0.06/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.06/0.12	% Command  : lash -P picomus -M modes -p tstp -t %d %s
0.12/0.33	% Computer : n015.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 : 1440
0.12/0.33	% WCLimit  : 180
0.12/0.33	% DateTime : Mon Jul  3 08:01:09 EDT 2023
0.12/0.33	% CPUTime  : 
0.18/0.51	% SZS status Theorem
0.18/0.51	% Mode: cade22sinegrackle2x6978
0.18/0.51	% Steps: 1869
0.18/0.51	% SZS output start Proof
0.18/0.51	thf(ty_denota231621370t_unit, type, denota231621370t_unit : $tType).
0.18/0.51	thf(ty_real, type, real : $tType).
0.18/0.51	thf(ty_set_Sum_sum_c_c, type, set_Sum_sum_c_c : $tType).
0.18/0.51	thf(ty_set_Su1783761653um_b_c, type, set_Su1783761653um_b_c : $tType).
0.18/0.51	thf(ty_a, type, a : $tType).
0.18/0.51	thf(ty_finite1398487019real_c, type, finite1398487019real_c : $tType).
0.18/0.51	thf(ty_sum_su737395349um_b_c, type, sum_su737395349um_b_c : $tType).
0.18/0.51	thf(ty_set_a, type, set_a : $tType).
0.18/0.51	thf(ty_produc190496183real_c, type, produc190496183real_c : $tType).
0.18/0.51	thf(ty_trm_a_c, type, trm_a_c : $tType).
0.18/0.51	thf(ty_plus_a_c, type, plus_a_c : (trm_a_c>trm_a_c>trm_a_c)).
0.18/0.51	thf(ty_nu2, type, nu2 : produc190496183real_c).
0.18/0.51	thf(ty_static_FVDiff_a_c, type, static_FVDiff_a_c : (trm_a_c>set_Sum_sum_c_c)).
0.18/0.51	thf(ty_produc314122909real_c, type, produc314122909real_c : (produc190496183real_c>finite1398487019real_c)).
0.18/0.51	thf(ty_member_a, type, member_a : (a>set_a>$o)).
0.18/0.51	thf(ty_j, type, j : denota231621370t_unit).
0.18/0.51	thf(ty_denota229585092_a_b_c, type, denota229585092_a_b_c : (denota231621370t_unit>trm_a_c>finite1398487019real_c>finite1398487019real_c>real)).
0.18/0.51	thf(ty_t1, type, t1 : trm_a_c).
0.18/0.51	thf(ty_denota1997846518gree_c, type, denota1997846518gree_c : (produc190496183real_c>produc190496183real_c>set_Sum_sum_c_c>$o)).
0.18/0.51	thf(ty_nu, type, nu : produc190496183real_c).
0.18/0.51	thf(ty_static_SIGT_a_c, type, static_SIGT_a_c : (trm_a_c>set_a)).
0.18/0.51	thf(ty_produc2010422875real_c, type, produc2010422875real_c : (produc190496183real_c>finite1398487019real_c)).
0.18/0.51	thf(ty_collec2086029184um_b_c, type, collec2086029184um_b_c : ((sum_su737395349um_b_c>$o)>set_Su1783761653um_b_c)).
0.18/0.51	thf(ty_i, type, i : denota231621370t_unit).
0.18/0.51	thf(ty_sum_In2139678582um_b_c, type, sum_In2139678582um_b_c : (a>sum_su737395349um_b_c)).
0.18/0.51	thf(ty_t2, type, t2 : trm_a_c).
0.18/0.51	thf(ty_denota69106024_a_b_c, type, denota69106024_a_b_c : (denota231621370t_unit>denota231621370t_unit>set_Su1783761653um_b_c>$o)).
0.18/0.51	thf(sP1,plain,sP1 <=> (![X1:produc190496183real_c]:(![X2:produc190496183real_c]:(![X3:trm_a_c]:(![X4:trm_a_c]:((((denota1997846518gree_c @ X1) @ X2) @ (static_FVDiff_a_c @ ((plus_a_c @ X3) @ X4))) => (((denota1997846518gree_c @ X1) @ X2) @ (static_FVDiff_a_c @ X4))))))),introduced(definition,[new_symbols(definition,[sP1])])).
0.18/0.51	thf(sP2,plain,sP2 <=> (((denota1997846518gree_c @ nu) @ nu2) @ (static_FVDiff_a_c @ t2)),introduced(definition,[new_symbols(definition,[sP2])])).
0.18/0.51	thf(sP3,plain,sP3 <=> ((((denota1997846518gree_c @ nu) @ nu2) @ (static_FVDiff_a_c @ ((plus_a_c @ t1) @ t2))) => sP2),introduced(definition,[new_symbols(definition,[sP3])])).
0.18/0.51	thf(sP4,plain,sP4 <=> (![X1:trm_a_c]:((((denota1997846518gree_c @ nu) @ nu2) @ (static_FVDiff_a_c @ ((plus_a_c @ t1) @ X1))) => (((denota1997846518gree_c @ nu) @ nu2) @ (static_FVDiff_a_c @ X1)))),introduced(definition,[new_symbols(definition,[sP4])])).
0.18/0.51	thf(sP5,plain,sP5 <=> (((denota1997846518gree_c @ nu) @ nu2) @ (static_FVDiff_a_c @ ((plus_a_c @ t1) @ t2))),introduced(definition,[new_symbols(definition,[sP5])])).
0.18/0.51	thf(sP6,plain,sP6 <=> (![X1:trm_a_c]:(![X2:trm_a_c]:((((denota1997846518gree_c @ nu) @ nu2) @ (static_FVDiff_a_c @ ((plus_a_c @ X1) @ X2))) => (((denota1997846518gree_c @ nu) @ nu2) @ (static_FVDiff_a_c @ X2))))),introduced(definition,[new_symbols(definition,[sP6])])).
0.18/0.51	thf(sP7,plain,sP7 <=> (((denota69106024_a_b_c @ i) @ j) @ (collec2086029184um_b_c @ (^[X1:sum_su737395349um_b_c]:(~((![X2:a]:((X1 = (sum_In2139678582um_b_c @ X2)) => (~(((member_a @ X2) @ (static_SIGT_a_c @ t2))))))))))),introduced(definition,[new_symbols(definition,[sP7])])).
0.18/0.51	thf(sP8,plain,sP8 <=> (((denota1997846518gree_c @ nu) @ nu2) @ (static_FVDiff_a_c @ t1)),introduced(definition,[new_symbols(definition,[sP8])])).
0.18/0.51	thf(sP9,plain,sP9 <=> (![X1:produc190496183real_c]:(![X2:trm_a_c]:(![X3:trm_a_c]:((((denota1997846518gree_c @ nu) @ X1) @ (static_FVDiff_a_c @ ((plus_a_c @ X2) @ X3))) => (((denota1997846518gree_c @ nu) @ X1) @ (static_FVDiff_a_c @ X3)))))),introduced(definition,[new_symbols(definition,[sP9])])).
0.18/0.51	thf(conj_0,conjecture,sP2).
0.18/0.51	thf(h0,negated_conjecture,(~(sP2)),inference(assume_negation,[status(cth)],[conj_0])).
0.18/0.51	thf(h1,assumption,(~(sP8)),introduced(assumption,[])).
0.18/0.51	thf(h2,assumption,((((denota69106024_a_b_c @ i) @ j) @ (collec2086029184um_b_c @ (^[X1:sum_su737395349um_b_c]:(~((![X2:a]:(((member_a @ X2) @ (static_SIGT_a_c @ t1)) => (~((X1 = (sum_In2139678582um_b_c @ X2))))))))))) => (((((denota229585092_a_b_c @ i) @ t1) @ (produc2010422875real_c @ nu)) @ (produc314122909real_c @ nu)) = ((((denota229585092_a_b_c @ j) @ t1) @ (produc2010422875real_c @ nu2)) @ (produc314122909real_c @ nu2)))),introduced(assumption,[])).
0.18/0.51	thf(h3,assumption,(~(sP2)),introduced(assumption,[])).
0.18/0.51	thf(h4,assumption,(sP7 => (((((denota229585092_a_b_c @ i) @ t2) @ (produc2010422875real_c @ nu)) @ (produc314122909real_c @ nu)) = ((((denota229585092_a_b_c @ j) @ t2) @ (produc2010422875real_c @ nu2)) @ (produc314122909real_c @ nu2)))),introduced(assumption,[])).
0.18/0.51	thf(fact_3_agree1,axiom,sP8).
0.18/0.51	thf(1,plain,$false,inference(tab_conflict,[status(thm),assumptions([h3,h1,h0])],[fact_3_agree1,h1])).
0.18/0.51	thf(h5,assumption,(~(sP7)),introduced(assumption,[])).
0.18/0.51	thf(h6,assumption,(((((denota229585092_a_b_c @ i) @ t2) @ (produc2010422875real_c @ nu)) @ (produc314122909real_c @ nu)) = ((((denota229585092_a_b_c @ j) @ t2) @ (produc2010422875real_c @ nu2)) @ (produc314122909real_c @ nu2))),introduced(assumption,[])).
0.18/0.51	thf(fact_34_IA2,axiom,sP7).
0.18/0.51	thf(2,plain,$false,inference(tab_conflict,[status(thm),assumptions([h5,h4,h1,h0])],[fact_34_IA2,h5])).
0.18/0.51	thf(3,plain,$false,inference(tab_conflict,[status(thm),assumptions([h6,h4,h1,h0])],[fact_3_agree1,h1])).
0.18/0.51	thf(4,plain,$false,inference(tab_imp,[status(thm),assumptions([h4,h1,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[h4,2,3,h5,h6])).
0.18/0.51	thf(fact_22_IH2,axiom,(sP2 => (sP7 => (((((denota229585092_a_b_c @ i) @ t2) @ (produc2010422875real_c @ nu)) @ (produc314122909real_c @ nu)) = ((((denota229585092_a_b_c @ j) @ t2) @ (produc2010422875real_c @ nu2)) @ (produc314122909real_c @ nu2)))))).
0.18/0.51	thf(5,plain,$false,inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[fact_22_IH2,1,4,h3,h4])).
0.18/0.51	thf(h7,assumption,(~((((denota69106024_a_b_c @ i) @ j) @ (collec2086029184um_b_c @ (^[X1:sum_su737395349um_b_c]:(~((![X2:a]:(((member_a @ X2) @ (static_SIGT_a_c @ t1)) => (~((X1 = (sum_In2139678582um_b_c @ X2))))))))))))),introduced(assumption,[])).
0.18/0.51	thf(h8,assumption,(((((denota229585092_a_b_c @ i) @ t1) @ (produc2010422875real_c @ nu)) @ (produc314122909real_c @ nu)) = ((((denota229585092_a_b_c @ j) @ t1) @ (produc2010422875real_c @ nu2)) @ (produc314122909real_c @ nu2))),introduced(assumption,[])).
0.18/0.51	thf(6,plain,((~(sP3) | ~(sP5)) | sP2),inference(prop_rule,[status(thm)],[])).
0.18/0.51	thf(7,plain,(~(sP4) | sP3),inference(all_rule,[status(thm)],[])).
0.18/0.51	thf(8,plain,(~(sP6) | sP4),inference(all_rule,[status(thm)],[])).
0.18/0.51	thf(9,plain,(~(sP9) | sP6),inference(all_rule,[status(thm)],[])).
0.18/0.51	thf(10,plain,(~(sP1) | sP9),inference(all_rule,[status(thm)],[])).
0.18/0.51	thf(fact_2_agree,axiom,sP5).
0.18/0.51	thf(fact_1_agree__plus2,axiom,sP1).
0.18/0.51	thf(11,plain,$false,inference(prop_unsat,[status(thm),assumptions([h3,h7,h2,h0])],[6,7,8,9,10,fact_2_agree,fact_1_agree__plus2,h3])).
0.18/0.51	thf(12,plain,$false,inference(tab_conflict,[status(thm),assumptions([h5,h4,h7,h2,h0])],[fact_34_IA2,h5])).
0.18/0.51	thf(13,plain,((~(sP3) | ~(sP5)) | sP2),inference(prop_rule,[status(thm)],[])).
0.18/0.51	thf(14,plain,(~(sP4) | sP3),inference(all_rule,[status(thm)],[])).
0.18/0.51	thf(15,plain,(~(sP6) | sP4),inference(all_rule,[status(thm)],[])).
0.18/0.51	thf(16,plain,(~(sP9) | sP6),inference(all_rule,[status(thm)],[])).
0.18/0.51	thf(17,plain,(~(sP1) | sP9),inference(all_rule,[status(thm)],[])).
0.18/0.51	thf(18,plain,$false,inference(prop_unsat,[status(thm),assumptions([h6,h4,h7,h2,h0])],[13,14,15,16,17,fact_2_agree,fact_1_agree__plus2,h0])).
0.18/0.51	thf(19,plain,$false,inference(tab_imp,[status(thm),assumptions([h4,h7,h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[h4,12,18,h5,h6])).
0.18/0.51	thf(20,plain,$false,inference(tab_imp,[status(thm),assumptions([h7,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[fact_22_IH2,11,19,h3,h4])).
0.18/0.51	thf(21,plain,((~(sP3) | ~(sP5)) | sP2),inference(prop_rule,[status(thm)],[])).
0.18/0.51	thf(22,plain,(~(sP4) | sP3),inference(all_rule,[status(thm)],[])).
0.18/0.51	thf(23,plain,(~(sP6) | sP4),inference(all_rule,[status(thm)],[])).
0.18/0.51	thf(24,plain,(~(sP9) | sP6),inference(all_rule,[status(thm)],[])).
0.18/0.51	thf(25,plain,(~(sP1) | sP9),inference(all_rule,[status(thm)],[])).
0.18/0.51	thf(26,plain,$false,inference(prop_unsat,[status(thm),assumptions([h3,h8,h2,h0])],[21,22,23,24,25,fact_2_agree,fact_1_agree__plus2,h3])).
0.18/0.51	thf(27,plain,$false,inference(tab_conflict,[status(thm),assumptions([h5,h4,h8,h2,h0])],[fact_34_IA2,h5])).
0.18/0.51	thf(28,plain,((~(sP3) | ~(sP5)) | sP2),inference(prop_rule,[status(thm)],[])).
0.18/0.51	thf(29,plain,(~(sP4) | sP3),inference(all_rule,[status(thm)],[])).
0.18/0.51	thf(30,plain,(~(sP6) | sP4),inference(all_rule,[status(thm)],[])).
0.18/0.51	thf(31,plain,(~(sP9) | sP6),inference(all_rule,[status(thm)],[])).
0.18/0.51	thf(32,plain,(~(sP1) | sP9),inference(all_rule,[status(thm)],[])).
0.18/0.51	thf(33,plain,$false,inference(prop_unsat,[status(thm),assumptions([h6,h4,h8,h2,h0])],[28,29,30,31,32,fact_2_agree,fact_1_agree__plus2,h0])).
0.18/0.51	thf(34,plain,$false,inference(tab_imp,[status(thm),assumptions([h4,h8,h2,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[h4,27,33,h5,h6])).
0.18/0.51	thf(35,plain,$false,inference(tab_imp,[status(thm),assumptions([h8,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[fact_22_IH2,26,34,h3,h4])).
0.18/0.51	thf(36,plain,$false,inference(tab_imp,[status(thm),assumptions([h2,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h2,20,35,h7,h8])).
0.18/0.51	thf(fact_35_IH1,axiom,(sP8 => ((((denota69106024_a_b_c @ i) @ j) @ (collec2086029184um_b_c @ (^[X1:sum_su737395349um_b_c]:(~((![X2:a]:(((member_a @ X2) @ (static_SIGT_a_c @ t1)) => (~((X1 = (sum_In2139678582um_b_c @ X2))))))))))) => (((((denota229585092_a_b_c @ i) @ t1) @ (produc2010422875real_c @ nu)) @ (produc314122909real_c @ nu)) = ((((denota229585092_a_b_c @ j) @ t1) @ (produc2010422875real_c @ nu2)) @ (produc314122909real_c @ nu2)))))).
0.18/0.51	thf(37,plain,$false,inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_35_IH1,5,36,h1,h2])).
0.18/0.51	thf(0,theorem,sP2,inference(contra,[status(thm),contra(discharge,[h0])],[37,h0])).
0.18/0.51	% SZS output end Proof
0.18/0.52	EOF