! [A:option_trm] : (((~ (A = none_trm)) = (? [B:trm]: (A = (some_trm @ B)))))),inference(cnf,[status(esa)],[250])).
% 132.99/59.63 thf(252,plain,(! [A:option_trm] : (((~ (A = none_trm)) = (? [B:trm]: (A = (some_trm @ B)))))),inference(lifteq,[status(thm)],[251])).
% 132.99/59.63 thf(583,plain,(((insert_nat @ zero_zero_nat @ bot_bot_set_nat) = zero_zero_set_nat)),inference(lifteq,[status(thm)],[582])).
% 132.99/59.63 thf(174,axiom,((! [A:variable,B:set_variable,C:set_variable]: ((member_variable @ A @ B) => (member_variable @ A @ (sup_sup_set_variable @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_UnI1)).
% 132.99/59.63 thf(830,plain,((! [A:variable,B:set_variable,C:set_variable]: ((member_variable @ A @ B) => (member_variable @ A @ (sup_sup_set_variable @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])).
% 132.99/59.63 thf(2495,plain,(! [B:variable,A:set_variable] : (((^ [C:variable]: (member_variable @ C @ (collect_variable @ (^ [D:variable]: (member_variable @ D @ A))))) != (^ [C:variable]: (($false)))) | (A != (set_option_variable2 @ (some_variable @ B))))),inference(paramod_ordered,[status(thm)],[543,2488])).
% 132.99/59.63 thf(2496,plain,(! [A:variable] : (((^ [B:variable]: (member_variable @ B @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (set_option_variable2 @ (some_variable @ A))))))) != (^ [B:variable]: (($false)))))),inference(pattern_uni,[status(thm)],[2495:[bind(A, $thf(set_option_variable2 @ (some_variable @ D))),bind(B, $thf(D))]])).
% 132.99/59.63 thf(2498,plain,(! [A:variable] : (((^ [B:variable]: (member_variable @ B @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (set_option_variable2 @ (some_variable @ A))))))) != (^ [B:variable]: (($false)))))),inference(simp,[status(thm)],[2496])).
% 132.99/59.63 thf(3831,plain,((~ (denota1419872369iation @ (f @ zero_zero_real) @ (omega) @ (sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (set_option_variable2 @ (some_variable @ (dVar @ x)))) @ u)))),inference(rewrite,[status(thm)],[249,784])).
% 132.99/59.63 thf(2508,plain,(! [B:variable,A:set_variable] : (((^ [C:variable]: (member_variable @ C @ (collect_variable @ (^ [D:variable]: (member_variable @ D @ (collect_variable @ (^ [E:variable]: (member_variable @ E @ A)))))))) != (^ [C:variable]: (($false)))) | (A != (set_option_variable2 @ (some_variable @ B))))),inference(paramod_ordered,[status(thm)],[543,2498])).
% 132.99/59.63 thf(2509,plain,(! [A:variable] : (((^ [B:variable]: (member_variable @ B @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (collect_variable @ (^ [D:variable]: (member_variable @ D @ (set_option_variable2 @ (some_variable @ A)))))))))) != (^ [B:variable]: (($false)))))),inference(pattern_uni,[status(thm)],[2508:[bind(A, $thf(set_option_variable2 @ (some_variable @ D))),bind(B, $thf(D))]])).
% 132.99/59.63 thf(2515,plain,(! [A:variable] : (((^ [B:variable]: (member_variable @ B @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (collect_variable @ (^ [D:variable]: (member_variable @ D @ (set_option_variable2 @ (some_variable @ A)))))))))) != (^ [B:variable]: (($false)))))),inference(simp,[status(thm)],[2509])).
% 132.99/59.63 thf(20,axiom,((some_trm = some_trm)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_Aterm__Some)).
% 132.99/59.63 thf(317,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])).
% 132.99/59.63 thf(223,axiom,((! [A:variable,B:variable,C:variable,D:variable]: (((insert_variable @ A @ (insert_variable @ B @ bot_bot_set_variable)) = (insert_variable @ C @ (insert_variable @ D @ bot_bot_set_variable))) = (((A = C) & (B = D)) | ((A = D) & (B = C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_doubleton__eq__iff)).
% 132.99/59.63 thf(980,plain,((! [A:variable,B:variable,C:variable,D:variable]: (((insert_variable @ A @ (insert_variable @ B @ bot_bot_set_variable)) = (insert_variable @ C @ (insert_variable @ D @ bot_bot_set_variable))) = (((A = C) & (B = D)) | ((A = D) & (B = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])).
% 132.99/59.63 thf(25,axiom,((! [A:trm,B:trm]: ((uSubst918876924Timeso @ (some_trm @ A) @ (some_trm @ B)) = (some_trm @ (times @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_Timeso_Osimps_I1_J)).
% 132.99/59.63 thf(354,plain,((! [A:trm,B:trm]: ((uSubst918876924Timeso @ (some_trm @ A) @ (some_trm @ B)) = (some_trm @ (times @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])).
% 132.99/59.63 thf(355,plain,(! [B:trm,A:trm] : (((uSubst918876924Timeso @ (some_trm @ A) @ (some_trm @ B)) = (some_trm @ (times @ A @ B))))),inference(cnf,[status(esa)],[354])).
% 132.99/59.63 thf(356,plain,(! [B:trm,A:trm] : (((uSubst918876924Timeso @ (some_trm @ A) @ (some_trm @ B)) = (some_trm @ (times @ A @ B))))),inference(lifteq,[status(thm)],[355])).
% 132.99/59.63 thf(41,axiom,((! [A:set_variable]: ((inf_inf_set_variable @ A @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_inf_Oidem)).
% 132.99/59.63 thf(418,plain,((! [A:set_variable]: ((inf_inf_set_variable @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])).
% 132.99/59.63 thf(419,plain,(! [A:set_variable] : (((inf_inf_set_variable @ A @ A) = A))),inference(cnf,[status(esa)],[418])).
% 132.99/59.63 thf(420,plain,(! [A:set_variable] : (((inf_inf_set_variable @ A @ A) = A))),inference(lifteq,[status(thm)],[419])).
% 132.99/59.63 thf(182,axiom,((! [A:char,B:char]: (((dVar @ A) = (dVar @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_variable_Oinject_I2_J)).
% 132.99/59.63 thf(857,plain,((! [A:char,B:char]: (((dVar @ A) = (dVar @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])).
% 132.99/59.63 thf(63,axiom,((! [A:set_variable]: (ord_le282106107riable @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_order__refl)).
% 132.99/59.63 thf(488,plain,((! [A:set_variable]: (ord_le282106107riable @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])).
% 132.99/59.63 thf(85,axiom,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_zero__reorient)).
% 132.99/59.63 thf(552,plain,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])).
% 132.99/59.63 thf(553,plain,(! [A:nat] : (((zero_zero_nat = A) = (A = zero_zero_nat)))),inference(cnf,[status(esa)],[552])).
% 132.99/59.63 thf(554,plain,(! [A:nat] : (((zero_zero_nat = A) = (A = zero_zero_nat)))),inference(lifteq,[status(thm)],[553])).
% 132.99/59.63 thf(320,plain,(! [C:option_trm,B:option_trm,A:option_trm] : ((~ ((uSubst918876924Timeso @ A @ B) = C)) | (B = (some_trm @ (sk11 @ C @ B @ A))) | (sk9 @ A @ C @ B))),inference(cnfConj,[status(thm)],[319])).
% 132.99/59.63 thf(329,plain,(! [C:option_trm,B:option_trm,A:option_trm] : (((uSubst918876924Timeso @ A @ B) != C) | ((some_trm @ (sk11 @ C @ B @ A)) = B) | (sk9 @ A @ C @ B))),inference(lifteq,[status(thm)],[320])).
% 132.99/59.63 thf(330,plain,(! [B:option_trm,A:option_trm] : (((some_trm @ (sk11 @ (uSubst918876924Timeso @ A @ B) @ B @ A)) = B) | (sk9 @ A @ (uSubst918876924Timeso @ A @ B) @ B))),inference(simp,[status(thm)],[329])).
% 132.99/59.63 thf(4347,plain,(! [C:trm,B:option_trm,A:option_trm] : ((sk9 @ A @ (uSubst918876924Timeso @ A @ B) @ B) | (B != none_trm) | ((some_trm @ (sk11 @ (uSubst918876924Timeso @ A @ B) @ B @ A)) != (some_trm @ C)))),inference(paramod_ordered,[status(thm)],[330,369])).
% 132.99/59.63 thf(4348,plain,(! [B:option_trm,A:option_trm] : ((sk9 @ B @ (uSubst918876924Timeso @ B @ A) @ A) | (A != none_trm))),inference(pattern_uni,[status(thm)],[4347:[bind(A, $thf(F)),bind(B, $thf(E)),bind(C, $thf(sk11 @ (uSubst918876924Timeso @ F @ E) @ E @ F))]])).
% 132.99/59.63 thf(4416,plain,(! [A:option_trm] : ((sk9 @ A @ (uSubst918876924Timeso @ A @ none_trm) @ none_trm))),inference(simp,[status(thm)],[4348])).
% 132.99/59.63 thf(325,plain,(! [C:option_trm,B:option_trm,A:option_trm] : ((~ ((uSubst918876924Timeso @ A @ B) = C)) | (~ (sk9 @ A @ C @ B)) | (C = none_trm) | (C = none_trm))),inference(cnfConj,[status(thm)],[319])).
% 132.99/59.63 thf(331,plain,(! [C:option_trm,B:option_trm,A:option_trm] : (((uSubst918876924Timeso @ A @ B) != C) | (C = none_trm) | (C = none_trm) | (~ (sk9 @ A @ C @ B)))),inference(lifteq,[status(thm)],[325])).
% 132.99/59.63 thf(332,plain,(! [B:option_trm,A:option_trm] : (((uSubst918876924Timeso @ A @ B) = none_trm) | (~ (sk9 @ A @ (uSubst918876924Timeso @ A @ B) @ B)))),inference(simp,[status(thm)],[331])).
% 132.99/59.63 thf(5670,plain,(! [C:option_trm,B:option_trm,A:option_trm] : (((uSubst918876924Timeso @ B @ C) = none_trm) | ~ (($true)) | ((sk9 @ A @ (uSubst918876924Timeso @ A @ none_trm) @ none_trm) != (sk9 @ B @ (uSubst918876924Timeso @ B @ C) @ C)))),inference(paramod_ordered,[status(thm)],[4416,332])).
% 132.99/59.63 thf(5671,plain,(! [C:option_trm,B:option_trm,A:option_trm] : (((uSubst918876924Timeso @ B @ C) = none_trm) | ((sk9 @ A @ (uSubst918876924Timeso @ A @ none_trm) @ none_trm) != (sk9 @ B @ (uSubst918876924Timeso @ B @ C) @ C)))),inference(simp,[status(thm)],[5670])).
% 132.99/59.63 thf(5672,plain,(! [A:option_trm] : (((uSubst918876924Timeso @ A @ none_trm) = none_trm))),inference(pattern_uni,[status(thm)],[5671:[bind(A, $thf(A)),bind(B, $thf(A)),bind(C, $thf(none_trm))]])).
% 132.99/59.63 thf(5791,plain,(! [A:option_trm] : ((sk9 @ A @ none_trm @ none_trm))),inference(rewrite,[status(thm)],[4416,5672])).
% 132.99/59.63 thf(128,axiom,((! [A:set_variable]: ((! [B:variable]: ~ (member_variable @ B @ A)) => (A = bot_bot_set_variable)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_equals0I)).
% 132.99/59.63 thf(686,plain,((! [A:set_variable]: ((! [B:variable]: ~ (member_variable @ B @ A)) => (A = bot_bot_set_variable)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])).
% 132.99/59.63 thf(114,axiom,((! [A:variable,B:variable,C:set_variable]: ((insert_variable @ A @ (insert_variable @ B @ C)) = (insert_variable @ B @ (insert_variable @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_insert__commute)).
% 132.99/59.63 thf(642,plain,((! [A:variable,B:variable,C:set_variable]: ((insert_variable @ A @ (insert_variable @ B @ C)) = (insert_variable @ B @ (insert_variable @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])).
% 132.99/59.63 thf(112,axiom,((! [A:(variable > real),B:(variable > real),C:set_variable]: ((denota1419872369iation @ A @ B @ C) => (denota1419872369iation @ B @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_Uvariation__sym__rel)).
% 132.99/59.63 thf(637,plain,((! [A:(variable > real),B:(variable > real),C:set_variable]: ((denota1419872369iation @ (A) @ (B) @ C) => (denota1419872369iation @ (B) @ (A) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])).
% 132.99/59.63 thf(489,plain,(! [A:set_variable] : ((ord_le282106107riable @ A @ A))),inference(cnf,[status(esa)],[488])).
% 132.99/59.63 thf(134,axiom,((! [A:char]: ((size_variable @ (rVar @ A)) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_variable_Osize__gen_I1_J)).
% 132.99/59.63 thf(704,plain,((! [A:char]: ((size_variable @ (rVar @ A)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])).
% 132.99/59.63 thf(705,plain,(! [A:char] : (((size_variable @ (rVar @ A)) = zero_zero_nat))),inference(cnf,[status(esa)],[704])).
% 132.99/59.63 thf(706,plain,(! [A:char] : (((size_variable @ (rVar @ A)) = zero_zero_nat))),inference(lifteq,[status(thm)],[705])).
% 132.99/59.63 thf(235,axiom,((! [A:variable,B:set_variable,C:(variable > $o)]: ((! [D:variable]: ((member_variable @ D @ (insert_variable @ A @ B)) => (C @ D))) = ((C @ A) & ! [D:variable]: ((member_variable @ D @ B) => (C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_ball__insert)).
% 132.99/59.63 thf(1016,plain,((! [A:variable,B:set_variable,C:(variable > $o)]: ((! [D:variable]: ((member_variable @ D @ (insert_variable @ A @ B)) => (C @ D))) = ((C @ A) & ! [D:variable]: ((member_variable @ D @ B) => (C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])).
% 132.99/59.63 thf(97,axiom,((! [A:(variable > real),B:(variable > real),C:set_variable]: ((denotational_Vagree @ A @ B @ C) => (denotational_Vagree @ B @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_Vagree__sym__rel)).
% 132.99/59.63 thf(590,plain,((! [A:(variable > real),B:(variable > real),C:set_variable]: ((denotational_Vagree @ (A) @ (B) @ C) => (denotational_Vagree @ (B) @ (A) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])).
% 132.99/59.63 thf(679,plain,(((denota1419872369iation) = (^ [A:(variable > real),B:(variable > real),C:set_variable]: ! [D:variable]: ((~ (member_variable @ D @ C)) => ((A @ D) = (B @ D)))))),inference(lifteq,[status(thm)],[678])).
% 132.99/59.63 thf(219,axiom,((! [A:real]: (((uminus_uminus_real @ A) = A) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_neg__equal__zero)).
% 132.99/59.63 thf(970,plain,((! [A:real]: (((uminus_uminus_real @ A) = A) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])).
% 132.99/59.63 thf(109,axiom,((! [A:variable,B:set_variable,C:set_variable]: ((member_variable @ A @ (sup_sup_set_variable @ B @ C)) = ((member_variable @ A @ B) | (member_variable @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_union__or)).
% 132.99/59.63 thf(622,plain,((! [A:variable,B:set_variable,C:set_variable]: ((member_variable @ A @ (sup_sup_set_variable @ B @ C)) = ((member_variable @ A @ B) | (member_variable @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])).
% 132.99/59.63 thf(144,axiom,((! [A:char]: ((size_size_variable @ (rVar @ A)) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_variable_Osize_I3_J)).
% 132.99/59.63 thf(736,plain,((! [A:char]: ((size_size_variable @ (rVar @ A)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])).
% 132.99/59.63 thf(737,plain,(! [A:char] : (((size_size_variable @ (rVar @ A)) = zero_zero_nat))),inference(cnf,[status(esa)],[736])).
% 132.99/59.63 thf(738,plain,(! [A:char] : (((size_size_variable @ (rVar @ A)) = zero_zero_nat))),inference(lifteq,[status(thm)],[737])).
% 132.99/59.63 thf(118,axiom,((! [A:char]: ((size_variable @ (dVar @ A)) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_variable_Osize__gen_I2_J)).
% 132.99/59.63 thf(654,plain,((! [A:char]: ((size_variable @ (dVar @ A)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])).
% 132.99/59.63 thf(200,axiom,((! [A:variable,B:set_option_variable]: ((these_variable @ (insert1340772453riable @ (some_variable @ A) @ B)) = (insert_variable @ A @ (these_variable @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_these__insert__Some)).
% 132.99/59.63 thf(911,plain,((! [A:variable,B:set_option_variable]: ((these_variable @ (insert1340772453riable @ (some_variable @ A) @ B)) = (insert_variable @ A @ (these_variable @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])).
% 132.99/59.63 thf(140,axiom,((! [A:set_variable]: ((sup_sup_set_variable @ bot_bot_set_variable @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_sup__bot_Oleft__neutral)).
% 132.99/59.63 thf(721,plain,((! [A:set_variable]: ((sup_sup_set_variable @ bot_bot_set_variable @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])).
% 132.99/59.63 thf(6784,plain,(! [B:variable,A:set_variable] : (((uminus1851247844riable @ A) != (uminus1851247844riable @ (collect_variable @ (^ [C:variable]: (($false)))))) | ((uminus1851247844riable @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ A)))) != (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ B)))))),inference(paramod_ordered,[status(thm)],[4864,6774])).
% 132.99/59.63 thf(6815,plain,(! [B:variable,A:set_variable] : ((A != (collect_variable @ (^ [C:variable]: (($false))))) | ((uminus1851247844riable @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ A)))) != (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ B)))))),inference(simp,[status(thm)],[6784])).
% 132.99/59.63 thf(6850,plain,(! [A:variable] : (((uminus1851247844riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ (collect_variable @ (^ [C:variable]: (($false)))))))) != (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ A)))))),inference(simp,[status(thm)],[6815])).
% 132.99/59.63 thf(9990,plain,(! [A:variable] : (((uminus1851247844riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ bot_bot_set_variable)))) != (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ A)))))),inference(rewrite,[status(thm)],[6850,1242])).
% 132.99/59.63 thf(158,axiom,((! [A:(variable > real),B:variable,C:real]: ((denotational_Vagree @ A @ (denotational_repv @ A @ B @ C) @ (insert_variable @ B @ bot_bot_set_variable)) = (C = (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_Vagree__repv__self)).
% 132.99/59.63 thf(779,plain,((! [A:(variable > real),B:variable,C:real]: ((denotational_Vagree @ (A) @ (denotational_repv @ A @ B @ C) @ (insert_variable @ B @ bot_bot_set_variable)) = (C = (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])).
% 132.99/59.63 thf(69,axiom,((! [A:set_variable_real,B:(variable > real),C:set_variable]: ((static_selectlike @ (uminus430703407e_real @ (static_selectlike @ A @ B @ C)) @ B @ C) = (static_selectlike @ (uminus430703407e_real @ A) @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_selectlike__co__selectlike)).
% 132.99/59.63 thf(503,plain,((! [A:set_variable_real,B:(variable > real),C:set_variable]: ((static_selectlike @ (uminus430703407e_real @ (static_selectlike @ A @ (B) @ C)) @ (B) @ C) = (static_selectlike @ (uminus430703407e_real @ A) @ (B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])).
% 132.99/59.63 thf(246,axiom,((! [A:set_variable,B:set_variable,C:variable]: (((sup_sup_set_variable @ A @ B) = (insert_variable @ C @ bot_bot_set_variable)) = (((A = bot_bot_set_variable) & (B = (insert_variable @ C @ bot_bot_set_variable))) | ((A = (insert_variable @ C @ bot_bot_set_variable)) & (B = bot_bot_set_variable)) | ((A = (insert_variable @ C @ bot_bot_set_variable)) & (B = (insert_variable @ C @ bot_bot_set_variable))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_Un__singleton__iff)).
% 132.99/59.63 thf(1050,plain,((! [A:set_variable,B:set_variable,C:variable]: (((sup_sup_set_variable @ A @ B) = (insert_variable @ C @ bot_bot_set_variable)) = (((A = bot_bot_set_variable) & (B = (insert_variable @ C @ bot_bot_set_variable))) | ((A = (insert_variable @ C @ bot_bot_set_variable)) & (B = bot_bot_set_variable)) | ((A = (insert_variable @ C @ bot_bot_set_variable)) & (B = (insert_variable @ C @ bot_bot_set_variable))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])).
% 132.99/59.63 thf(52,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_le__zero__eq)).
% 132.99/59.63 thf(457,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])).
% 132.99/59.63 thf(8,axiom,((! [A:(variable > real),B:set_variable_real]: ((member_variable_real @ A @ (uminus430703407e_real @ B)) = (~ (member_variable_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_Compl__iff)).
% 132.99/59.63 thf(264,plain,((! [A:(variable > real),B:set_variable_real]: ((member_variable_real @ (A) @ (uminus430703407e_real @ B)) = (~ (member_variable_real @ (A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])).
% 132.99/59.63 thf(265,plain,(! [B:set_variable_real,A:(variable > real)] : (((member_variable_real @ (A) @ (uminus430703407e_real @ B)) = (~ (member_variable_real @ (A) @ B))))),inference(cnf,[status(esa)],[264])).
% 132.99/59.63 thf(266,plain,(! [B:set_variable_real,A:(variable > real)] : (((member_variable_real @ (A) @ (uminus430703407e_real @ B)) = (~ (member_variable_real @ (A) @ B))))),inference(lifteq,[status(thm)],[265])).
% 132.99/59.63 thf(71,axiom,((! [A:variable,B:set_variable,C:(variable > real),D:(variable > real)]: ((member_variable @ A @ B) => ((stateinterpol @ C @ D @ B @ A) = (C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_stateinterpol__left)).
% 132.99/59.63 thf(508,plain,((! [A:variable,B:set_variable,C:(variable > real),D:(variable > real)]: ((member_variable @ A @ B) => ((stateinterpol @ (C) @ (D) @ B @ A) = (C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])).
% 132.99/59.63 thf(303,plain,((! [A:option_trm,B:(trm > $o)]: ((! [C:trm]: ((member_trm @ C @ (set_option_trm2 @ A)) => (B @ C))) => (! [C:trm]: ((A = (some_trm @ C)) => (B @ C)))))),inference(miniscope,[status(thm)],[302])).
% 132.99/59.63 thf(304,plain,(! [C:trm,B:(trm > $o),A:option_trm] : ((((member_trm @ (sk8 @ (B) @ A) @ (set_option_trm2 @ A)) | ~ (A = (some_trm @ C)) | (B @ C)) & (~ (B @ (sk8 @ (B) @ A)) | ~ (A = (some_trm @ C)) | (B @ C))))),inference(cnf,[status(esa)],[303])).
% 132.99/59.63 thf(306,plain,(! [C:trm,B:(trm > $o),A:option_trm] : ((~ (B @ (sk8 @ (B) @ A))) | (~ (A = (some_trm @ C))) | (B @ C))),inference(cnfConj,[status(thm)],[304])).
% 132.99/59.63 thf(310,plain,(! [C:trm,B:(trm > $o),A:option_trm] : ((A != (some_trm @ C)) | (~ (B @ (sk8 @ (B) @ A))) | (B @ C))),inference(lifteq,[status(thm)],[306])).
% 132.99/59.63 thf(311,plain,(! [B:trm,A:(trm > $o)] : ((~ (A @ (sk8 @ (A) @ (some_trm @ B)))) | (A @ B))),inference(simp,[status(thm)],[310])).
% 132.99/59.63 thf(119,axiom,((! [A:(variable > $o)]: (((collect_variable @ A) = bot_bot_set_variable) = (! [B:variable]: ~ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_Collect__empty__eq)).
% 132.99/59.63 thf(657,plain,((! [A:(variable > $o)]: (((collect_variable @ (A)) = bot_bot_set_variable) = (! [B:variable]: ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])).
% 132.99/59.63 thf(154,axiom,((! [A:set_variable]: ((sup_sup_set_variable @ A @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_Un__absorb)).
% 132.99/59.63 thf(765,plain,((! [A:set_variable]: ((sup_sup_set_variable @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])).
% 132.99/59.63 thf(242,axiom,((! [A:variable,B:set_variable,C:set_variable]: ((~ (member_variable @ A @ (sup_sup_set_variable @ B @ C))) = (~ (member_variable @ A @ B) & ~ (member_variable @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_not__union__or)).
% 132.99/59.63 thf(1035,plain,((! [A:variable,B:set_variable,C:set_variable]: ((~ (member_variable @ A @ (sup_sup_set_variable @ B @ C))) = (~ (member_variable @ A @ B) & ~ (member_variable @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])).
% 132.99/59.63 thf(1514,plain,(((^ [A:(variable > real),B:(variable > real)]: (denotational_Vagree @ B @ A)) = (denotational_Vagree)) | ((^ [A:(variable > real),B:(variable > real),C:set_variable]: (A)) != (^ [A:(variable > real),B:(variable > real),C:set_variable]: (B))) | ((^ [A:(variable > real),B:(variable > real),C:set_variable]: ! [D:variable]: ((member_variable @ D @ C) => ((A @ D) = (B @ D)))) != (^ [A:(variable > real),B:(variable > real),C:set_variable]: ! [D:variable]: ((member_variable @ D @ C) => ((A @ D) = (B @ D)))))),inference(paramod_ordered,[status(thm)],[1330,1338])).
% 132.99/59.63 thf(1515,plain,(((^ [A:(variable > real),B:(variable > real)]: (denotational_Vagree @ B @ A)) = (denotational_Vagree)) | ((^ [A:(variable > real),B:(variable > real),C:set_variable]: (A)) != (^ [A:(variable > real),B:(variable > real),C:set_variable]: (B)))),inference(pattern_uni,[status(thm)],[1514:[]])).
% 132.99/59.63 thf(239,axiom,((! [A:(variable > $o)]: ((bot_bot_set_variable = (collect_variable @ A)) = (! [B:variable]: ~ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_empty__Collect__eq)).
% 132.99/59.63 thf(1026,plain,((! [A:(variable > $o)]: ((bot_bot_set_variable = (collect_variable @ (A))) = (! [B:variable]: ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])).
% 132.99/59.63 thf(2608,plain,(((insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)) != u) | ((insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)) != u)),inference(simp,[status(thm)],[2605])).
% 132.99/59.63 thf(2620,plain,(((insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)) != u)),inference(simp,[status(thm)],[2608])).
% 132.99/59.63 thf(3841,plain,(((insert_variable @ (rVar @ x) @ (set_option_variable2 @ (some_variable @ (dVar @ x)))) != u)),inference(rewrite,[status(thm)],[2620,784])).
% 132.99/59.63 thf(139,axiom,((! [A:denotational_interp,B:(real > (variable > real)),C:char,D:trm,E:real]: ((denota1778088425es_ODE @ A @ B @ C @ D) => (denotational_Vagree @ (B @ E) @ (B @ zero_zero_real) @ (uminus1851247844riable @ (insert_variable @ (rVar @ C) @ (insert_variable @ (dVar @ C) @ bot_bot_set_variable))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_solves__Vagree)).
% 132.99/59.63 thf(718,plain,((! [A:denotational_interp,B:(real > (variable > real)),C:char,D:trm,E:real]: ((denota1778088425es_ODE @ A @ (B) @ C @ D) => (denotational_Vagree @ (B @ E) @ (B @ zero_zero_real) @ (uminus1851247844riable @ (insert_variable @ (rVar @ C) @ (insert_variable @ (dVar @ C) @ bot_bot_set_variable))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])).
% 132.99/59.63 thf(886,plain,((~ (? [A:char,B:char]: ((rVar @ A) = (dVar @ B))))),inference(miniscope,[status(thm)],[885])).
% 132.99/59.63 thf(887,plain,(! [B:char,A:char] : ((~ ((rVar @ A) = (dVar @ B))))),inference(cnf,[status(esa)],[886])).
% 132.99/59.63 thf(888,plain,(! [B:char,A:char] : (((rVar @ A) != (dVar @ B)))),inference(lifteq,[status(thm)],[887])).
% 132.99/59.63 thf(17,axiom,((! [A:(option_trm > $o),B:option_trm]: ((! [C:trm]: (A @ (some_trm @ C))) => ((A @ none_trm) => (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_Differentialo_Oinduct)).
% 132.99/59.63 thf(296,plain,((! [A:(option_trm > $o),B:option_trm]: ((! [C:trm]: (A @ (some_trm @ C))) => ((A @ none_trm) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])).
% 132.99/59.63 thf(297,plain,((! [A:(option_trm > $o)]: ((! [B:trm]: (A @ (some_trm @ B))) => ((A @ none_trm) => (! [B:option_trm]: (A @ B)))))),inference(miniscope,[status(thm)],[296])).
% 132.99/59.63 thf(298,plain,(! [B:option_trm,A:(option_trm > $o)] : ((~ (A @ (some_trm @ (sk7 @ (A))))) | (~ (A @ none_trm)) | (A @ B))),inference(cnf,[status(esa)],[297])).
% 132.99/59.63 thf(45,axiom,((! [A:set_variable,B:set_variable]: ((ord_le282106107riable @ (uminus1851247844riable @ A) @ (uminus1851247844riable @ B)) = (ord_le282106107riable @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_compl__le__compl__iff)).
% 132.99/59.63 thf(430,plain,((! [A:set_variable,B:set_variable]: ((ord_le282106107riable @ (uminus1851247844riable @ A) @ (uminus1851247844riable @ B)) = (ord_le282106107riable @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])).
% 132.99/59.63 thf(4765,plain,(! [B:variable,A:set_variable] : (((^ [C:variable]: (member_variable @ C @ (uminus1851247844riable @ (collect_variable @ (^ [D:variable]: (member_variable @ D @ (uminus1851247844riable @ A))))))) != (^ [C:variable]: (($false)))) | (A != (set_option_variable2 @ (some_variable @ B))))),inference(paramod_ordered,[status(thm)],[1610,2488])).
% 132.99/59.63 thf(4766,plain,(! [A:variable] : (((^ [B:variable]: (member_variable @ B @ (uminus1851247844riable @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ A))))))))) != (^ [B:variable]: (($false)))))),inference(pattern_uni,[status(thm)],[4765:[bind(A, $thf(set_option_variable2 @ (some_variable @ D))),bind(B, $thf(D))]])).
% 132.99/59.63 thf(4872,plain,(! [A:variable] : (((^ [B:variable]: (member_variable @ B @ (uminus1851247844riable @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ A))))))))) != (^ [B:variable]: (($false)))))),inference(simp,[status(thm)],[4766])).
% 132.99/59.63 thf(2609,plain,(! [A:set_variable] : ((A != (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)))) | ((sup_sup_set_variable @ A @ bot_bot_set_variable) != (sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)) @ u)))),inference(paramod_ordered,[status(thm)],[729,2605])).
% 132.99/59.63 thf(2616,plain,(((sup_sup_set_variable @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable))) @ bot_bot_set_variable) != (sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)) @ u))),inference(simp,[status(thm)],[2609])).
% 132.99/59.63 thf(5451,plain,(((sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable))) != (sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (set_option_variable2 @ (some_variable @ (dVar @ x)))) @ u))),inference(rewrite,[status(thm)],[2616,784,729])).
% 132.99/59.63 thf(50,axiom,((! [A:variable,B:option_variable]: ((member_variable @ A @ (set_option_variable2 @ B)) = (B = (some_variable @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_elem__set)).
% 132.99/59.63 thf(444,plain,((! [A:variable,B:option_variable]: ((member_variable @ A @ (set_option_variable2 @ B)) = (B = (some_variable @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])).
% 132.99/59.63 thf(31,axiom,((! [A:trm,B:trm,C:trm,D:trm]: (((times @ A @ B) = (times @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_trm_Oinject_I6_J)).
% 132.99/59.63 thf(373,plain,((! [A:trm,B:trm,C:trm,D:trm]: (((times @ A @ B) = (times @ C @ D)) = ((A = C) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])).
% 132.99/59.63 thf(374,plain,(! [D:trm,C:trm,B:trm,A:trm] : ((((times @ A @ B) = (times @ C @ D)) = ((A = C) & (B = D))))),inference(cnf,[status(esa)],[373])).
% 132.99/59.63 thf(375,plain,(! [D:trm,C:trm,B:trm,A:trm] : ((((times @ A @ B) = (times @ C @ D)) = ((A = C) & (B = D))))),inference(lifteq,[status(thm)],[374])).
% 132.99/59.63 thf(102,axiom,((! [A:(variable > real)]: ((denota1419872369iation @ A @ (f @ zero_zero_real) @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)))) => ((denota1863255036rm_sem @ i @ (the_trm @ (uSubst516392818stappt @ sigma @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable))) @ theta)) @ A) = (denota1863255036rm_sem @ (uSubst1599435252djoint @ sigma @ i @ (f @ zero_zero_real)) @ theta @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_IH)).
% 132.99/59.63 thf(601,plain,((! [A:(variable > real)]: ((denota1419872369iation @ (A) @ (f @ zero_zero_real) @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)))) => ((denota1863255036rm_sem @ i @ (the_trm @ (uSubst516392818stappt @ sigma @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable))) @ theta)) @ (A)) = (denota1863255036rm_sem @ (uSubst1599435252djoint @ sigma @ i @ (f @ zero_zero_real)) @ theta @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])).
% 132.99/59.63 thf(4994,plain,(! [B:variable,A:set_variable] : ((is_sin155454833riable @ (uminus1851247844riable @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ A))))) | (A != (collect_variable @ (^ [C:variable]: (member_variable @ C @ (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ B))))))))),inference(paramod_ordered,[status(thm)],[543,4888])).
% 132.99/59.63 thf(4995,plain,(! [A:variable] : ((is_sin155454833riable @ (uminus1851247844riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ A))))))))))))),inference(pattern_uni,[status(thm)],[4994:[bind(A, $thf(collect_variable @ (^ [C:variable]: (member_variable @ C @ (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ B))))))),bind(B, $thf(B))]])).
% 132.99/59.63 thf(5016,plain,(! [A:variable] : ((is_sin155454833riable @ (uminus1851247844riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ A))))))))))))),inference(simp,[status(thm)],[4995])).
% 132.99/59.63 thf(92,axiom,((! [A:option_trm]: ((A != none_trm) => ((some_trm @ (the_trm @ A)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_option_Ocollapse)).
% 132.99/59.63 thf(573,plain,((! [A:option_trm]: ((~ (A = none_trm)) => ((some_trm @ (the_trm @ A)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])).
% 132.99/59.63 thf(96,axiom,((! [A:produc1418842292n_game,B:set_variable,C:trm,D:trm]: (((uSubst516392818stappt @ A @ B @ (times @ C @ D)) != none_trm) => (((uSubst516392818stappt @ A @ B @ C) != none_trm) & ((uSubst516392818stappt @ A @ B @ D) != none_trm))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_usubstappt__times__conv)).
% 132.99/59.63 thf(584,plain,((! [A:produc1418842292n_game,B:set_variable,C:trm,D:trm]: ((~ ((uSubst516392818stappt @ A @ B @ (times @ C @ D)) = none_trm)) => (~ ((uSubst516392818stappt @ A @ B @ C) = none_trm) & ~ ((uSubst516392818stappt @ A @ B @ D) = none_trm))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])).
% 132.99/59.63 thf(36,axiom,((! [A:trm]: (none_trm != (some_trm @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_option_Odistinct_I1_J)).
% 132.99/59.63 thf(402,plain,((! [A:trm]: ~ (none_trm = (some_trm @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])).
% 132.99/59.63 thf(94,axiom,((! [A:set_variable]: ((uminus1851247844riable @ (uminus1851247844riable @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_double__compl)).
% 132.99/59.63 thf(579,plain,((! [A:set_variable]: ((uminus1851247844riable @ (uminus1851247844riable @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])).
% 132.99/59.63 thf(83,axiom,((! [A:set_variable,B:set_variable]: ((! [C:variable]: ((member_variable @ C @ A) => (member_variable @ C @ B))) => (ord_le282106107riable @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_subsetI)).
% 132.99/59.63 thf(545,plain,((! [A:set_variable,B:set_variable]: ((! [C:variable]: ((member_variable @ C @ A) => (member_variable @ C @ B))) => (ord_le282106107riable @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])).
% 132.99/59.63 thf(12,axiom,((! [A:trm]: ((the_trm @ (some_trm @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_option_Osel)).
% 132.99/59.63 thf(281,plain,((! [A:trm]: ((the_trm @ (some_trm @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])).
% 132.99/59.63 thf(209,axiom,((! [A:variable,B:variable]: (((insert_variable @ A @ bot_bot_set_variable) = (insert_variable @ B @ bot_bot_set_variable)) => (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_singleton__inject)).
% 132.99/59.63 thf(936,plain,((! [A:variable,B:variable]: (((insert_variable @ A @ bot_bot_set_variable) = (insert_variable @ B @ bot_bot_set_variable)) => (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])).
% 132.99/59.63 thf(307,plain,(! [C:trm,B:(trm > $o),A:option_trm] : ((~ ((sk8 @ (B) @ A) = (sk8 @ ((=) @ trm @ (sk8 @ B @ A)) @ A))) | (~ (A = (some_trm @ C))) | ((sk8 @ (B) @ A) = C))),inference(replace_leibeq,[status(thm)],[306:[bind(A, $thf(A)),bind(B, $thf((=) @ trm @ (sk8 @ B @ A)))]])).
% 132.99/59.63 thf(312,plain,(! [C:trm,B:(trm > $o),A:option_trm] : (((sk8 @ (B) @ A) != (sk8 @ ((=) @ trm @ (sk8 @ B @ A)) @ A)) | (A != (some_trm @ C)) | ((sk8 @ (B) @ A) = C))),inference(lifteq,[status(thm)],[307])).
% 132.99/59.63 thf(313,plain,(! [B:trm,A:(trm > $o)] : (((sk8 @ (A) @ (some_trm @ B)) != (sk8 @ ((=) @ trm @ (sk8 @ A @ (some_trm @ B))) @ (some_trm @ B))) | ((sk8 @ (A) @ (some_trm @ B)) = B))),inference(simp,[status(thm)],[312])).
% 132.99/59.63 thf(105,axiom,((! [A:variable,B:set_variable,C:set_variable]: ((member_variable @ A @ (sup_sup_set_variable @ B @ C)) => ((~ (member_variable @ A @ B)) => (member_variable @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_UnE)).
% 132.99/59.63 thf(611,plain,((! [A:variable,B:set_variable,C:set_variable]: ((member_variable @ A @ (sup_sup_set_variable @ B @ C)) => ((~ (member_variable @ A @ B)) => (member_variable @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])).
% 132.99/59.63 thf(248,axiom,((! [A:(variable > real),B:(variable > real),C:set_variable,D:produc1418842292n_game,E:trm,F:denotational_interp]: ((denota1419872369iation @ A @ B @ C) => (((uSubst516392818stappt @ D @ C @ E) != none_trm) => ((denota1863255036rm_sem @ F @ (the_trm @ (uSubst516392818stappt @ D @ C @ E)) @ A) = (denota1863255036rm_sem @ (uSubst1599435252djoint @ D @ F @ B) @ E @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_usubst__term)).
% 132.99/59.63 thf(1058,plain,((! [A:(variable > real),B:(variable > real),C:set_variable,D:produc1418842292n_game,E:trm,F:denotational_interp]: ((denota1419872369iation @ (A) @ (B) @ C) => ((~ ((uSubst516392818stappt @ D @ C @ E) = none_trm)) => ((denota1863255036rm_sem @ F @ (the_trm @ (uSubst516392818stappt @ D @ C @ E)) @ (A)) = (denota1863255036rm_sem @ (uSubst1599435252djoint @ D @ F @ (B)) @ E @ (A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])).
% 132.99/59.63 thf(213,axiom,((! [A:variable,B:set_variable,C:set_variable]: ((~ (member_variable @ A @ B)) => ((~ (member_variable @ A @ C)) => (((insert_variable @ A @ B) = (insert_variable @ A @ C)) = (B = C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_insert__ident)).
% 132.99/59.63 thf(947,plain,((! [A:variable,B:set_variable,C:set_variable]: ((~ (member_variable @ A @ B)) => ((~ (member_variable @ A @ C)) => (((insert_variable @ A @ B) = (insert_variable @ A @ C)) = (B = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])).
% 132.99/59.63 thf(722,plain,(! [A:set_variable] : (((sup_sup_set_variable @ bot_bot_set_variable @ A) = A))),inference(cnf,[status(esa)],[721])).
% 132.99/59.63 thf(723,plain,(! [A:set_variable] : (((sup_sup_set_variable @ bot_bot_set_variable @ A) = A))),inference(lifteq,[status(thm)],[722])).
% 132.99/59.63 thf(2133,plain,(! [A:set_variable] : ((~ (denota1419872369iation @ (f @ zero_zero_real) @ (omega) @ A)) | ((sup_sup_set_variable @ A @ bot_bot_set_variable) != (sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)) @ u)))),inference(paramod_ordered,[status(thm)],[729,249])).
% 132.99/59.63 thf(2142,plain,(! [A:set_variable] : ((~ (denota1419872369iation @ (f @ zero_zero_real) @ (omega) @ A)) | (A != (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable))) | (u != bot_bot_set_variable))),inference(simp,[status(thm)],[2133])).
% 132.99/59.63 thf(2145,plain,((~ (denota1419872369iation @ (f @ zero_zero_real) @ (omega) @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)))) | (u != bot_bot_set_variable)),inference(simp,[status(thm)],[2142])).
% 132.99/59.63 thf(2587,plain,(~ (($true)) | (u != bot_bot_set_variable) | ((denota1419872369iation @ (f @ zero_zero_real) @ (omega) @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)))) != (denota1419872369iation @ (f @ zero_zero_real) @ (omega) @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable))))),inference(paramod_ordered,[status(thm)],[860,2145])).
% 132.99/59.63 thf(2588,plain,((u != bot_bot_set_variable) | ((denota1419872369iation @ (f @ zero_zero_real) @ (omega) @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)))) != (denota1419872369iation @ (f @ zero_zero_real) @ (omega) @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable))))),inference(simp,[status(thm)],[2587])).
% 132.99/59.63 thf(2601,plain,((u != bot_bot_set_variable) | ((f @ zero_zero_real) != (f @ zero_zero_real)) | ((omega) != (omega)) | ((sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable))) != (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)))),inference(simp,[status(thm)],[2588])).
% 132.99/59.63 thf(2606,plain,((u != bot_bot_set_variable) | ((sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable))) != (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)))),inference(simp,[status(thm)],[2601])).
% 132.99/59.63 thf(3291,plain,(! [A:set_variable] : ((u != bot_bot_set_variable) | (A != (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable))) | ((sup_sup_set_variable @ bot_bot_set_variable @ A) != (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)))))),inference(paramod_ordered,[status(thm)],[723,2606])).
% 132.99/59.63 thf(3301,plain,((u != bot_bot_set_variable) | (u != bot_bot_set_variable) | ((insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)) != (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)))),inference(simp,[status(thm)],[3291])).
% 132.99/59.63 thf(3302,plain,((u != bot_bot_set_variable)),inference(simp,[status(thm)],[3301])).
% 132.99/59.63 thf(23,axiom,((! [A:(variable > real),B:set_variable_real]: ((~ (member_variable_real @ A @ B)) => (member_variable_real @ A @ (uminus430703407e_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_ComplI)).
% 132.99/59.63 thf(350,plain,((! [A:(variable > real),B:set_variable_real]: ((~ (member_variable_real @ (A) @ B)) => (member_variable_real @ (A) @ (uminus430703407e_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])).
% 132.99/59.63 thf(123,axiom,((! [A:set_variable,B:set_variable,C:set_variable]: ((sup_sup_set_variable @ (sup_sup_set_variable @ A @ B) @ C) = (sup_sup_set_variable @ A @ (sup_sup_set_variable @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_inf__sup__aci_I6_J)).
% 132.99/59.63 thf(672,plain,((! [A:set_variable,B:set_variable,C:set_variable]: ((sup_sup_set_variable @ (sup_sup_set_variable @ A @ B) @ C) = (sup_sup_set_variable @ A @ (sup_sup_set_variable @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])).
% 132.99/59.63 thf(103,axiom,((! [A:variable,B:trm,C:denotational_interp,D:(variable > real),E:(variable > real),F:set_variable]: ((~ (member_variable @ A @ (static_FVT @ B))) => ((denota1863255036rm_sem @ C @ B @ (stateinterpol @ D @ E @ F)) = (denota1863255036rm_sem @ C @ B @ (stateinterpol @ D @ E @ (insert_variable @ A @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_stateinterpol__FVT)).
% 132.99/59.63 thf(604,plain,((! [A:variable,B:trm,C:denotational_interp,D:(variable > real),E:(variable > real),F:set_variable]: ((~ (member_variable @ A @ (static_FVT @ B))) => ((denota1863255036rm_sem @ C @ B @ (stateinterpol @ D @ E @ F)) = (denota1863255036rm_sem @ C @ B @ (stateinterpol @ D @ E @ (insert_variable @ A @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])).
% 132.99/59.63 thf(37,axiom,((! [A:trm,B:option_trm]: ((member_trm @ A @ (set_option_trm2 @ B)) = (B = (some_trm @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_elem__set)).
% 132.99/59.63 thf(406,plain,((! [A:trm,B:option_trm]: ((member_trm @ A @ (set_option_trm2 @ B)) = (B = (some_trm @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])).
% 132.99/59.63 thf(2493,plain,(! [A:variable] : ((member_variable @ (sk87 @ A) @ (set_option_variable2 @ (some_variable @ A))))),inference(func_ext,[status(esa)],[2488])).
% 132.99/59.63 thf(234,axiom,((! [A:set_variable,B:set_variable,C:set_variable,D:set_variable]: ((A = (sup_sup_set_variable @ B @ C)) => ((sup_sup_set_variable @ D @ A) = (sup_sup_set_variable @ B @ (sup_sup_set_variable @ D @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_boolean__algebra__cancel_Osup2)).
% 132.99/59.63 thf(1011,plain,((! [A:set_variable,B:set_variable,C:set_variable,D:set_variable]: ((A = (sup_sup_set_variable @ B @ C)) => ((sup_sup_set_variable @ D @ A) = (sup_sup_set_variable @ B @ (sup_sup_set_variable @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])).
% 132.99/59.63 thf(703,plain,(! [B:set_variable,A:(variable > real)] : ((denota1419872369iation @ (A) @ (A) @ B))),inference(cnf,[status(esa)],[702])).
% 132.99/59.63 thf(7996,plain,(! [B:set_variable,A:(variable > real)] : (~ (($true)) | ((denota1419872369iation @ (A) @ (A) @ B) != (denota1419872369iation @ (f @ zero_zero_real) @ (omega) @ (sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (set_option_variable2 @ (some_variable @ (dVar @ x)))) @ u))))),inference(paramod_ordered,[status(thm)],[703,3831])).
% 132.99/59.63 thf(7997,plain,(! [B:set_variable,A:(variable > real)] : (((denota1419872369iation @ (A) @ (A) @ B) != (denota1419872369iation @ (f @ zero_zero_real) @ (omega) @ (sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (set_option_variable2 @ (some_variable @ (dVar @ x)))) @ u))))),inference(simp,[status(thm)],[7996])).
% 132.99/59.63 thf(8024,plain,(! [B:set_variable,A:(variable > real)] : (((A) != (f @ zero_zero_real)) | ((A) != (omega)) | (B != (sup_sup_set_variable @ (insert_variable @ (rVar @ x) @ (set_option_variable2 @ (some_variable @ (dVar @ x)))) @ u)))),inference(simp,[status(thm)],[7997])).
% 132.99/59.63 thf(8047,plain,(((f @ zero_zero_real) != (omega))),inference(simp,[status(thm)],[8024])).
% 132.99/59.63 thf(107,axiom,((! [A:set_variable,B:set_variable,C:set_variable]: ((sup_sup_set_variable @ (sup_sup_set_variable @ A @ B) @ C) = (sup_sup_set_variable @ A @ (sup_sup_set_variable @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_Un__assoc)).
% 132.99/59.63 thf(616,plain,((! [A:set_variable,B:set_variable,C:set_variable]: ((sup_sup_set_variable @ (sup_sup_set_variable @ A @ B) @ C) = (sup_sup_set_variable @ A @ (sup_sup_set_variable @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])).
% 132.99/59.63 thf(10,axiom,((! [A:(option_trm > $o),B:option_trm]: ((A @ none_trm) => ((! [C:trm]: (A @ (some_trm @ C))) => (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_option_Oinducts)).
% 132.99/59.63 thf(271,plain,((! [A:(option_trm > $o),B:option_trm]: ((A @ none_trm) => ((! [C:trm]: (A @ (some_trm @ C))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])).
% 132.99/59.63 thf(101,axiom,((! [A:(variable > real),B:(variable > real)]: (denotational_Vagree @ A @ B @ bot_bot_set_variable))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_Vagree__empty)).
% 132.99/59.63 thf(599,plain,((! [A:(variable > real),B:(variable > real)]: (denotational_Vagree @ (A) @ (B) @ bot_bot_set_variable))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])).
% 132.99/59.63 thf(28,axiom,((! [A:produc1418842292n_game,B:set_variable,C:trm,D:trm]: ((uSubst516392818stappt @ A @ B @ (times @ C @ D)) = (uSubst918876924Timeso @ (uSubst516392818stappt @ A @ B @ C) @ (uSubst516392818stappt @ A @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_usubstappt_Osimps_I6_J)).
% 132.99/59.63 thf(362,plain,((! [A:produc1418842292n_game,B:set_variable,C:trm,D:trm]: ((uSubst516392818stappt @ A @ B @ (times @ C @ D)) = (uSubst918876924Timeso @ (uSubst516392818stappt @ A @ B @ C) @ (uSubst516392818stappt @ A @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])).
% 132.99/59.63 thf(90,axiom,((! [A:option_trm]: ((A != none_trm) => (A = (some_trm @ (the_trm @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_option_Oexhaust__sel)).
% 132.99/59.63 thf(567,plain,((! [A:option_trm]: ((~ (A = none_trm)) => (A = (some_trm @ (the_trm @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])).
% 132.99/59.63 thf(66,axiom,((! [A:variable,B:(variable > real),C:(variable > real)]: ((~ (member_variable @ A @ (statediff @ B @ C))) => ((B @ A) = (C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_nostatediff)).
% 132.99/59.63 thf(494,plain,((! [A:variable,B:(variable > real),C:(variable > real)]: ((~ (member_variable @ A @ (statediff @ (B) @ (C)))) => ((B @ A) = (C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])).
% 132.99/59.63 thf(99,axiom,((! [A:set_variable,B:set_variable]: (((uminus1851247844riable @ A) = (uminus1851247844riable @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_Compl__eq__Compl__iff)).
% 132.99/59.63 thf(594,plain,((! [A:set_variable,B:set_variable]: (((uminus1851247844riable @ A) = (uminus1851247844riable @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])).
% 132.99/59.63 thf(122,axiom,((! [A:variable,B:variable,C:(variable > real),D:real,E:set_variable_real]: ((A != B) => ((member_variable_real @ (denotational_repv @ C @ A @ D) @ (static_selectlike @ E @ C @ (insert_variable @ B @ bot_bot_set_variable))) = (member_variable_real @ (denotational_repv @ C @ A @ D) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_repv__selectlike__other)).
% 132.99/59.63 thf(668,plain,((! [A:variable,B:variable,C:(variable > real),D:real,E:set_variable_real]: ((~ (A = B)) => ((member_variable_real @ (denotational_repv @ C @ A @ D) @ (static_selectlike @ E @ (C) @ (insert_variable @ B @ bot_bot_set_variable))) = (member_variable_real @ (denotational_repv @ C @ A @ D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])).
% 132.99/59.63 thf(240,axiom,((! [A:set_variable]: ((sup_sup_set_variable @ A @ bot_bot_set_variable) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_sup__bot_Oright__neutral)).
% 132.99/59.63 thf(1029,plain,((! [A:set_variable]: ((sup_sup_set_variable @ A @ bot_bot_set_variable) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])).
% 132.99/59.63 thf(195,axiom,((! [A:variable,B:set_variable]: ((member_variable @ A @ B) => ((insert_variable @ A @ B) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_insert__absorb)).
% 132.99/59.63 thf(895,plain,((! [A:variable,B:set_variable]: ((member_variable @ A @ B) => ((insert_variable @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])).
% 132.99/59.63 thf(211,axiom,((zero_zero_set_real = (insert_real @ zero_zero_real @ bot_bot_set_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_set__zero)).
% 132.99/59.63 thf(943,plain,((zero_zero_set_real = (insert_real @ zero_zero_real @ bot_bot_set_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])).
% 132.99/59.63 thf(237,axiom,((! [A:(variable > $o)]: (((collect_variable @ A) = bot_bot_set_variable) = (A = bot_bot_variable_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_Collect__empty__eq__bot)).
% 132.99/59.63 thf(1022,plain,((! [A:(variable > $o)]: (((collect_variable @ (A)) = bot_bot_set_variable) = ((A) = (bot_bot_variable_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])).
% 132.99/59.63 thf(208,axiom,((! [A:variable,B:set_variable,C:variable,D:set_variable]: ((~ (member_variable @ A @ B)) => ((~ (member_variable @ C @ D)) => (((insert_variable @ A @ B) = (insert_variable @ C @ D)) = (((A = C) => (B = D)) & ((A != C) => (? [E:set_variable]: ((B = (insert_variable @ C @ E)) & ~ (member_variable @ C @ E) & (D = (insert_variable @ A @ E)) & ~ (member_variable @ A @ E)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_insert__eq__iff)).
% 132.99/59.63 thf(932,plain,((! [A:variable,B:set_variable,C:variable,D:set_variable]: ((~ (member_variable @ A @ B)) => ((~ (member_variable @ C @ D)) => (((insert_variable @ A @ B) = (insert_variable @ C @ D)) = (((A = C) => (B = D)) & ((~ (A = C)) => (? [E:set_variable]: ((B = (insert_variable @ C @ E)) & ~ (member_variable @ C @ E) & (D = (insert_variable @ A @ E)) & ~ (member_variable @ A @ E)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])).
% 132.99/59.63 thf(75,axiom,((! [A:set_variable,B:set_variable]: ((inf_inf_set_variable @ (inf_inf_set_variable @ A @ B) @ B) = (inf_inf_set_variable @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_inf_Oright__idem)).
% 132.99/59.63 thf(521,plain,((! [A:set_variable,B:set_variable]: ((inf_inf_set_variable @ (inf_inf_set_variable @ A @ B) @ B) = (inf_inf_set_variable @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])).
% 132.99/59.63 thf(224,axiom,((! [A:set_variable,B:set_variable,C:set_variable]: ((ord_le282106107riable @ (sup_sup_set_variable @ A @ B) @ C) = ((ord_le282106107riable @ A @ C) & (ord_le282106107riable @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_sup_Obounded__iff)).
% 132.99/59.63 thf(983,plain,((! [A:set_variable,B:set_variable,C:set_variable]: ((ord_le282106107riable @ (sup_sup_set_variable @ A @ B) @ C) = ((ord_le282106107riable @ A @ C) & (ord_le282106107riable @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])).
% 132.99/59.63 thf(35,axiom,((! [A:trm,B:trm]: (((some_trm @ A) = (some_trm @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_option_Oinject)).
% 132.99/59.63 thf(399,plain,((! [A:trm,B:trm]: (((some_trm @ A) = (some_trm @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])).
% 132.99/59.63 thf(104,axiom,((! [A:set_variable,B:set_variable]: ((sup_sup_set_variable @ A @ (sup_sup_set_variable @ A @ B)) = (sup_sup_set_variable @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_inf__sup__aci_I8_J)).
% 132.99/59.63 thf(608,plain,((! [A:set_variable,B:set_variable]: ((sup_sup_set_variable @ A @ (sup_sup_set_variable @ A @ B)) = (sup_sup_set_variable @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])).
% 132.99/59.63 thf(4890,plain,(! [A:variable] : (((uminus1851247844riable @ bot_bot_set_variable) != bot_bot_set_variable) | ((collect_variable @ (^ [B:variable]: (member_variable @ B @ (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ A)))))) != (collect_variable @ (^ [B:variable]: (($false))))))),inference(paramod_ordered,[status(thm)],[1242,4866])).
% 132.99/59.63 thf(4918,plain,(! [A:variable] : (((uminus1851247844riable @ bot_bot_set_variable) != bot_bot_set_variable) | ((^ [B:variable]: (member_variable @ B @ (uminus1851247844riable @ (set_option_variable2 @ (some_variable @ A))))) != (^ [B:variable]: (($false)))))),inference(simp,[status(thm)],[4890])).
% 132.99/59.63 thf(204,axiom,((! [A:real]: (((uminus_uminus_real @ A) = zero_zero_real) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_neg__equal__0__iff__equal)).
% 132.99/59.63 thf(922,plain,((! [A:real]: (((uminus_uminus_real @ A) = zero_zero_real) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])).
% 132.99/59.63 thf(216,axiom,((! [A:set_variable,B:set_variable]: ((sup_sup_set_variable @ (sup_sup_set_variable @ A @ B) @ B) = (sup_sup_set_variable @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_sup_Oright__idem)).
% 132.99/59.63 thf(959,plain,((! [A:set_variable,B:set_variable]: ((sup_sup_set_variable @ (sup_sup_set_variable @ A @ B) @ B) = (sup_sup_set_variable @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])).
% 132.99/59.63 thf(2163,plain,(! [B:set_variable,A:variable] : ((bot_bot_set_variable != bot_bot_set_variable) | ((collect_variable @ (^ [C:variable]: (member_variable @ C @ (insert_variable @ A @ B)))) != (collect_variable @ (^ [C:variable]: (($false))))))),inference(paramod_ordered,[status(thm)],[1242,1608])).
% 132.99/59.63 thf(2164,plain,(! [B:set_variable,A:variable] : (((collect_variable @ (^ [C:variable]: (member_variable @ C @ (insert_variable @ A @ B)))) != (collect_variable @ (^ [C:variable]: (($false))))))),inference(simp,[status(thm)],[2163])).
% 132.99/59.63 thf(2171,plain,(! [B:set_variable,A:variable] : (((^ [C:variable]: (member_variable @ C @ (insert_variable @ A @ B))) != (^ [C:variable]: (($false)))))),inference(simp,[status(thm)],[2164])).
% 132.99/59.63 thf(155,axiom,((! [A:set_variable_real,B:(variable > real),C:set_variable,D:set_variable_real]: (((static_selectlike @ A @ B @ C) = (static_selectlike @ D @ B @ C)) = (! [E:(variable > real)]: ((denota1419872369iation @ E @ B @ (uminus1851247844riable @ C)) => ((member_variable_real @ E @ A) = (member_variable_real @ E @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_selectlike__equal__cond)).
% 132.99/59.63 thf(768,plain,((! [A:set_variable_real,B:(variable > real),C:set_variable,D:set_variable_real]: (((static_selectlike @ A @ (B) @ C) = (static_selectlike @ D @ (B) @ C)) = (! [E:(variable > real)]: ((denota1419872369iation @ (E) @ (B) @ (uminus1851247844riable @ C)) => ((member_variable_real @ (E) @ A) = (member_variable_real @ (E) @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])).
% 132.99/59.63 thf(957,plain,(! [A:variable] : (((the_elem_variable @ (insert_variable @ A @ bot_bot_set_variable)) = A))),inference(cnf,[status(esa)],[956])).
% 132.99/59.63 thf(958,plain,(! [A:variable] : (((the_elem_variable @ (insert_variable @ A @ bot_bot_set_variable)) = A))),inference(lifteq,[status(thm)],[957])).
% 132.99/59.63 thf(3838,plain,(! [A:variable] : (((the_elem_variable @ (set_option_variable2 @ (some_variable @ A))) = A))),inference(rewrite,[status(thm)],[958,784])).
% 132.99/59.63 thf(33,axiom,((! [A:(variable > real),B:set_variable_real]: ((member_variable_real @ A @ (uminus430703407e_real @ B)) => (~ (member_variable_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_ComplD)).
% 132.99/59.63 thf(394,plain,((! [A:(variable > real),B:set_variable_real]: ((member_variable_real @ (A) @ (uminus430703407e_real @ B)) => (~ (member_variable_real @ (A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])).
% 132.99/59.63 thf(225,axiom,((sup_sup_set_variable = (^ [A:set_variable,B:set_variable]: (sup_sup_set_variable @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_sup__commute)).
% 132.99/59.63 thf(986,plain,(((sup_sup_set_variable) = (^ [A:set_variable,B:set_variable]: (sup_sup_set_variable @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])).
% 132.99/59.63 thf(180,axiom,((! [A:variable,B:variable]: ((member_variable @ A @ (insert_variable @ B @ bot_bot_set_variable)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_singleton__iff)).
% 132.99/59.63 thf(851,plain,((! [A:variable,B:variable]: ((member_variable @ A @ (insert_variable @ B @ bot_bot_set_variable)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])).
% 132.99/59.63 thf(206,axiom,((! [A:char]: ((size_size_variable @ (dVar @ A)) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_variable_Osize_I4_J)).
% 132.99/59.63 thf(927,plain,((! [A:char]: ((size_size_variable @ (dVar @ A)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])).
% 132.99/59.63 thf(254,plain,((! [A:(char > (option_trm > $o))]: ((! [B:char,C:trm]: (A @ B @ (some_trm @ C))) => ((! [B:char]: (A @ B @ none_trm)) => (! [B:char,C:option_trm]: (A @ B @ C)))))),inference(miniscope,[status(thm)],[253])).
% 132.99/59.63 thf(255,plain,(! [C:option_trm,B:char,A:(char > (option_trm > $o))] : ((~ (A @ (sk1 @ (A)) @ (some_trm @ (sk2 @ (A))))) | (~ (A @ (sk3 @ (A)) @ none_trm)) | (A @ B @ C))),inference(cnf,[status(esa)],[254])).
% 132.99/59.63 thf(210,axiom,((! [A:variable]: ((! [B:char]: (A != (rVar @ B))) => (~ (! [B:char]: (A != (dVar @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_variable_Oexhaust)).
% 132.99/59.63 thf(939,plain,((! [A:variable]: ((! [B:char]: ~ (A = (rVar @ B))) => (~ (! [B:char]: ~ (A = (dVar @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])).
% 132.99/59.63 thf(327,plain,(! [C:option_trm,B:option_trm,A:option_trm] : ((~ ((uSubst918876924Timeso @ A @ B) = C)) | (~ (sk9 @ A @ C @ B)) | (A = none_trm) | (A = (some_trm @ (sk12 @ C @ B @ A))))),inference(cnfConj,[status(thm)],[319])).
% 132.99/59.63 thf(341,plain,(! [C:option_trm,B:option_trm,A:option_trm] : (((uSubst918876924Timeso @ A @ B) != C) | (A = none_trm) | ((some_trm @ (sk12 @ C @ B @ A)) = A) | (~ (sk9 @ A @ C @ B)))),inference(lifteq,[status(thm)],[327])).
% 132.99/59.63 thf(342,plain,(! [B:option_trm,A:option_trm] : ((A = none_trm) | ((some_trm @ (sk12 @ (uSubst918876924Timeso @ A @ B) @ B @ A)) = A) | (~ (sk9 @ A @ (uSubst918876924Timeso @ A @ B) @ B)))),inference(simp,[status(thm)],[341])).
% 132.99/59.63 thf(151,axiom,((! [A:(variable > real),B:variable,C:real]: (denotational_Vagree @ A @ (denotational_repv @ A @ B @ C) @ (uminus1851247844riable @ (insert_variable @ B @ bot_bot_set_variable))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_Vagree__repv)).
% 132.99/59.63 thf(754,plain,((! [A:(variable > real),B:variable,C:real]: (denotational_Vagree @ (A) @ (denotational_repv @ A @ B @ C) @ (uminus1851247844riable @ (insert_variable @ B @ bot_bot_set_variable))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])).
% 132.99/59.63 thf(176,axiom,((! [A:(real > (variable > real)),B:trm,C:real]: ((denota1778088425es_ODE @ i @ A @ x @ (the_trm @ (uSubst516392818stappt @ sigma @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable))) @ B))) => (denota1419872369iation @ (A @ C) @ (A @ zero_zero_real) @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_vaflow1)).
% 132.99/59.63 thf(836,plain,((! [A:(real > (variable > real)),B:trm,C:real]: ((denota1778088425es_ODE @ i @ (A) @ x @ (the_trm @ (uSubst516392818stappt @ sigma @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable))) @ B))) => (denota1419872369iation @ (A @ C) @ (A @ zero_zero_real) @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])).
% 132.99/59.63 thf(3849,plain,((denota1419872369iation @ (f @ zero_zero_real) @ (omega) @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (set_option_variable2 @ (some_variable @ (dVar @ x))))))),inference(rewrite,[status(thm)],[860,784])).
% 132.99/59.63 thf(64,axiom,((stateinterpol = (^ [A:(variable > real),B:(variable > real),C:set_variable,D:variable]: (if_real @ (member_variable @ D @ C) @ (A @ D) @ (B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_stateinterpol__def)).
% 132.99/59.63 thf(490,plain,(((stateinterpol) = (^ [A:(variable > real),B:(variable > real),C:set_variable,D:variable]: (if_real @ (member_variable @ D @ C) @ (A @ D) @ (B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])).
% 132.99/59.63 thf(124,axiom,((! [A:set_option_variable]: (((these_variable @ A) = bot_bot_set_variable) = ((A = bot_bo266290559riable) | (A = (insert1340772453riable @ none_variable @ bot_bo266290559riable)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_these__empty__eq)).
% 132.99/59.63 thf(675,plain,((! [A:set_option_variable]: (((these_variable @ A) = bot_bot_set_variable) = ((A = bot_bo266290559riable) | (A = (insert1340772453riable @ none_variable @ bot_bo266290559riable)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])).
% 132.99/59.63 thf(78,axiom,((! [A:(variable > real),B:set_variable_real,C:set_variable_real]: ((member_variable_real @ A @ B) => ((member_variable_real @ A @ C) => (member_variable_real @ A @ (inf_in1556002680e_real @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_IntI)).
% 132.99/59.63 thf(531,plain,((! [A:(variable > real),B:set_variable_real,C:set_variable_real]: ((member_variable_real @ (A) @ B) => ((member_variable_real @ (A) @ C) => (member_variable_real @ (A) @ (inf_in1556002680e_real @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])).
% 132.99/59.63 thf(944,plain,(((insert_real @ zero_zero_real @ bot_bot_set_real) = zero_zero_set_real)),inference(lifteq,[status(thm)],[943])).
% 132.99/59.63 thf(164,axiom,((! [A:set_variable]: ((sup_sup_set_variable @ bot_bot_set_variable @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_Un__empty__left)).
% 132.99/59.63 thf(795,plain,((! [A:set_variable]: ((sup_sup_set_variable @ bot_bot_set_variable @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])).
% 132.99/59.63 thf(126,axiom,((! [A:set_variable,B:set_variable,C:(variable > $o)]: ((? [D:variable]: ((member_variable @ D @ (sup_sup_set_variable @ A @ B)) & (C @ D))) = (? [D:variable]: ((member_variable @ D @ A) & (C @ D)) | ? [D:variable]: ((member_variable @ D @ B) & (C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_bex__Un)).
% 132.99/59.63 thf(680,plain,((! [A:set_variable,B:set_variable,C:(variable > $o)]: ((? [D:variable]: ((member_variable @ D @ (sup_sup_set_variable @ A @ B)) & (C @ D))) = (? [D:variable]: ((member_variable @ D @ A) & (C @ D)) | ? [D:variable]: ((member_variable @ D @ B) & (C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])).
% 132.99/59.63 thf(116,axiom,((! [A:variable,B:variable,C:set_variable]: ((member_variable @ A @ (insert_variable @ B @ C)) => ((A != B) => (member_variable @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_insertE)).
% 132.99/59.63 thf(648,plain,((! [A:variable,B:variable,C:set_variable]: ((member_variable @ A @ (insert_variable @ B @ C)) => ((~ (A = B)) => (member_variable @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])).
% 132.99/59.63 thf(486,plain,(! [A:option_trm] : (((uSubst918876924Timeso @ none_trm @ A) = none_trm))),inference(cnf,[status(esa)],[485])).
% 132.99/59.63 thf(487,plain,(! [A:option_trm] : (((uSubst918876924Timeso @ none_trm @ A) = none_trm))),inference(lifteq,[status(thm)],[486])).
% 132.99/59.63 thf(491,plain,(((stateinterpol) = (^ [A:(variable > real),B:(variable > real),C:set_variable,D:variable]: (if_real @ (member_variable @ D @ C) @ (A @ D) @ (B @ D))))),inference(lifteq,[status(thm)],[490])).
% 132.99/59.63 thf(1081,plain,(! [A:(variable > real)] : (((stateinterpol @ A) = (^ [B:(variable > real),C:set_variable,D:variable]: (if_real @ (member_variable @ D @ C) @ (A @ D) @ (B @ D)))))),inference(func_ext,[status(esa)],[491])).
% 132.99/59.63 thf(149,axiom,((! [A:variable,B:set_variable,C:variable]: ((member_variable @ A @ B) => (member_variable @ A @ (insert_variable @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_insertI2)).
% 132.99/59.63 thf(749,plain,((! [A:variable,B:set_variable,C:variable]: ((member_variable @ A @ B) => (member_variable @ A @ (insert_variable @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])).
% 132.99/59.63 thf(129,axiom,((! [A:set_variable,B:set_variable,C:set_variable]: ((sup_sup_set_variable @ A @ (sup_sup_set_variable @ B @ C)) = (sup_sup_set_variable @ B @ (sup_sup_set_variable @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_sup__left__commute)).
% 132.99/59.63 thf(690,plain,((! [A:set_variable,B:set_variable,C:set_variable]: ((sup_sup_set_variable @ A @ (sup_sup_set_variable @ B @ C)) = (sup_sup_set_variable @ B @ (sup_sup_set_variable @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])).
% 132.99/59.63 thf(238,axiom,((denota1778088425es_ODE @ (uSubst1599435252djoint @ sigma @ i @ omega) @ f @ x @ theta)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_a1)).
% 132.99/59.63 thf(1025,plain,((denota1778088425es_ODE @ (uSubst1599435252djoint @ sigma @ i @ (omega)) @ (f) @ x @ theta)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])).
% 132.99/59.63 thf(187,axiom,(((uminus_uminus_real @ zero_zero_real) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_add_Oinverse__neutral)).
% 132.99/59.63 thf(871,plain,(((uminus_uminus_real @ zero_zero_real) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])).
% 132.99/59.63 thf(872,plain,(((uminus_uminus_real @ zero_zero_real) = zero_zero_real)),inference(lifteq,[status(thm)],[871])).
% 132.99/59.63 thf(135,axiom,((! [A:(variable > real),B:(variable > real),C:set_variable,D:set_variable]: ((denotational_Vagree @ A @ B @ C) => ((denotational_Vagree @ A @ B @ D) => (denotational_Vagree @ A @ B @ (sup_sup_set_variable @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_Vagree__union)).
% 132.99/59.63 thf(707,plain,((! [A:(variable > real),B:(variable > real),C:set_variable,D:set_variable]: ((denotational_Vagree @ (A) @ (B) @ C) => ((denotational_Vagree @ (A) @ (B) @ D) => (denotational_Vagree @ (A) @ (B) @ (sup_sup_set_variable @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])).
% 132.99/59.63 thf(40,axiom,((! [A:(variable > real),B:(variable > real),C:trm,D:denotational_interp]: ((denotational_Vagree @ A @ B @ (static_FVT @ C)) => ((denota1863255036rm_sem @ D @ C @ A) = (denota1863255036rm_sem @ D @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_coincidence__term)).
% 132.99/59.63 thf(414,plain,((! [A:(variable > real),B:(variable > real),C:trm,D:denotational_interp]: ((denotational_Vagree @ (A) @ (B) @ (static_FVT @ C)) => ((denota1863255036rm_sem @ D @ C @ (A)) = (denota1863255036rm_sem @ D @ C @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])).
% 132.99/59.63 thf(821,plain,(((is_sin155454833riable) = (^ [A:set_variable]: (A = (insert_variable @ (the_elem_variable @ A) @ bot_bot_set_variable))))),inference(lifteq,[status(thm)],[820])).
% 132.99/59.63 thf(1341,plain,(((^ [A:set_variable]: (A = (insert_variable @ (the_elem_variable @ A) @ bot_bot_set_variable))) = (^ [A:set_variable]: ? [B:variable]: (A = (insert_variable @ B @ bot_bot_set_variable)))) | ((is_sin155454833riable) != (is_sin155454833riable))),inference(paramod_ordered,[status(thm)],[821,740])).
% 132.99/59.63 thf(1342,plain,(((^ [A:set_variable]: (A = (insert_variable @ (the_elem_variable @ A) @ bot_bot_set_variable))) = (^ [A:set_variable]: ? [B:variable]: (A = (insert_variable @ B @ bot_bot_set_variable))))),inference(pattern_uni,[status(thm)],[1341:[]])).
% 132.99/59.63 thf(3833,plain,(((^ [A:set_variable]: (A = (set_option_variable2 @ (some_variable @ (the_elem_variable @ A))))) = (^ [A:set_variable]: ? [B:variable]: (A = (set_option_variable2 @ (some_variable @ B)))))),inference(rewrite,[status(thm)],[1342,784])).
% 132.99/59.63 thf(38,axiom,((! [A:(variable > real),B:(variable > real),C:set_variable]: ((denotational_Vagree @ A @ B @ C) => (ord_le282106107riable @ (statediff @ A @ B) @ (uminus1851247844riable @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_Vagree__statediff)).
% 132.99/59.63 thf(409,plain,((! [A:(variable > real),B:(variable > real),C:set_variable]: ((denotational_Vagree @ (A) @ (B) @ C) => (ord_le282106107riable @ (statediff @ (A) @ (B)) @ (uminus1851247844riable @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])).
% 132.99/59.63 thf(262,plain,(! [B:set_variable_real,A:set_variable_real] : ((((uminus430703407e_real @ A) = (uminus430703407e_real @ B)) = (A = B)))),inference(cnf,[status(esa)],[261])).
% 132.99/59.63 thf(263,plain,(! [B:set_variable_real,A:set_variable_real] : ((((uminus430703407e_real @ A) = (uminus430703407e_real @ B)) = (A = B)))),inference(lifteq,[status(thm)],[262])).
% 132.99/59.63 thf(247,axiom,((~ (! [A:(trm > (denotational_interp > (trm > (denotational_interp > (char > ((real > (variable > real)) > (variable > real)))))))]: ~ (! [B:trm,C:denotational_interp,D:trm,E:denotational_interp,F:char,G:(real > (variable > real))]: ((? [H:(variable > real)]: ((denota1419872369iation @ H @ (G @ zero_zero_real) @ (insert_variable @ (rVar @ F) @ (insert_variable @ (dVar @ F) @ bot_bot_set_variable))) & ((denota1863255036rm_sem @ E @ D @ H) != (denota1863255036rm_sem @ C @ B @ H)))) = ((denota1419872369iation @ (A @ B @ C @ D @ E @ F @ G) @ (G @ zero_zero_real) @ (insert_variable @ (rVar @ F) @ (insert_variable @ (dVar @ F) @ bot_bot_set_variable))) & ((denota1863255036rm_sem @ E @ D @ (A @ B @ C @ D @ E @ F @ G)) != (denota1863255036rm_sem @ C @ B @ (A @ B @ C @ D @ E @ F @ G))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rr_O_A_092_060forall_062x0_Ax1_Ax2_Ax3_Ax4_Ax5_O_A_I_092_060exists_062v6_O_AUvariation_Av6_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_Av6_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_Av6_J_A_061_A_IUvariation_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)).
% 132.99/59.63 thf(1053,plain,((~ (! [A:(trm > (denotational_interp > (trm > (denotational_interp > (char > ((real > (variable > real)) > (variable > real)))))))]: ~ (! [B:trm,C:denotational_interp,D:trm,E:denotational_interp,F:char,G:(real > (variable > real))]: ((? [H:(variable > real)]: ((denota1419872369iation @ (H) @ (G @ zero_zero_real) @ (insert_variable @ (rVar @ F) @ (insert_variable @ (dVar @ F) @ bot_bot_set_variable))) & ~ ((denota1863255036rm_sem @ E @ D @ (H)) = (denota1863255036rm_sem @ C @ B @ (H))))) = ((denota1419872369iation @ (A @ B @ C @ D @ E @ F @ G) @ (G @ zero_zero_real) @ (insert_variable @ (rVar @ F) @ (insert_variable @ (dVar @ F) @ bot_bot_set_variable))) & ~ ((denota1863255036rm_sem @ E @ D @ (A @ B @ C @ D @ E @ F @ G)) = (denota1863255036rm_sem @ C @ B @ (A @ B @ C @ D @ E @ F @ G))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])).
% 132.99/59.63 thf(5571,plain,(! [C:trm,B:option_trm,A:option_trm] : ((sk9 @ A @ (uSubst918876924Timeso @ A @ B) @ B) | (A != none_trm) | ((some_trm @ (sk10 @ (uSubst918876924Timeso @ A @ B) @ B @ A)) != (some_trm @ C)))),inference(paramod_ordered,[status(thm)],[340,369])).
% 132.99/59.63 thf(5572,plain,(! [B:option_trm,A:option_trm] : ((sk9 @ B @ (uSubst918876924Timeso @ B @ A) @ A) | (B != none_trm))),inference(pattern_uni,[status(thm)],[5571:[bind(A, $thf(F)),bind(B, $thf(E)),bind(C, $thf(sk10 @ (uSubst918876924Timeso @ F @ E) @ E @ F))]])).
% 132.99/59.63 thf(5630,plain,(! [A:option_trm] : ((sk9 @ none_trm @ (uSubst918876924Timeso @ none_trm @ A) @ A))),inference(simp,[status(thm)],[5572])).
% 132.99/59.63 thf(6912,plain,(! [A:option_trm] : ((sk9 @ none_trm @ none_trm @ A))),inference(rewrite,[status(thm)],[5630,487])).
% 132.99/59.63 thf(49,axiom,((! [A:option_trm,B:option_trm]: (((uSubst918876924Timeso @ A @ B) = none_trm) = ((A = none_trm) | (B = none_trm))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_Timeso__undef)).
% 132.99/59.63 thf(441,plain,((! [A:option_trm,B:option_trm]: (((uSubst918876924Timeso @ A @ B) = none_trm) = ((A = none_trm) | (B = none_trm))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])).
% 132.99/59.63 thf(328,plain,(! [C:option_trm,B:option_trm,A:option_trm] : ((~ ((uSubst918876924Timeso @ A @ B) = C)) | (C = (some_trm @ (times @ (sk10 @ C @ B @ A) @ (sk11 @ C @ B @ A)))) | (sk9 @ A @ C @ B))),inference(cnfConj,[status(thm)],[319])).
% 132.99/59.63 thf(337,plain,(! [C:option_trm,B:option_trm,A:option_trm] : (((uSubst918876924Timeso @ A @ B) != C) | ((some_trm @ (times @ (sk10 @ C @ B @ A) @ (sk11 @ C @ B @ A))) = C) | (sk9 @ A @ C @ B))),inference(lifteq,[status(thm)],[328])).
% 132.99/59.63 thf(338,plain,(! [B:option_trm,A:option_trm] : (((some_trm @ (times @ (sk10 @ (uSubst918876924Timeso @ A @ B) @ B @ A) @ (sk11 @ (uSubst918876924Timeso @ A @ B) @ B @ A))) = (uSubst918876924Timeso @ A @ B)) | (sk9 @ A @ (uSubst918876924Timeso @ A @ B) @ B))),inference(simp,[status(thm)],[337])).
% 132.99/59.63 thf(93,axiom,((! [A:(variable > real),B:variable]: ((denotational_repv @ A @ B @ (A @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_repv__self)).
% 132.99/59.63 thf(576,plain,((! [A:(variable > real),B:variable]: ((denotational_repv @ A @ B @ (A @ B)) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])).
% 132.99/59.63 thf(27,axiom,((! [A:set_variable_real,B:set_variable_real]: (((uminus430703407e_real @ A) = (uminus430703407e_real @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_compl__eq__compl__iff)).
% 132.99/59.63 thf(359,plain,((! [A:set_variable_real,B:set_variable_real]: (((uminus430703407e_real @ A) = (uminus430703407e_real @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])).
% 132.99/59.63 thf(82,axiom,((none_trm = none_trm)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_undeft__None)).
% 132.99/59.63 thf(544,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])).
% 132.99/59.63 thf(243,axiom,((! [A:variable,B:set_variable]: ((insert_variable @ A @ (insert_variable @ A @ B)) = (insert_variable @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_insert__absorb2)).
% 132.99/59.63 thf(1038,plain,((! [A:variable,B:set_variable]: ((insert_variable @ A @ (insert_variable @ A @ B)) = (insert_variable @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])).
% 132.99/59.63 thf(214,axiom,((! [A:variable,B:set_variable]: ((member_variable @ A @ B) => (~ (! [C:set_variable]: ((B = (insert_variable @ A @ C)) => (member_variable @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_Set_Oset__insert)).
% 132.99/59.63 thf(951,plain,((! [A:variable,B:set_variable]: ((member_variable @ A @ B) => (~ (! [C:set_variable]: ((B = (insert_variable @ A @ C)) => (member_variable @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])).
% 132.99/59.63 thf(233,axiom,(((uSubst516392818stappt @ sigma @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable))) @ theta) != none_trm)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_subdef)).
% 132.99/59.63 thf(1008,plain,((~ ((uSubst516392818stappt @ sigma @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable))) @ theta) = none_trm))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])).
% 132.99/59.63 thf(1009,plain,((~ ((uSubst516392818stappt @ sigma @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable))) @ theta) = none_trm))),inference(polarity_switch,[status(thm)],[1008])).
% 132.99/59.63 thf(1010,plain,(((uSubst516392818stappt @ sigma @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable))) @ theta) != none_trm)),inference(lifteq,[status(thm)],[1009])).
% 132.99/59.63 thf(3847,plain,(((uSubst516392818stappt @ sigma @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (set_option_variable2 @ (some_variable @ (dVar @ x))))) @ theta) != none_trm)),inference(rewrite,[status(thm)],[1010,784])).
% 132.99/59.63 thf(655,plain,(! [A:char] : (((size_variable @ (dVar @ A)) = zero_zero_nat))),inference(cnf,[status(esa)],[654])).
% 132.99/59.63 thf(656,plain,(! [A:char] : (((size_variable @ (dVar @ A)) = zero_zero_nat))),inference(lifteq,[status(thm)],[655])).
% 132.99/59.63 thf(106,axiom,((! [A:char,B:char]: (((rVar @ A) = (rVar @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_variable_Oinject_I1_J)).
% 132.99/59.63 thf(613,plain,((! [A:char,B:char]: (((rVar @ A) = (rVar @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])).
% 132.99/59.63 thf(600,plain,(! [B:(variable > real),A:(variable > real)] : ((denotational_Vagree @ (A) @ (B) @ bot_bot_set_variable))),inference(cnf,[status(esa)],[599])).
% 132.99/59.63 thf(185,axiom,((! [A:(real > (variable > real)),B:trm,C:real]: ((denota1778088425es_ODE @ (uSubst1599435252djoint @ sigma @ i @ omega) @ A @ x @ B) => (denota1419872369iation @ (A @ C) @ (A @ zero_zero_real) @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_vaflow2)).
% 132.99/59.63 thf(864,plain,((! [A:(real > (variable > real)),B:trm,C:real]: ((denota1778088425es_ODE @ (uSubst1599435252djoint @ sigma @ i @ (omega)) @ (A) @ x @ B) => (denota1419872369iation @ (A @ C) @ (A @ zero_zero_real) @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])).
% 132.99/59.63 thf(222,axiom,((! [A:variable]: (member_variable @ A @ (insert_variable @ A @ bot_bot_set_variable)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_singletonI)).
% 132.99/59.63 thf(978,plain,((! [A:variable]: (member_variable @ A @ (insert_variable @ A @ bot_bot_set_variable)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])).
% 132.99/59.63 thf(19,axiom,((! [A:set_variable_real]: ((uminus430703407e_real @ (uminus430703407e_real @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_double__compl)).
% 132.99/59.63 thf(314,plain,((! [A:set_variable_real]: ((uminus430703407e_real @ (uminus430703407e_real @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])).
% 132.99/59.63 thf(67,axiom,((! [A:set_variable,B:set_variable]: ((inf_inf_set_variable @ (inf_inf_set_variable @ A @ B) @ B) = (inf_inf_set_variable @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_inf__right__idem)).
% 132.99/59.63 thf(497,plain,((! [A:set_variable,B:set_variable]: ((inf_inf_set_variable @ (inf_inf_set_variable @ A @ B) @ B) = (inf_inf_set_variable @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])).
% 132.99/59.63 thf(189,axiom,((! [A:variable]: ~ (member_variable @ A @ bot_bot_set_variable))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_empty__iff)).
% 132.99/59.63 thf(876,plain,((! [A:variable]: ~ (member_variable @ A @ bot_bot_set_variable))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])).
% 132.99/59.63 thf(179,axiom,((! [A:(variable > real),B:set_variable,C:set_variable_real,D:set_variable_real]: ((! [E:(variable > real)]: ((denota1419872369iation @ E @ A @ (uminus1851247844riable @ B)) => ((member_variable_real @ E @ C) = (member_variable_real @ E @ D)))) => ((static_selectlike @ C @ A @ B) = (static_selectlike @ D @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_selectlike__equal__cocond__rule)).
% 132.99/59.63 thf(845,plain,((! [A:(variable > real),B:set_variable,C:set_variable_real,D:set_variable_real]: ((! [E:(variable > real)]: ((denota1419872369iation @ (E) @ (A) @ (uminus1851247844riable @ B)) => ((member_variable_real @ (E) @ C) = (member_variable_real @ (E) @ D)))) => ((static_selectlike @ C @ (A) @ B) = (static_selectlike @ D @ (A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])).
% 132.99/59.63 thf(221,axiom,((! [A:(variable > real),B:variable,C:real]: (denota1419872369iation @ A @ (denotational_repv @ A @ B @ C) @ (insert_variable @ B @ bot_bot_set_variable)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_Uvariation__repv)).
% 132.99/59.63 thf(976,plain,((! [A:(variable > real),B:variable,C:real]: (denota1419872369iation @ (A) @ (denotational_repv @ A @ B @ C) @ (insert_variable @ B @ bot_bot_set_variable)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])).
% 132.99/59.63 thf(76,axiom,((! [A:produc1418842292n_game,B:set_variable,C:trm,D:set_variable]: (((uSubst516392818stappt @ A @ B @ C) != none_trm) => (((uSubst516392818stappt @ A @ D @ C) != none_trm) => ((uSubst516392818stappt @ A @ B @ C) = (uSubst516392818stappt @ A @ D @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_usubstappt__det)).
% 132.99/59.63 thf(524,plain,((! [A:produc1418842292n_game,B:set_variable,C:trm,D:set_variable]: ((~ ((uSubst516392818stappt @ A @ B @ C) = none_trm)) => ((~ ((uSubst516392818stappt @ A @ D @ C) = none_trm)) => ((uSubst516392818stappt @ A @ B @ C) = (uSubst516392818stappt @ A @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])).
% 132.99/59.63 thf(153,axiom,((! [A:(variable > real),B:set_variable,C:set_variable_real,D:set_variable_real]: ((! [E:(variable > real)]: ((denota1419872369iation @ E @ A @ B) => ((member_variable_real @ E @ C) = (member_variable_real @ E @ D)))) => ((static_selectlike @ C @ A @ (uminus1851247844riable @ B)) = (static_selectlike @ D @ A @ (uminus1851247844riable @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_selectlike__equal__cocond__corule)).
% 132.99/59.63 thf(759,plain,((! [A:(variable > real),B:set_variable,C:set_variable_real,D:set_variable_real]: ((! [E:(variable > real)]: ((denota1419872369iation @ (E) @ (A) @ B) => ((member_variable_real @ (E) @ C) = (member_variable_real @ (E) @ D)))) => ((static_selectlike @ C @ (A) @ (uminus1851247844riable @ B)) = (static_selectlike @ D @ (A) @ (uminus1851247844riable @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])).
% 132.99/59.63 thf(156,axiom,((! [A:set_variable]: ((! [B:variable]: ~ (member_variable @ B @ A)) = (A = bot_bot_set_variable)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_all__not__in__conv)).
% 132.99/59.63 thf(771,plain,((! [A:set_variable]: ((! [B:variable]: ~ (member_variable @ B @ A)) = (A = bot_bot_set_variable)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])).
% 132.99/59.63 thf(979,plain,(! [A:variable] : ((member_variable @ A @ (insert_variable @ A @ bot_bot_set_variable)))),inference(cnf,[status(esa)],[978])).
% 132.99/59.63 thf(2525,plain,(! [B:variable,A:variable] : (~ (($true)) | ((member_variable @ A @ (insert_variable @ A @ bot_bot_set_variable)) != (member_variable @ B @ bot_bot_set_variable)))),inference(paramod_ordered,[status(thm)],[979,621])).
% 132.99/59.63 thf(2526,plain,(! [B:variable,A:variable] : (((member_variable @ A @ (insert_variable @ A @ bot_bot_set_variable)) != (member_variable @ B @ bot_bot_set_variable)))),inference(simp,[status(thm)],[2525])).
% 132.99/59.63 thf(2546,plain,(! [B:variable,A:variable] : ((A != B) | ((insert_variable @ A @ bot_bot_set_variable) != bot_bot_set_variable))),inference(simp,[status(thm)],[2526])).
% 132.99/59.63 thf(2548,plain,(! [A:variable] : (((insert_variable @ A @ bot_bot_set_variable) != bot_bot_set_variable))),inference(simp,[status(thm)],[2546])).
% 132.99/59.63 thf(2554,plain,(! [B:variable,A:set_variable] : (((collect_variable @ (^ [C:variable]: (member_variable @ C @ A))) != bot_bot_set_variable) | (A != (insert_variable @ B @ bot_bot_set_variable)))),inference(paramod_ordered,[status(thm)],[543,2548])).
% 132.99/59.63 thf(2555,plain,(! [A:variable] : (((collect_variable @ (^ [B:variable]: (member_variable @ B @ (insert_variable @ A @ bot_bot_set_variable)))) != bot_bot_set_variable))),inference(pattern_uni,[status(thm)],[2554:[bind(A, $thf(insert_variable @ C @ bot_bot_set_variable)),bind(B, $thf(C))]])).
% 132.99/59.63 thf(2557,plain,(! [A:variable] : (((collect_variable @ (^ [B:variable]: (member_variable @ B @ (insert_variable @ A @ bot_bot_set_variable)))) != bot_bot_set_variable))),inference(simp,[status(thm)],[2555])).
% 132.99/59.63 thf(2558,plain,(! [A:variable] : ((bot_bot_set_variable != bot_bot_set_variable) | ((collect_variable @ (^ [B:variable]: (member_variable @ B @ (insert_variable @ A @ bot_bot_set_variable)))) != (collect_variable @ (^ [B:variable]: (($false))))))),inference(paramod_ordered,[status(thm)],[1242,2557])).
% 132.99/59.63 thf(2559,plain,(! [A:variable] : (((collect_variable @ (^ [B:variable]: (member_variable @ B @ (insert_variable @ A @ bot_bot_set_variable)))) != (collect_variable @ (^ [B:variable]: (($false))))))),inference(simp,[status(thm)],[2558])).
% 132.99/59.63 thf(2567,plain,(! [A:variable] : (((^ [B:variable]: (member_variable @ B @ (insert_variable @ A @ bot_bot_set_variable))) != (^ [B:variable]: (($false)))))),inference(simp,[status(thm)],[2559])).
% 132.99/59.63 thf(2571,plain,(! [A:variable] : ((member_variable @ (sk89 @ A) @ (insert_variable @ A @ bot_bot_set_variable)))),inference(func_ext,[status(esa)],[2567])).
% 132.99/59.63 thf(5386,plain,(! [A:variable] : ((member_variable @ (sk89 @ A) @ (set_option_variable2 @ (some_variable @ A))))),inference(rewrite,[status(thm)],[2571,784])).
% 132.99/59.63 thf(4829,plain,(! [B:variable,A:set_variable] : ((is_sin155454833riable @ (uminus1851247844riable @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (uminus1851247844riable @ A)))))) | (A != (collect_variable @ (^ [C:variable]: (member_variable @ C @ (set_option_variable2 @ (some_variable @ B)))))))),inference(paramod_ordered,[status(thm)],[1610,3843])).
% 132.99/59.63 thf(4830,plain,(! [A:variable] : ((is_sin155454833riable @ (uminus1851247844riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ (uminus1851247844riable @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (set_option_variable2 @ (some_variable @ A))))))))))))),inference(pattern_uni,[status(thm)],[4829:[bind(A, $thf(collect_variable @ (^ [C:variable]: (member_variable @ C @ (set_option_variable2 @ (some_variable @ B)))))),bind(B, $thf(B))]])).
% 132.99/59.63 thf(4873,plain,(! [A:variable] : ((is_sin155454833riable @ (uminus1851247844riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ (uminus1851247844riable @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (set_option_variable2 @ (some_variable @ A))))))))))))),inference(simp,[status(thm)],[4830])).
% 132.99/59.63 thf(132,axiom,((! [A:set_variable,B:set_variable,C:set_variable]: ((sup_sup_set_variable @ A @ (sup_sup_set_variable @ B @ C)) = (sup_sup_set_variable @ B @ (sup_sup_set_variable @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_sup_Oleft__commute)).
% 132.99/59.63 thf(699,plain,((! [A:set_variable,B:set_variable,C:set_variable]: ((sup_sup_set_variable @ A @ (sup_sup_set_variable @ B @ C)) = (sup_sup_set_variable @ B @ (sup_sup_set_variable @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])).
% 132.99/59.63 thf(1062,plain,(! [A:(variable > real)] : (((denotational_Vagree @ A) = (^ [B:(variable > real)]: (denotational_Vagree @ B @ A))))),inference(func_ext,[status(esa)],[466])).
% 132.99/59.63 thf(10288,plain,(! [B:option_trm,A:option_trm] : (~ (($true)) | (sk20 @ B @ A @ (^ [C:option_trm,D:option_trm]: (($true)))))),inference(prim_subst,[status(thm)],[384:[bind(A, $thf(A)),bind(B, $thf(^ [D:option_trm,E:option_trm]: (($true))))]])).
% 132.99/59.63 thf(10428,plain,(! [B:option_trm,A:option_trm] : ((sk20 @ B @ A @ (^ [C:option_trm,D:option_trm]: (($true)))))),inference(simp,[status(thm)],[10288])).
% 132.99/59.63 thf(228,axiom,((sup_sup_set_variable = (^ [A:set_variable,B:set_variable]: (sup_sup_set_variable @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_inf__sup__aci_I5_J)).
% 132.99/59.63 thf(995,plain,(((sup_sup_set_variable) = (^ [A:set_variable,B:set_variable]: (sup_sup_set_variable @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])).
% 132.99/59.63 thf(946,plain,(((these_variable @ bot_bo266290559riable) = bot_bot_set_variable)),inference(lifteq,[status(thm)],[945])).
% 132.99/59.63 thf(46,axiom,((! [A:(variable > real),B:set_variable_real,C:set_variable]: ((member_variable_real @ A @ (static_selectlike @ B @ A @ C)) = (member_variable_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_selectlike__self)).
% 132.99/59.63 thf(433,plain,((! [A:(variable > real),B:set_variable_real,C:set_variable]: ((member_variable_real @ (A) @ (static_selectlike @ B @ (A) @ C)) = (member_variable_real @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])).
% 132.99/59.63 thf(928,plain,(! [A:char] : (((size_size_variable @ (dVar @ A)) = zero_zero_nat))),inference(cnf,[status(esa)],[927])).
% 132.99/59.63 thf(929,plain,(! [A:char] : (((size_size_variable @ (dVar @ A)) = zero_zero_nat))),inference(lifteq,[status(thm)],[928])).
% 132.99/59.63 thf(84,axiom,((! [A:variable,B:set_variable,C:set_variable]: ((member_variable @ A @ B) => ((member_variable @ A @ C) => (member_variable @ A @ (inf_inf_set_variable @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_IntI)).
% 132.99/59.63 thf(549,plain,((! [A:variable,B:set_variable,C:set_variable]: ((member_variable @ A @ B) => ((member_variable @ A @ C) => (member_variable @ A @ (inf_inf_set_variable @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])).
% 132.99/59.63 thf(15,axiom,((! [A:option_trm]: ((A != none_trm) = (? [B:trm]: (A = (some_trm @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_not__None__eq)).
% 132.99/59.63 thf(290,plain,((! [A:option_trm]: ((~ (A = none_trm)) = (? [B:trm]: (A = (some_trm @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])).
% 132.99/59.63 thf(201,axiom,((! [A:real]: ((A = (uminus_uminus_real @ A)) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_equal__neg__zero)).
% 132.99/59.63 thf(914,plain,((! [A:real]: ((A = (uminus_uminus_real @ A)) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])).
% 132.99/59.63 thf(1077,plain,(! [A:(variable > real)] : (((denotational_repv @ A) = (^ [B:variable,C:real,D:variable]: (if_real @ (B = D) @ C @ (A @ D)))))),inference(func_ext,[status(esa)],[440])).
% 132.99/59.63 thf(60,axiom,((! [A:variable,B:(variable > $o)]: ((member_variable @ A @ (collect_variable @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_mem__Collect__eq)).
% 132.99/59.63 thf(478,plain,((! [A:variable,B:(variable > $o)]: ((member_variable @ A @ (collect_variable @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])).
% 132.99/59.63 thf(230,axiom,(((denota1778088425es_ODE @ i @ f @ x @ (the_trm @ (uSubst516392818stappt @ sigma @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable))) @ theta))) => (denota1778088425es_ODE @ (uSubst1599435252djoint @ sigma @ i @ omega) @ f @ x @ theta))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_l2r)).
% 132.99/59.63 thf(999,plain,(((denota1778088425es_ODE @ i @ (f) @ x @ (the_trm @ (uSubst516392818stappt @ sigma @ (sup_sup_set_variable @ u @ (insert_variable @ (rVar @ x) @ (insert_variable @ (dVar @ x) @ bot_bot_set_variable))) @ theta))) => (denota1778088425es_ODE @ (uSubst1599435252djoint @ sigma @ i @ (omega)) @ (f) @ x @ theta))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])).
% 132.99/59.63 thf(51,axiom,((! [A:option_trm,B:option_trm]: (((A = none_trm) = (B = none_trm)) => (((A != none_trm) => ((B != none_trm) => ((the_trm @ A) = (the_trm @ B)))) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_option_Oexpand)).
% 132.99/59.63 thf(447,plain,((! [A:option_trm,B:option_trm]: (((A = none_trm) = (B = none_trm)) => (((~ (A = none_trm)) => ((~ (B = none_trm)) => ((the_trm @ A) = (the_trm @ B)))) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])).
% 132.99/59.63 thf(175,axiom,((! [A:set_variable]: ((sup_sup_set_variable @ A @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_sup__idem)).
% 132.99/59.63 thf(833,plain,((! [A:set_variable]: ((sup_sup_set_variable @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])).
% 132.99/59.63 thf(4810,plain,(! [B:set_variable,A:set_variable] : (((uminus1851247844riable @ A) = B) | ((uminus1851247844riable @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (uminus1851247844riable @ A))))) != (uminus1851247844riable @ B)))),inference(paramod_ordered,[status(thm)],[1610,426])).
% 132.99/59.63 thf(4811,plain,(! [A:set_variable] : (((uminus1851247844riable @ A) = (collect_variable @ (^ [B:variable]: (member_variable @ B @ (uminus1851247844riable @ A))))))),inference(pattern_uni,[status(thm)],[4810:[bind(A, $thf(A)),bind(B, $thf(collect_variable @ (^ [C:variable]: (member_variable @ C @ (uminus1851247844riable @ A)))))]])).
% 132.99/59.63 thf(3837,plain,(((is_sin155454833riable) = (^ [A:set_variable]: (A = (set_option_variable2 @ (some_variable @ (the_elem_variable @ A))))))),inference(rewrite,[status(thm)],[821,784])).
% 132.99/59.63 thf(181,axiom,((! [A:variable,B:set_variable,C:set_variable]: (((insert_variable @ A @ bot_bot_set_variable) = (sup_sup_set_variable @ B @ C)) = (((B = bot_bot_set_variable) & (C = (insert_variable @ A @ bot_bot_set_variable))) | ((B = (insert_variable @ A @ bot_bot_set_variable)) & (C = bot_bot_set_variable)) | ((B = (insert_variable @ A @ bot_bot_set_variable)) & (C = (insert_variable @ A @ bot_bot_set_variable))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_singleton__Un__iff)).
% 132.99/59.63 thf(854,plain,((! [A:variable,B:set_variable,C:set_variable]: (((insert_variable @ A @ bot_bot_set_variable) = (sup_sup_set_variable @ B @ C)) = (((B = bot_bot_set_variable) & (C = (insert_variable @ A @ bot_bot_set_variable))) | ((B = (insert_variable @ A @ bot_bot_set_variable)) & (C = bot_bot_set_variable)) | ((B = (insert_variable @ A @ bot_bot_set_variable)) & (C = (insert_variable @ A @ bot_bot_set_variable))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])).
% 132.99/59.63 thf(162,axiom,((! [A:set_variable,B:set_variable,C:(variable > $o)]: ((! [D:variable]: ((member_variable @ D @ (sup_sup_set_variable @ A @ B)) => (C @ D))) = (! [D:variable]: ((member_variable @ D @ A) => (C @ D)) & ! [D:variable]: ((member_variable @ D @ B) => (C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_ball__Un)).
% 132.99/59.63 thf(790,plain,((! [A:set_variable,B:set_variable,C:(variable > $o)]: ((! [D:variable]: ((member_variable @ D @ (sup_sup_set_variable @ A @ B)) => (C @ D))) = (! [D:variable]: ((member_variable @ D @ A) => (C @ D)) & ! [D:variable]: ((member_variable @ D @ B) => (C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])).
% 132.99/59.63 thf(186,axiom,((! [A:variable,B:variable,C:(variable > real),D:real,E:set_variable_real]: ((A != B) => ((member_variable_real @ (denotational_repv @ C @ A @ D) @ E) = (member_variable_real @ (denotational_repv @ C @ A @ D) @ (static_selectlike @ E @ C @ (insert_variable @ B @ bot_bot_set_variable))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_repv__selectlike__other__converse)).
% 132.99/59.63 thf(867,plain,((! [A:variable,B:variable,C:(variable > real),D:real,E:set_variable_real]: ((~ (A = B)) => ((member_variable_real @ (denotational_repv @ C @ A @ D) @ E) = (member_variable_real @ (denotational_repv @ C @ A @ D) @ (static_selectlike @ E @ (C) @ (insert_variable @ B @ bot_bot_set_variable))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])).
% 132.99/59.63 thf(272,plain,((! [A:(option_trm > $o)]: ((A @ none_trm) => ((! [B:trm]: (A @ (some_trm @ B))) => (! [B:option_trm]: (A @ B)))))),inference(miniscope,[status(thm)],[271])).
% 132.99/59.63 thf(273,plain,(! [B:option_trm,A:(option_trm > $o)] : ((~ (A @ none_trm)) | (~ (A @ (some_trm @ (sk5 @ (A))))) | (A @ B))),inference(cnf,[status(esa)],[272])).
% 132.99/59.63 thf(89,axiom,((! [A:set_variable,B:set_variable,C:set_variable]: ((ord_le282106107riable @ A @ (inf_inf_set_variable @ B @ C)) = ((ord_le282106107riable @ A @ B) & (ord_le282106107riable @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_le__inf__iff)).
% 132.99/59.63 thf(564,plain,((! [A:set_variable,B:set_variable,C:set_variable]: ((ord_le282106107riable @ A @ (inf_inf_set_variable @ B @ C)) = ((ord_le282106107riable @ A @ B) & (ord_le282106107riable @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])).
% 132.99/59.63 thf(70,axiom,((! [A:(variable > real),B:(variable > real),C:set_variable]: (denotational_Vagree @ (stateinterpol @ A @ B @ C) @ A @ C))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_Vagree__stateinterpol)).
% 132.99/59.63 thf(506,plain,((! [A:(variable > real),B:(variable > real),C:set_variable]: (denotational_Vagree @ (stateinterpol @ A @ B @ C) @ (A) @ C))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])).
% 132.99/59.63 thf(1065,plain,(! [A:(variable > real)] : (((denota1419872369iation @ A) = (^ [B:(variable > real)]: (denota1419872369iation @ B @ A))))),inference(func_ext,[status(esa)],[598])).
% 132.99/59.63 thf(131,axiom,((! [A:(variable > real),B:(variable > real)]: ((denota1419872369iation @ A @ B @ bot_bot_set_variable) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_Uvariation__empty)).
% 132.99/59.63 thf(696,plain,((! [A:(variable > real),B:(variable > real)]: ((denota1419872369iation @ (A) @ (B) @ bot_bot_set_variable) = ((A) = (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])).
% 132.99/59.63 thf(282,plain,(! [A:trm] : (((the_trm @ (some_trm @ A)) = A))),inference(cnf,[status(esa)],[281])).
% 132.99/59.63 thf(283,plain,(! [A:trm] : (((the_trm @ (some_trm @ A)) = A))),inference(lifteq,[status(thm)],[282])).
% 132.99/59.63 thf(1409,plain,(((^ [A:(variable > real),B:(variable > real),C:set_variable]: ! [D:variable]: ((~ (member_variable @ D @ C)) => ((A @ D) = (B @ D)))) = (^ [A:(variable > real),B:(variable > real)]: (denota1419872369iation @ B @ A))) | ((denota1419872369iation) != (denota1419872369iation))),inference(paramod_ordered,[status(thm)],[679,598])).
% 132.99/59.63 thf(1410,plain,(((^ [A:(variable > real),B:(variable > real),C:set_variable]: ! [D:variable]: ((~ (member_variable @ D @ C)) => ((A @ D) = (B @ D)))) = (^ [A:(variable > real),B:(variable > real)]: (denota1419872369iation @ B @ A)))),inference(pattern_uni,[status(thm)],[1409:[]])).
% 132.99/59.63 thf(766,plain,(! [A:set_variable] : (((sup_sup_set_variable @ A @ A) = A))),inference(cnf,[status(esa)],[765])).
% 132.99/59.63 thf(767,plain,(! [A:set_variable] : (((sup_sup_set_variable @ A @ A) = A))),inference(lifteq,[status(thm)],[766])).
% 132.99/59.63 thf(8051,plain,(((f @ zero_zero_real @ sk132) != (omega @ sk132))),inference(func_ext,[status(esa)],[8047])).
% 132.99/59.63 thf(177,axiom,((! [A:set_variable_real,B:(variable > real),C:set_variable,D:set_variable_real]: (((static_selectlike @ A @ B @ (uminus1851247844riable @ C)) = (static_selectlike @ D @ B @ (uminus1851247844riable @ C))) = (! [E:(variable > real)]: ((denota1419872369iation @ E @ B @ C) => ((member_variable_real @ E @ A) = (member_variable_real @ E @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_selectlike__equal__cocond)).
% 132.99/59.63 thf(839,plain,((! [A:set_variable_real,B:(variable > real),C:set_variable,D:set_variable_real]: (((static_selectlike @ A @ (B) @ (uminus1851247844riable @ C)) = (static_selectlike @ D @ (B) @ (uminus1851247844riable @ C))) = (! [E:(variable > real)]: ((denota1419872369iation @ (E) @ (B) @ C) => ((member_variable_real @ (E) @ A) = (member_variable_real @ (E) @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])).
% 132.99/59.63 thf(44,axiom,((! [A:(variable > real),B:(variable > real)]: ((stateinterpol @ A @ B @ (statediff @ A @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_stateinterpol__diff)).
% 132.99/59.63 thf(427,plain,((! [A:(variable > real),B:(variable > real)]: ((stateinterpol @ A @ B @ (statediff @ A @ B)) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])).
% 132.99/59.63 thf(236,axiom,((! [A:trm,B:denotational_interp,C:trm,D:denotational_interp,E:char,F:(real > (variable > real))]: ((? [G:(variable > real)]: ((denota1419872369iation @ G @ (F @ zero_zero_real) @ (insert_variable @ (rVar @ E) @ (insert_variable @ (dVar @ E) @ bot_bot_set_variable))) & ((denota1863255036rm_sem @ D @ C @ G) != (denota1863255036rm_sem @ B @ A @ G)))) = ((denota1419872369iation @ (rr @ A @ B @ C @ D @ E @ F) @ (F @ zero_zero_real) @ (insert_variable @ (rVar @ E) @ (insert_variable @ (dVar @ E) @ bot_bot_set_variable))) & ((denota1863255036rm_sem @ D @ C @ (rr @ A @ B @ C @ D @ E @ F)) != (denota1863255036rm_sem @ B @ A @ (rr @ A @ B @ C @ D @ E @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155__092_060open_062_092_060forall_062x0_Ax1_Ax2_Ax3_Ax4_Ax5_O_A_I_092_060exists_062v6_O_AUvariation_Av6_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_Av6_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_Av6_J_A_061_A_IUvariation_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_Ix5_A0_J_A_123RVar_Ax4_M_ADVar_Ax4_125_A_092_060and_062_Aterm__sem_Ax3_Ax2_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_A_092_060noteq_062_Aterm__sem_Ax1_Ax0_A_Irr_Ax0_Ax1_Ax2_Ax3_Ax4_Ax5_J_J_092_060close_062)).
% 132.99/59.63 thf(1019,plain,((! [A:trm,B:denotational_interp,C:trm,D:denotational_interp,E:char,F:(real > (variable > real))]: ((? [G:(variable > real)]: ((denota1419872369iation @ (G) @ (F @ zero_zero_real) @ (insert_variable @ (rVar @ E) @ (insert_variable @ (dVar @ E) @ bot_bot_set_variable))) & ~ ((denota1863255036rm_sem @ D @ C @ (G)) = (denota1863255036rm_sem @ B @ A @ (G))))) = ((denota1419872369iation @ (rr @ A @ B @ C @ D @ E @ F) @ (F @ zero_zero_real) @ (insert_variable @ (rVar @ E) @ (insert_variable @ (dVar @ E) @ bot_bot_set_variable))) & ~ ((denota1863255036rm_sem @ D @ C @ (rr @ A @ B @ C @ D @ E @ F)) = (denota1863255036rm_sem @ B @ A @ (rr @ A @ B @ C @ D @ E @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])).
% 132.99/59.63 thf(77,axiom,((! [A:(variable > real),B:set_variable_real,C:set_variable_real]: ((member_variable_real @ A @ (inf_in1556002680e_real @ B @ C)) = ((member_variable_real @ A @ B) & (member_variable_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_Int__iff)).
% 132.99/59.63 thf(528,plain,((! [A:(variable > real),B:set_variable_real,C:set_variable_real]: ((member_variable_real @ (A) @ (inf_in1556002680e_real @ B @ C)) = ((member_variable_real @ (A) @ B) & (member_variable_real @ (A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])).
% 132.99/59.63 thf(458,plain,(! [A:nat] : (((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(cnf,[status(esa)],[457])).
% 132.99/59.63 thf(459,plain,(! [A:nat] : (((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(lifteq,[status(thm)],[458])).
% 132.99/59.63 thf(172,axiom,((! [A:variable,B:set_variable]: ((member_variable @ A @ B) => (? [C:set_variable]: ((B = (insert_variable @ A @ C)) & ~ (member_variable @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_mk__disjoint__insert)).
% 132.99/59.63 thf(822,plain,((! [A:variable,B:set_variable]: ((member_variable @ A @ B) => (? [C:set_variable]: ((B = (insert_variable @ A @ C)) & ~ (member_variable @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])).
% 132.99/59.63 thf(5039,plain,(! [B:variable,A:set_variable] : (((uminus1851247844riable @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ A)))) != (uminus1851247844riable @ bot_bot_set_variable)) | (A != (set_option_variable2 @ (some_variable @ B))))),inference(paramod_ordered,[status(thm)],[543,4956])).
% 132.99/59.63 thf(5040,plain,(! [A:variable] : (((uminus1851247844riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ (set_option_variable2 @ (some_variable @ A)))))) != (uminus1851247844riable @ bot_bot_set_variable)))),inference(pattern_uni,[status(thm)],[5039:[bind(A, $thf(set_option_variable2 @ (some_variable @ D))),bind(B, $thf(D))]])).
% 132.99/59.63 thf(5046,plain,(! [A:variable] : (((uminus1851247844riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ (set_option_variable2 @ (some_variable @ A)))))) != (uminus1851247844riable @ bot_bot_set_variable)))),inference(simp,[status(thm)],[5040])).
% 132.99/59.63 thf(199,axiom,((! [A:set_variable]: ((sup_sup_set_variable @ A @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_sup_Oidem)).
% 132.99/59.63 thf(908,plain,((! [A:set_variable]: ((sup_sup_set_variable @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])).
% 132.99/59.63 thf(227,axiom,((! [A:set_variable,B:set_variable]: (((sup_sup_set_variable @ A @ B) = bot_bot_set_variable) = ((A = bot_bot_set_variable) & (B = bot_bot_set_variable))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_sup__bot_Oeq__neutr__iff)).
% 132.99/59.63 thf(992,plain,((! [A:set_variable,B:set_variable]: (((sup_sup_set_variable @ A @ B) = bot_bot_set_variable) = ((A = bot_bot_set_variable) & (B = bot_bot_set_variable))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])).
% 132.99/59.63 thf(166,axiom,((! [A:set_variable]: ((? [B:variable]: (member_variable @ B @ A)) = (A != bot_bot_set_variable)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_ex__in__conv)).
% 132.99/59.63 thf(803,plain,((! [A:set_variable]: ((? [B:variable]: (member_variable @ B @ A)) = (~ (A = bot_bot_set_variable))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])).
% 132.99/59.63 thf(57,axiom,((! [A:variable,B:set_option_variable]: ((member_variable @ A @ (these_variable @ B)) = (member814448204riable @ (some_variable @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_in__these__eq)).
% 132.99/59.63 thf(469,plain,((! [A:variable,B:set_option_variable]: ((member_variable @ A @ (these_variable @ B)) = (member814448204riable @ (some_variable @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])).
% 132.99/59.63 thf(305,plain,(! [C:trm,B:(trm > $o),A:option_trm] : ((member_trm @ (sk8 @ (B) @ A) @ (set_option_trm2 @ A)) | (~ (A = (some_trm @ C))) | (B @ C))),inference(cnfConj,[status(thm)],[304])).
% 132.99/59.63 thf(308,plain,(! [C:trm,B:(trm > $o),A:option_trm] : ((A != (some_trm @ C)) | (member_trm @ (sk8 @ (B) @ A) @ (set_option_trm2 @ A)) | (B @ C))),inference(lifteq,[status(thm)],[305])).
% 132.99/59.63 thf(309,plain,(! [B:trm,A:(trm > $o)] : ((member_trm @ (sk8 @ (A) @ (some_trm @ B)) @ (set_option_trm2 @ (some_trm @ B))) | (A @ B))),inference(simp,[status(thm)],[308])).
% 132.99/59.63 thf(789,plain,(((insert_variable) = (^ [A:variable]: (sup_sup_set_variable @ (insert_variable @ A @ bot_bot_set_variable))))),inference(lifteq,[status(thm)],[788])).
% 132.99/59.63 thf(1246,plain,(! [A:variable] : (((insert_variable @ A) = (sup_sup_set_variable @ (insert_variable @ A @ bot_bot_set_variable))))),inference(func_ext,[status(esa)],[789])).
% 132.99/59.63 thf(4742,plain,(! [A:variable] : (((insert_variable @ A) = (sup_sup_set_variable @ (set_option_variable2 @ (some_variable @ A)))))),inference(rewrite,[status(thm)],[1246,784])).
% 132.99/59.63 thf(113,axiom,((! [A:set_variable,B:set_variable,C:set_variable]: ((sup_sup_set_variable @ A @ (sup_sup_set_variable @ B @ C)) = (sup_sup_set_variable @ B @ (sup_sup_set_variable @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_inf__sup__aci_I7_J)).
% 132.99/59.63 thf(639,plain,((! [A:set_variable,B:set_variable,C:set_variable]: ((sup_sup_set_variable @ A @ (sup_sup_set_variable @ B @ C)) = (sup_sup_set_variable @ B @ (sup_sup_set_variable @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])).
% 132.99/59.63 thf(98,axiom,((! [A:variable,B:set_variable]: ((~ (member_variable @ A @ B)) => (member_variable @ A @ (uminus1851247844riable @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_ComplI)).
% 132.99/59.63 thf(592,plain,((! [A:variable,B:set_variable]: ((~ (member_variable @ A @ B)) => (member_variable @ A @ (uminus1851247844riable @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])).
% 132.99/59.63 thf(363,plain,(! [D:trm,C:trm,B:set_variable,A:produc1418842292n_game] : (((uSubst516392818stappt @ A @ B @ (times @ C @ D)) = (uSubst918876924Timeso @ (uSubst516392818stappt @ A @ B @ C) @ (uSubst516392818stappt @ A @ B @ D))))),inference(cnf,[status(esa)],[362])).
% 132.99/59.63 thf(364,plain,(! [D:trm,C:trm,B:set_variable,A:produc1418842292n_game] : (((uSubst516392818stappt @ A @ B @ (times @ C @ D)) = (uSubst918876924Timeso @ (uSubst516392818stappt @ A @ B @ C) @ (uSubst516392818stappt @ A @ B @ D))))),inference(lifteq,[status(thm)],[363])).
% 132.99/59.63 thf(191,axiom,((! [A:set_variable,B:set_variable]: (((sup_sup_set_variable @ A @ B) = bot_bot_set_variable) = ((A = bot_bot_set_variable) & (B = bot_bot_set_variable))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_Un__empty)).
% 132.99/59.63 thf(882,plain,((! [A:set_variable,B:set_variable]: (((sup_sup_set_variable @ A @ B) = bot_bot_set_variable) = ((A = bot_bot_set_variable) & (B = bot_bot_set_variable))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])).
% 132.99/59.63 thf(2344,plain,(! [B:variable,A:set_variable] : ((is_sin155454833riable @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ A)))) | (A != (collect_variable @ (^ [C:variable]: (member_variable @ C @ (collect_variable @ (^ [D:variable]: (member_variable @ D @ (insert_variable @ B @ bot_bot_set_variable)))))))))),inference(paramod_ordered,[status(thm)],[543,2092])).
% 132.99/59.63 thf(2345,plain,(! [A:variable] : ((is_sin155454833riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (collect_variable @ (^ [D:variable]: (member_variable @ D @ (insert_variable @ A @ bot_bot_set_variable))))))))))))),inference(pattern_uni,[status(thm)],[2344:[bind(A, $thf(collect_variable @ (^ [C:variable]: (member_variable @ C @ (collect_variable @ (^ [D:variable]: (member_variable @ D @ (insert_variable @ B @ bot_bot_set_variable)))))))),bind(B, $thf(B))]])).
% 132.99/59.63 thf(2360,plain,(! [A:variable] : ((is_sin155454833riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (collect_variable @ (^ [D:variable]: (member_variable @ D @ (insert_variable @ A @ bot_bot_set_variable))))))))))))),inference(simp,[status(thm)],[2345])).
% 132.99/59.63 thf(6141,plain,(! [A:variable] : ((is_sin155454833riable @ (collect_variable @ (^ [B:variable]: (member_variable @ B @ (collect_variable @ (^ [C:variable]: (member_variable @ C @ (collect_variable @ (^ [D:variable]: (member_variable @ D @ (set_option_variable2 @ (some_variable @ A)))))))))))))),inference(rewrite,[status(thm)],[2360,784])).
% 132.99/59.63 thf(921,plain,(((is_empty_variable) = (^ [A:set_variable]: (A = bot_bot_set_variable)))),inference(lifteq,[status(thm)],[920])).
% 132.99/59.63 thf(1088,plain,(! [A:set_variable] : (((is_empty_variable @ A) = (A = bot_bot_set_variable)))),inference(func_ext,[status(esa)],[921])).
% 132.99/59.63 thf(20739,plain,(($false)),inference(e,[status(thm)],[809,365,347,518,962,555,645,892,628,249,481,352,4931,582,1005,683,730,1068,741,873,440,597,1041,861,3848,1608,384,500,715,945,340,538,930,5146,472,829,898,1001,2491,436,782,6872,973,885,651,257,724,2328,570,4866,4956,785,372,619,344,357,2466,460,1330,2444,917,702,3845,2488,559,3840,1087,421,284,289,261,817,902,475,492,756,376,253,485,514,4871,806,905,353,966,280,5096,774,396,660,1242,293,956,411,988,920,678,270,4888,793,925,1338,534,714,512,439,1047,798,746,302,598,820,424,693,788,815,729,260,349,467,1365,625,879,665,889,493,710,842,1032,252,583,830,2498,3831,2515,317,980,356,420,857,256,488,3846,554,5791,686,642,637,489,706,1016,590,679,970,622,997,738,654,911,721,9990,779,503,1050,457,266,508,311,541,657,765,1035,1515,1026,3841,718,888,298,965,430,4872,5451,264,745,296,444,375,601,5016,573,584,562,402,286,579,545,281,6774,936,313,611,713,1058,466,704,947,3302,350,672,604,406,2493,784,1011,736,8047,318,616,271,599,362,567,494,552,594,621,668,330,1029,895,943,1022,2329,932,521,983,399,608,563,4918,922,959,2171,768,3838,827,394,986,267,851,426,927,255,939,342,754,836,3849,490,675,531,944,795,2318,680,648,487,1081,749,690,1025,4864,872,707,414,3833,739,409,263,1053,6912,441,463,338,576,359,544,1038,370,951,3847,744,703,656,613,600,864,727,978,1008,314,497,876,845,976,524,759,771,250,465,5386,4873,699,1062,10428,418,995,946,258,433,929,5672,549,287,290,914,1077,478,999,752,447,833,4811,3837,854,790,373,867,273,564,506,358,1065,696,3843,1610,283,1410,767,8051,839,464,332,427,860,1019,528,459,723,822,5046,277,871,369,908,992,803,469,354,309,543,4742,639,592,364,882,6141,491,1088])).
% 132.99/59.63 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 132.99/59.63 % [INFO] Killing All external provers ...
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