0.12/0.12	% Problem  : SLH0350^1 : TPTP v8.2.0. Released v8.2.0.
0.12/0.12	% Command  : lash -P picomus -M modes -p tstp -t %d %s
0.12/0.33	% Computer : n028.cluster.edu
0.12/0.33	% Model    : x86_64 x86_64
0.12/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory   : 8042.1875MB
0.12/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit : 30
0.12/0.33	% WCLimit  : 30
0.12/0.33	% DateTime : Mon Jul  3 04:35:28 EDT 2023
0.12/0.33	% CPUTime  : 
16.12/16.38	% SZS status Theorem
16.12/16.38	% Mode: cade22sinegrackle2xfaf3
16.12/16.38	% Steps: 11080
16.12/16.38	% SZS output start Proof
16.12/16.38	thf(ty_joinTree_a, type, joinTree_a : $tType).
16.12/16.38	thf(ty_real, type, real : $tType).
16.12/16.38	thf(ty_a, type, a : $tType).
16.12/16.38	thf(ty_r, type, r : joinTree_a).
16.12/16.38	thf(ty_mirror_a, type, mirror_a : (joinTree_a>joinTree_a)).
16.12/16.38	thf(ty_card_a, type, card_a : ((a>real)>(a>a>real)>joinTree_a>real)).
16.12/16.38	thf(ty_ord_less_eq_real, type, ord_less_eq_real : (real>real>$o)).
16.12/16.38	thf(ty_sel_symm_a, type, sel_symm_a : ((a>a>real)>$o)).
16.12/16.38	thf(ty_join_a, type, join_a : (joinTree_a>joinTree_a>joinTree_a)).
16.12/16.38	thf(ty_zero_zero_real, type, zero_zero_real : real).
16.12/16.38	thf(ty_f, type, f : (a>a>real)).
16.12/16.38	thf(ty_times_times_real, type, times_times_real : (real>real>real)).
16.12/16.38	thf(ty_ord_less_real, type, ord_less_real : (real>real>$o)).
16.12/16.38	thf(ty_l, type, l : joinTree_a).
16.12/16.38	thf(ty_cf, type, cf : (a>real)).
16.12/16.38	thf(sP1,plain,sP1 <=> ((((card_a @ cf) @ f) @ l) = (((card_a @ cf) @ f) @ (mirror_a @ l))),introduced(definition,[new_symbols(definition,[sP1])])).
16.12/16.38	thf(sP2,plain,sP2 <=> ((((card_a @ cf) @ f) @ (mirror_a @ l)) = (((card_a @ cf) @ f) @ l)),introduced(definition,[new_symbols(definition,[sP2])])).
16.12/16.38	thf(sP3,plain,sP3 <=> ((sel_symm_a @ f) => ((((card_a @ cf) @ f) @ (mirror_a @ r)) = (((card_a @ cf) @ f) @ r))),introduced(definition,[new_symbols(definition,[sP3])])).
16.12/16.38	thf(sP4,plain,sP4 <=> ((ord_less_eq_real @ (((card_a @ cf) @ f) @ ((join_a @ l) @ r))) @ ((times_times_real @ (((card_a @ cf) @ f) @ r)) @ (((card_a @ cf) @ f) @ l))),introduced(definition,[new_symbols(definition,[sP4])])).
16.12/16.38	thf(sP5,plain,sP5 <=> $false,introduced(definition,[new_symbols(definition,[sP5])])).
16.12/16.38	thf(sP6,plain,sP6 <=> (((ord_less_eq_real @ (((card_a @ cf) @ f) @ (mirror_a @ ((join_a @ l) @ r)))) @ ((times_times_real @ (((card_a @ cf) @ f) @ (mirror_a @ r))) @ (((card_a @ cf) @ f) @ (mirror_a @ l)))) => (~(((ord_less_real @ zero_zero_real) @ (((card_a @ cf) @ f) @ (mirror_a @ ((join_a @ l) @ r))))))),introduced(definition,[new_symbols(definition,[sP6])])).
16.12/16.38	thf(sP7,plain,sP7 <=> ((((card_a @ cf) @ f) @ (mirror_a @ ((join_a @ l) @ r))) = (((card_a @ cf) @ f) @ ((join_a @ l) @ r))),introduced(definition,[new_symbols(definition,[sP7])])).
16.12/16.38	thf(sP8,plain,sP8 <=> ((ord_less_eq_real @ (((card_a @ cf) @ f) @ (mirror_a @ ((join_a @ l) @ r)))) @ ((times_times_real @ (((card_a @ cf) @ f) @ (mirror_a @ r))) @ (((card_a @ cf) @ f) @ (mirror_a @ l)))),introduced(definition,[new_symbols(definition,[sP8])])).
16.12/16.38	thf(sP9,plain,sP9 <=> ((~(sP6)) = (~((sP4 => (~(((ord_less_real @ zero_zero_real) @ (((card_a @ cf) @ f) @ ((join_a @ l) @ r))))))))),introduced(definition,[new_symbols(definition,[sP9])])).
16.12/16.38	thf(sP10,plain,sP10 <=> ((((card_a @ cf) @ f) @ (mirror_a @ r)) = (((card_a @ cf) @ f) @ r)),introduced(definition,[new_symbols(definition,[sP10])])).
16.12/16.38	thf(sP11,plain,sP11 <=> ((sel_symm_a @ f) => sP2),introduced(definition,[new_symbols(definition,[sP11])])).
16.12/16.38	thf(sP12,plain,sP12 <=> (((times_times_real @ (((card_a @ cf) @ f) @ r)) @ (((card_a @ cf) @ f) @ l)) = ((times_times_real @ (((card_a @ cf) @ f) @ (mirror_a @ r))) @ (((card_a @ cf) @ f) @ (mirror_a @ l)))),introduced(definition,[new_symbols(definition,[sP12])])).
16.12/16.38	thf(sP13,plain,sP13 <=> ((((card_a @ cf) @ f) @ ((join_a @ l) @ r)) = (((card_a @ cf) @ f) @ (mirror_a @ ((join_a @ l) @ r)))),introduced(definition,[new_symbols(definition,[sP13])])).
16.12/16.38	thf(sP14,plain,sP14 <=> (((times_times_real @ (((card_a @ cf) @ f) @ (mirror_a @ r))) @ (((card_a @ cf) @ f) @ (mirror_a @ l))) = ((times_times_real @ (((card_a @ cf) @ f) @ r)) @ (((card_a @ cf) @ f) @ l))),introduced(definition,[new_symbols(definition,[sP14])])).
16.12/16.38	thf(sP15,plain,sP15 <=> (![X1:a>real]:(![X2:joinTree_a]:((sel_symm_a @ f) => ((((card_a @ X1) @ f) @ (mirror_a @ X2)) = (((card_a @ X1) @ f) @ X2))))),introduced(definition,[new_symbols(definition,[sP15])])).
16.12/16.38	thf(sP16,plain,sP16 <=> (sel_symm_a @ f),introduced(definition,[new_symbols(definition,[sP16])])).
16.12/16.38	thf(sP17,plain,sP17 <=> ((ord_less_real @ zero_zero_real) @ (((card_a @ cf) @ f) @ (mirror_a @ ((join_a @ l) @ r)))),introduced(definition,[new_symbols(definition,[sP17])])).
16.12/16.38	thf(sP18,plain,sP18 <=> (![X1:a>a>real]:(![X2:a>real]:(![X3:joinTree_a]:((sel_symm_a @ X1) => ((((card_a @ X2) @ X1) @ (mirror_a @ X3)) = (((card_a @ X2) @ X1) @ X3)))))),introduced(definition,[new_symbols(definition,[sP18])])).
16.12/16.38	thf(sP19,plain,sP19 <=> (sP16 => sP7),introduced(definition,[new_symbols(definition,[sP19])])).
16.12/16.38	thf(sP20,plain,sP20 <=> (![X1:joinTree_a]:(sP16 => ((((card_a @ cf) @ f) @ (mirror_a @ X1)) = (((card_a @ cf) @ f) @ X1)))),introduced(definition,[new_symbols(definition,[sP20])])).
16.12/16.38	thf(sP21,plain,sP21 <=> ((((card_a @ cf) @ f) @ r) = (((card_a @ cf) @ f) @ (mirror_a @ r))),introduced(definition,[new_symbols(definition,[sP21])])).
16.12/16.38	thf(sP22,plain,sP22 <=> (sP4 => (~(((ord_less_real @ zero_zero_real) @ (((card_a @ cf) @ f) @ ((join_a @ l) @ r)))))),introduced(definition,[new_symbols(definition,[sP22])])).
16.12/16.38	thf(sP23,plain,sP23 <=> ((ord_less_real @ zero_zero_real) @ (((card_a @ cf) @ f) @ ((join_a @ l) @ r))),introduced(definition,[new_symbols(definition,[sP23])])).
16.12/16.38	thf(conj_0,conjecture,sP9).
16.12/16.38	thf(h0,negated_conjecture,(~(sP9)),inference(assume_negation,[status(cth)],[conj_0])).
16.12/16.38	thf(1,plain,((sP12 | ~(sP1)) | ~(sP21)),inference(prop_rule,[status(thm)],[])).
16.12/16.38	thf(2,plain,(~(sP12) | sP14),inference(symeq,[status(thm)],[])).
16.12/16.38	thf(3,plain,(~(sP7) | sP13),inference(symeq,[status(thm)],[])).
16.12/16.38	thf(4,plain,(~(sP2) | sP1),inference(symeq,[status(thm)],[])).
16.12/16.38	thf(5,plain,(~(sP10) | sP21),inference(symeq,[status(thm)],[])).
16.12/16.38	thf(6,plain,(((~(sP17) | sP23) | ~(sP7)) | sP5),inference(mating_rule,[status(thm)],[])).
16.12/16.38	thf(7,plain,(((~(sP8) | sP4) | ~(sP14)) | ~(sP7)),inference(mating_rule,[status(thm)],[])).
16.12/16.38	thf(8,plain,(((~(sP23) | sP17) | ~(sP13)) | sP5),inference(mating_rule,[status(thm)],[])).
16.12/16.38	thf(9,plain,(((~(sP4) | sP8) | ~(sP12)) | ~(sP13)),inference(mating_rule,[status(thm)],[])).
16.12/16.38	thf(10,plain,((~(sP19) | ~(sP16)) | sP7),inference(prop_rule,[status(thm)],[])).
16.12/16.38	thf(11,plain,((~(sP11) | ~(sP16)) | sP2),inference(prop_rule,[status(thm)],[])).
16.12/16.38	thf(12,plain,((~(sP3) | ~(sP16)) | sP10),inference(prop_rule,[status(thm)],[])).
16.12/16.38	thf(13,plain,~(sP5),inference(prop_rule,[status(thm)],[])).
16.12/16.38	thf(14,plain,(~(sP20) | sP19),inference(all_rule,[status(thm)],[])).
16.12/16.38	thf(15,plain,(~(sP20) | sP11),inference(all_rule,[status(thm)],[])).
16.12/16.38	thf(16,plain,(~(sP20) | sP3),inference(all_rule,[status(thm)],[])).
16.12/16.38	thf(17,plain,((~(sP22) | ~(sP4)) | ~(sP23)),inference(prop_rule,[status(thm)],[])).
16.12/16.38	thf(18,plain,(sP22 | sP23),inference(prop_rule,[status(thm)],[])).
16.12/16.38	thf(19,plain,(sP22 | sP4),inference(prop_rule,[status(thm)],[])).
16.12/16.38	thf(20,plain,(~(sP15) | sP20),inference(all_rule,[status(thm)],[])).
16.12/16.38	thf(21,plain,((~(sP6) | ~(sP8)) | ~(sP17)),inference(prop_rule,[status(thm)],[])).
16.12/16.38	thf(22,plain,(sP6 | sP17),inference(prop_rule,[status(thm)],[])).
16.12/16.38	thf(23,plain,(sP6 | sP8),inference(prop_rule,[status(thm)],[])).
16.12/16.38	thf(24,plain,((sP9 | sP6) | sP22),inference(prop_rule,[status(thm)],[])).
16.12/16.38	thf(25,plain,((sP9 | ~(sP6)) | ~(sP22)),inference(prop_rule,[status(thm)],[])).
16.12/16.38	thf(26,plain,(~(sP18) | sP15),inference(all_rule,[status(thm)],[])).
16.12/16.38	thf(fact_569_mirror__card__eq,axiom,sP18).
16.12/16.38	thf(fact_224_Join_Oprems_I1_J,axiom,sP16).
16.12/16.38	thf(27,plain,$false,inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,h0,fact_569_mirror__card__eq,fact_224_Join_Oprems_I1_J])).
16.12/16.38	thf(0,theorem,sP9,inference(contra,[status(thm),contra(discharge,[h0])],[27,h0])).
16.12/16.38	% SZS output end Proof
16.12/16.38	EOF