%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : LCL951^24 : TPTP v9.3.1. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n026.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 01:02:56 PM UTC 2026 % Result : Theorem 0.21s 0.50s % Output : Proof 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL951^24 : TPTP v9.3.1. Released v8.1.0. % 0.00/0.04 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.10/0.36 % Computer : n026.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Sat Sep 5 06:12:41 UTC 2026 % 0.10/0.36 % CPUTime : % 0.21/0.50 % SZS status Theorem % 0.21/0.50 % Mode: mode213 % 0.21/0.50 % Inferences: 245 % 0.21/0.50 % SZS output start Proof % 0.21/0.50 thf(ty_mworld, type, mworld : $tType). % 0.21/0.50 thf(ty_eigen__6, type, eigen__6 : $i). % 0.21/0.50 thf(ty_singleton, type, singleton : ($i>$i)). % 0.21/0.50 thf(ty_eiw_di, type, eiw_di : ($i>mworld>$o)). % 0.21/0.50 thf(ty_eigen__2, type, eigen__2 : mworld). % 0.21/0.50 thf(ty_eigen__1, type, eigen__1 : $i). % 0.21/0.50 thf(ty_eigen__0, type, eigen__0 : mworld). % 0.21/0.50 thf(ty_eigen__4, type, eigen__4 : mworld). % 0.21/0.50 thf(ty_eigen__5, type, eigen__5 : $i). % 0.21/0.50 thf(ty_mrel, type, mrel : (mworld>mworld>$o)). % 0.21/0.50 thf(ty_eigen__3, type, eigen__3 : $i). % 0.21/0.50 thf(ty_empty, type, empty : ($i>mworld>$o)). % 0.21/0.50 thf(ty_mactual, type, mactual : mworld). % 0.21/0.50 thf(ty_qmltpeq, type, qmltpeq : ($i>$i>mworld>$o)). % 0.21/0.50 thf(ty_empty_set, type, empty_set : $i). % 0.21/0.50 thf(ty_in, type, in : ($i>$i>mworld>$o)). % 0.21/0.50 thf(sP1,plain,sP1 <=> (![X1:mworld]:(((mrel @ eigen__4) @ X1) => (~((![X2:mworld]:(((mrel @ X1) @ X2) => (((qmltpeq @ eigen__1) @ empty_set) @ X2))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 0.21/0.50 thf(sP2,plain,sP2 <=> ((eiw_di @ eigen__1) @ eigen__0),introduced(definition,[new_symbols(definition,[sP2])])). % 0.21/0.50 thf(sP3,plain,sP3 <=> (sP2 => (![X1:mworld]:(((mrel @ eigen__0) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (![X3:mworld]:(((mrel @ X1) @ X3) => ((![X4:mworld]:(((mrel @ X3) @ X4) => (~((![X5:mworld]:(((mrel @ X4) @ X5) => (((qmltpeq @ eigen__1) @ (singleton @ X2)) @ X5))))))) => ((![X4:mworld]:(((mrel @ X3) @ X4) => (~((![X5:mworld]:(((mrel @ X4) @ X5) => (((qmltpeq @ eigen__1) @ empty_set) @ X5))))))) => (~((![X4:mworld]:(((mrel @ X3) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((![X7:mworld]:(((mrel @ X6) @ X7) => (((in @ X5) @ eigen__1) @ X7))) => (~((![X7:mworld]:(((mrel @ X6) @ X7) => (~((![X8:mworld]:(((mrel @ X7) @ X8) => (((qmltpeq @ X5) @ X2) @ X8))))))))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP3])])). % 0.21/0.50 thf(sP4,plain,sP4 <=> (![X1:mworld]:(((mrel @ eigen__0) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (![X3:mworld]:(((mrel @ X1) @ X3) => ((![X4:mworld]:(((mrel @ X3) @ X4) => (~((![X5:mworld]:(((mrel @ X4) @ X5) => (((qmltpeq @ eigen__1) @ (singleton @ X2)) @ X5))))))) => ((![X4:mworld]:(((mrel @ X3) @ X4) => (~((![X5:mworld]:(((mrel @ X4) @ X5) => (((qmltpeq @ eigen__1) @ empty_set) @ X5))))))) => (~((![X4:mworld]:(((mrel @ X3) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((![X7:mworld]:(((mrel @ X6) @ X7) => (((in @ X5) @ eigen__1) @ X7))) => (~((![X7:mworld]:(((mrel @ X6) @ X7) => (~((![X8:mworld]:(((mrel @ X7) @ X8) => (((qmltpeq @ X5) @ X2) @ X8)))))))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 0.21/0.50 thf(sP5,plain,sP5 <=> (((mrel @ mactual) @ eigen__0) => (![X1:$i]:(((eiw_di @ X1) @ eigen__0) => (![X2:mworld]:(((mrel @ eigen__0) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => ((![X5:mworld]:(((mrel @ X4) @ X5) => (~((![X6:mworld]:(((mrel @ X5) @ X6) => (((qmltpeq @ X1) @ (singleton @ X3)) @ X6))))))) => ((![X5:mworld]:(((mrel @ X4) @ X5) => (~((![X6:mworld]:(((mrel @ X5) @ X6) => (((qmltpeq @ X1) @ empty_set) @ X6))))))) => (~((![X5:mworld]:(((mrel @ X4) @ X5) => (![X6:$i]:(((eiw_di @ X6) @ X5) => (![X7:mworld]:(((mrel @ X5) @ X7) => ((![X8:mworld]:(((mrel @ X7) @ X8) => (((in @ X6) @ X1) @ X8))) => (~((![X8:mworld]:(((mrel @ X7) @ X8) => (~((![X9:mworld]:(((mrel @ X8) @ X9) => (((qmltpeq @ X6) @ X3) @ X9))))))))))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP5])])). % 0.21/0.50 thf(sP6,plain,sP6 <=> ((eiw_di @ eigen__3) @ eigen__2),introduced(definition,[new_symbols(definition,[sP6])])). % 0.21/0.50 thf(sP7,plain,sP7 <=> (sP6 => (![X1:mworld]:(((mrel @ eigen__2) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (~((![X3:mworld]:(((mrel @ X2) @ X3) => (((qmltpeq @ eigen__1) @ (singleton @ eigen__3)) @ X3))))))) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (~((![X3:mworld]:(((mrel @ X2) @ X3) => (((qmltpeq @ eigen__1) @ empty_set) @ X3))))))) => (~((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => ((![X5:mworld]:(((mrel @ X4) @ X5) => (((in @ X3) @ eigen__1) @ X5))) => (~((![X5:mworld]:(((mrel @ X4) @ X5) => (~((![X6:mworld]:(((mrel @ X5) @ X6) => (((qmltpeq @ X3) @ eigen__3) @ X6))))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP7])])). % 0.21/0.50 thf(sP8,plain,sP8 <=> ((![X1:mworld]:(((mrel @ eigen__4) @ X1) => (~((![X2:mworld]:(((mrel @ X1) @ X2) => (((qmltpeq @ eigen__1) @ (singleton @ eigen__3)) @ X2))))))) => (sP1 => (~((![X1:mworld]:(((mrel @ eigen__4) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (![X3:mworld]:(((mrel @ X1) @ X3) => ((![X4:mworld]:(((mrel @ X3) @ X4) => (((in @ X2) @ eigen__1) @ X4))) => (~((![X4:mworld]:(((mrel @ X3) @ X4) => (~((![X5:mworld]:(((mrel @ X4) @ X5) => (((qmltpeq @ X2) @ eigen__3) @ X5)))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP8])])). % 0.21/0.50 thf(sP9,plain,sP9 <=> (![X1:$i]:(((eiw_di @ X1) @ eigen__0) => (![X2:mworld]:(((mrel @ eigen__0) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => ((![X5:mworld]:(((mrel @ X4) @ X5) => (~((![X6:mworld]:(((mrel @ X5) @ X6) => (((qmltpeq @ X1) @ (singleton @ X3)) @ X6))))))) => ((![X5:mworld]:(((mrel @ X4) @ X5) => (~((![X6:mworld]:(((mrel @ X5) @ X6) => (((qmltpeq @ X1) @ empty_set) @ X6))))))) => (~((![X5:mworld]:(((mrel @ X4) @ X5) => (![X6:$i]:(((eiw_di @ X6) @ X5) => (![X7:mworld]:(((mrel @ X5) @ X7) => ((![X8:mworld]:(((mrel @ X7) @ X8) => (((in @ X6) @ X1) @ X8))) => (~((![X8:mworld]:(((mrel @ X7) @ X8) => (~((![X9:mworld]:(((mrel @ X8) @ X9) => (((qmltpeq @ X6) @ X3) @ X9)))))))))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP9])])). % 0.21/0.50 thf(sP10,plain,sP10 <=> ((mrel @ eigen__0) @ eigen__2),introduced(definition,[new_symbols(definition,[sP10])])). % 0.21/0.50 thf(sP11,plain,sP11 <=> (sP10 => (![X1:$i]:(((eiw_di @ X1) @ eigen__2) => (![X2:mworld]:(((mrel @ eigen__2) @ X2) => ((![X3:mworld]:(((mrel @ X2) @ X3) => (~((![X4:mworld]:(((mrel @ X3) @ X4) => (((qmltpeq @ eigen__1) @ (singleton @ X1)) @ X4))))))) => ((![X3:mworld]:(((mrel @ X2) @ X3) => (~((![X4:mworld]:(((mrel @ X3) @ X4) => (((qmltpeq @ eigen__1) @ empty_set) @ X4))))))) => (~((![X3:mworld]:(((mrel @ X2) @ X3) => (![X4:$i]:(((eiw_di @ X4) @ X3) => (![X5:mworld]:(((mrel @ X3) @ X5) => ((![X6:mworld]:(((mrel @ X5) @ X6) => (((in @ X4) @ eigen__1) @ X6))) => (~((![X6:mworld]:(((mrel @ X5) @ X6) => (~((![X7:mworld]:(((mrel @ X6) @ X7) => (((qmltpeq @ X4) @ X1) @ X7))))))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP11])])). % 0.21/0.50 thf(sP12,plain,sP12 <=> (sP1 => (~((![X1:mworld]:(((mrel @ eigen__4) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (![X3:mworld]:(((mrel @ X1) @ X3) => ((![X4:mworld]:(((mrel @ X3) @ X4) => (((in @ X2) @ eigen__1) @ X4))) => (~((![X4:mworld]:(((mrel @ X3) @ X4) => (~((![X5:mworld]:(((mrel @ X4) @ X5) => (((qmltpeq @ X2) @ eigen__3) @ X5))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP12])])). % 0.21/0.50 thf(sP13,plain,sP13 <=> (![X1:mworld]:(((mrel @ eigen__2) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (~((![X3:mworld]:(((mrel @ X2) @ X3) => (((qmltpeq @ eigen__1) @ (singleton @ eigen__3)) @ X3))))))) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (~((![X3:mworld]:(((mrel @ X2) @ X3) => (((qmltpeq @ eigen__1) @ empty_set) @ X3))))))) => (~((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => ((![X5:mworld]:(((mrel @ X4) @ X5) => (((in @ X3) @ eigen__1) @ X5))) => (~((![X5:mworld]:(((mrel @ X4) @ X5) => (~((![X6:mworld]:(((mrel @ X5) @ X6) => (((qmltpeq @ X3) @ eigen__3) @ X6)))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP13])])). % 0.21/0.50 thf(sP14,plain,sP14 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (![X3:mworld]:(((mrel @ X1) @ X3) => (![X4:$i]:(((eiw_di @ X4) @ X3) => (![X5:mworld]:(((mrel @ X3) @ X5) => ((![X6:mworld]:(((mrel @ X5) @ X6) => (~((![X7:mworld]:(((mrel @ X6) @ X7) => (((qmltpeq @ X2) @ (singleton @ X4)) @ X7))))))) => ((![X6:mworld]:(((mrel @ X5) @ X6) => (~((![X7:mworld]:(((mrel @ X6) @ X7) => (((qmltpeq @ X2) @ empty_set) @ X7))))))) => (~((![X6:mworld]:(((mrel @ X5) @ X6) => (![X7:$i]:(((eiw_di @ X7) @ X6) => (![X8:mworld]:(((mrel @ X6) @ X8) => ((![X9:mworld]:(((mrel @ X8) @ X9) => (((in @ X7) @ X2) @ X9))) => (~((![X9:mworld]:(((mrel @ X8) @ X9) => (~((![X10:mworld]:(((mrel @ X9) @ X10) => (((qmltpeq @ X7) @ X4) @ X10)))))))))))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP14])])). % 0.21/0.50 thf(sP15,plain,sP15 <=> (![X1:mworld]:(((mrel @ eigen__4) @ X1) => (~((![X2:mworld]:(((mrel @ X1) @ X2) => (((qmltpeq @ eigen__1) @ (singleton @ eigen__3)) @ X2))))))),introduced(definition,[new_symbols(definition,[sP15])])). % 0.21/0.50 thf(sP16,plain,sP16 <=> (![X1:mworld]:(((mrel @ eigen__4) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (![X3:mworld]:(((mrel @ X1) @ X3) => ((![X4:mworld]:(((mrel @ X3) @ X4) => (((in @ X2) @ eigen__1) @ X4))) => (~((![X4:mworld]:(((mrel @ X3) @ X4) => (~((![X5:mworld]:(((mrel @ X4) @ X5) => (((qmltpeq @ X2) @ eigen__3) @ X5)))))))))))))))),introduced(definition,[new_symbols(definition,[sP16])])). % 0.21/0.50 thf(sP17,plain,sP17 <=> ((mrel @ mactual) @ eigen__0),introduced(definition,[new_symbols(definition,[sP17])])). % 0.21/0.50 thf(sP18,plain,sP18 <=> (((mrel @ eigen__2) @ eigen__4) => sP8),introduced(definition,[new_symbols(definition,[sP18])])). % 0.21/0.50 thf(sP19,plain,sP19 <=> (![X1:$i]:(((eiw_di @ X1) @ eigen__2) => (![X2:mworld]:(((mrel @ eigen__2) @ X2) => ((![X3:mworld]:(((mrel @ X2) @ X3) => (~((![X4:mworld]:(((mrel @ X3) @ X4) => (((qmltpeq @ eigen__1) @ (singleton @ X1)) @ X4))))))) => ((![X3:mworld]:(((mrel @ X2) @ X3) => (~((![X4:mworld]:(((mrel @ X3) @ X4) => (((qmltpeq @ eigen__1) @ empty_set) @ X4))))))) => (~((![X3:mworld]:(((mrel @ X2) @ X3) => (![X4:$i]:(((eiw_di @ X4) @ X3) => (![X5:mworld]:(((mrel @ X3) @ X5) => ((![X6:mworld]:(((mrel @ X5) @ X6) => (((in @ X4) @ eigen__1) @ X6))) => (~((![X6:mworld]:(((mrel @ X5) @ X6) => (~((![X7:mworld]:(((mrel @ X6) @ X7) => (((qmltpeq @ X4) @ X1) @ X7)))))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP19])])). % 0.21/0.50 thf(sP20,plain,sP20 <=> ((mrel @ eigen__2) @ eigen__4),introduced(definition,[new_symbols(definition,[sP20])])). % 0.21/0.50 thf(def_mlocal,definition,(mlocal = (^[X1:mworld>$o]:(X1 @ mactual)))). % 0.21/0.50 thf(def_mnot,definition,(mnot = (^[X1:mworld>$o]:(^[X2:mworld]:(~((X1 @ X2))))))). % 0.21/0.50 thf(def_mand,definition,(mand = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))). % 0.21/0.50 thf(def_mor,definition,(mor = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((~((X1 @ X3))) => (X2 @ X3))))))). % 0.21/0.50 thf(def_mimplies,definition,(mimplies = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) => (X2 @ X3))))))). % 0.21/0.50 thf(def_mequiv,definition,(mequiv = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) = (X2 @ X3))))))). % 0.21/0.50 thf(def_mbox,definition,(mbox = (^[X1:mworld>$o]:(^[X2:mworld]:(![X3:mworld]:(((mrel @ X2) @ X3) => (X1 @ X3))))))). % 0.21/0.50 thf(def_mdia,definition,(mdia = (^[X1:mworld>$o]:(^[X2:mworld]:(~((![X3:mworld]:(((mrel @ X2) @ X3) => (~((X1 @ X3))))))))))). % 0.21/0.50 thf(def_mforall_di,definition,(mforall_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(![X3:$i]:(((eiw_di @ X3) @ X2) => ((X1 @ X3) @ X2))))))). % 0.21/0.50 thf(def_mexists_di,definition,(mexists_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(~((![X3:$i]:(((eiw_di @ X3) @ X2) => (~(((X1 @ X3) @ X2))))))))))). % 0.21/0.50 thf(t41_zfmisc_1,conjecture,(![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (![X3:mworld]:(((mrel @ X1) @ X3) => (![X4:$i]:(((eiw_di @ X4) @ X3) => (![X5:mworld]:(((mrel @ X3) @ X5) => (~((~(((![X6:mworld]:(((mrel @ X5) @ X6) => (~((![X7:mworld]:(((mrel @ X6) @ X7) => (((qmltpeq @ X2) @ (singleton @ X4)) @ X7))))))) => (~((~(((![X6:mworld]:(((mrel @ X5) @ X6) => (~((![X7:mworld]:(((mrel @ X6) @ X7) => (((qmltpeq @ X2) @ empty_set) @ X7))))))) => (~((![X6:mworld]:(((mrel @ X5) @ X6) => (![X7:$i]:(((eiw_di @ X7) @ X6) => (![X8:mworld]:(((mrel @ X6) @ X8) => (~((~(((![X9:mworld]:(((mrel @ X8) @ X9) => (((in @ X7) @ X2) @ X9))) => (~((![X9:mworld]:(((mrel @ X8) @ X9) => (~((![X10:mworld]:(((mrel @ X9) @ X10) => (((qmltpeq @ X7) @ X4) @ X10))))))))))))))))))))))))))))))))))))))))))). % 0.21/0.50 thf(h0,negated_conjecture,(~(sP14)),inference(assume_negation,[status(cth)],[t41_zfmisc_1])). % 0.21/0.50 thf(h1,assumption,(~(sP5)),introduced(assumption,[])). % 0.21/0.50 thf(h2,assumption,sP17,introduced(assumption,[])). % 0.21/0.50 thf(h3,assumption,(~(sP9)),introduced(assumption,[])). % 0.21/0.50 thf(h4,assumption,(~(sP3)),introduced(assumption,[])). % 0.21/0.50 thf(h5,assumption,sP2,introduced(assumption,[])). % 0.21/0.50 thf(h6,assumption,(~(sP4)),introduced(assumption,[])). % 0.21/0.50 thf(h7,assumption,(~(sP11)),introduced(assumption,[])). % 0.21/0.50 thf(h8,assumption,sP10,introduced(assumption,[])). % 0.21/0.50 thf(h9,assumption,(~(sP19)),introduced(assumption,[])). % 0.21/0.50 thf(h10,assumption,(~(sP7)),introduced(assumption,[])). % 0.21/0.50 thf(h11,assumption,sP6,introduced(assumption,[])). % 0.21/0.50 thf(h12,assumption,(~(sP13)),introduced(assumption,[])). % 0.21/0.50 thf(h13,assumption,(~(sP18)),introduced(assumption,[])). % 0.21/0.50 thf(h14,assumption,sP20,introduced(assumption,[])). % 0.21/0.50 thf(h15,assumption,(~(sP8)),introduced(assumption,[])). % 0.21/0.50 thf(h16,assumption,sP15,introduced(assumption,[])). % 0.21/0.50 thf(h17,assumption,(~(sP12)),introduced(assumption,[])). % 0.21/0.50 thf(h18,assumption,sP1,introduced(assumption,[])). % 0.21/0.50 thf(h19,assumption,sP16,introduced(assumption,[])). % 0.21/0.50 thf(h20,assumption,(~((((eiw_di @ eigen__5) @ mactual) => (~((![X1:mworld]:(((mrel @ mactual) @ X1) => ((empty @ eigen__5) @ X1)))))))),introduced(assumption,[])). % 0.21/0.50 thf(h21,assumption,((eiw_di @ eigen__5) @ mactual),introduced(assumption,[])). % 0.21/0.50 thf(h22,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((empty @ eigen__5) @ X1))),introduced(assumption,[])). % 0.21/0.50 thf(h23,assumption,(~((((eiw_di @ eigen__6) @ mactual) => (~((![X1:mworld]:(((mrel @ mactual) @ X1) => (~((![X2:mworld]:(((mrel @ X1) @ X2) => ((empty @ eigen__6) @ X2)))))))))))),introduced(assumption,[])). % 0.21/0.50 thf(h24,assumption,((eiw_di @ eigen__6) @ mactual),introduced(assumption,[])). % 0.21/0.50 thf(h25,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => (~((![X2:mworld]:(((mrel @ X1) @ X2) => ((empty @ eigen__6) @ X2))))))),introduced(assumption,[])). % 0.21/0.50 thf(1,plain,(~(sP13) | sP18),inference(all_rule,[status(thm)],[])). % 0.21/0.50 thf(2,plain,((~(sP18) | ~(sP20)) | sP8),inference(prop_rule,[status(thm)],[])). % 0.21/0.50 thf(3,plain,((~(sP8) | ~(sP15)) | sP12),inference(prop_rule,[status(thm)],[])). % 0.21/0.50 thf(4,plain,((~(sP12) | ~(sP1)) | ~(sP16)),inference(prop_rule,[status(thm)],[])). % 0.21/0.50 thf(5,plain,(~(sP19) | sP7),inference(all_rule,[status(thm)],[])). % 0.21/0.50 thf(6,plain,((~(sP7) | ~(sP6)) | sP13),inference(prop_rule,[status(thm)],[])). % 0.21/0.50 thf(7,plain,(~(sP4) | sP11),inference(all_rule,[status(thm)],[])). % 0.21/0.50 thf(8,plain,((~(sP11) | ~(sP10)) | sP19),inference(prop_rule,[status(thm)],[])). % 0.21/0.50 thf(9,plain,(~(sP9) | sP3),inference(all_rule,[status(thm)],[])). % 0.21/0.50 thf(10,plain,((~(sP3) | ~(sP2)) | sP4),inference(prop_rule,[status(thm)],[])). % 0.21/0.50 thf(11,plain,(~(sP14) | sP5),inference(all_rule,[status(thm)],[])). % 0.21/0.50 thf(12,plain,((~(sP5) | ~(sP17)) | sP9),inference(prop_rule,[status(thm)],[])). % 0.21/0.50 thf(l45_zfmisc_1,axiom,(mlocal @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (mnot @ ((mand @ (mbox @ (mnot @ (mbox @ ((qmltpeq @ X1) @ (singleton @ X2)))))) @ ((mand @ (mbox @ (mnot @ (mbox @ ((qmltpeq @ X1) @ empty_set))))) @ (mbox @ (mforall_di @ (^[X3:$i]:(mbox @ (mnot @ ((mand @ (mbox @ ((in @ X3) @ X1))) @ (mbox @ (mnot @ (mbox @ ((qmltpeq @ X3) @ X2)))))))))))))))))))))). % 0.21/0.50 thf(13,plain,sP14,inference(preprocess,[status(thm)],[l45_zfmisc_1]). % 0.21/0.50 thf(14,plain,$false,inference(prop_unsat,[status(thm),assumptions([h24,h25,h23,h21,h22,h20,h18,h19,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,h2,h5,h8,h11,h14,h16,h18,h19])). % 0.21/0.50 thf(15,plain,$false,inference(tab_negimp,[status(thm),assumptions([h23,h21,h22,h20,h18,h19,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h24,h25])],[h23,14,h24,h25])). % 0.21/0.50 thf(rc2_xboole_0,axiom,(mlocal @ (mexists_di @ (^[X1:$i]:(mbox @ (mnot @ (mbox @ (empty @ X1)))))))). % 0.21/0.50 thf(16,plain,(~((![X1:$i]:(((eiw_di @ X1) @ mactual) => (~((![X2:mworld]:(((mrel @ mactual) @ X2) => (~((![X3:mworld]:(((mrel @ X2) @ X3) => ((empty @ X1) @ X3))))))))))))),inference(preprocess,[status(thm)],[rc2_xboole_0]). % 0.21/0.50 thf(17,plain,$false,inference(tab_negall,[status(thm),assumptions([h21,h22,h20,h18,h19,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__6)],[16,15,h23])). % 0.21/0.50 thf(18,plain,$false,inference(tab_negimp,[status(thm),assumptions([h20,h18,h19,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h21,h22])],[h20,17,h21,h22])). % 0.21/0.50 thf(rc1_xboole_0,axiom,(mlocal @ (mexists_di @ (^[X1:$i]:(mbox @ (empty @ X1)))))). % 0.21/0.50 thf(19,plain,(~((![X1:$i]:(((eiw_di @ X1) @ mactual) => (~((![X2:mworld]:(((mrel @ mactual) @ X2) => ((empty @ X1) @ X2))))))))),inference(preprocess,[status(thm)],[rc1_xboole_0]). % 0.21/0.50 thf(20,plain,$false,inference(tab_negall,[status(thm),assumptions([h18,h19,h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__5)],[19,18,h20])). % 0.21/0.50 thf(21,plain,$false,inference(tab_negimp,[status(thm),assumptions([h16,h17,h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h18,h19])],[h17,20,h18,h19])). % 0.21/0.50 thf(22,plain,$false,inference(tab_negimp,[status(thm),assumptions([h14,h15,h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,21,h16,h17])). % 0.21/0.50 thf(23,plain,$false,inference(tab_negimp,[status(thm),assumptions([h13,h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,22,h14,h15])). % 0.21/0.50 thf(24,plain,$false,inference(tab_negall,[status(thm),assumptions([h11,h12,h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__4)],[h12,23,h13])). % 0.21/0.50 thf(25,plain,$false,inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,24,h11,h12])). % 0.21/0.50 thf(26,plain,$false,inference(tab_negall,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__3)],[h9,25,h10])). % 0.21/0.50 thf(27,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,26,h8,h9])). % 0.21/0.50 thf(28,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,27,h7])). % 0.21/0.50 thf(29,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,28,h5,h6])). % 0.21/0.50 thf(30,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,29,h4])). % 0.21/0.50 thf(31,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,30,h2,h3])). % 0.21/0.50 thf(32,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,31,h1])). % 0.21/0.50 thf(0,theorem,(![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (![X3:mworld]:(((mrel @ X1) @ X3) => (![X4:$i]:(((eiw_di @ X4) @ X3) => (![X5:mworld]:(((mrel @ X3) @ X5) => (~((~(((![X6:mworld]:(((mrel @ X5) @ X6) => (~((![X7:mworld]:(((mrel @ X6) @ X7) => (((qmltpeq @ X2) @ (singleton @ X4)) @ X7))))))) => (~((~(((![X6:mworld]:(((mrel @ X5) @ X6) => (~((![X7:mworld]:(((mrel @ X6) @ X7) => (((qmltpeq @ X2) @ empty_set) @ X7))))))) => (~((![X6:mworld]:(((mrel @ X5) @ X6) => (![X7:$i]:(((eiw_di @ X7) @ X6) => (![X8:mworld]:(((mrel @ X6) @ X8) => (~((~(((![X9:mworld]:(((mrel @ X8) @ X9) => (((in @ X7) @ X2) @ X9))) => (~((![X9:mworld]:(((mrel @ X8) @ X9) => (~((![X10:mworld]:(((mrel @ X9) @ X10) => (((qmltpeq @ X7) @ X4) @ X10)))))))))))))))))))))))))))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[32,h0])). % 0.21/0.50 % SZS output end Proof %------------------------------------------------------------------------------