TSTP Solution File: ITP133^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP133^1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 00:29:13 EDT 2022
% Result : Theorem 100.04s 99.92s
% Output : Proof 100.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP133^1 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jun 3 08:26:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 100.04/99.92 % SZS status Theorem
% 100.04/99.92 % Mode: mode498:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=1.:SINE_DEPTH=0
% 100.04/99.92 % Inferences: 2425
% 100.04/99.92 % SZS output start Proof
% 100.04/99.92 thf(ty_set_nat, type, set_nat : $tType).
% 100.04/99.92 thf(ty_nat, type, nat : $tType).
% 100.04/99.92 thf(ty_p, type, p : (nat>nat)).
% 100.04/99.92 thf(ty_set_ord_atMost_nat, type, set_ord_atMost_nat : (nat>set_nat)).
% 100.04/99.92 thf(ty_eigen__7, type, eigen__7 : nat).
% 100.04/99.92 thf(ty_eigen__0, type, eigen__0 : nat).
% 100.04/99.92 thf(ty_times_times_nat, type, times_times_nat : (nat>nat>nat)).
% 100.04/99.92 thf(ty_zero_zero_nat, type, zero_zero_nat : nat).
% 100.04/99.92 thf(ty_groups1842438620at_nat, type, groups1842438620at_nat : ((nat>nat)>set_nat>nat)).
% 100.04/99.92 thf(ty_one_one_nat, type, one_one_nat : nat).
% 100.04/99.92 thf(ty_ord_less_eq_nat, type, ord_less_eq_nat : (nat>nat>$o)).
% 100.04/99.92 thf(sP1,plain,sP1 <=> (p = (^[X1:nat]:zero_zero_nat)),introduced(definition,[new_symbols(definition,[sP1])])).
% 100.04/99.92 thf(sP2,plain,sP2 <=> ((p @ eigen__7) = zero_zero_nat),introduced(definition,[new_symbols(definition,[sP2])])).
% 100.04/99.92 thf(sP3,plain,sP3 <=> (![X1:nat]:((p @ X1) = zero_zero_nat)),introduced(definition,[new_symbols(definition,[sP3])])).
% 100.04/99.92 thf(conj_0,conjecture,((~(((![X1:nat]:((~(((p @ X1) = zero_zero_nat))) => (~((((ord_less_eq_nat @ one_one_nat) @ X1) => (~(((ord_less_eq_nat @ X1) @ zero_zero_nat)))))))) => (~((((groups1842438620at_nat @ (^[X1:nat]:((times_times_nat @ (p @ X1)) @ X1))) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat)))))) = sP1)).
% 100.04/99.92 thf(h0,negated_conjecture,(~(((~(((![X1:nat]:((~(((p @ X1) = zero_zero_nat))) => (~((((ord_less_eq_nat @ one_one_nat) @ X1) => (~(((ord_less_eq_nat @ X1) @ zero_zero_nat)))))))) => (~((((groups1842438620at_nat @ (^[X1:nat]:((times_times_nat @ (p @ X1)) @ X1))) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat)))))) = sP1))),inference(assume_negation,[status(cth)],[conj_0])).
% 100.04/99.92 thf(h1,assumption,(~(((![X1:nat]:((~(((p @ X1) = zero_zero_nat))) => (~((((ord_less_eq_nat @ one_one_nat) @ X1) => (~(((ord_less_eq_nat @ X1) @ zero_zero_nat)))))))) => (~((((groups1842438620at_nat @ (^[X1:nat]:((times_times_nat @ (p @ X1)) @ X1))) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat)))))),introduced(assumption,[])).
% 100.04/99.92 thf(h2,assumption,sP1,introduced(assumption,[])).
% 100.04/99.92 thf(h3,assumption,((![X1:nat]:((~(((p @ X1) = zero_zero_nat))) => (~((((ord_less_eq_nat @ one_one_nat) @ X1) => (~(((ord_less_eq_nat @ X1) @ zero_zero_nat)))))))) => (~((((groups1842438620at_nat @ (^[X1:nat]:((times_times_nat @ (p @ X1)) @ X1))) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat)))),introduced(assumption,[])).
% 100.04/99.92 thf(h4,assumption,(~(sP1)),introduced(assumption,[])).
% 100.04/99.92 thf(h5,assumption,(![X1:nat]:((~(((p @ X1) = zero_zero_nat))) => (~((((ord_less_eq_nat @ one_one_nat) @ X1) => (~(((ord_less_eq_nat @ X1) @ zero_zero_nat)))))))),introduced(assumption,[])).
% 100.04/99.92 thf(h6,assumption,(((groups1842438620at_nat @ (^[X1:nat]:((times_times_nat @ (p @ X1)) @ X1))) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat),introduced(assumption,[])).
% 100.04/99.92 thf(h7,assumption,(~(sP3)),introduced(assumption,[])).
% 100.04/99.92 thf(h8,assumption,(~(((p @ eigen__0) = zero_zero_nat))),introduced(assumption,[])).
% 100.04/99.92 thf(ax1961, axiom, (~(p116)|p125), file('<stdin>', ax1961)).
% 100.04/99.92 thf(ax1962, axiom, (~(p125)|p114|~(p124)), file('<stdin>', ax1962)).
% 100.04/99.92 thf(ax1971, axiom, p116, file('<stdin>', ax1971)).
% 100.04/99.92 thf(ax1973, axiom, ~(p114), file('<stdin>', ax1973)).
% 100.04/99.92 thf(ax1644, axiom, (~(p103)|p407), file('<stdin>', ax1644)).
% 100.04/99.92 thf(ax386, axiom, (~(p37)|p1409), file('<stdin>', ax386)).
% 100.04/99.92 thf(ax80, axiom, (~(p407)|p1620), file('<stdin>', ax80)).
% 100.04/99.92 thf(ax1984, axiom, p103, file('<stdin>', ax1984)).
% 100.04/99.92 thf(ax163, axiom, (~(p1409)|~(p1354)|p1544), file('<stdin>', ax163)).
% 100.04/99.92 thf(ax454, axiom, (p124|p1354), file('<stdin>', ax454)).
% 100.04/99.92 thf(ax2050, axiom, p37, file('<stdin>', ax2050)).
% 100.04/99.92 thf(ax81, axiom, (~(p1620)|~(p1553)|~(p1544)), file('<stdin>', ax81)).
% 100.04/99.92 thf(ax1915, axiom, (~(p110)|p169), file('<stdin>', ax1915)).
% 100.04/99.92 thf(pax1544, axiom, (p1544=>(f__0)=(fzero_zero_nat)), file('<stdin>', pax1544)).
% 100.04/99.92 thf(nax34, axiom, (p34<=(fzero_zero_nat)=(fone_one_nat)), file('<stdin>', nax34)).
% 100.04/99.92 thf(ax2053, axiom, ~(p34), file('<stdin>', ax2053)).
% 100.04/99.92 thf(ax207, axiom, (~(p169)|p1557), file('<stdin>', ax207)).
% 100.04/99.92 thf(ax1977, axiom, p110, file('<stdin>', ax1977)).
% 100.04/99.92 thf(pax1547, axiom, (p1547=>(fone_one_nat)=(f__0)), file('<stdin>', pax1547)).
% 100.04/99.92 thf(ax209, axiom, (~(p1556)|~(p1353)|p1553), file('<stdin>', ax209)).
% 100.04/99.92 thf(ax455, axiom, (p124|p1353), file('<stdin>', ax455)).
% 100.04/99.92 thf(ax208, axiom, (~(p1557)|p1547|p1556), file('<stdin>', ax208)).
% 100.04/99.92 thf(c_0_22, plain, (~p116|p125), inference(fof_simplification,[status(thm)],[ax1961])).
% 100.04/99.92 thf(c_0_23, plain, (~p125|p114|~p124), inference(fof_simplification,[status(thm)],[ax1962])).
% 100.04/99.92 thf(c_0_24, plain, (p125|~p116), inference(split_conjunct,[status(thm)],[c_0_22])).
% 100.04/99.92 thf(c_0_25, plain, p116, inference(split_conjunct,[status(thm)],[ax1971])).
% 100.04/99.92 thf(c_0_26, plain, ~p114, inference(fof_simplification,[status(thm)],[ax1973])).
% 100.04/99.92 thf(c_0_27, plain, (~p103|p407), inference(fof_simplification,[status(thm)],[ax1644])).
% 100.04/99.92 thf(c_0_28, plain, (p114|~p125|~p124), inference(split_conjunct,[status(thm)],[c_0_23])).
% 100.04/99.92 thf(c_0_29, plain, p125, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24, c_0_25])])).
% 100.04/99.92 thf(c_0_30, plain, ~p114, inference(split_conjunct,[status(thm)],[c_0_26])).
% 100.04/99.92 thf(c_0_31, plain, (~p37|p1409), inference(fof_simplification,[status(thm)],[ax386])).
% 100.04/99.92 thf(c_0_32, plain, (~p407|p1620), inference(fof_simplification,[status(thm)],[ax80])).
% 100.04/99.92 thf(c_0_33, plain, (p407|~p103), inference(split_conjunct,[status(thm)],[c_0_27])).
% 100.04/99.92 thf(c_0_34, plain, p103, inference(split_conjunct,[status(thm)],[ax1984])).
% 100.04/99.92 thf(c_0_35, plain, (~p1409|~p1354|p1544), inference(fof_simplification,[status(thm)],[ax163])).
% 100.04/99.92 thf(c_0_36, plain, (p124|p1354), inference(split_conjunct,[status(thm)],[ax454])).
% 100.04/99.92 thf(c_0_37, plain, ~p124, inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28, c_0_29])]), c_0_30])).
% 100.04/99.92 thf(c_0_38, plain, (p1409|~p37), inference(split_conjunct,[status(thm)],[c_0_31])).
% 100.04/99.92 thf(c_0_39, plain, p37, inference(split_conjunct,[status(thm)],[ax2050])).
% 100.04/99.92 thf(c_0_40, plain, (~p1620|~p1553|~p1544), inference(fof_simplification,[status(thm)],[ax81])).
% 100.04/99.92 thf(c_0_41, plain, (p1620|~p407), inference(split_conjunct,[status(thm)],[c_0_32])).
% 100.04/99.92 thf(c_0_42, plain, p407, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33, c_0_34])])).
% 100.04/99.92 thf(c_0_43, plain, (~p110|p169), inference(fof_simplification,[status(thm)],[ax1915])).
% 100.04/99.92 thf(c_0_44, plain, (~p1544|(f__0)=(fzero_zero_nat)), inference(fof_nnf,[status(thm)],[pax1544])).
% 100.04/99.92 thf(c_0_45, plain, (p1544|~p1409|~p1354), inference(split_conjunct,[status(thm)],[c_0_35])).
% 100.04/99.92 thf(c_0_46, plain, p1354, inference(sr,[status(thm)],[c_0_36, c_0_37])).
% 100.04/99.92 thf(c_0_47, plain, p1409, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38, c_0_39])])).
% 100.04/99.92 thf(c_0_48, plain, ((fzero_zero_nat)!=(fone_one_nat)|p34), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax34])])).
% 100.04/99.92 thf(c_0_49, plain, ~p34, inference(fof_simplification,[status(thm)],[ax2053])).
% 100.04/99.92 thf(c_0_50, plain, (~p1620|~p1553|~p1544), inference(split_conjunct,[status(thm)],[c_0_40])).
% 100.04/99.92 thf(c_0_51, plain, p1620, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41, c_0_42])])).
% 100.04/99.92 thf(c_0_52, plain, (~p169|p1557), inference(fof_simplification,[status(thm)],[ax207])).
% 100.04/99.92 thf(c_0_53, plain, (p169|~p110), inference(split_conjunct,[status(thm)],[c_0_43])).
% 100.04/99.92 thf(c_0_54, plain, p110, inference(split_conjunct,[status(thm)],[ax1977])).
% 100.04/99.92 thf(c_0_55, plain, (~p1547|(fone_one_nat)=(f__0)), inference(fof_nnf,[status(thm)],[pax1547])).
% 100.04/99.92 thf(c_0_56, plain, ((f__0)=(fzero_zero_nat)|~p1544), inference(split_conjunct,[status(thm)],[c_0_44])).
% 100.04/99.92 thf(c_0_57, plain, p1544, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45, c_0_46]), c_0_47])])).
% 100.04/99.92 thf(c_0_58, plain, (p34|(fzero_zero_nat)!=(fone_one_nat)), inference(split_conjunct,[status(thm)],[c_0_48])).
% 100.04/99.92 thf(c_0_59, plain, ~p34, inference(split_conjunct,[status(thm)],[c_0_49])).
% 100.04/99.92 thf(c_0_60, plain, (~p1556|~p1353|p1553), inference(fof_simplification,[status(thm)],[ax209])).
% 100.04/99.92 thf(c_0_61, plain, (p124|p1353), inference(split_conjunct,[status(thm)],[ax455])).
% 100.04/99.92 thf(c_0_62, plain, (~p1544|~p1553), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50, c_0_51])])).
% 100.04/99.92 thf(c_0_63, plain, (~p1557|p1547|p1556), inference(fof_simplification,[status(thm)],[ax208])).
% 100.04/99.92 thf(c_0_64, plain, (p1557|~p169), inference(split_conjunct,[status(thm)],[c_0_52])).
% 100.04/99.92 thf(c_0_65, plain, p169, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53, c_0_54])])).
% 100.04/99.92 thf(c_0_66, plain, ((fone_one_nat)=(f__0)|~p1547), inference(split_conjunct,[status(thm)],[c_0_55])).
% 100.04/99.92 thf(c_0_67, plain, (f__0)=(fzero_zero_nat), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56, c_0_57])])).
% 100.04/99.92 thf(c_0_68, plain, (fone_one_nat)!=(fzero_zero_nat), inference(sr,[status(thm)],[c_0_58, c_0_59])).
% 100.04/99.92 thf(c_0_69, plain, (p1553|~p1556|~p1353), inference(split_conjunct,[status(thm)],[c_0_60])).
% 100.04/99.92 thf(c_0_70, plain, p1353, inference(sr,[status(thm)],[c_0_61, c_0_37])).
% 100.04/99.92 thf(c_0_71, plain, ~p1553, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62, c_0_57])])).
% 100.04/99.92 thf(c_0_72, plain, (p1547|p1556|~p1557), inference(split_conjunct,[status(thm)],[c_0_63])).
% 100.04/99.92 thf(c_0_73, plain, p1557, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64, c_0_65])])).
% 100.04/99.92 thf(c_0_74, plain, ~p1547, inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_66, c_0_67]), c_0_68])).
% 100.04/99.92 thf(c_0_75, plain, ~p1556, inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69, c_0_70])]), c_0_71])).
% 100.04/99.92 thf(c_0_76, plain, ($false), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72, c_0_73])]), c_0_74]), c_0_75]), ['proof']).
% 100.04/99.92 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h8,h7,h5,h6,h1,h2,h0])],[])).
% 100.04/99.92 thf(2,plain,$false,inference(tab_negall,[status(thm),assumptions([h7,h5,h6,h1,h2,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__0)],[h7,1,h8])).
% 100.04/99.92 thf(3,plain,$false,inference(tab_fe,[status(thm),assumptions([h5,h6,h1,h2,h0]),tab_fe(discharge,[h7])],[h2,2,h7])).
% 100.04/99.92 thf(4,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h1,3,h5,h6])).
% 100.04/99.92 thf(h9,assumption,(~((![X1:nat]:((~(((p @ X1) = zero_zero_nat))) => (~((((ord_less_eq_nat @ one_one_nat) @ X1) => (~(((ord_less_eq_nat @ X1) @ zero_zero_nat)))))))))),introduced(assumption,[])).
% 100.04/99.92 thf(h10,assumption,(~((((groups1842438620at_nat @ (^[X1:nat]:((times_times_nat @ (p @ X1)) @ X1))) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat))),introduced(assumption,[])).
% 100.04/99.92 thf(h11,assumption,(~(((~(sP2)) => (~((((ord_less_eq_nat @ one_one_nat) @ eigen__7) => (~(((ord_less_eq_nat @ eigen__7) @ zero_zero_nat))))))))),introduced(assumption,[])).
% 100.04/99.92 thf(h12,assumption,(~(sP2)),introduced(assumption,[])).
% 100.04/99.92 thf(h13,assumption,(((ord_less_eq_nat @ one_one_nat) @ eigen__7) => (~(((ord_less_eq_nat @ eigen__7) @ zero_zero_nat)))),introduced(assumption,[])).
% 100.04/99.92 thf(h14,assumption,(~(((ord_less_eq_nat @ one_one_nat) @ eigen__7))),introduced(assumption,[])).
% 100.04/99.92 thf(h15,assumption,(~(((ord_less_eq_nat @ eigen__7) @ zero_zero_nat))),introduced(assumption,[])).
% 100.04/99.92 thf(5,plain,(~(sP3) | sP2),inference(all_rule,[status(thm)],[])).
% 100.04/99.92 thf(6,plain,(~(sP1) | sP3),inference(prop_rule,[status(thm)],[])).
% 100.04/99.92 thf(7,plain,$false,inference(prop_unsat,[status(thm),assumptions([h14,h12,h13,h11,h9,h3,h4,h0])],[5,6,h12,h4])).
% 100.04/99.92 thf(8,plain,(~(sP3) | sP2),inference(all_rule,[status(thm)],[])).
% 100.04/99.92 thf(9,plain,(~(sP1) | sP3),inference(prop_rule,[status(thm)],[])).
% 100.04/99.92 thf(10,plain,$false,inference(prop_unsat,[status(thm),assumptions([h15,h12,h13,h11,h9,h3,h4,h0])],[8,9,h12,h4])).
% 100.04/99.92 thf(11,plain,$false,inference(tab_imp,[status(thm),assumptions([h12,h13,h11,h9,h3,h4,h0]),tab_imp(discharge,[h14]),tab_imp(discharge,[h15])],[h13,7,10,h14,h15])).
% 100.04/99.92 thf(12,plain,$false,inference(tab_negimp,[status(thm),assumptions([h11,h9,h3,h4,h0]),tab_negimp(discharge,[h12,h13])],[h11,11,h12,h13])).
% 100.04/99.92 thf(13,plain,$false,inference(tab_negall,[status(thm),assumptions([h9,h3,h4,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__7)],[h9,12,h11])).
% 100.04/99.92 thf(ax4044, axiom, (~(p35)|p592), file('<stdin>', ax4044)).
% 100.04/99.92 thf(ax4007, axiom, (~(p1639)|p1674), file('<stdin>', ax4007)).
% 100.04/99.92 thf(ax4045, axiom, (~(p592)|p591), file('<stdin>', ax4045)).
% 100.04/99.92 thf(ax4127, axiom, p35, file('<stdin>', ax4127)).
% 100.04/99.92 thf(pax1674, axiom, (p1674=>![X42:nat]:(fp @ X42)=(fzero_zero_nat)), file('<stdin>', pax1674)).
% 100.04/99.92 thf(ax4048, axiom, p1639, file('<stdin>', ax4048)).
% 100.04/99.92 thf(ax4046, axiom, (~(p591)|p115|~(p590)), file('<stdin>', ax4046)).
% 100.04/99.92 thf(ax4047, axiom, ~(p115), file('<stdin>', ax4047)).
% 100.04/99.92 thf(ax2631, axiom, (~(p46)|p486), file('<stdin>', ax2631)).
% 100.04/99.92 thf(nax590, axiom, (p590<=![X163:nat]:(fmember_nat @ X163 @ (fset_ord_atMost_nat @ fzero_zero_nat)=>(ftimes_times_nat @ (fp @ X163) @ X163)=(fzero_zero_nat))), file('<stdin>', nax590)).
% 100.04/99.92 thf(pax486, axiom, (p486=>![X177:nat]:(fzero_zero_nat)=(ftimes_times_nat @ fzero_zero_nat @ X177)), file('<stdin>', pax486)).
% 100.04/99.92 thf(ax4116, axiom, p46, file('<stdin>', ax4116)).
% 100.04/99.92 thf(c_0_12, plain, (~p35|p592), inference(fof_simplification,[status(thm)],[ax4044])).
% 100.04/99.92 thf(c_0_13, plain, (~p1639|p1674), inference(fof_simplification,[status(thm)],[ax4007])).
% 100.04/99.92 thf(c_0_14, plain, (~p592|p591), inference(fof_simplification,[status(thm)],[ax4045])).
% 100.04/99.92 thf(c_0_15, plain, (p592|~p35), inference(split_conjunct,[status(thm)],[c_0_12])).
% 100.04/99.92 thf(c_0_16, plain, p35, inference(split_conjunct,[status(thm)],[ax4127])).
% 100.04/99.92 thf(c_0_17, plain, ![X932:nat]:(~p1674|(fp @ X932)=(fzero_zero_nat)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax1674])])])).
% 100.04/99.92 thf(c_0_18, plain, (p1674|~p1639), inference(split_conjunct,[status(thm)],[c_0_13])).
% 100.04/99.92 thf(c_0_19, plain, p1639, inference(split_conjunct,[status(thm)],[ax4048])).
% 100.04/99.92 thf(c_0_20, plain, (~p591|p115|~p590), inference(fof_simplification,[status(thm)],[ax4046])).
% 100.04/99.92 thf(c_0_21, plain, (p591|~p592), inference(split_conjunct,[status(thm)],[c_0_14])).
% 100.04/99.92 thf(c_0_22, plain, p592, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15, c_0_16])])).
% 100.04/99.92 thf(c_0_23, plain, ~p115, inference(fof_simplification,[status(thm)],[ax4047])).
% 100.04/99.92 thf(c_0_24, plain, (~p46|p486), inference(fof_simplification,[status(thm)],[ax2631])).
% 100.04/99.92 thf(c_0_25, plain, ((fmember_nat @ esk746_0 @ (fset_ord_atMost_nat @ fzero_zero_nat)|p590)&((ftimes_times_nat @ (fp @ esk746_0) @ esk746_0)!=(fzero_zero_nat)|p590)), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax590])])])])])).
% 100.04/99.92 thf(c_0_26, plain, ![X1:nat]:((fp @ X1)=(fzero_zero_nat)|~p1674), inference(split_conjunct,[status(thm)],[c_0_17])).
% 100.04/99.92 thf(c_0_27, plain, p1674, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18, c_0_19])])).
% 100.04/99.92 thf(c_0_28, plain, (p115|~p591|~p590), inference(split_conjunct,[status(thm)],[c_0_20])).
% 100.04/99.92 thf(c_0_29, plain, p591, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21, c_0_22])])).
% 100.04/99.92 thf(c_0_30, plain, ~p115, inference(split_conjunct,[status(thm)],[c_0_23])).
% 100.04/99.92 thf(c_0_31, plain, ![X1924:nat]:(~p486|(fzero_zero_nat)=(ftimes_times_nat @ fzero_zero_nat @ X1924)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax486])])])).
% 100.04/99.92 thf(c_0_32, plain, (p486|~p46), inference(split_conjunct,[status(thm)],[c_0_24])).
% 100.04/99.92 thf(c_0_33, plain, p46, inference(split_conjunct,[status(thm)],[ax4116])).
% 100.04/99.92 thf(c_0_34, plain, (p590|(ftimes_times_nat @ (fp @ esk746_0) @ esk746_0)!=(fzero_zero_nat)), inference(split_conjunct,[status(thm)],[c_0_25])).
% 100.04/99.92 thf(c_0_35, plain, ![X1:nat]:(fp @ X1)=(fzero_zero_nat), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26, c_0_27])])).
% 100.04/99.92 thf(c_0_36, plain, ~p590, inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28, c_0_29])]), c_0_30])).
% 100.04/99.92 thf(c_0_37, plain, ![X1:nat]:((fzero_zero_nat)=(ftimes_times_nat @ fzero_zero_nat @ X1)|~p486), inference(split_conjunct,[status(thm)],[c_0_31])).
% 100.04/99.92 thf(c_0_38, plain, p486, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32, c_0_33])])).
% 100.04/99.92 thf(c_0_39, plain, (ftimes_times_nat @ fzero_zero_nat @ esk746_0)!=(fzero_zero_nat), inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_34, c_0_35]), c_0_36])).
% 100.04/99.92 thf(c_0_40, plain, ![X1:nat]:(ftimes_times_nat @ fzero_zero_nat @ X1)=(fzero_zero_nat), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37, c_0_38])])).
% 100.04/99.92 thf(c_0_41, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39, c_0_40])]), ['proof']).
% 100.04/99.92 thf(14,plain,$false,inference(eprover,[status(thm),assumptions([h10,h3,h4,h0])],[])).
% 100.04/99.92 thf(15,plain,$false,inference(tab_imp,[status(thm),assumptions([h3,h4,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[h3,13,14,h9,h10])).
% 100.04/99.92 thf(16,plain,$false,inference(tab_be,[status(thm),assumptions([h0]),tab_be(discharge,[h1,h2]),tab_be(discharge,[h3,h4])],[h0,4,15,h1,h2,h3,h4])).
% 100.04/99.92 thf(0,theorem,((~(((![X1:nat]:((~(((p @ X1) = zero_zero_nat))) => (~((((ord_less_eq_nat @ one_one_nat) @ X1) => (~(((ord_less_eq_nat @ X1) @ zero_zero_nat)))))))) => (~((((groups1842438620at_nat @ (^[X1:nat]:((times_times_nat @ (p @ X1)) @ X1))) @ (set_ord_atMost_nat @ zero_zero_nat)) = zero_zero_nat)))))) = sP1),inference(contra,[status(thm),contra(discharge,[h0])],[16,h0])).
% 100.04/99.92 % SZS output end Proof
%------------------------------------------------------------------------------