%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : SWV426^4 : TPTP v9.2.0. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n003.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 : 300s % DateTime : Thu Oct 9 03:07:20 PM UTC 2025 % Result : Theorem 0.13s 0.41s % Output : Proof 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : SWV426^4 : TPTP v9.2.0. Released v3.6.0. % 0.13/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n003.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Wed Oct 8 14:24:08 EDT 2025 % 0.13/0.35 % CPUTime : % 0.13/0.41 % SZS status Theorem % 0.13/0.41 % Mode: mode213 % 0.13/0.41 % Inferences: 605 % 0.13/0.41 % SZS output start Proof % 0.13/0.41 thf(ty_a, type, a : ($i>$o)). % 0.13/0.41 thf(ty_eigen__2, type, eigen__2 : $i). % 0.13/0.41 thf(ty_s, type, s : ($i>$o)). % 0.13/0.41 thf(ty_eigen__1, type, eigen__1 : $i). % 0.13/0.41 thf(ty_b, type, b : ($i>$o)). % 0.13/0.41 thf(ty_eigen__0, type, eigen__0 : $i). % 0.13/0.41 thf(ty_eigen__4, type, eigen__4 : $i). % 0.13/0.41 thf(ty_eigen__3, type, eigen__3 : $i). % 0.13/0.41 thf(ty_rel, type, rel : ($i>$i>$o)). % 0.13/0.41 thf(sP1,plain,sP1 <=> ((rel @ eigen__3) @ eigen__4),introduced(definition,[new_symbols(definition,[sP1])])). % 0.13/0.41 thf(sP2,plain,sP2 <=> (![X1:$i]:(((rel @ eigen__1) @ X1) => ((~((![X2:$i]:(((rel @ X1) @ X2) => ((a @ X2) => (b @ X2)))))) => (![X2:$i]:(((rel @ X1) @ X2) => (s @ X2)))))),introduced(definition,[new_symbols(definition,[sP2])])). % 0.13/0.41 thf(sP3,plain,sP3 <=> ((a @ eigen__3) => (b @ eigen__3)),introduced(definition,[new_symbols(definition,[sP3])])). % 0.13/0.41 thf(sP4,plain,sP4 <=> (![X1:$i]:(((rel @ eigen__2) @ X1) => ((~((a @ X1))) => (![X2:$i]:(((rel @ X1) @ X2) => (s @ X2)))))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.13/0.41 thf(sP5,plain,sP5 <=> (((rel @ eigen__2) @ eigen__3) => sP3),introduced(definition,[new_symbols(definition,[sP5])])). % 0.13/0.41 thf(sP6,plain,sP6 <=> (sP1 => (s @ eigen__4)),introduced(definition,[new_symbols(definition,[sP6])])). % 0.13/0.41 thf(sP7,plain,sP7 <=> ((![X1:$i]:(((rel @ eigen__2) @ X1) => (s @ X1))) => (![X1:$i]:(((rel @ eigen__2) @ X1) => (![X2:$i]:(((rel @ X1) @ X2) => (s @ X2)))))),introduced(definition,[new_symbols(definition,[sP7])])). % 0.13/0.41 thf(sP8,plain,sP8 <=> (![X1:$i]:(((rel @ eigen__2) @ X1) => (![X2:$i]:(((rel @ X1) @ X2) => (s @ X2))))),introduced(definition,[new_symbols(definition,[sP8])])). % 0.13/0.41 thf(sP9,plain,sP9 <=> ((rel @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP9])])). % 0.13/0.41 thf(sP10,plain,sP10 <=> (((rel @ eigen__2) @ eigen__3) => (![X1:$i]:(((rel @ eigen__3) @ X1) => (s @ X1)))),introduced(definition,[new_symbols(definition,[sP10])])). % 0.13/0.41 thf(sP11,plain,sP11 <=> (sP9 => ((~((![X1:$i]:(((rel @ eigen__2) @ X1) => ((a @ X1) => (b @ X1)))))) => (![X1:$i]:(((rel @ eigen__2) @ X1) => (s @ X1))))),introduced(definition,[new_symbols(definition,[sP11])])). % 0.13/0.41 thf(sP12,plain,sP12 <=> (![X1:$i]:(((rel @ eigen__2) @ X1) => (s @ X1))),introduced(definition,[new_symbols(definition,[sP12])])). % 0.13/0.41 thf(sP13,plain,sP13 <=> ((~((a @ eigen__3))) => (![X1:$i]:(((rel @ eigen__3) @ X1) => (s @ X1)))),introduced(definition,[new_symbols(definition,[sP13])])). % 0.13/0.41 thf(sP14,plain,sP14 <=> (![X1:$i>$o]:(![X2:$i]:((![X3:$i]:(((rel @ X2) @ X3) => (X1 @ X3))) => (![X3:$i]:(((rel @ X2) @ X3) => (![X4:$i]:(((rel @ X3) @ X4) => (X1 @ X4)))))))),introduced(definition,[new_symbols(definition,[sP14])])). % 0.13/0.41 thf(sP15,plain,sP15 <=> (![X1:$i]:(((rel @ eigen__3) @ X1) => (s @ X1))),introduced(definition,[new_symbols(definition,[sP15])])). % 0.13/0.41 thf(sP16,plain,sP16 <=> (b @ eigen__3),introduced(definition,[new_symbols(definition,[sP16])])). % 0.13/0.41 thf(sP17,plain,sP17 <=> (s @ eigen__4),introduced(definition,[new_symbols(definition,[sP17])])). % 0.13/0.41 thf(sP18,plain,sP18 <=> (![X1:$i]:((![X2:$i]:(((rel @ X1) @ X2) => (s @ X2))) => (![X2:$i]:(((rel @ X1) @ X2) => (![X3:$i]:(((rel @ X2) @ X3) => (s @ X3))))))),introduced(definition,[new_symbols(definition,[sP18])])). % 0.13/0.41 thf(sP19,plain,sP19 <=> (a @ eigen__3),introduced(definition,[new_symbols(definition,[sP19])])). % 0.13/0.41 thf(sP20,plain,sP20 <=> ((~((![X1:$i]:(((rel @ eigen__2) @ X1) => ((a @ X1) => (b @ X1)))))) => sP12),introduced(definition,[new_symbols(definition,[sP20])])). % 0.13/0.41 thf(sP21,plain,sP21 <=> (((rel @ eigen__2) @ eigen__3) => sP13),introduced(definition,[new_symbols(definition,[sP21])])). % 0.13/0.41 thf(sP22,plain,sP22 <=> (![X1:$i]:(((rel @ eigen__2) @ X1) => ((a @ X1) => (b @ X1)))),introduced(definition,[new_symbols(definition,[sP22])])). % 0.13/0.41 thf(sP23,plain,sP23 <=> ((rel @ eigen__2) @ eigen__3),introduced(definition,[new_symbols(definition,[sP23])])). % 0.13/0.41 thf(def_mfalse,definition,(mfalse = (^[X1:$i]:$false))). % 0.13/0.41 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 0.13/0.41 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 0.13/0.41 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 0.13/0.41 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 0.13/0.41 thf(def_mimpl,definition,(mimpl = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 0.13/0.41 thf(def_miff,definition,(miff = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimpl @ X1) @ X2)) @ ((mimpl @ X2) @ X1)))))). % 0.13/0.41 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 0.13/0.41 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~((![X4:$i]:(((X1 @ X3) @ X4) => (~((X2 @ X4)))))))))))). % 0.13/0.41 thf(def_mall,definition,(mall = (^[X1:individuals>$i>$o]:(^[X2:$i]:(![X3:individuals]:((X1 @ X3) @ X2)))))). % 0.13/0.41 thf(def_mexists,definition,(mexists = (^[X1:individuals>$i>$o]:(^[X2:$i]:(~((![X3:individuals]:(~(((X1 @ X3) @ X2)))))))))). % 0.13/0.41 thf(def_mvalid,definition,(mvalid = (!!))). % 0.13/0.41 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 0.13/0.41 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 0.13/0.41 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 0.13/0.41 thf(def_icl_atom,definition,(icl_atom = (mbox @ rel))). % 0.13/0.41 thf(def_icl_princ,definition,(icl_princ = (^[X1:$i>$o]:X1))). % 0.13/0.41 thf(def_icl_and,definition,(icl_and = mand)). % 0.13/0.41 thf(def_icl_or,definition,(icl_or = mor)). % 0.13/0.41 thf(def_icl_impl,definition,(icl_impl = (^[X1:$i>$o]:(^[X2:$i>$o]:((mbox @ rel) @ ((mimpl @ X1) @ X2)))))). % 0.13/0.41 thf(def_icl_true,definition,(icl_true = mtrue)). % 0.13/0.41 thf(def_icl_false,definition,(icl_false = mfalse)). % 0.13/0.41 thf(def_icl_says,definition,(icl_says = (^[X1:$i>$o]:(^[X2:$i>$o]:((mbox @ rel) @ ((mor @ X1) @ X2)))))). % 0.13/0.41 thf(def_iclval,definition,(iclval = mvalid)). % 0.13/0.41 thf(cuc,conjecture,(![X1:$i]:(![X2:$i]:(((rel @ X1) @ X2) => ((~((~((![X3:$i]:(((rel @ X2) @ X3) => ((~((![X4:$i]:(((rel @ X3) @ X4) => ((~((~((a @ X4))))) => (b @ X4)))))) => (![X4:$i]:(((rel @ X3) @ X4) => (s @ X4)))))))))) => (![X3:$i]:(((rel @ X2) @ X3) => ((~((~((![X4:$i]:(((rel @ X3) @ X4) => ((~((a @ X4))) => (![X5:$i]:(((rel @ X4) @ X5) => (s @ X5)))))))))) => (![X4:$i]:(((rel @ X3) @ X4) => ((~((b @ X4))) => (![X5:$i]:(((rel @ X4) @ X5) => (s @ X5)))))))))))))). % 0.13/0.41 thf(h0,negated_conjecture,(~((![X1:$i]:(![X2:$i]:(((rel @ X1) @ X2) => ((![X3:$i]:(((rel @ X2) @ X3) => ((~((![X4:$i]:(((rel @ X3) @ X4) => ((a @ X4) => (b @ X4)))))) => (![X4:$i]:(((rel @ X3) @ X4) => (s @ X4)))))) => (![X3:$i]:(((rel @ X2) @ X3) => ((![X4:$i]:(((rel @ X3) @ X4) => ((~((a @ X4))) => (![X5:$i]:(((rel @ X4) @ X5) => (s @ X5)))))) => (![X4:$i]:(((rel @ X3) @ X4) => ((~((b @ X4))) => (![X5:$i]:(((rel @ X4) @ X5) => (s @ X5))))))))))))))),inference(assume_negation,[status(cth)],[cuc])). % 0.13/0.41 thf(h1,assumption,(~((![X1:$i]:(((rel @ eigen__0) @ X1) => ((![X2:$i]:(((rel @ X1) @ X2) => ((~((![X3:$i]:(((rel @ X2) @ X3) => ((a @ X3) => (b @ X3)))))) => (![X3:$i]:(((rel @ X2) @ X3) => (s @ X3)))))) => (![X2:$i]:(((rel @ X1) @ X2) => ((![X3:$i]:(((rel @ X2) @ X3) => ((~((a @ X3))) => (![X4:$i]:(((rel @ X3) @ X4) => (s @ X4)))))) => (![X3:$i]:(((rel @ X2) @ X3) => ((~((b @ X3))) => (![X4:$i]:(((rel @ X3) @ X4) => (s @ X4)))))))))))))),introduced(assumption,[])). % 0.13/0.41 thf(h2,assumption,(~((((rel @ eigen__0) @ eigen__1) => (sP2 => (![X1:$i]:(((rel @ eigen__1) @ X1) => ((![X2:$i]:(((rel @ X1) @ X2) => ((~((a @ X2))) => (![X3:$i]:(((rel @ X2) @ X3) => (s @ X3)))))) => (![X2:$i]:(((rel @ X1) @ X2) => ((~((b @ X2))) => (![X3:$i]:(((rel @ X2) @ X3) => (s @ X3))))))))))))),introduced(assumption,[])). % 0.13/0.41 thf(h3,assumption,((rel @ eigen__0) @ eigen__1),introduced(assumption,[])). % 0.13/0.41 thf(h4,assumption,(~((sP2 => (![X1:$i]:(((rel @ eigen__1) @ X1) => ((![X2:$i]:(((rel @ X1) @ X2) => ((~((a @ X2))) => (![X3:$i]:(((rel @ X2) @ X3) => (s @ X3)))))) => (![X2:$i]:(((rel @ X1) @ X2) => ((~((b @ X2))) => (![X3:$i]:(((rel @ X2) @ X3) => (s @ X3)))))))))))),introduced(assumption,[])). % 0.13/0.41 thf(h5,assumption,sP2,introduced(assumption,[])). % 0.13/0.41 thf(h6,assumption,(~((![X1:$i]:(((rel @ eigen__1) @ X1) => ((![X2:$i]:(((rel @ X1) @ X2) => ((~((a @ X2))) => (![X3:$i]:(((rel @ X2) @ X3) => (s @ X3)))))) => (![X2:$i]:(((rel @ X1) @ X2) => ((~((b @ X2))) => (![X3:$i]:(((rel @ X2) @ X3) => (s @ X3))))))))))),introduced(assumption,[])). % 0.13/0.41 thf(h7,assumption,(~((sP9 => (sP4 => (![X1:$i]:(((rel @ eigen__2) @ X1) => ((~((b @ X1))) => (![X2:$i]:(((rel @ X1) @ X2) => (s @ X2)))))))))),introduced(assumption,[])). % 0.13/0.41 thf(h8,assumption,sP9,introduced(assumption,[])). % 0.13/0.41 thf(h9,assumption,(~((sP4 => (![X1:$i]:(((rel @ eigen__2) @ X1) => ((~((b @ X1))) => (![X2:$i]:(((rel @ X1) @ X2) => (s @ X2))))))))),introduced(assumption,[])). % 0.13/0.41 thf(h10,assumption,sP4,introduced(assumption,[])). % 0.13/0.41 thf(h11,assumption,(~((![X1:$i]:(((rel @ eigen__2) @ X1) => ((~((b @ X1))) => (![X2:$i]:(((rel @ X1) @ X2) => (s @ X2)))))))),introduced(assumption,[])). % 0.13/0.41 thf(h12,assumption,(~((sP23 => ((~(sP16)) => sP15)))),introduced(assumption,[])). % 0.13/0.41 thf(h13,assumption,sP23,introduced(assumption,[])). % 0.13/0.41 thf(h14,assumption,(~(((~(sP16)) => sP15))),introduced(assumption,[])). % 0.13/0.41 thf(h15,assumption,(~(sP16)),introduced(assumption,[])). % 0.13/0.41 thf(h16,assumption,(~(sP15)),introduced(assumption,[])). % 0.13/0.41 thf(h17,assumption,(~(sP6)),introduced(assumption,[])). % 0.13/0.41 thf(h18,assumption,sP1,introduced(assumption,[])). % 0.13/0.41 thf(h19,assumption,(~(sP17)),introduced(assumption,[])). % 0.13/0.41 thf(1,plain,(~(sP8) | sP10),inference(all_rule,[status(thm)],[])). % 0.13/0.41 thf(2,plain,((~(sP10) | ~(sP23)) | sP15),inference(prop_rule,[status(thm)],[])). % 0.13/0.41 thf(3,plain,(~(sP18) | sP7),inference(all_rule,[status(thm)],[])). % 0.13/0.41 thf(4,plain,((~(sP7) | ~(sP12)) | sP8),inference(prop_rule,[status(thm)],[])). % 0.13/0.41 thf(5,plain,(~(sP14) | sP18),inference(all_rule,[status(thm)],[])). % 0.13/0.41 thf(6,plain,(~(sP22) | sP5),inference(all_rule,[status(thm)],[])). % 0.13/0.41 thf(7,plain,((~(sP5) | ~(sP23)) | sP3),inference(prop_rule,[status(thm)],[])). % 0.13/0.41 thf(8,plain,((~(sP3) | ~(sP19)) | sP16),inference(prop_rule,[status(thm)],[])). % 0.13/0.41 thf(9,plain,(~(sP2) | sP11),inference(all_rule,[status(thm)],[])). % 0.13/0.41 thf(10,plain,((~(sP11) | ~(sP9)) | sP20),inference(prop_rule,[status(thm)],[])). % 0.13/0.41 thf(11,plain,((~(sP20) | sP22) | sP12),inference(prop_rule,[status(thm)],[])). % 0.13/0.41 thf(12,plain,(~(sP15) | sP6),inference(all_rule,[status(thm)],[])). % 0.13/0.41 thf(13,plain,((~(sP6) | ~(sP1)) | sP17),inference(prop_rule,[status(thm)],[])). % 0.13/0.41 thf(14,plain,(~(sP4) | sP21),inference(all_rule,[status(thm)],[])). % 0.13/0.41 thf(15,plain,((~(sP21) | ~(sP23)) | sP13),inference(prop_rule,[status(thm)],[])). % 0.13/0.41 thf(16,plain,((~(sP13) | sP19) | sP15),inference(prop_rule,[status(thm)],[])). % 0.13/0.41 thf(trans_axiom,axiom,(![X1:$i>$o]:(mvalid @ ((mimpl @ ((mbox @ rel) @ X1)) @ ((mbox @ rel) @ ((mbox @ rel) @ X1)))))). % 0.13/0.41 thf(17,plain,sP14,inference(preprocess,[status(thm)],[trans_axiom]). % 0.13/0.41 thf(18,plain,$false,inference(prop_unsat,[status(thm),assumptions([h18,h19,h17,h15,h16,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,h5,h8,h10,h13,h15,h18,h19])). % 0.13/0.41 thf(19,plain,$false,inference(tab_negimp,[status(thm),assumptions([h17,h15,h16,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h18,h19])],[h17,18,h18,h19])). % 0.13/0.41 thf(20,plain,$false,inference(tab_negall,[status(thm),assumptions([h15,h16,h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__4)],[h16,19,h17])). % 0.13/0.41 thf(21,plain,$false,inference(tab_negimp,[status(thm),assumptions([h13,h14,h12,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,20,h15,h16])). % 0.13/0.41 thf(22,plain,$false,inference(tab_negimp,[status(thm),assumptions([h12,h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,21,h13,h14])). % 0.13/0.41 thf(23,plain,$false,inference(tab_negall,[status(thm),assumptions([h10,h11,h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__3)],[h11,22,h12])). % 0.13/0.41 thf(24,plain,$false,inference(tab_negimp,[status(thm),assumptions([h8,h9,h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,23,h10,h11])). % 0.13/0.41 thf(25,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,24,h8,h9])). % 0.13/0.41 thf(26,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,25,h7])). % 0.13/0.41 thf(27,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,26,h5,h6])). % 0.13/0.41 thf(28,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,27,h3,h4])). % 0.13/0.41 thf(29,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,28,h2])). % 0.13/0.41 thf(30,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,29,h1])). % 0.13/0.41 thf(0,theorem,(![X1:$i]:(![X2:$i]:(((rel @ X1) @ X2) => ((~((~((![X3:$i]:(((rel @ X2) @ X3) => ((~((![X4:$i]:(((rel @ X3) @ X4) => ((~((~((a @ X4))))) => (b @ X4)))))) => (![X4:$i]:(((rel @ X3) @ X4) => (s @ X4)))))))))) => (![X3:$i]:(((rel @ X2) @ X3) => ((~((~((![X4:$i]:(((rel @ X3) @ X4) => ((~((a @ X4))) => (![X5:$i]:(((rel @ X4) @ X5) => (s @ X5)))))))))) => (![X4:$i]:(((rel @ X3) @ X4) => ((~((b @ X4))) => (![X5:$i]:(((rel @ X4) @ X5) => (s @ X5))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[30,h0])). % 0.13/0.41 % SZS output end Proof %------------------------------------------------------------------------------