%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : PUZ087^1 : TPTP v9.2.0. Released v4.0.0. % 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 : 300s % DateTime : Thu Oct 9 02:15:36 PM UTC 2025 % Result : Theorem 196.82s 196.57s % Output : Proof 196.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : PUZ087^1 : TPTP v9.2.0. Released v4.0.0. % 0.04/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n006.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 17:21:38 EDT 2025 % 0.13/0.35 % CPUTime : % 196.82/196.57 % SZS status Theorem % 196.82/196.57 % Mode: mode455:USE_SINE=true:SINE_TOLERANCE=1.0:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=3.:SINE_DEPTH=0 % 196.82/196.57 % Inferences: 1839 % 196.82/196.57 % SZS output start Proof % 196.82/196.57 thf(ty_a, type, a : ($i>$i>$o)). % 196.82/196.57 thf(ty_fool, type, fool : ($i>$i>$o)). % 196.82/196.57 thf(ty_eigen__2, type, eigen__2 : $i). % 196.82/196.57 thf(ty_eigen__1, type, eigen__1 : $i). % 196.82/196.57 thf(ty_b, type, b : ($i>$i>$o)). % 196.82/196.57 thf(ty_eigen__0, type, eigen__0 : $i). % 196.82/196.57 thf(ty_eigen__4, type, eigen__4 : $i). % 196.82/196.57 thf(ty_ws, type, ws : (($i>$i>$o)>$i>$o)). % 196.82/196.57 thf(ty_c, type, c : ($i>$i>$o)). % 196.82/196.57 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 196.82/196.57 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((((a @ eigen__1) @ X1) => ((ws @ a) @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 196.82/196.57 thf(eigendef_eigen__4, definition, eigen__4 = (eps__0 @ (^[X1:$i]:(~((((b @ eigen__1) @ X1) => ((ws @ b) @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__4])])). % 196.82/196.57 thf(sP1,plain,sP1 <=> (![X1:$i]:(((fool @ eigen__1) @ X1) => ((~(((ws @ a) @ X1))) => ((~(((ws @ b) @ X1))) => ((ws @ c) @ X1))))),introduced(definition,[new_symbols(definition,[sP1])])). % 196.82/196.57 thf(sP2,plain,sP2 <=> ((~(((ws @ b) @ eigen__4))) => ((ws @ c) @ eigen__4)),introduced(definition,[new_symbols(definition,[sP2])])). % 196.82/196.57 thf(sP3,plain,sP3 <=> ((~(((ws @ a) @ eigen__4))) => sP2),introduced(definition,[new_symbols(definition,[sP3])])). % 196.82/196.57 thf(sP4,plain,sP4 <=> (((a @ eigen__1) @ eigen__2) => ((ws @ a) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP4])])). % 196.82/196.57 thf(sP5,plain,sP5 <=> (![X1:$i]:(((a @ eigen__1) @ X1) => ((ws @ a) @ X1))),introduced(definition,[new_symbols(definition,[sP5])])). % 196.82/196.57 thf(sP6,plain,sP6 <=> ((ws @ a) @ eigen__4),introduced(definition,[new_symbols(definition,[sP6])])). % 196.82/196.57 thf(sP7,plain,sP7 <=> ((ws @ c) @ eigen__1),introduced(definition,[new_symbols(definition,[sP7])])). % 196.82/196.57 thf(sP8,plain,sP8 <=> (((a @ eigen__1) @ eigen__2) => (~((![X1:$i]:(((b @ eigen__2) @ X1) => (~(((ws @ a) @ X1)))))))),introduced(definition,[new_symbols(definition,[sP8])])). % 196.82/196.57 thf(sP9,plain,sP9 <=> (![X1:$i]:(((b @ eigen__1) @ X1) => ((ws @ b) @ X1))),introduced(definition,[new_symbols(definition,[sP9])])). % 196.82/196.57 thf(sP10,plain,sP10 <=> (![X1:$i>$o]:((![X2:$i]:(((fool @ eigen__1) @ X2) => (X1 @ X2))) => (![X2:$i]:(((a @ eigen__1) @ X2) => (X1 @ X2))))),introduced(definition,[new_symbols(definition,[sP10])])). % 196.82/196.57 thf(sP11,plain,sP11 <=> ((~(sP7)) => (![X1:$i]:(((b @ eigen__1) @ X1) => (~(((ws @ c) @ X1)))))),introduced(definition,[new_symbols(definition,[sP11])])). % 196.82/196.57 thf(sP12,plain,sP12 <=> (((b @ eigen__1) @ eigen__4) => ((ws @ b) @ eigen__4)),introduced(definition,[new_symbols(definition,[sP12])])). % 196.82/196.57 thf(sP13,plain,sP13 <=> (((b @ eigen__1) @ eigen__4) => (~(sP6))),introduced(definition,[new_symbols(definition,[sP13])])). % 196.82/196.57 thf(sP14,plain,sP14 <=> (![X1:$i>$o]:((~((![X2:$i]:(((b @ eigen__1) @ X2) => (X1 @ X2))))) => (![X2:$i]:(((a @ eigen__1) @ X2) => (~((![X3:$i]:(((b @ X2) @ X3) => (X1 @ X3))))))))),introduced(definition,[new_symbols(definition,[sP14])])). % 196.82/196.57 thf(sP15,plain,sP15 <=> (![X1:$i>$o]:((![X2:$i]:(((fool @ eigen__1) @ X2) => (X1 @ X2))) => (X1 @ eigen__1))),introduced(definition,[new_symbols(definition,[sP15])])). % 196.82/196.57 thf(sP16,plain,sP16 <=> (![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((b @ X1) @ X3) => (X2 @ X3))))) => (![X3:$i]:(((a @ X1) @ X3) => (~((![X4:$i]:(((b @ X3) @ X4) => (X2 @ X4)))))))))),introduced(definition,[new_symbols(definition,[sP16])])). % 196.82/196.57 thf(sP17,plain,sP17 <=> ((a @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP17])])). % 196.82/196.57 thf(sP18,plain,sP18 <=> (![X1:$i]:(((fool @ eigen__1) @ X1) => ((~(((ws @ c) @ X1))) => (![X2:$i]:(((b @ X1) @ X2) => (~(((ws @ c) @ X2)))))))),introduced(definition,[new_symbols(definition,[sP18])])). % 196.82/196.57 thf(sP19,plain,sP19 <=> ((~((![X1:$i]:(((b @ eigen__1) @ X1) => (~(((ws @ a) @ X1))))))) => (![X1:$i]:(((a @ eigen__1) @ X1) => (~((![X2:$i]:(((b @ X1) @ X2) => (~(((ws @ a) @ X2)))))))))),introduced(definition,[new_symbols(definition,[sP19])])). % 196.82/196.57 thf(sP20,plain,sP20 <=> (![X1:$i>$o]:((![X2:$i]:(((fool @ eigen__1) @ X2) => (X1 @ X2))) => (![X2:$i]:(((b @ eigen__1) @ X2) => (X1 @ X2))))),introduced(definition,[new_symbols(definition,[sP20])])). % 196.82/196.57 thf(sP21,plain,sP21 <=> ((b @ eigen__1) @ eigen__4),introduced(definition,[new_symbols(definition,[sP21])])). % 196.82/196.57 thf(sP22,plain,sP22 <=> (![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((fool @ X1) @ X3) => (X2 @ X3))) => (![X3:$i]:(((b @ X1) @ X3) => (X2 @ X3)))))),introduced(definition,[new_symbols(definition,[sP22])])). % 196.82/196.57 thf(sP23,plain,sP23 <=> (![X1:$i]:(~((![X2:$i]:(((b @ X1) @ X2) => ((ws @ b) @ X2)))))),introduced(definition,[new_symbols(definition,[sP23])])). % 196.82/196.57 thf(sP24,plain,sP24 <=> (![X1:$i]:(![X2:$i]:(((fool @ X1) @ X2) => ((~(((ws @ c) @ X2))) => (![X3:$i]:(((b @ X2) @ X3) => (~(((ws @ c) @ X3))))))))),introduced(definition,[new_symbols(definition,[sP24])])). % 196.82/196.57 thf(sP25,plain,sP25 <=> (sP21 => (~(((ws @ c) @ eigen__4)))),introduced(definition,[new_symbols(definition,[sP25])])). % 196.82/196.57 thf(sP26,plain,sP26 <=> (![X1:$i]:(((b @ eigen__1) @ X1) => (~(((ws @ c) @ X1))))),introduced(definition,[new_symbols(definition,[sP26])])). % 196.82/196.57 thf(sP27,plain,sP27 <=> (![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((fool @ X1) @ X3) => (X2 @ X3))) => (![X3:$i]:(((a @ X1) @ X3) => (X2 @ X3)))))),introduced(definition,[new_symbols(definition,[sP27])])). % 196.82/196.57 thf(sP28,plain,sP28 <=> (sP17 => ((~(((ws @ a) @ eigen__2))) => (![X1:$i]:(((b @ eigen__2) @ X1) => (~(((ws @ a) @ X1))))))),introduced(definition,[new_symbols(definition,[sP28])])). % 196.82/196.57 thf(sP29,plain,sP29 <=> ((![X1:$i]:(((fool @ eigen__1) @ X1) => ((~(((ws @ a) @ X1))) => (![X2:$i]:(((b @ X1) @ X2) => (~(((ws @ a) @ X2)))))))) => (![X1:$i]:(((a @ eigen__1) @ X1) => ((~(((ws @ a) @ X1))) => (![X2:$i]:(((b @ X1) @ X2) => (~(((ws @ a) @ X2))))))))),introduced(definition,[new_symbols(definition,[sP29])])). % 196.82/196.57 thf(sP30,plain,sP30 <=> (![X1:$i]:(![X2:$i]:(((fool @ X1) @ X2) => ((~(((ws @ a) @ X2))) => ((~(((ws @ b) @ X2))) => ((ws @ c) @ X2)))))),introduced(definition,[new_symbols(definition,[sP30])])). % 196.82/196.57 thf(sP31,plain,sP31 <=> (![X1:$i]:(![X2:$i]:(((fool @ X1) @ X2) => ((~(((ws @ a) @ X2))) => (![X3:$i]:(((b @ X2) @ X3) => (~(((ws @ a) @ X3))))))))),introduced(definition,[new_symbols(definition,[sP31])])). % 196.82/196.57 thf(sP32,plain,sP32 <=> (![X1:$i]:(((b @ eigen__1) @ X1) => ((~(((ws @ a) @ X1))) => ((~(((ws @ b) @ X1))) => ((ws @ c) @ X1))))),introduced(definition,[new_symbols(definition,[sP32])])). % 196.82/196.57 thf(sP33,plain,sP33 <=> (sP18 => sP11),introduced(definition,[new_symbols(definition,[sP33])])). % 196.82/196.57 thf(sP34,plain,sP34 <=> (![X1:$i]:(((a @ eigen__1) @ X1) => (~((![X2:$i]:(((b @ X1) @ X2) => (~(((ws @ a) @ X2))))))))),introduced(definition,[new_symbols(definition,[sP34])])). % 196.82/196.57 thf(sP35,plain,sP35 <=> (![X1:$i]:(~((![X2:$i]:(((a @ X1) @ X2) => ((ws @ a) @ X2)))))),introduced(definition,[new_symbols(definition,[sP35])])). % 196.82/196.57 thf(sP36,plain,sP36 <=> (sP21 => sP3),introduced(definition,[new_symbols(definition,[sP36])])). % 196.82/196.57 thf(sP37,plain,sP37 <=> ((~(((ws @ a) @ eigen__2))) => (![X1:$i]:(((b @ eigen__2) @ X1) => (~(((ws @ a) @ X1)))))),introduced(definition,[new_symbols(definition,[sP37])])). % 196.82/196.57 thf(sP38,plain,sP38 <=> (![X1:$i]:(((b @ eigen__1) @ X1) => (~(((ws @ a) @ X1))))),introduced(definition,[new_symbols(definition,[sP38])])). % 196.82/196.57 thf(sP39,plain,sP39 <=> ((ws @ b) @ eigen__4),introduced(definition,[new_symbols(definition,[sP39])])). % 196.82/196.57 thf(sP40,plain,sP40 <=> (![X1:$i]:(((b @ eigen__2) @ X1) => (~(((ws @ a) @ X1))))),introduced(definition,[new_symbols(definition,[sP40])])). % 196.82/196.57 thf(sP41,plain,sP41 <=> (![X1:$i]:(![X2:$i>$o]:((![X3:$i]:(((fool @ X1) @ X3) => (X2 @ X3))) => (X2 @ X1)))),introduced(definition,[new_symbols(definition,[sP41])])). % 196.82/196.57 thf(sP42,plain,sP42 <=> (sP1 => sP32),introduced(definition,[new_symbols(definition,[sP42])])). % 196.82/196.57 thf(sP43,plain,sP43 <=> (![X1:$i]:(((a @ eigen__1) @ X1) => ((~(((ws @ a) @ X1))) => (![X2:$i]:(((b @ X1) @ X2) => (~(((ws @ a) @ X2)))))))),introduced(definition,[new_symbols(definition,[sP43])])). % 196.82/196.57 thf(sP44,plain,sP44 <=> (![X1:$i]:(((fool @ eigen__1) @ X1) => ((~(((ws @ a) @ X1))) => (![X2:$i]:(((b @ X1) @ X2) => (~(((ws @ a) @ X2)))))))),introduced(definition,[new_symbols(definition,[sP44])])). % 196.82/196.57 thf(sP45,plain,sP45 <=> ((ws @ c) @ eigen__4),introduced(definition,[new_symbols(definition,[sP45])])). % 196.82/196.57 thf(sP46,plain,sP46 <=> ((ws @ a) @ eigen__2),introduced(definition,[new_symbols(definition,[sP46])])). % 196.82/196.57 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 196.82/196.57 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 196.82/196.57 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 196.82/196.57 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 196.82/196.57 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 196.82/196.57 thf(def_mvalid,definition,(mvalid = (!!))). % 196.82/196.57 thf(conj,conjecture,(![X1:$i]:(![X2:$i]:(((c @ X1) @ X2) => ((ws @ c) @ X2))))). % 196.82/196.57 thf(h1,negated_conjecture,(~((![X1:$i]:(![X2:$i]:(((c @ X1) @ X2) => ((ws @ c) @ X2)))))),inference(assume_negation,[status(cth)],[conj])). % 196.82/196.57 thf(h2,assumption,(~((![X1:$i]:(((c @ eigen__0) @ X1) => ((ws @ c) @ X1))))),introduced(assumption,[])). % 196.82/196.57 thf(h3,assumption,(~((((c @ eigen__0) @ eigen__1) => sP7))),introduced(assumption,[])). % 196.82/196.57 thf(h4,assumption,((c @ eigen__0) @ eigen__1),introduced(assumption,[])). % 196.82/196.57 thf(h5,assumption,(~(sP7)),introduced(assumption,[])). % 196.82/196.57 thf(1,plain,(~(sP14) | sP19),inference(all_rule,[status(thm)],[])). % 196.82/196.57 thf(2,plain,((~(sP19) | sP38) | sP34),inference(prop_rule,[status(thm)],[])). % 196.82/196.57 thf(3,plain,(~(sP34) | sP8),inference(all_rule,[status(thm)],[])). % 196.82/196.57 thf(4,plain,((~(sP8) | ~(sP17)) | ~(sP40)),inference(prop_rule,[status(thm)],[])). % 196.82/196.57 thf(5,plain,(~(sP43) | sP28),inference(all_rule,[status(thm)],[])). % 196.82/196.57 thf(6,plain,((~(sP28) | ~(sP17)) | sP37),inference(prop_rule,[status(thm)],[])). % 196.82/196.57 thf(7,plain,(~(sP32) | sP36),inference(all_rule,[status(thm)],[])). % 196.82/196.57 thf(8,plain,((~(sP36) | ~(sP21)) | sP3),inference(prop_rule,[status(thm)],[])). % 196.82/196.57 thf(9,plain,((~(sP3) | sP6) | sP2),inference(prop_rule,[status(thm)],[])). % 196.82/196.57 thf(10,plain,((~(sP2) | sP39) | sP45),inference(prop_rule,[status(thm)],[])). % 196.82/196.57 thf(11,plain,(~(sP38) | sP13),inference(all_rule,[status(thm)],[])). % 196.82/196.57 thf(12,plain,((~(sP13) | ~(sP21)) | ~(sP6)),inference(prop_rule,[status(thm)],[])). % 196.82/196.57 thf(13,plain,(~(sP26) | sP25),inference(all_rule,[status(thm)],[])). % 196.82/196.57 thf(14,plain,((~(sP25) | ~(sP21)) | ~(sP45)),inference(prop_rule,[status(thm)],[])). % 196.82/196.57 thf(15,plain,(sP12 | ~(sP39)),inference(prop_rule,[status(thm)],[])). % 196.82/196.57 thf(16,plain,(sP12 | sP21),inference(prop_rule,[status(thm)],[])). % 196.82/196.57 thf(17,plain,(sP9 | ~(sP12)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4])). % 196.82/196.57 thf(18,plain,((~(sP37) | sP46) | sP40),inference(prop_rule,[status(thm)],[])). % 196.82/196.57 thf(19,plain,(sP4 | ~(sP46)),inference(prop_rule,[status(thm)],[])). % 196.82/196.57 thf(20,plain,(sP4 | sP17),inference(prop_rule,[status(thm)],[])). % 196.82/196.57 thf(21,plain,(sP5 | ~(sP4)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). % 196.82/196.57 thf(22,plain,((~(sP11) | sP7) | sP26),inference(prop_rule,[status(thm)],[])). % 196.82/196.57 thf(23,plain,(~(sP15) | sP33),inference(all_rule,[status(thm)],[])). % 196.82/196.57 thf(24,plain,((~(sP33) | ~(sP18)) | sP11),inference(prop_rule,[status(thm)],[])). % 196.82/196.57 thf(25,plain,(~(sP10) | sP29),inference(all_rule,[status(thm)],[])). % 196.82/196.57 thf(26,plain,((~(sP29) | ~(sP44)) | sP43),inference(prop_rule,[status(thm)],[])). % 196.82/196.57 thf(27,plain,(~(sP20) | sP42),inference(all_rule,[status(thm)],[])). % 196.82/196.57 thf(28,plain,((~(sP42) | ~(sP1)) | sP32),inference(prop_rule,[status(thm)],[])). % 196.82/196.57 thf(29,plain,(~(sP23) | ~(sP9)),inference(all_rule,[status(thm)],[])). % 196.82/196.57 thf(30,plain,(~(sP35) | ~(sP5)),inference(all_rule,[status(thm)],[])). % 196.82/196.57 thf(31,plain,(~(sP16) | sP14),inference(all_rule,[status(thm)],[])). % 196.82/196.57 thf(32,plain,(~(sP22) | sP20),inference(all_rule,[status(thm)],[])). % 196.82/196.57 thf(33,plain,(~(sP27) | sP10),inference(all_rule,[status(thm)],[])). % 196.82/196.57 thf(34,plain,(~(sP41) | sP15),inference(all_rule,[status(thm)],[])). % 196.82/196.57 thf(35,plain,(~(sP24) | sP18),inference(all_rule,[status(thm)],[])). % 196.82/196.57 thf(36,plain,(~(sP31) | sP44),inference(all_rule,[status(thm)],[])). % 196.82/196.57 thf(37,plain,(~(sP30) | sP1),inference(all_rule,[status(thm)],[])). % 196.82/196.57 thf(axiom_5,axiom,(mvalid @ (mnot @ ((mbox @ b) @ (ws @ b))))). % 196.82/196.57 thf(38,plain,sP23,inference(preprocess,[status(thm)],[axiom_5]). % 196.82/196.57 thf(axiom_4,axiom,(mvalid @ (mnot @ ((mbox @ a) @ (ws @ a))))). % 196.82/196.57 thf(39,plain,sP35,inference(preprocess,[status(thm)],[axiom_4]). % 196.82/196.57 thf(a6_axiom_for_fool_b_a,axiom,(mvalid @ (mforall_prop @ (^[X1:$i>$o]:((mimplies @ (mnot @ ((mbox @ b) @ X1))) @ ((mbox @ a) @ (mnot @ ((mbox @ b) @ X1)))))))). % 196.82/196.57 thf(40,plain,sP16,inference(preprocess,[status(thm)],[a6_axiom_for_fool_b_a]). % 196.82/196.57 thf(i_axiom_for_fool_b,axiom,(mvalid @ (mforall_prop @ (^[X1:$i>$o]:((mimplies @ ((mbox @ fool) @ X1)) @ ((mbox @ b) @ X1)))))). % 196.82/196.57 thf(41,plain,sP22,inference(preprocess,[status(thm)],[i_axiom_for_fool_b]). % 196.82/196.57 thf(i_axiom_for_fool_a,axiom,(mvalid @ (mforall_prop @ (^[X1:$i>$o]:((mimplies @ ((mbox @ fool) @ X1)) @ ((mbox @ a) @ X1)))))). % 196.82/196.57 thf(42,plain,sP27,inference(preprocess,[status(thm)],[i_axiom_for_fool_a]). % 196.82/196.57 thf(t_axiom_for_fool,axiom,(mvalid @ (mforall_prop @ (^[X1:$i>$o]:((mimplies @ ((mbox @ fool) @ X1)) @ X1))))). % 196.82/196.57 thf(43,plain,sP41,inference(preprocess,[status(thm)],[t_axiom_for_fool]). % 196.82/196.57 thf(axiom_3_c_b,axiom,(mvalid @ ((mbox @ fool) @ ((mimplies @ (mnot @ (ws @ c))) @ ((mbox @ b) @ (mnot @ (ws @ c))))))). % 196.82/196.57 thf(44,plain,sP24,inference(preprocess,[status(thm)],[axiom_3_c_b]). % 196.82/196.57 thf(axiom_3_a_b,axiom,(mvalid @ ((mbox @ fool) @ ((mimplies @ (mnot @ (ws @ a))) @ ((mbox @ b) @ (mnot @ (ws @ a))))))). % 196.82/196.57 thf(45,plain,sP31,inference(preprocess,[status(thm)],[axiom_3_a_b]). % 196.82/196.57 thf(axiom_1,axiom,(mvalid @ ((mbox @ fool) @ ((mor @ (ws @ a)) @ ((mor @ (ws @ b)) @ (ws @ c)))))). % 196.82/196.57 thf(46,plain,sP30,inference(preprocess,[status(thm)],[axiom_1]). % 196.82/196.57 thf(47,plain,$false,inference(prop_unsat,[status(thm),assumptions([h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,h5,38,39,40,41,42,43,44,45,46])). % 196.82/196.57 thf(48,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,47,h4,h5])). % 196.82/196.57 thf(49,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,48,h3])). % 196.82/196.57 thf(50,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,49,h2])). % 196.82/196.57 thf(51,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[50,h0])). % 196.82/196.57 thf(0,theorem,(![X1:$i]:(![X2:$i]:(((c @ X1) @ X2) => ((ws @ c) @ X2)))),inference(contra,[status(thm),contra(discharge,[h1])],[50,h1])). % 196.82/196.57 % SZS output end Proof %------------------------------------------------------------------------------