TSTP Solution File: SEU627^2 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU627^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n020.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 : Tue Jul 19 13:54:37 EDT 2022
% Result : Theorem 43.89s 44.13s
% Output : Proof 43.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU627^2 : TPTP v8.1.0. Released v3.7.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n020.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 : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 14:18:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 43.89/44.13 % SZS status Theorem
% 43.89/44.13 % Mode: mode459
% 43.89/44.13 % Inferences: 38
% 43.89/44.13 % SZS output start Proof
% 43.89/44.13 thf(def_subsetI2,definition,(subsetI2 = (![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))))).
% 43.89/44.13 thf(def_singletoninpowunion,definition,(singletoninpowunion = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ ((setadjoin @ X3) @ emptyset)) @ (powerset @ ((binunion @ X1) @ X2))))))))).
% 43.89/44.13 thf(def_upairset2E,definition,(upairset2E = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))))).
% 43.89/44.13 thf(def_upairinpowunion,definition,(upairinpowunion = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))))).
% 43.89/44.13 thf(ubforcartprodlem1,conjecture,((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ ((setadjoin @ X3) @ emptyset)) @ (powerset @ ((binunion @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2)))))))))))))).
% 43.89/44.13 thf(h0,negated_conjecture,(~(((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ ((setadjoin @ X3) @ emptyset)) @ (powerset @ ((binunion @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))))))))),inference(assume_negation,[status(cth)],[ubforcartprodlem1])).
% 43.89/44.13 thf(ax100, axiom, (p1|~(p3)), file('<stdin>', ax100)).
% 43.89/44.13 thf(ax102, axiom, ~(p1), file('<stdin>', ax102)).
% 43.89/44.13 thf(ax98, axiom, (p3|~(p5)), file('<stdin>', ax98)).
% 43.89/44.13 thf(ax94, axiom, (p5|~(p9)), file('<stdin>', ax94)).
% 43.89/44.13 thf(ax91, axiom, (p9|~(p12)), file('<stdin>', ax91)).
% 43.89/44.13 thf(ax89, axiom, (p12|~(p14)), file('<stdin>', ax89)).
% 43.89/44.13 thf(ax88, axiom, (p14|~(p15)), file('<stdin>', ax88)).
% 43.89/44.13 thf(ax79, axiom, (~(p2)|p24), file('<stdin>', ax79)).
% 43.89/44.13 thf(ax101, axiom, (p1|p2), file('<stdin>', ax101)).
% 43.89/44.13 thf(ax87, axiom, (p15|~(p16)), file('<stdin>', ax87)).
% 43.89/44.13 thf(ax80, axiom, (~(p24)|p23), file('<stdin>', ax80)).
% 43.89/44.13 thf(ax85, axiom, (p16|~(p18)), file('<stdin>', ax85)).
% 43.89/44.13 thf(ax71, axiom, (~(p8)|p33), file('<stdin>', ax71)).
% 43.89/44.13 thf(ax95, axiom, (p5|p8), file('<stdin>', ax95)).
% 43.89/44.13 thf(ax81, axiom, (~(p23)|~(p22)|p21), file('<stdin>', ax81)).
% 43.89/44.13 thf(ax84, axiom, (p18|~(p19)), file('<stdin>', ax84)).
% 43.89/44.13 thf(ax72, axiom, (~(p33)|p32), file('<stdin>', ax72)).
% 43.89/44.13 thf(ax82, axiom, (p19|~(p21)), file('<stdin>', ax82)).
% 43.89/44.13 thf(ax73, axiom, (~(p32)|p31), file('<stdin>', ax73)).
% 43.89/44.13 thf(ax78, axiom, (p22|~(p25)), file('<stdin>', ax78)).
% 43.89/44.13 thf(ax74, axiom, (~(p31)|~(p26)|p30), file('<stdin>', ax74)).
% 43.89/44.13 thf(ax77, axiom, (p25|p26), file('<stdin>', ax77)).
% 43.89/44.13 thf(pax30, axiom, (p30=>(~((f__5)=(fsetadjoin @ f__3 @ femptyset))=>(f__5)=(fsetadjoin @ f__3 @ (fsetadjoin @ f__4 @ femptyset)))), file('<stdin>', pax30)).
% 43.89/44.13 thf(pax4, axiom, (p4=>![X1:$i, X2:$i, X3:$i]:(fin @ X3 @ X1=>fin @ (fsetadjoin @ X3 @ femptyset) @ (fpowerset @ (fbinunion @ X1 @ X2)))), file('<stdin>', pax4)).
% 43.89/44.13 thf(ax99, axiom, (p3|p4), file('<stdin>', ax99)).
% 43.89/44.13 thf(nax28, axiom, (p28<=(f__5)=(fsetadjoin @ f__3 @ (fsetadjoin @ f__4 @ femptyset))), file('<stdin>', nax28)).
% 43.89/44.13 thf(pax17, axiom, (p17=>fin @ f__3 @ f__1), file('<stdin>', pax17)).
% 43.89/44.13 thf(ax86, axiom, (p16|p17), file('<stdin>', ax86)).
% 43.89/44.13 thf(nax25, axiom, (p25<=(fin @ f__5 @ (fsetadjoin @ (fsetadjoin @ f__3 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ f__3 @ (fsetadjoin @ f__4 @ femptyset)) @ femptyset))=>fin @ f__5 @ (fpowerset @ (fbinunion @ f__1 @ f__2)))), file('<stdin>', nax25)).
% 43.89/44.13 thf(pax11, axiom, (p11=>![X1:$i, X2:$i, X3:$i]:(fin @ X3 @ X1=>![X4:$i]:(fin @ X4 @ X2=>fin @ (fsetadjoin @ X3 @ (fsetadjoin @ X4 @ femptyset)) @ (fpowerset @ (fbinunion @ X1 @ X2))))), file('<stdin>', pax11)).
% 43.89/44.13 thf(ax92, axiom, (p9|p11), file('<stdin>', ax92)).
% 43.89/44.13 thf(pax28, axiom, (p28=>(f__5)=(fsetadjoin @ f__3 @ (fsetadjoin @ f__4 @ femptyset))), file('<stdin>', pax28)).
% 43.89/44.13 thf(pax20, axiom, (p20=>fin @ f__4 @ f__2), file('<stdin>', pax20)).
% 43.89/44.13 thf(ax83, axiom, (p19|p20), file('<stdin>', ax83)).
% 43.89/44.13 thf(c_0_34, plain, (p1|~p3), inference(fof_simplification,[status(thm)],[ax100])).
% 43.89/44.13 thf(c_0_35, plain, ~p1, inference(fof_simplification,[status(thm)],[ax102])).
% 43.89/44.13 thf(c_0_36, plain, (p3|~p5), inference(fof_simplification,[status(thm)],[ax98])).
% 43.89/44.13 thf(c_0_37, plain, (p1|~p3), inference(split_conjunct,[status(thm)],[c_0_34])).
% 43.89/44.13 thf(c_0_38, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_35])).
% 43.89/44.13 thf(c_0_39, plain, (p5|~p9), inference(fof_simplification,[status(thm)],[ax94])).
% 43.89/44.13 thf(c_0_40, plain, (p3|~p5), inference(split_conjunct,[status(thm)],[c_0_36])).
% 43.89/44.13 thf(c_0_41, plain, ~p3, inference(sr,[status(thm)],[c_0_37, c_0_38])).
% 43.89/44.13 thf(c_0_42, plain, (p9|~p12), inference(fof_simplification,[status(thm)],[ax91])).
% 43.89/44.13 thf(c_0_43, plain, (p5|~p9), inference(split_conjunct,[status(thm)],[c_0_39])).
% 43.89/44.13 thf(c_0_44, plain, ~p5, inference(sr,[status(thm)],[c_0_40, c_0_41])).
% 43.89/44.13 thf(c_0_45, plain, (p12|~p14), inference(fof_simplification,[status(thm)],[ax89])).
% 43.89/44.13 thf(c_0_46, plain, (p9|~p12), inference(split_conjunct,[status(thm)],[c_0_42])).
% 43.89/44.13 thf(c_0_47, plain, ~p9, inference(sr,[status(thm)],[c_0_43, c_0_44])).
% 43.89/44.13 thf(c_0_48, plain, (p14|~p15), inference(fof_simplification,[status(thm)],[ax88])).
% 43.89/44.13 thf(c_0_49, plain, (p12|~p14), inference(split_conjunct,[status(thm)],[c_0_45])).
% 43.89/44.13 thf(c_0_50, plain, ~p12, inference(sr,[status(thm)],[c_0_46, c_0_47])).
% 43.89/44.13 thf(c_0_51, plain, (~p2|p24), inference(fof_simplification,[status(thm)],[ax79])).
% 43.89/44.13 thf(c_0_52, plain, (p1|p2), inference(split_conjunct,[status(thm)],[ax101])).
% 43.89/44.13 thf(c_0_53, plain, (p15|~p16), inference(fof_simplification,[status(thm)],[ax87])).
% 43.89/44.13 thf(c_0_54, plain, (p14|~p15), inference(split_conjunct,[status(thm)],[c_0_48])).
% 43.89/44.13 thf(c_0_55, plain, ~p14, inference(sr,[status(thm)],[c_0_49, c_0_50])).
% 43.89/44.13 thf(c_0_56, plain, (~p24|p23), inference(fof_simplification,[status(thm)],[ax80])).
% 43.89/44.13 thf(c_0_57, plain, (p24|~p2), inference(split_conjunct,[status(thm)],[c_0_51])).
% 43.89/44.13 thf(c_0_58, plain, p2, inference(sr,[status(thm)],[c_0_52, c_0_38])).
% 43.89/44.13 thf(c_0_59, plain, (p16|~p18), inference(fof_simplification,[status(thm)],[ax85])).
% 43.89/44.13 thf(c_0_60, plain, (p15|~p16), inference(split_conjunct,[status(thm)],[c_0_53])).
% 43.89/44.13 thf(c_0_61, plain, ~p15, inference(sr,[status(thm)],[c_0_54, c_0_55])).
% 43.89/44.13 thf(c_0_62, plain, (~p8|p33), inference(fof_simplification,[status(thm)],[ax71])).
% 43.89/44.13 thf(c_0_63, plain, (p5|p8), inference(split_conjunct,[status(thm)],[ax95])).
% 43.89/44.13 thf(c_0_64, plain, (~p23|~p22|p21), inference(fof_simplification,[status(thm)],[ax81])).
% 43.89/44.13 thf(c_0_65, plain, (p23|~p24), inference(split_conjunct,[status(thm)],[c_0_56])).
% 43.89/44.13 thf(c_0_66, plain, p24, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57, c_0_58])])).
% 43.89/44.13 thf(c_0_67, plain, (p18|~p19), inference(fof_simplification,[status(thm)],[ax84])).
% 43.89/44.13 thf(c_0_68, plain, (p16|~p18), inference(split_conjunct,[status(thm)],[c_0_59])).
% 43.89/44.13 thf(c_0_69, plain, ~p16, inference(sr,[status(thm)],[c_0_60, c_0_61])).
% 43.89/44.13 thf(c_0_70, plain, (~p33|p32), inference(fof_simplification,[status(thm)],[ax72])).
% 43.89/44.13 thf(c_0_71, plain, (p33|~p8), inference(split_conjunct,[status(thm)],[c_0_62])).
% 43.89/44.13 thf(c_0_72, plain, p8, inference(sr,[status(thm)],[c_0_63, c_0_44])).
% 43.89/44.13 thf(c_0_73, plain, (p19|~p21), inference(fof_simplification,[status(thm)],[ax82])).
% 43.89/44.13 thf(c_0_74, plain, (p21|~p23|~p22), inference(split_conjunct,[status(thm)],[c_0_64])).
% 43.89/44.13 thf(c_0_75, plain, p23, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65, c_0_66])])).
% 43.89/44.13 thf(c_0_76, plain, (p18|~p19), inference(split_conjunct,[status(thm)],[c_0_67])).
% 43.89/44.13 thf(c_0_77, plain, ~p18, inference(sr,[status(thm)],[c_0_68, c_0_69])).
% 43.89/44.13 thf(c_0_78, plain, (~p32|p31), inference(fof_simplification,[status(thm)],[ax73])).
% 43.89/44.13 thf(c_0_79, plain, (p32|~p33), inference(split_conjunct,[status(thm)],[c_0_70])).
% 43.89/44.13 thf(c_0_80, plain, p33, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71, c_0_72])])).
% 43.89/44.13 thf(c_0_81, plain, (p19|~p21), inference(split_conjunct,[status(thm)],[c_0_73])).
% 43.89/44.13 thf(c_0_82, plain, (p21|~p22), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74, c_0_75])])).
% 43.89/44.13 thf(c_0_83, plain, ~p19, inference(sr,[status(thm)],[c_0_76, c_0_77])).
% 43.89/44.13 thf(c_0_84, plain, (p22|~p25), inference(fof_simplification,[status(thm)],[ax78])).
% 43.89/44.13 thf(c_0_85, plain, (~p31|~p26|p30), inference(fof_simplification,[status(thm)],[ax74])).
% 43.89/44.13 thf(c_0_86, plain, (p31|~p32), inference(split_conjunct,[status(thm)],[c_0_78])).
% 43.89/44.13 thf(c_0_87, plain, p32, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79, c_0_80])])).
% 43.89/44.13 thf(c_0_88, plain, ~p22, inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_82]), c_0_83])).
% 43.89/44.13 thf(c_0_89, plain, (p22|~p25), inference(split_conjunct,[status(thm)],[c_0_84])).
% 43.89/44.13 thf(c_0_90, plain, (p30|~p31|~p26), inference(split_conjunct,[status(thm)],[c_0_85])).
% 43.89/44.13 thf(c_0_91, plain, p31, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86, c_0_87])])).
% 43.89/44.13 thf(c_0_92, plain, (p25|p26), inference(split_conjunct,[status(thm)],[ax77])).
% 43.89/44.13 thf(c_0_93, plain, ~p25, inference(spm,[status(thm)],[c_0_88, c_0_89])).
% 43.89/44.13 thf(c_0_94, plain, (~p30|((f__5)=(fsetadjoin @ f__3 @ femptyset)|(f__5)=(fsetadjoin @ f__3 @ (fsetadjoin @ f__4 @ femptyset)))), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax30])])).
% 43.89/44.13 thf(c_0_95, plain, (p30|~p26), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90, c_0_91])])).
% 43.89/44.13 thf(c_0_96, plain, p26, inference(sr,[status(thm)],[c_0_92, c_0_93])).
% 43.89/44.13 thf(c_0_97, plain, ![X261:$i, X262:$i, X263:$i]:(~p4|(~fin @ X263 @ X261|fin @ (fsetadjoin @ X263 @ femptyset) @ (fpowerset @ (fbinunion @ X261 @ X262)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax4])])])).
% 43.89/44.13 thf(c_0_98, plain, (p3|p4), inference(split_conjunct,[status(thm)],[ax99])).
% 43.89/44.13 thf(c_0_99, plain, ((f__5)!=(fsetadjoin @ f__3 @ (fsetadjoin @ f__4 @ femptyset))|p28), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax28])])).
% 43.89/44.13 thf(c_0_100, plain, ((f__5)=(fsetadjoin @ f__3 @ femptyset)|(f__5)=(fsetadjoin @ f__3 @ (fsetadjoin @ f__4 @ femptyset))|~p30), inference(split_conjunct,[status(thm)],[c_0_94])).
% 43.89/44.13 thf(c_0_101, plain, p30, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_95, c_0_96])])).
% 43.89/44.13 thf(c_0_102, plain, ![X1:$i, X3:$i, X2:$i]:(fin @ (fsetadjoin @ X1 @ femptyset) @ (fpowerset @ (fbinunion @ X2 @ X3))|~p4|~fin @ X1 @ X2), inference(split_conjunct,[status(thm)],[c_0_97])).
% 43.89/44.13 thf(c_0_103, plain, p4, inference(sr,[status(thm)],[c_0_98, c_0_41])).
% 43.89/44.13 thf(c_0_104, plain, (p28|(f__5)!=(fsetadjoin @ f__3 @ (fsetadjoin @ f__4 @ femptyset))), inference(split_conjunct,[status(thm)],[c_0_99])).
% 43.89/44.13 thf(c_0_105, plain, ((fsetadjoin @ f__3 @ (fsetadjoin @ f__4 @ femptyset))=(f__5)|(fsetadjoin @ f__3 @ femptyset)=(f__5)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_100, c_0_101])])).
% 43.89/44.13 thf(c_0_106, plain, (~p17|fin @ f__3 @ f__1), inference(fof_nnf,[status(thm)],[pax17])).
% 43.89/44.13 thf(c_0_107, plain, (p16|p17), inference(split_conjunct,[status(thm)],[ax86])).
% 43.89/44.13 thf(c_0_108, plain, ((fin @ f__5 @ (fsetadjoin @ (fsetadjoin @ f__3 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ f__3 @ (fsetadjoin @ f__4 @ femptyset)) @ femptyset))|p25)&(~fin @ f__5 @ (fpowerset @ (fbinunion @ f__1 @ f__2))|p25)), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax25])])])).
% 43.89/44.13 thf(c_0_109, plain, ![X1:$i, X3:$i, X2:$i]:(fin @ (fsetadjoin @ X1 @ femptyset) @ (fpowerset @ (fbinunion @ X2 @ X3))|~fin @ X1 @ X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_102, c_0_103])])).
% 43.89/44.13 thf(c_0_110, plain, ((fsetadjoin @ f__3 @ femptyset)=(f__5)|p28), inference(spm,[status(thm)],[c_0_104, c_0_105])).
% 43.89/44.13 thf(c_0_111, plain, (fin @ f__3 @ f__1|~p17), inference(split_conjunct,[status(thm)],[c_0_106])).
% 43.89/44.13 thf(c_0_112, plain, p17, inference(sr,[status(thm)],[c_0_107, c_0_69])).
% 43.89/44.13 thf(c_0_113, plain, (p25|~fin @ f__5 @ (fpowerset @ (fbinunion @ f__1 @ f__2))), inference(split_conjunct,[status(thm)],[c_0_108])).
% 43.89/44.13 thf(c_0_114, plain, ![X2:$i, X1:$i]:(fin @ f__5 @ (fpowerset @ (fbinunion @ X1 @ X2))|p28|~fin @ f__3 @ X1), inference(spm,[status(thm)],[c_0_109, c_0_110])).
% 43.89/44.13 thf(c_0_115, plain, fin @ f__3 @ f__1, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_111, c_0_112])])).
% 43.89/44.13 thf(c_0_116, plain, ![X197:$i, X198:$i, X199:$i, X200:$i]:(~p11|(~fin @ X199 @ X197|(~fin @ X200 @ X198|fin @ (fsetadjoin @ X199 @ (fsetadjoin @ X200 @ femptyset)) @ (fpowerset @ (fbinunion @ X197 @ X198))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax11])])])).
% 43.89/44.13 thf(c_0_117, plain, (p9|p11), inference(split_conjunct,[status(thm)],[ax92])).
% 43.89/44.13 thf(c_0_118, plain, (~p28|(f__5)=(fsetadjoin @ f__3 @ (fsetadjoin @ f__4 @ femptyset))), inference(fof_nnf,[status(thm)],[pax28])).
% 43.89/44.13 thf(c_0_119, plain, ~fin @ f__5 @ (fpowerset @ (fbinunion @ f__1 @ f__2)), inference(sr,[status(thm)],[c_0_113, c_0_93])).
% 43.89/44.13 thf(c_0_120, plain, ![X1:$i]:(fin @ f__5 @ (fpowerset @ (fbinunion @ f__1 @ X1))|p28), inference(spm,[status(thm)],[c_0_114, c_0_115])).
% 43.89/44.13 thf(c_0_121, plain, ![X1:$i, X2:$i, X3:$i, X4:$i]:(fin @ (fsetadjoin @ X1 @ (fsetadjoin @ X3 @ femptyset)) @ (fpowerset @ (fbinunion @ X2 @ X4))|~p11|~fin @ X1 @ X2|~fin @ X3 @ X4), inference(split_conjunct,[status(thm)],[c_0_116])).
% 43.89/44.13 thf(c_0_122, plain, p11, inference(sr,[status(thm)],[c_0_117, c_0_47])).
% 43.89/44.13 thf(c_0_123, plain, ((f__5)=(fsetadjoin @ f__3 @ (fsetadjoin @ f__4 @ femptyset))|~p28), inference(split_conjunct,[status(thm)],[c_0_118])).
% 43.89/44.13 thf(c_0_124, plain, p28, inference(spm,[status(thm)],[c_0_119, c_0_120])).
% 43.89/44.13 thf(c_0_125, plain, (~p20|fin @ f__4 @ f__2), inference(fof_nnf,[status(thm)],[pax20])).
% 43.89/44.13 thf(c_0_126, plain, (p19|p20), inference(split_conjunct,[status(thm)],[ax83])).
% 43.89/44.13 thf(c_0_127, plain, ![X2:$i, X1:$i, X4:$i, X3:$i]:(fin @ (fsetadjoin @ X1 @ (fsetadjoin @ X2 @ femptyset)) @ (fpowerset @ (fbinunion @ X3 @ X4))|~fin @ X2 @ X4|~fin @ X1 @ X3), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_121, c_0_122])])).
% 43.89/44.13 thf(c_0_128, plain, (fsetadjoin @ f__3 @ (fsetadjoin @ f__4 @ femptyset))=(f__5), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_123, c_0_124])])).
% 43.89/44.13 thf(c_0_129, plain, (fin @ f__4 @ f__2|~p20), inference(split_conjunct,[status(thm)],[c_0_125])).
% 43.89/44.13 thf(c_0_130, plain, p20, inference(sr,[status(thm)],[c_0_126, c_0_83])).
% 43.89/44.13 thf(c_0_131, plain, ![X2:$i, X1:$i]:(fin @ f__5 @ (fpowerset @ (fbinunion @ X1 @ X2))|~fin @ f__4 @ X2|~fin @ f__3 @ X1), inference(spm,[status(thm)],[c_0_127, c_0_128])).
% 43.89/44.13 thf(c_0_132, plain, fin @ f__4 @ f__2, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_129, c_0_130])])).
% 43.89/44.13 thf(c_0_133, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119, c_0_131]), c_0_132]), c_0_115])]), ['proof']).
% 43.89/44.13 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 43.89/44.13 thf(0,theorem,((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => ((in @ ((setadjoin @ X3) @ emptyset)) @ (powerset @ ((binunion @ X1) @ X2))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((in @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))) => (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((subset @ ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) @ (powerset @ ((binunion @ X1) @ X2))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 43.89/44.13 % SZS output end Proof
%------------------------------------------------------------------------------