TSTP Solution File: SEU807^2 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU807^2 : 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 : n006.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 14:07:53 EDT 2022
% Result : Theorem 43.95s 44.08s
% Output : Proof 43.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU807^2 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Mon Jun 20 07:41:55 EDT 2022
% 0.11/0.33 % CPUTime :
% 43.95/44.08 % SZS status Theorem
% 43.95/44.08 % Mode: mode459
% 43.95/44.08 % Inferences: 92
% 43.95/44.08 % SZS output start Proof
% 43.95/44.08 thf(def_foundationAx,definition,(foundationAx = (![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (~((![X2:$i]:(((in @ X2) @ X1) => (~((![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ X1))))))))))))))).
% 43.95/44.08 thf(def_setadjoinIL,definition,(setadjoinIL = (![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))))).
% 43.95/44.08 thf(def_setadjoinIR,definition,(setadjoinIR = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ ((setadjoin @ X1) @ X2)))))))).
% 43.95/44.08 thf(def_in__Cong,definition,(in__Cong = (![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) = ((in @ X4) @ X2)))))))))).
% 43.95/44.08 thf(def_upairset2E,definition,(upairset2E = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))))).
% 43.95/44.08 thf(notinself2,conjecture,((![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (~((![X2:$i]:(((in @ X2) @ X1) => (~((![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ X1))))))))))))) => ((![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ ((setadjoin @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) = ((in @ X4) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))) => (![X1:$i]:(![X2:$i]:(((in @ X1) @ X2) => (~(((in @ X2) @ X1)))))))))))).
% 43.95/44.08 thf(h0,negated_conjecture,(~(((![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (~((![X2:$i]:(((in @ X2) @ X1) => (~((![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ X1))))))))))))) => ((![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ ((setadjoin @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) = ((in @ X4) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))) => (![X1:$i]:(![X2:$i]:(((in @ X1) @ X2) => (~(((in @ X2) @ X1))))))))))))),inference(assume_negation,[status(cth)],[notinself2])).
% 43.95/44.08 thf(ax124, axiom, (p1|~(p3)), file('<stdin>', ax124)).
% 43.95/44.08 thf(ax126, axiom, ~(p1), file('<stdin>', ax126)).
% 43.95/44.08 thf(ax122, axiom, (p3|~(p5)), file('<stdin>', ax122)).
% 43.95/44.08 thf(ax118, axiom, (p5|~(p9)), file('<stdin>', ax118)).
% 43.95/44.08 thf(ax115, axiom, (p9|~(p12)), file('<stdin>', ax115)).
% 43.95/44.08 thf(pax2, axiom, (p2=>![X1:$i]:(~(![X2:$i]:~(fin @ X2 @ X1))=>~(![X2:$i]:(fin @ X2 @ X1=>~(![X3:$i]:(fin @ X3 @ X2=>~(fin @ X3 @ X1))))))), file('<stdin>', pax2)).
% 43.95/44.08 thf(ax125, axiom, (p1|p2), file('<stdin>', ax125)).
% 43.95/44.08 thf(pax4, axiom, (p4=>![X1:$i, X2:$i]:fin @ X1 @ (fsetadjoin @ X1 @ X2)), file('<stdin>', pax4)).
% 43.95/44.08 thf(ax123, axiom, (p3|p4), file('<stdin>', ax123)).
% 43.95/44.08 thf(pax14, axiom, (p14=>![X1:$i, X2:$i, X3:$i]:(fin @ X3 @ (fsetadjoin @ X1 @ (fsetadjoin @ X2 @ femptyset))=>(~((X3)=(X1))=>(X3)=(X2)))), file('<stdin>', pax14)).
% 43.95/44.08 thf(ax113, axiom, (p12|p14), file('<stdin>', ax113)).
% 43.95/44.08 thf(pax8, axiom, (p8=>![X1:$i, X2:$i, X3:$i]:(fin @ X3 @ X2=>fin @ X3 @ (fsetadjoin @ X1 @ X2))), file('<stdin>', pax8)).
% 43.95/44.08 thf(ax119, axiom, (p5|p8), file('<stdin>', ax119)).
% 43.95/44.08 thf(nax12, axiom, (p12<=(![X1:$i, X2:$i, X3:$i]:(fin @ X3 @ (fsetadjoin @ X1 @ (fsetadjoin @ X2 @ femptyset))=>(~((X3)=(X1))=>(X3)=(X2)))=>![X1:$i, X2:$i]:(fin @ X1 @ X2=>~(fin @ X2 @ X1)))), file('<stdin>', nax12)).
% 43.95/44.08 thf(c_0_14, plain, (p1|~p3), inference(fof_simplification,[status(thm)],[ax124])).
% 43.95/44.08 thf(c_0_15, plain, ~p1, inference(fof_simplification,[status(thm)],[ax126])).
% 43.95/44.08 thf(c_0_16, plain, (p3|~p5), inference(fof_simplification,[status(thm)],[ax122])).
% 43.95/44.08 thf(c_0_17, plain, (p1|~p3), inference(split_conjunct,[status(thm)],[c_0_14])).
% 43.95/44.08 thf(c_0_18, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_15])).
% 43.95/44.08 thf(c_0_19, plain, (p5|~p9), inference(fof_simplification,[status(thm)],[ax118])).
% 43.95/44.08 thf(c_0_20, plain, (p3|~p5), inference(split_conjunct,[status(thm)],[c_0_16])).
% 43.95/44.08 thf(c_0_21, plain, ~p3, inference(sr,[status(thm)],[c_0_17, c_0_18])).
% 43.95/44.08 thf(c_0_22, plain, (p9|~p12), inference(fof_simplification,[status(thm)],[ax115])).
% 43.95/44.08 thf(c_0_23, plain, (p5|~p9), inference(split_conjunct,[status(thm)],[c_0_19])).
% 43.95/44.08 thf(c_0_24, plain, ~p5, inference(sr,[status(thm)],[c_0_20, c_0_21])).
% 43.95/44.08 thf(c_0_25, plain, (p9|~p12), inference(split_conjunct,[status(thm)],[c_0_22])).
% 43.95/44.08 thf(c_0_26, plain, ~p9, inference(sr,[status(thm)],[c_0_23, c_0_24])).
% 43.95/44.08 thf(c_0_27, plain, ![X158:$i, X159:$i, X161:$i]:((fin @ (esk78_1 @ X158) @ X158|~fin @ X159 @ X158|~p2)&(~fin @ X161 @ (esk78_1 @ X158)|~fin @ X161 @ X158|~fin @ X159 @ X158|~p2)), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax2])])])])])])).
% 43.95/44.08 thf(c_0_28, plain, (p1|p2), inference(split_conjunct,[status(thm)],[ax125])).
% 43.95/44.08 thf(c_0_29, plain, ![X154:$i, X155:$i]:(~p4|fin @ X154 @ (fsetadjoin @ X154 @ X155)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax4])])])).
% 43.95/44.08 thf(c_0_30, plain, (p3|p4), inference(split_conjunct,[status(thm)],[ax123])).
% 43.95/44.08 thf(c_0_31, plain, ![X120:$i, X121:$i, X122:$i]:(~p14|(~fin @ X122 @ (fsetadjoin @ X120 @ (fsetadjoin @ X121 @ femptyset))|((X122)=(X120)|(X122)=(X121)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax14])])])])).
% 43.95/44.08 thf(c_0_32, plain, (p12|p14), inference(split_conjunct,[status(thm)],[ax113])).
% 43.95/44.08 thf(c_0_33, plain, ~p12, inference(sr,[status(thm)],[c_0_25, c_0_26])).
% 43.95/44.08 thf(c_0_34, plain, ![X2:$i, X1:$i]:(fin @ (esk78_1 @ X1) @ X1|~fin @ X2 @ X1|~p2), inference(split_conjunct,[status(thm)],[c_0_27])).
% 43.95/44.08 thf(c_0_35, plain, p2, inference(sr,[status(thm)],[c_0_28, c_0_18])).
% 43.95/44.08 thf(c_0_36, plain, ![X1:$i, X2:$i]:(fin @ X1 @ (fsetadjoin @ X1 @ X2)|~p4), inference(split_conjunct,[status(thm)],[c_0_29])).
% 43.95/44.08 thf(c_0_37, plain, p4, inference(sr,[status(thm)],[c_0_30, c_0_21])).
% 43.95/44.08 thf(c_0_38, plain, ![X1:$i, X2:$i, X3:$i]:((X1)=(X2)|(X1)=(X3)|~p14|~fin @ X1 @ (fsetadjoin @ X2 @ (fsetadjoin @ X3 @ femptyset))), inference(split_conjunct,[status(thm)],[c_0_31])).
% 43.95/44.08 thf(c_0_39, plain, p14, inference(sr,[status(thm)],[c_0_32, c_0_33])).
% 43.95/44.08 thf(c_0_40, plain, ![X2:$i, X1:$i]:(fin @ (esk78_1 @ X1) @ X1|~fin @ X2 @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34, c_0_35])])).
% 43.95/44.08 thf(c_0_41, plain, ![X1:$i, X2:$i]:fin @ X1 @ (fsetadjoin @ X1 @ X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36, c_0_37])])).
% 43.95/44.08 thf(c_0_42, plain, ![X1:$i, X3:$i, X2:$i]:(~fin @ X1 @ (esk78_1 @ X2)|~fin @ X1 @ X2|~fin @ X3 @ X2|~p2), inference(split_conjunct,[status(thm)],[c_0_27])).
% 43.95/44.08 thf(c_0_43, plain, ![X1:$i, X2:$i, X3:$i]:((X1)=(X2)|(X1)=(X3)|~fin @ X1 @ (fsetadjoin @ X2 @ (fsetadjoin @ X3 @ femptyset))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38, c_0_39])])).
% 43.95/44.08 thf(c_0_44, plain, ![X1:$i, X2:$i]:fin @ (esk78_1 @ (fsetadjoin @ X1 @ X2)) @ (fsetadjoin @ X1 @ X2), inference(spm,[status(thm)],[c_0_40, c_0_41])).
% 43.95/44.08 thf(c_0_45, plain, ![X1:$i, X3:$i, X2:$i]:(~fin @ X1 @ (esk78_1 @ X2)|~fin @ X3 @ X2|~fin @ X1 @ X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42, c_0_35])])).
% 43.95/44.08 thf(c_0_46, plain, ![X1:$i, X2:$i]:((esk78_1 @ (fsetadjoin @ X1 @ (fsetadjoin @ X2 @ femptyset)))=(X1)|(esk78_1 @ (fsetadjoin @ X1 @ (fsetadjoin @ X2 @ femptyset)))=(X2)), inference(spm,[status(thm)],[c_0_43, c_0_44])).
% 43.95/44.08 thf(c_0_47, plain, ![X1:$i, X4:$i, X3:$i, X2:$i]:((esk78_1 @ (fsetadjoin @ X1 @ (fsetadjoin @ X2 @ femptyset)))=(X1)|~fin @ X3 @ (fsetadjoin @ X1 @ (fsetadjoin @ X2 @ femptyset))|~fin @ X4 @ (fsetadjoin @ X1 @ (fsetadjoin @ X2 @ femptyset))|~fin @ X4 @ X2), inference(spm,[status(thm)],[c_0_45, c_0_46])).
% 43.95/44.08 thf(c_0_48, plain, ![X140:$i, X141:$i, X142:$i]:(~p8|(~fin @ X142 @ X141|fin @ X142 @ (fsetadjoin @ X140 @ X141))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax8])])])).
% 43.95/44.08 thf(c_0_49, plain, (p5|p8), inference(split_conjunct,[status(thm)],[ax119])).
% 43.95/44.08 thf(c_0_50, plain, ![X1:$i, X3:$i, X2:$i]:((esk78_1 @ (fsetadjoin @ X1 @ (fsetadjoin @ X2 @ femptyset)))=(X1)|~fin @ X3 @ (fsetadjoin @ X1 @ (fsetadjoin @ X2 @ femptyset))|~fin @ X3 @ X2), inference(spm,[status(thm)],[c_0_47, c_0_44])).
% 43.95/44.08 thf(c_0_51, plain, ![X1:$i, X3:$i, X2:$i]:(fin @ X1 @ (fsetadjoin @ X3 @ X2)|~p8|~fin @ X1 @ X2), inference(split_conjunct,[status(thm)],[c_0_48])).
% 43.95/44.08 thf(c_0_52, plain, p8, inference(sr,[status(thm)],[c_0_49, c_0_24])).
% 43.95/44.08 thf(c_0_53, plain, ![X1:$i, X2:$i]:((esk78_1 @ (fsetadjoin @ X1 @ (fsetadjoin @ X2 @ femptyset)))=(X1)|~fin @ X1 @ X2), inference(spm,[status(thm)],[c_0_50, c_0_41])).
% 43.95/44.08 thf(c_0_54, plain, ![X1:$i, X2:$i, X3:$i]:(fin @ X1 @ (fsetadjoin @ X2 @ X3)|~fin @ X1 @ X3), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51, c_0_52])])).
% 43.95/44.08 thf(c_0_55, plain, ![X1:$i, X2:$i, X4:$i, X3:$i]:(~fin @ X1 @ (fsetadjoin @ X2 @ (fsetadjoin @ X3 @ femptyset))|~fin @ X4 @ (fsetadjoin @ X2 @ (fsetadjoin @ X3 @ femptyset))|~fin @ X4 @ X2|~fin @ X2 @ X3), inference(spm,[status(thm)],[c_0_45, c_0_53])).
% 43.95/44.08 thf(c_0_56, plain, ![X1:$i, X2:$i, X3:$i]:((X1)=(X2)|(X1)=(X3)|~fin @ X1 @ (fsetadjoin @ X3 @ femptyset)), inference(spm,[status(thm)],[c_0_43, c_0_54])).
% 43.95/44.08 thf(c_0_57, plain, ![X1:$i, X2:$i, X3:$i]:(~fin @ X1 @ (fsetadjoin @ X2 @ (fsetadjoin @ X3 @ femptyset))|~fin @ X1 @ X2|~fin @ X2 @ X3), inference(spm,[status(thm)],[c_0_55, c_0_44])).
% 43.95/44.08 thf(c_0_58, plain, ![X1:$i, X2:$i]:((esk78_1 @ (fsetadjoin @ X1 @ femptyset))=(X1)|(esk78_1 @ (fsetadjoin @ X1 @ femptyset))=(X2)), inference(spm,[status(thm)],[c_0_56, c_0_44])).
% 43.95/44.08 thf(c_0_59, plain, ![X131:$i, X132:$i, X133:$i]:((~fin @ X133 @ (fsetadjoin @ X131 @ (fsetadjoin @ X132 @ femptyset))|((X133)=(X131)|(X133)=(X132))|p12)&((fin @ esk65_0 @ esk66_0|p12)&(fin @ esk66_0 @ esk65_0|p12))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax12])])])])])])).
% 43.95/44.08 thf(c_0_60, plain, ![X1:$i, X3:$i, X2:$i]:(~fin @ X1 @ (fsetadjoin @ X2 @ femptyset)|~fin @ X1 @ X3|~fin @ X3 @ X2), inference(spm,[status(thm)],[c_0_57, c_0_54])).
% 43.95/44.08 thf(c_0_61, plain, ![X1:$i]:(esk78_1 @ (fsetadjoin @ X1 @ femptyset))=(X1), inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_58])])).
% 43.95/44.08 thf(c_0_62, plain, (fin @ esk65_0 @ esk66_0|p12), inference(split_conjunct,[status(thm)],[c_0_59])).
% 43.95/44.08 thf(c_0_63, plain, (fin @ esk66_0 @ esk65_0|p12), inference(split_conjunct,[status(thm)],[c_0_59])).
% 43.95/44.08 thf(c_0_64, plain, ![X2:$i, X1:$i]:(~fin @ X1 @ X2|~fin @ X2 @ X1), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_44]), c_0_61])).
% 43.95/44.08 thf(c_0_65, plain, fin @ esk65_0 @ esk66_0, inference(sr,[status(thm)],[c_0_62, c_0_33])).
% 43.95/44.08 thf(c_0_66, plain, fin @ esk66_0 @ esk65_0, inference(sr,[status(thm)],[c_0_63, c_0_33])).
% 43.95/44.08 thf(c_0_67, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_65]), c_0_66])]), ['proof']).
% 43.95/44.08 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 43.95/44.08 thf(0,theorem,((![X1:$i]:((~((![X2:$i]:(~(((in @ X2) @ X1)))))) => (~((![X2:$i]:(((in @ X2) @ X1) => (~((![X3:$i]:(((in @ X3) @ X2) => (~(((in @ X3) @ X1))))))))))))) => ((![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X2) => ((in @ X3) @ ((setadjoin @ X1) @ X2)))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) = ((in @ X4) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) => ((~((X3 = X1))) => (X3 = X2)))))) => (![X1:$i]:(![X2:$i]:(((in @ X1) @ X2) => (~(((in @ X2) @ X1))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 43.95/44.08 % SZS output end Proof
%------------------------------------------------------------------------------