0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s 0.12/0.34 Computer : n005.cluster.edu 0.12/0.34 Model : x86_64 x86_64 0.12/0.34 CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 RAMPerCPU : 8042.1875MB 0.12/0.34 OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 1440 0.12/0.34 % DateTime : Mon Jul 3 03:28:15 EDT 2023 0.12/0.34 % CPUTime : 123.46/122.97 % SZS status Theorem 123.46/122.97 % Mode: mode94:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=3.:SINE_DEPTH=0 123.46/122.97 % Inferences: 179 123.46/122.97 % SZS output start Proof 123.46/122.97 thf(ty_a, type, a : $tType). 123.46/122.97 thf(ty_nat, type, nat : $tType). 123.46/122.97 thf(ty_set_Product_prod_a_a, type, set_Product_prod_a_a : $tType). 123.46/122.97 thf(ty_set_a, type, set_a : $tType). 123.46/122.97 thf(ty_member_a, type, member_a : (a>set_a>$o)). 123.46/122.97 thf(ty_finite_finite_a, type, finite_finite_a : (set_a>$o)). 123.46/122.97 thf(ty_relation, type, relation : set_Product_prod_a_a). 123.46/122.97 thf(ty_finite_card_a, type, finite_card_a : (set_a>nat)). 123.46/122.97 thf(ty_prefer1676310729than_a, type, prefer1676310729than_a : (a>set_a>set_Product_prod_a_a>set_a)). 123.46/122.97 thf(ty_y, type, y : a). 123.46/122.97 thf(ty_ord_less_eq_set_a, type, ord_less_eq_set_a : (set_a>set_a>$o)). 123.46/122.97 thf(ty_finite179568208od_a_a, type, finite179568208od_a_a : (set_Product_prod_a_a>$o)). 123.46/122.97 thf(ty_ord_less_eq_nat, type, ord_less_eq_nat : (nat>nat>$o)). 123.46/122.97 thf(ty_carrier, type, carrier : set_a). 123.46/122.97 thf(ty_x, type, x : a). 123.46/122.97 thf(sP1,plain,sP1 <=> (((ord_less_eq_set_a @ (((prefer1676310729than_a @ y) @ carrier) @ relation)) @ (((prefer1676310729than_a @ x) @ carrier) @ relation)) => (((ord_less_eq_nat @ (finite_card_a @ (((prefer1676310729than_a @ x) @ carrier) @ relation))) @ (finite_card_a @ (((prefer1676310729than_a @ y) @ carrier) @ relation))) => ((((prefer1676310729than_a @ y) @ carrier) @ relation) = (((prefer1676310729than_a @ x) @ carrier) @ relation)))),introduced(definition,[new_symbols(definition,[sP1])])). 123.46/122.97 thf(sP2,plain,sP2 <=> (![X1:set_a]:(![X2:set_a]:((finite_finite_a @ X1) => (((ord_less_eq_set_a @ X2) @ X1) => (((ord_less_eq_nat @ (finite_card_a @ X1)) @ (finite_card_a @ X2)) => (X2 = X1)))))),introduced(definition,[new_symbols(definition,[sP2])])). 123.46/122.97 thf(sP3,plain,sP3 <=> ((ord_less_eq_nat @ (finite_card_a @ (((prefer1676310729than_a @ x) @ carrier) @ relation))) @ (finite_card_a @ (((prefer1676310729than_a @ y) @ carrier) @ relation))),introduced(definition,[new_symbols(definition,[sP3])])). 123.46/122.97 thf(sP4,plain,sP4 <=> ((ord_less_eq_set_a @ (((prefer1676310729than_a @ x) @ carrier) @ relation)) @ (((prefer1676310729than_a @ y) @ carrier) @ relation)),introduced(definition,[new_symbols(definition,[sP4])])). 123.46/122.97 thf(sP5,plain,sP5 <=> (![X1:a]:(![X2:a]:((~(((ord_less_eq_set_a @ (((prefer1676310729than_a @ X2) @ carrier) @ relation)) @ (((prefer1676310729than_a @ X1) @ carrier) @ relation)))) => ((ord_less_eq_set_a @ (((prefer1676310729than_a @ X1) @ carrier) @ relation)) @ (((prefer1676310729than_a @ X2) @ carrier) @ relation))))),introduced(definition,[new_symbols(definition,[sP5])])). 123.46/122.97 thf(sP6,plain,sP6 <=> (![X1:set_a]:(((((prefer1676310729than_a @ y) @ carrier) @ relation) = X1) => ((ord_less_eq_set_a @ X1) @ (((prefer1676310729than_a @ y) @ carrier) @ relation)))),introduced(definition,[new_symbols(definition,[sP6])])). 123.46/122.97 thf(sP7,plain,sP7 <=> ((member_a @ x) @ carrier),introduced(definition,[new_symbols(definition,[sP7])])). 123.46/122.97 thf(sP8,plain,sP8 <=> (finite_finite_a @ (((prefer1676310729than_a @ x) @ carrier) @ relation)),introduced(definition,[new_symbols(definition,[sP8])])). 123.46/122.97 thf(sP9,plain,sP9 <=> ((ord_less_eq_set_a @ (((prefer1676310729than_a @ y) @ carrier) @ relation)) @ (((prefer1676310729than_a @ x) @ carrier) @ relation)),introduced(definition,[new_symbols(definition,[sP9])])). 123.46/122.97 thf(sP10,plain,sP10 <=> (![X1:set_a]:(![X2:set_a]:((X1 = X2) => ((ord_less_eq_set_a @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP10])])). 123.46/122.97 thf(sP11,plain,sP11 <=> ((((prefer1676310729than_a @ y) @ carrier) @ relation) = (((prefer1676310729than_a @ x) @ carrier) @ relation)),introduced(definition,[new_symbols(definition,[sP11])])). 123.46/122.97 thf(sP12,plain,sP12 <=> (sP7 => sP8),introduced(definition,[new_symbols(definition,[sP12])])). 123.46/122.97 thf(sP13,plain,sP13 <=> (sP3 => sP11),introduced(definition,[new_symbols(definition,[sP13])])). 123.46/122.97 thf(sP14,plain,sP14 <=> (sP11 => sP4),introduced(definition,[new_symbols(definition,[sP14])])). 123.46/122.97 thf(sP15,plain,sP15 <=> (![X1:a]:(((member_a @ X1) @ carrier) => (finite_finite_a @ (((prefer1676310729than_a @ X1) @ carrier) @ relation)))),introduced(definition,[new_symbols(definition,[sP15])])). 123.46/122.97 thf(sP16,plain,sP16 <=> (![X1:a]:((~(((ord_less_eq_set_a @ (((prefer1676310729than_a @ X1) @ carrier) @ relation)) @ (((prefer1676310729than_a @ x) @ carrier) @ relation)))) => ((ord_less_eq_set_a @ (((prefer1676310729than_a @ x) @ carrier) @ relation)) @ (((prefer1676310729than_a @ X1) @ carrier) @ relation)))),introduced(definition,[new_symbols(definition,[sP16])])). 123.46/122.97 thf(sP17,plain,sP17 <=> (![X1:set_a]:(sP8 => (((ord_less_eq_set_a @ X1) @ (((prefer1676310729than_a @ x) @ carrier) @ relation)) => (((ord_less_eq_nat @ (finite_card_a @ (((prefer1676310729than_a @ x) @ carrier) @ relation))) @ (finite_card_a @ X1)) => (X1 = (((prefer1676310729than_a @ x) @ carrier) @ relation)))))),introduced(definition,[new_symbols(definition,[sP17])])). 123.46/122.97 thf(sP18,plain,sP18 <=> ((~(sP9)) => sP4),introduced(definition,[new_symbols(definition,[sP18])])). 123.46/122.97 thf(sP19,plain,sP19 <=> (sP8 => sP1),introduced(definition,[new_symbols(definition,[sP19])])). 123.46/122.97 thf(sP20,plain,sP20 <=> (finite_finite_a @ carrier),introduced(definition,[new_symbols(definition,[sP20])])). 123.46/122.97 thf(conj_0,conjecture,sP4). 123.46/122.97 thf(h0,negated_conjecture,(~(sP4)),inference(assume_negation,[status(cth)],[conj_0])). 123.46/122.97 thf(h1,assumption,(~(sP20)),introduced(assumption,[])). 123.46/122.97 thf(h2,assumption,(finite179568208od_a_a @ relation),introduced(assumption,[])). 123.46/122.97 thf(fact_7__092_060open_062finite_Acarrier_092_060close_062,axiom,sP20). 123.46/122.97 thf(1,plain,$false,inference(tab_conflict,[status(thm),assumptions([h1,h0])],[fact_7__092_060open_062finite_Acarrier_092_060close_062,h1])). 123.46/122.97 thf(2,plain,((~(sP12) | ~(sP7)) | sP8),inference(prop_rule,[status(thm)],[])). 123.46/122.97 thf(3,plain,(~(sP17) | sP19),inference(all_rule,[status(thm)],[])). 123.46/122.97 thf(4,plain,((~(sP19) | ~(sP8)) | sP1),inference(prop_rule,[status(thm)],[])). 123.46/122.97 thf(5,plain,((~(sP1) | ~(sP9)) | sP13),inference(prop_rule,[status(thm)],[])). 123.46/122.97 thf(6,plain,((~(sP13) | ~(sP3)) | sP11),inference(prop_rule,[status(thm)],[])). 123.46/122.97 thf(7,plain,(~(sP2) | sP17),inference(all_rule,[status(thm)],[])). 123.46/122.97 thf(8,plain,(~(sP10) | sP6),inference(all_rule,[status(thm)],[])). 123.46/122.97 thf(9,plain,(~(sP6) | sP14),inference(all_rule,[status(thm)],[])). 123.46/122.97 thf(10,plain,((~(sP14) | ~(sP11)) | sP4),inference(prop_rule,[status(thm)],[])). 123.46/122.97 thf(11,plain,(~(sP15) | sP12),inference(all_rule,[status(thm)],[])). 123.46/122.97 thf(12,plain,(~(sP16) | sP18),inference(all_rule,[status(thm)],[])). 123.46/122.97 thf(13,plain,((~(sP18) | sP9) | sP4),inference(prop_rule,[status(thm)],[])). 123.46/122.97 thf(14,plain,(~(sP5) | sP16),inference(all_rule,[status(thm)],[])). 123.46/122.97 thf(fact_4_nbt__nest,axiom,sP5). 123.46/122.97 thf(fact_15_fnt__carrier__fnt__nbt,axiom,sP15). 123.46/122.97 thf(fact_150_equalityD2,axiom,sP10). 123.46/122.97 thf(fact_211_card__seteq,axiom,sP2). 123.46/122.97 thf(fact_3__092_060open_062card_A_Ino__better__than_Ax_Acarrier_Arelation_J_A_092_060le_062_Acard_A_Ino__better__than_Ay_Acarrier_Arelation_J_092_060close_062,axiom,sP3). 123.46/122.97 thf(fact_1_assms_I1_J,axiom,sP7). 123.46/122.97 thf(15,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h0])],[2,3,4,5,6,7,8,9,10,11,12,13,14,fact_4_nbt__nest,h0,fact_15_fnt__carrier__fnt__nbt,fact_150_equalityD2,fact_211_card__seteq,fact_3__092_060open_062card_A_Ino__better__than_Ax_Acarrier_Arelation_J_A_092_060le_062_Acard_A_Ino__better__than_Ay_Acarrier_Arelation_J_092_060close_062,fact_1_assms_I1_J])). 123.46/122.97 thf(fact_105_fnt__carrier__fnt__rel,axiom,(sP20 => (finite179568208od_a_a @ relation))). 123.46/122.97 thf(16,plain,$false,inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_105_fnt__carrier__fnt__rel,1,15,h1,h2])). 123.46/122.97 thf(0,theorem,sP4,inference(contra,[status(thm),contra(discharge,[h0])],[16,h0])). 123.46/122.97 % SZS output end Proof 123.46/122.97 EOF