TSTP Solution File: SEU599^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU599^2 : 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 : n024.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 13:54:00 EDT 2022
% Result : Theorem 2.79s 3.05s
% Output : Proof 2.79s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU599^2 : 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
% 0.12/0.33 % Computer : n024.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 : Mon Jun 20 06:28:32 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.79/3.05 % SZS status Theorem
% 2.79/3.05 % Mode: mode506
% 2.79/3.05 % Inferences: 20971
% 2.79/3.05 % SZS output start Proof
% 2.79/3.05 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)))))))))).
% 2.79/3.05 thf(def_subsetI1,definition,(subsetI1 = (![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))))).
% 2.79/3.05 thf(def_binintersectER,definition,(binintersectER = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X2))))))).
% 2.79/3.05 thf(binintersectSubset1,conjecture,((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) = ((in @ X4) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X2))))) => (![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X1) => ((subset @ X1) @ X2)))))))).
% 2.79/3.05 thf(h0,negated_conjecture,(~(((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) = ((in @ X4) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((![X3:$i]:(((in @ X3) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X2))))) => (![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X1) => ((subset @ X1) @ X2))))))))),inference(assume_negation,[status(cth)],[binintersectSubset1])).
% 2.79/3.05 thf(ax1173, axiom, (p1|~(p3)), file('<stdin>', ax1173)).
% 2.79/3.05 thf(ax1175, axiom, ~(p1), file('<stdin>', ax1175)).
% 2.79/3.05 thf(ax1171, axiom, (p3|~(p5)), file('<stdin>', ax1171)).
% 2.79/3.05 thf(ax1169, axiom, (p5|~(p7)), file('<stdin>', ax1169)).
% 2.79/3.05 thf(ax1168, axiom, (p7|~(p8)), file('<stdin>', ax1168)).
% 2.79/3.05 thf(ax1132, axiom, (~(p4)|p45), file('<stdin>', ax1132)).
% 2.79/3.05 thf(ax1172, axiom, (p3|p4), file('<stdin>', ax1172)).
% 2.79/3.05 thf(ax1167, axiom, (p8|~(p9)), file('<stdin>', ax1167)).
% 2.79/3.05 thf(ax1133, axiom, (~(p45)|p44), file('<stdin>', ax1133)).
% 2.79/3.05 thf(nax3, axiom, (p3<=(![X1:$i, X2:$i]:(![X3:$i]:(fin @ X3 @ X1=>fin @ X3 @ X2)=>fsubset @ X1 @ X2)=>(![X1:$i, X2:$i, X3:$i]:(fin @ X3 @ (fbinintersect @ X1 @ X2)=>fin @ X3 @ X2)=>![X1:$i, X2:$i]:((fbinintersect @ X1 @ X2)=(X1)=>fsubset @ X1 @ X2)))), file('<stdin>', nax3)).
% 2.79/3.05 thf(nax9, axiom, (p9<=((fbinintersect @ f__0 @ f__1)=(f__0)=>fsubset @ f__0 @ f__1)), file('<stdin>', nax9)).
% 2.79/3.05 thf(pax44, axiom, (p44=>(![X1:$i]:(fin @ X1 @ f__0=>fin @ X1 @ f__1)=>fsubset @ f__0 @ f__1)), file('<stdin>', pax44)).
% 2.79/3.05 thf(c_0_12, plain, (p1|~p3), inference(fof_simplification,[status(thm)],[ax1173])).
% 2.79/3.05 thf(c_0_13, plain, ~p1, inference(fof_simplification,[status(thm)],[ax1175])).
% 2.79/3.05 thf(c_0_14, plain, (p3|~p5), inference(fof_simplification,[status(thm)],[ax1171])).
% 2.79/3.05 thf(c_0_15, plain, (p1|~p3), inference(split_conjunct,[status(thm)],[c_0_12])).
% 2.79/3.05 thf(c_0_16, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_13])).
% 2.79/3.05 thf(c_0_17, plain, (p5|~p7), inference(fof_simplification,[status(thm)],[ax1169])).
% 2.79/3.05 thf(c_0_18, plain, (p3|~p5), inference(split_conjunct,[status(thm)],[c_0_14])).
% 2.79/3.05 thf(c_0_19, plain, ~p3, inference(sr,[status(thm)],[c_0_15, c_0_16])).
% 2.79/3.05 thf(c_0_20, plain, (p7|~p8), inference(fof_simplification,[status(thm)],[ax1168])).
% 2.79/3.05 thf(c_0_21, plain, (p5|~p7), inference(split_conjunct,[status(thm)],[c_0_17])).
% 2.79/3.05 thf(c_0_22, plain, ~p5, inference(sr,[status(thm)],[c_0_18, c_0_19])).
% 2.79/3.05 thf(c_0_23, plain, (~p4|p45), inference(fof_simplification,[status(thm)],[ax1132])).
% 2.79/3.05 thf(c_0_24, plain, (p3|p4), inference(split_conjunct,[status(thm)],[ax1172])).
% 2.79/3.05 thf(c_0_25, plain, (p8|~p9), inference(fof_simplification,[status(thm)],[ax1167])).
% 2.79/3.05 thf(c_0_26, plain, (p7|~p8), inference(split_conjunct,[status(thm)],[c_0_20])).
% 2.79/3.05 thf(c_0_27, plain, ~p7, inference(sr,[status(thm)],[c_0_21, c_0_22])).
% 2.79/3.05 thf(c_0_28, plain, (~p45|p44), inference(fof_simplification,[status(thm)],[ax1133])).
% 2.79/3.05 thf(c_0_29, plain, (p45|~p4), inference(split_conjunct,[status(thm)],[c_0_23])).
% 2.79/3.05 thf(c_0_30, plain, p4, inference(sr,[status(thm)],[c_0_24, c_0_19])).
% 2.79/3.05 thf(c_0_31, plain, ![X1032:$i, X1033:$i, X1035:$i, X1036:$i, X1037:$i]:(((fin @ (esk516_2 @ X1032 @ X1033) @ X1032|fsubset @ X1032 @ X1033|p3)&(~fin @ (esk516_2 @ X1032 @ X1033) @ X1033|fsubset @ X1032 @ X1033|p3))&((~fin @ X1037 @ (fbinintersect @ X1035 @ X1036)|fin @ X1037 @ X1036|p3)&(((fbinintersect @ esk517_0 @ esk518_0)=(esk517_0)|p3)&(~fsubset @ esk517_0 @ esk518_0|p3)))), 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)],[nax3])])])])])])).
% 2.79/3.05 thf(c_0_32, plain, (((fbinintersect @ f__0 @ f__1)=(f__0)|p9)&(~fsubset @ f__0 @ f__1|p9)), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax9])])])).
% 2.79/3.05 thf(c_0_33, plain, (p8|~p9), inference(split_conjunct,[status(thm)],[c_0_25])).
% 2.79/3.05 thf(c_0_34, plain, ~p8, inference(sr,[status(thm)],[c_0_26, c_0_27])).
% 2.79/3.05 thf(c_0_35, plain, ((fin @ esk473_0 @ f__0|fsubset @ f__0 @ f__1|~p44)&(~fin @ esk473_0 @ f__1|fsubset @ f__0 @ f__1|~p44)), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax44])])])])).
% 2.79/3.05 thf(c_0_36, plain, (p44|~p45), inference(split_conjunct,[status(thm)],[c_0_28])).
% 2.79/3.05 thf(c_0_37, plain, p45, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29, c_0_30])])).
% 2.79/3.05 thf(c_0_38, plain, ![X1:$i, X2:$i, X3:$i]:(fin @ X1 @ X3|p3|~fin @ X1 @ (fbinintersect @ X2 @ X3)), inference(split_conjunct,[status(thm)],[c_0_31])).
% 2.79/3.05 thf(c_0_39, plain, ((fbinintersect @ f__0 @ f__1)=(f__0)|p9), inference(split_conjunct,[status(thm)],[c_0_32])).
% 2.79/3.05 thf(c_0_40, plain, ~p9, inference(sr,[status(thm)],[c_0_33, c_0_34])).
% 2.79/3.05 thf(c_0_41, plain, (fin @ esk473_0 @ f__0|fsubset @ f__0 @ f__1|~p44), inference(split_conjunct,[status(thm)],[c_0_35])).
% 2.79/3.05 thf(c_0_42, plain, p44, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36, c_0_37])])).
% 2.79/3.05 thf(c_0_43, plain, (p9|~fsubset @ f__0 @ f__1), inference(split_conjunct,[status(thm)],[c_0_32])).
% 2.79/3.05 thf(c_0_44, plain, (fsubset @ f__0 @ f__1|~fin @ esk473_0 @ f__1|~p44), inference(split_conjunct,[status(thm)],[c_0_35])).
% 2.79/3.05 thf(c_0_45, plain, ![X1:$i, X3:$i, X2:$i]:(fin @ X1 @ X2|~fin @ X1 @ (fbinintersect @ X3 @ X2)), inference(sr,[status(thm)],[c_0_38, c_0_19])).
% 2.79/3.05 thf(c_0_46, plain, (fbinintersect @ f__0 @ f__1)=(f__0), inference(sr,[status(thm)],[c_0_39, c_0_40])).
% 2.79/3.05 thf(c_0_47, plain, (fsubset @ f__0 @ f__1|fin @ esk473_0 @ f__0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41, c_0_42])])).
% 2.79/3.05 thf(c_0_48, plain, ~fsubset @ f__0 @ f__1, inference(sr,[status(thm)],[c_0_43, c_0_40])).
% 2.79/3.05 thf(c_0_49, plain, (fsubset @ f__0 @ f__1|~fin @ esk473_0 @ f__1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44, c_0_42])])).
% 2.79/3.05 thf(c_0_50, plain, ![X1:$i]:(fin @ X1 @ f__1|~fin @ X1 @ f__0), inference(spm,[status(thm)],[c_0_45, c_0_46])).
% 2.79/3.05 thf(c_0_51, plain, fin @ esk473_0 @ f__0, inference(sr,[status(thm)],[c_0_47, c_0_48])).
% 2.79/3.05 thf(c_0_52, plain, ~fin @ esk473_0 @ f__1, inference(sr,[status(thm)],[c_0_49, c_0_48])).
% 2.79/3.05 thf(c_0_53, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_51]), c_0_52]), ['proof']).
% 2.79/3.05 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 2.79/3.05 thf(0,theorem,((![X1:$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) @ X1) => ((in @ X3) @ X2))) => ((subset @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((binintersect @ X1) @ X2)) => ((in @ X3) @ X2))))) => (![X1:$i]:(![X2:$i]:((((binintersect @ X1) @ X2) = X1) => ((subset @ X1) @ X2))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 2.79/3.05 % SZS output end Proof
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