0.10/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.11 % Command : lash -P picomus -M modes -p tstp -t %d %s 0.11/0.32 % Computer : n021.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 960 0.11/0.32 % WCLimit : 120 0.11/0.32 % DateTime : Tue Aug 9 04:41:05 EDT 2022 0.11/0.32 % CPUTime : 9.96/10.09 % SZS status Theorem 9.96/10.09 % Mode: cade22grackle2x6978 9.96/10.09 % Steps: 250906 9.96/10.09 % SZS output start Proof 9.96/10.09 thf(ty_nat, type, nat : $tType). 9.96/10.09 thf(ty_real, type, real : $tType). 9.96/10.09 thf(ty_genClo1015804716orrect, type, genClo1015804716orrect : (nat>real>$o)). 9.96/10.09 thf(ty_q, type, q : nat). 9.96/10.09 thf(ty_p, type, p : nat). 9.96/10.09 thf(ty_plus_plus_nat, type, plus_plus_nat : (nat>nat>nat)). 9.96/10.09 thf(ty_genClo1163638703lle_te, type, genClo1163638703lle_te : (nat>nat>real)). 9.96/10.09 thf(ty_ord_less_eq_real, type, ord_less_eq_real : (real>real>$o)). 9.96/10.09 thf(ty_abs_abs_real, type, abs_abs_real : (real>real)). 9.96/10.09 thf(ty_one_one_nat, type, one_one_nat : nat). 9.96/10.09 thf(ty_minus_minus_real, type, minus_minus_real : (real>real>real)). 9.96/10.09 thf(ty_genClo1278781456e_beta, type, genClo1278781456e_beta : real). 9.96/10.09 thf(ty_i, type, i : nat). 9.96/10.09 thf(ty_plus_plus_real, type, plus_plus_real : (real>real>real)). 9.96/10.09 thf(sP1,plain,sP1 <=> (![X1:real]:(![X2:real]:(((ord_less_eq_real @ ((minus_minus_real @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat))) @ X1)) @ X2) = ((ord_less_eq_real @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat))) @ ((plus_plus_real @ X2) @ X1))))),introduced(definition,[new_symbols(definition,[sP1])])). 9.96/10.09 thf(sP2,plain,sP2 <=> (![X1:real]:(![X2:real]:(((ord_less_eq_real @ ((minus_minus_real @ ((genClo1163638703lle_te @ q) @ ((plus_plus_nat @ i) @ one_one_nat))) @ X1)) @ X2) = ((ord_less_eq_real @ ((genClo1163638703lle_te @ q) @ ((plus_plus_nat @ i) @ one_one_nat))) @ ((plus_plus_real @ X2) @ X1))))),introduced(definition,[new_symbols(definition,[sP2])])). 9.96/10.09 thf(sP3,plain,sP3 <=> ((genClo1015804716orrect @ q) @ ((genClo1163638703lle_te @ q) @ ((plus_plus_nat @ i) @ one_one_nat))),introduced(definition,[new_symbols(definition,[sP3])])). 9.96/10.09 thf(sP4,plain,sP4 <=> ((ord_less_eq_real @ ((minus_minus_real @ ((genClo1163638703lle_te @ q) @ ((plus_plus_nat @ i) @ one_one_nat))) @ genClo1278781456e_beta)) @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat))),introduced(definition,[new_symbols(definition,[sP4])])). 9.96/10.09 thf(sP5,plain,sP5 <=> (sP3 => (~(((genClo1015804716orrect @ p) @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat)))))),introduced(definition,[new_symbols(definition,[sP5])])). 9.96/10.09 thf(sP6,plain,sP6 <=> (![X1:real]:(![X2:real]:(![X3:real]:(((ord_less_eq_real @ (abs_abs_real @ ((minus_minus_real @ X1) @ X2))) @ X3) = (~((((ord_less_eq_real @ ((minus_minus_real @ X2) @ X3)) @ X1) => (~(((ord_less_eq_real @ X1) @ ((plus_plus_real @ X2) @ X3))))))))))),introduced(definition,[new_symbols(definition,[sP6])])). 9.96/10.09 thf(sP7,plain,sP7 <=> (![X1:real]:(![X2:real]:(![X3:real]:(((ord_less_eq_real @ ((minus_minus_real @ X1) @ X2)) @ X3) = ((ord_less_eq_real @ X1) @ ((plus_plus_real @ X3) @ X2)))))),introduced(definition,[new_symbols(definition,[sP7])])). 9.96/10.09 thf(sP8,plain,sP8 <=> (![X1:real]:(![X2:real]:(((ord_less_eq_real @ (abs_abs_real @ ((minus_minus_real @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat))) @ X1))) @ X2) = (~((((ord_less_eq_real @ ((minus_minus_real @ X1) @ X2)) @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat))) => (~(((ord_less_eq_real @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat))) @ ((plus_plus_real @ X1) @ X2)))))))))),introduced(definition,[new_symbols(definition,[sP8])])). 9.96/10.09 thf(sP9,plain,sP9 <=> ((ord_less_eq_real @ (abs_abs_real @ ((minus_minus_real @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat))) @ ((genClo1163638703lle_te @ q) @ ((plus_plus_nat @ i) @ one_one_nat))))) @ genClo1278781456e_beta),introduced(definition,[new_symbols(definition,[sP9])])). 9.96/10.09 thf(sP10,plain,sP10 <=> (![X1:real]:(((ord_less_eq_real @ (abs_abs_real @ ((minus_minus_real @ ((genClo1163638703lle_te @ q) @ ((plus_plus_nat @ i) @ one_one_nat))) @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat))))) @ X1) = (~((((ord_less_eq_real @ ((minus_minus_real @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat))) @ X1)) @ ((genClo1163638703lle_te @ q) @ ((plus_plus_nat @ i) @ one_one_nat))) => (~(((ord_less_eq_real @ ((genClo1163638703lle_te @ q) @ ((plus_plus_nat @ i) @ one_one_nat))) @ ((plus_plus_real @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat))) @ X1))))))))),introduced(definition,[new_symbols(definition,[sP10])])). 9.96/10.09 thf(sP11,plain,sP11 <=> ((genClo1015804716orrect @ p) @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat))),introduced(definition,[new_symbols(definition,[sP11])])). 9.96/10.09 thf(sP12,plain,sP12 <=> (sP9 = (~((sP4 => (~(((ord_less_eq_real @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat))) @ ((plus_plus_real @ ((genClo1163638703lle_te @ q) @ ((plus_plus_nat @ i) @ one_one_nat))) @ genClo1278781456e_beta)))))))),introduced(definition,[new_symbols(definition,[sP12])])). 9.96/10.09 thf(sP13,plain,sP13 <=> (![X1:real]:(![X2:real]:(((ord_less_eq_real @ (abs_abs_real @ ((minus_minus_real @ ((genClo1163638703lle_te @ q) @ ((plus_plus_nat @ i) @ one_one_nat))) @ X1))) @ X2) = (~((((ord_less_eq_real @ ((minus_minus_real @ X1) @ X2)) @ ((genClo1163638703lle_te @ q) @ ((plus_plus_nat @ i) @ one_one_nat))) => (~(((ord_less_eq_real @ ((genClo1163638703lle_te @ q) @ ((plus_plus_nat @ i) @ one_one_nat))) @ ((plus_plus_real @ X1) @ X2)))))))))),introduced(definition,[new_symbols(definition,[sP13])])). 9.96/10.09 thf(sP14,plain,sP14 <=> ((ord_less_eq_real @ ((genClo1163638703lle_te @ q) @ ((plus_plus_nat @ i) @ one_one_nat))) @ ((plus_plus_real @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat))) @ genClo1278781456e_beta)),introduced(definition,[new_symbols(definition,[sP14])])). 9.96/10.09 thf(sP15,plain,sP15 <=> (![X1:nat]:(![X2:nat]:((~((((genClo1015804716orrect @ q) @ ((genClo1163638703lle_te @ q) @ X2)) => (~(((genClo1015804716orrect @ X1) @ ((genClo1163638703lle_te @ X1) @ X2))))))) => ((ord_less_eq_real @ (abs_abs_real @ ((minus_minus_real @ ((genClo1163638703lle_te @ q) @ X2)) @ ((genClo1163638703lle_te @ X1) @ X2)))) @ genClo1278781456e_beta)))),introduced(definition,[new_symbols(definition,[sP15])])). 9.96/10.09 thf(sP16,plain,sP16 <=> (![X1:nat]:(![X2:nat]:(![X3:nat]:((~((((genClo1015804716orrect @ X1) @ ((genClo1163638703lle_te @ X1) @ X3)) => (~(((genClo1015804716orrect @ X2) @ ((genClo1163638703lle_te @ X2) @ X3))))))) => ((ord_less_eq_real @ (abs_abs_real @ ((minus_minus_real @ ((genClo1163638703lle_te @ X1) @ X3)) @ ((genClo1163638703lle_te @ X2) @ X3)))) @ genClo1278781456e_beta))))),introduced(definition,[new_symbols(definition,[sP16])])). 9.96/10.09 thf(sP17,plain,sP17 <=> (![X1:real]:(((ord_less_eq_real @ (abs_abs_real @ ((minus_minus_real @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat))) @ ((genClo1163638703lle_te @ q) @ ((plus_plus_nat @ i) @ one_one_nat))))) @ X1) = (~((((ord_less_eq_real @ ((minus_minus_real @ ((genClo1163638703lle_te @ q) @ ((plus_plus_nat @ i) @ one_one_nat))) @ X1)) @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat))) => (~(((ord_less_eq_real @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat))) @ ((plus_plus_real @ ((genClo1163638703lle_te @ q) @ ((plus_plus_nat @ i) @ one_one_nat))) @ X1))))))))),introduced(definition,[new_symbols(definition,[sP17])])). 9.96/10.09 thf(sP18,plain,sP18 <=> ((ord_less_eq_real @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat))) @ ((plus_plus_real @ ((genClo1163638703lle_te @ q) @ ((plus_plus_nat @ i) @ one_one_nat))) @ genClo1278781456e_beta)),introduced(definition,[new_symbols(definition,[sP18])])). 9.96/10.09 thf(sP19,plain,sP19 <=> (![X1:real]:(((ord_less_eq_real @ ((minus_minus_real @ ((genClo1163638703lle_te @ q) @ ((plus_plus_nat @ i) @ one_one_nat))) @ genClo1278781456e_beta)) @ X1) = ((ord_less_eq_real @ ((genClo1163638703lle_te @ q) @ ((plus_plus_nat @ i) @ one_one_nat))) @ ((plus_plus_real @ X1) @ genClo1278781456e_beta)))),introduced(definition,[new_symbols(definition,[sP19])])). 9.96/10.09 thf(sP20,plain,sP20 <=> (![X1:nat]:((~((((genClo1015804716orrect @ q) @ ((genClo1163638703lle_te @ q) @ X1)) => (~(((genClo1015804716orrect @ p) @ ((genClo1163638703lle_te @ p) @ X1))))))) => ((ord_less_eq_real @ (abs_abs_real @ ((minus_minus_real @ ((genClo1163638703lle_te @ q) @ X1)) @ ((genClo1163638703lle_te @ p) @ X1)))) @ genClo1278781456e_beta))),introduced(definition,[new_symbols(definition,[sP20])])). 9.96/10.09 thf(sP21,plain,sP21 <=> (sP4 = sP14),introduced(definition,[new_symbols(definition,[sP21])])). 9.96/10.09 thf(sP22,plain,sP22 <=> (((ord_less_eq_real @ (abs_abs_real @ ((minus_minus_real @ ((genClo1163638703lle_te @ q) @ ((plus_plus_nat @ i) @ one_one_nat))) @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat))))) @ genClo1278781456e_beta) = (~((((ord_less_eq_real @ ((minus_minus_real @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat))) @ genClo1278781456e_beta)) @ ((genClo1163638703lle_te @ q) @ ((plus_plus_nat @ i) @ one_one_nat))) => (~(sP14)))))),introduced(definition,[new_symbols(definition,[sP22])])). 9.96/10.09 thf(sP23,plain,sP23 <=> (((ord_less_eq_real @ ((minus_minus_real @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat))) @ genClo1278781456e_beta)) @ ((genClo1163638703lle_te @ q) @ ((plus_plus_nat @ i) @ one_one_nat))) = sP18),introduced(definition,[new_symbols(definition,[sP23])])). 9.96/10.09 thf(sP24,plain,sP24 <=> ((~(sP5)) => ((ord_less_eq_real @ (abs_abs_real @ ((minus_minus_real @ ((genClo1163638703lle_te @ q) @ ((plus_plus_nat @ i) @ one_one_nat))) @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat))))) @ genClo1278781456e_beta)),introduced(definition,[new_symbols(definition,[sP24])])). 9.96/10.09 thf(sP25,plain,sP25 <=> ((ord_less_eq_real @ (abs_abs_real @ ((minus_minus_real @ ((genClo1163638703lle_te @ q) @ ((plus_plus_nat @ i) @ one_one_nat))) @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat))))) @ genClo1278781456e_beta),introduced(definition,[new_symbols(definition,[sP25])])). 9.96/10.09 thf(sP26,plain,sP26 <=> (sP4 => (~(sP18))),introduced(definition,[new_symbols(definition,[sP26])])). 9.96/10.09 thf(sP27,plain,sP27 <=> (((ord_less_eq_real @ ((minus_minus_real @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat))) @ genClo1278781456e_beta)) @ ((genClo1163638703lle_te @ q) @ ((plus_plus_nat @ i) @ one_one_nat))) => (~(sP14))),introduced(definition,[new_symbols(definition,[sP27])])). 9.96/10.09 thf(sP28,plain,sP28 <=> (![X1:real]:(((ord_less_eq_real @ ((minus_minus_real @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat))) @ genClo1278781456e_beta)) @ X1) = ((ord_less_eq_real @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat))) @ ((plus_plus_real @ X1) @ genClo1278781456e_beta)))),introduced(definition,[new_symbols(definition,[sP28])])). 9.96/10.09 thf(sP29,plain,sP29 <=> ((ord_less_eq_real @ ((minus_minus_real @ ((genClo1163638703lle_te @ p) @ ((plus_plus_nat @ i) @ one_one_nat))) @ genClo1278781456e_beta)) @ ((genClo1163638703lle_te @ q) @ ((plus_plus_nat @ i) @ one_one_nat))),introduced(definition,[new_symbols(definition,[sP29])])). 9.96/10.09 thf(conj_0,conjecture,sP9). 9.96/10.09 thf(h0,negated_conjecture,(~(sP9)),inference(assume_negation,[status(cth)],[conj_0])). 9.96/10.09 thf(1,plain,((~(sP5) | ~(sP3)) | ~(sP11)),inference(prop_rule,[status(thm)],[])). 9.96/10.09 thf(2,plain,((~(sP24) | sP5) | sP25),inference(prop_rule,[status(thm)],[])). 9.96/10.09 thf(3,plain,(~(sP20) | sP24),inference(all_rule,[status(thm)],[])). 9.96/10.09 thf(4,plain,(~(sP15) | sP20),inference(all_rule,[status(thm)],[])). 9.96/10.09 thf(5,plain,((~(sP26) | ~(sP4)) | ~(sP18)),inference(prop_rule,[status(thm)],[])). 9.96/10.09 thf(6,plain,((~(sP12) | sP9) | sP26),inference(prop_rule,[status(thm)],[])). 9.96/10.09 thf(7,plain,(sP27 | sP14),inference(prop_rule,[status(thm)],[])). 9.96/10.09 thf(8,plain,(sP27 | sP29),inference(prop_rule,[status(thm)],[])). 9.96/10.09 thf(9,plain,(~(sP17) | sP12),inference(all_rule,[status(thm)],[])). 9.96/10.09 thf(10,plain,((~(sP22) | ~(sP25)) | ~(sP27)),inference(prop_rule,[status(thm)],[])). 9.96/10.09 thf(11,plain,(~(sP8) | sP17),inference(all_rule,[status(thm)],[])). 9.96/10.09 thf(12,plain,(~(sP10) | sP22),inference(all_rule,[status(thm)],[])). 9.96/10.09 thf(13,plain,((~(sP23) | ~(sP29)) | sP18),inference(prop_rule,[status(thm)],[])). 9.96/10.09 thf(14,plain,(~(sP28) | sP23),inference(all_rule,[status(thm)],[])). 9.96/10.09 thf(15,plain,(~(sP1) | sP28),inference(all_rule,[status(thm)],[])). 9.96/10.09 thf(16,plain,((~(sP21) | sP4) | ~(sP14)),inference(prop_rule,[status(thm)],[])). 9.96/10.09 thf(17,plain,(~(sP6) | sP8),inference(all_rule,[status(thm)],[])). 9.96/10.09 thf(18,plain,(~(sP7) | sP1),inference(all_rule,[status(thm)],[])). 9.96/10.09 thf(19,plain,(~(sP13) | sP10),inference(all_rule,[status(thm)],[])). 9.96/10.09 thf(20,plain,(~(sP19) | sP21),inference(all_rule,[status(thm)],[])). 9.96/10.09 thf(21,plain,(~(sP2) | sP19),inference(all_rule,[status(thm)],[])). 9.96/10.09 thf(22,plain,(~(sP16) | sP15),inference(all_rule,[status(thm)],[])). 9.96/10.09 thf(23,plain,(~(sP6) | sP13),inference(all_rule,[status(thm)],[])). 9.96/10.09 thf(24,plain,(~(sP7) | sP2),inference(all_rule,[status(thm)],[])). 9.96/10.09 thf(fact_1_corr__p,axiom,sP11). 9.96/10.09 thf(fact_192_diff__le__eq,axiom,sP7). 9.96/10.09 thf(fact_2_corr__q__tq,axiom,sP3). 9.96/10.09 thf(fact_0_rts2b,axiom,sP16). 9.96/10.09 thf(fact_199_abs__diff__le__iff,axiom,sP6). 9.96/10.09 thf(25,plain,$false,inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,fact_1_corr__p,fact_192_diff__le__eq,fact_2_corr__q__tq,h0,fact_0_rts2b,fact_199_abs__diff__le__iff])). 9.96/10.09 thf(0,theorem,sP9,inference(contra,[status(thm),contra(discharge,[h0])],[25,h0])). 9.96/10.09 % SZS output end Proof 9.96/10.09 EOF