%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : GEG012^1 : TPTP v9.2.0. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n017.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 01:27:38 PM UTC 2025 % Result : Theorem 70.79s 70.93s % Output : Proof 70.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.05/0.14 % Problem : GEG012^1 : TPTP v9.2.0. Released v4.1.0. % 0.05/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.15/0.36 % Computer : n017.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Wed Oct 8 12:31:23 EDT 2025 % 0.15/0.36 % CPUTime : % 70.79/70.93 % SZS status Theorem % 70.79/70.93 % Mode: mode398 % 70.79/70.93 % Inferences: 12731 % 70.79/70.93 % SZS output start Proof % 70.79/70.93 thf(ty_reg, type, reg : $tType). % 70.79/70.93 thf(ty_a, type, a : ($i>$i>$o)). % 70.79/70.93 thf(ty_eigen__2, type, eigen__2 : reg). % 70.79/70.93 thf(ty_spain, type, spain : reg). % 70.79/70.93 thf(ty_catalunya, type, catalunya : reg). % 70.79/70.93 thf(ty_eigen__7, type, eigen__7 : reg). % 70.79/70.93 thf(ty_eigen__24, type, eigen__24 : reg). % 70.79/70.93 thf(ty_eigen__1, type, eigen__1 : $i). % 70.79/70.93 thf(ty_paris, type, paris : reg). % 70.79/70.93 thf(ty_eigen__0, type, eigen__0 : $i). % 70.79/70.93 thf(ty_eigen__4, type, eigen__4 : reg). % 70.79/70.93 thf(ty_eigen__5, type, eigen__5 : reg). % 70.79/70.93 thf(ty_eigen__19, type, eigen__19 : reg). % 70.79/70.93 thf(ty_eigen__3, type, eigen__3 : reg). % 70.79/70.93 thf(ty_eigen__8, type, eigen__8 : reg). % 70.79/70.93 thf(ty_eigen__41, type, eigen__41 : reg). % 70.79/70.93 thf(ty_eigen__9, type, eigen__9 : reg). % 70.79/70.93 thf(ty_france, type, france : reg). % 70.79/70.93 thf(ty_eigen__54, type, eigen__54 : reg). % 70.79/70.93 thf(ty_c, type, c : (reg>reg>$o)). % 70.79/70.93 thf(h0, assumption, (![X1:reg>$o]:(![X2:reg]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 70.79/70.93 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:reg]:(~(((~((((c @ X1) @ paris) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))))) => (((c @ X1) @ eigen__2) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ eigen__2))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__3])])). % 70.79/70.93 thf(h1, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])). % 70.79/70.93 thf(eigendef_eigen__1, definition, eigen__1 = (eps__1 @ (^[X1:$i]:(~((((a @ eigen__0) @ X1) => (![X2:reg]:((~(((~(((~(((![X3:reg]:(((c @ X3) @ france) => ((c @ X3) @ X2))) => (![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france)))))) => (~((![X3:reg]:((~((((c @ X3) @ france) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ france)))))))))))) => (((c @ X3) @ X2) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X2))))))))))))))))) => ((~(((![X3:reg]:(((c @ X3) @ spain) => ((c @ X3) @ X2))) => (![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ spain)))))) => (~((![X3:reg]:((~((((c @ X3) @ spain) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ spain)))))))))))) => (((c @ X3) @ X2) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X2)))))))))))))))))) => (~(((~(((~(((![X3:reg]:(((c @ X3) @ paris) => ((c @ X3) @ X2))) => (![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))) => (~((![X3:reg]:((~((((c @ X3) @ paris) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ paris)))))))))))) => (((c @ X3) @ X2) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X2))))))))))))))))) => ((~(((![X3:reg]:(((c @ X3) @ catalunya) => ((c @ X3) @ X2))) => (![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya)))))) => (~((![X3:reg]:((~((((c @ X3) @ catalunya) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ catalunya)))))))))))) => (((c @ X3) @ X2) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X2))))))))))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 70.79/70.93 thf(eigendef_eigen__0, definition, eigen__0 = (eps__1 @ (^[X1:$i]:(~((![X2:$i]:(((a @ X1) @ X2) => (![X3:reg]:((~(((~(((~(((![X4:reg]:(((c @ X4) @ france) => ((c @ X4) @ X3))) => (![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ france)))))) => (~((![X4:reg]:((~((((c @ X4) @ france) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ france)))))))))))) => (((c @ X4) @ X3) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3))))))))))))))))) => ((~(((![X4:reg]:(((c @ X4) @ spain) => ((c @ X4) @ X3))) => (![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ spain)))))) => (~((![X4:reg]:((~((((c @ X4) @ spain) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ spain)))))))))))) => (((c @ X4) @ X3) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3)))))))))))))))))) => (~(((~(((~(((![X4:reg]:(((c @ X4) @ paris) => ((c @ X4) @ X3))) => (![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ paris)))))) => (~((![X4:reg]:((~((((c @ X4) @ paris) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ paris)))))))))))) => (((c @ X4) @ X3) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3))))))))))))))))) => ((~(((![X4:reg]:(((c @ X4) @ catalunya) => ((c @ X4) @ X3))) => (![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ catalunya)))))) => (~((![X4:reg]:((~((((c @ X4) @ catalunya) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ catalunya)))))))))))) => (((c @ X4) @ X3) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3)))))))))))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 70.79/70.93 thf(eigendef_eigen__8, definition, eigen__8 = (eps__0 @ (^[X1:reg]:(~((((c @ X1) @ paris) => ((c @ X1) @ eigen__2)))))), introduced(definition,[new_symbols(definition,[eigen__8])])). % 70.79/70.93 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:reg]:(~(((~(((~(((~(((![X2:reg]:(((c @ X2) @ france) => ((c @ X2) @ X1))) => (![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ france)))))) => (~((![X2:reg]:((~((((c @ X2) @ france) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ france)))))))))))) => (((c @ X2) @ X1) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X1))))))))))))))))) => ((~(((![X2:reg]:(((c @ X2) @ spain) => ((c @ X2) @ X1))) => (![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain)))))) => (~((![X2:reg]:((~((((c @ X2) @ spain) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ spain)))))))))))) => (((c @ X2) @ X1) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X1)))))))))))))))))) => (~(((~(((~(((![X2:reg]:(((c @ X2) @ paris) => ((c @ X2) @ X1))) => (![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))) => (~((![X2:reg]:((~((((c @ X2) @ paris) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ paris)))))))))))) => (((c @ X2) @ X1) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X1))))))))))))))))) => ((~(((![X2:reg]:(((c @ X2) @ catalunya) => ((c @ X2) @ X1))) => (![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya)))))) => (~((![X2:reg]:((~((((c @ X2) @ catalunya) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ catalunya)))))))))))) => (((c @ X2) @ X1) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X1))))))))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__2])])). % 70.79/70.93 thf(eigendef_eigen__4, definition, eigen__4 = (eps__0 @ (^[X1:reg]:(~(((~((((c @ X1) @ catalunya) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya)))))))))))) => (((c @ X1) @ eigen__2) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ eigen__2))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__4])])). % 70.79/70.93 thf(eigendef_eigen__41, definition, eigen__41 = (eps__0 @ (^[X1:reg]:(~((((c @ X1) @ eigen__19) => ((c @ X1) @ eigen__2)))))), introduced(definition,[new_symbols(definition,[eigen__41])])). % 70.79/70.93 thf(eigendef_eigen__9, definition, eigen__9 = (eps__0 @ (^[X1:reg]:(~((((c @ X1) @ catalunya) => ((c @ X1) @ eigen__2)))))), introduced(definition,[new_symbols(definition,[eigen__9])])). % 70.79/70.93 thf(eigendef_eigen__7, definition, eigen__7 = (eps__0 @ (^[X1:reg]:(~((((c @ X1) @ eigen__2) => ((c @ X1) @ spain)))))), introduced(definition,[new_symbols(definition,[eigen__7])])). % 70.79/70.93 thf(eigendef_eigen__5, definition, eigen__5 = (eps__0 @ (^[X1:reg]:(~((((c @ X1) @ eigen__2) => ((c @ X1) @ france)))))), introduced(definition,[new_symbols(definition,[eigen__5])])). % 70.79/70.93 thf(eigendef_eigen__54, definition, eigen__54 = (eps__0 @ (^[X1:reg]:(~((((c @ X1) @ eigen__24) => ((c @ X1) @ eigen__2)))))), introduced(definition,[new_symbols(definition,[eigen__54])])). % 70.79/70.93 thf(eigendef_eigen__24, definition, eigen__24 = (eps__0 @ (^[X1:reg]:(~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__4))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain)))))))))), introduced(definition,[new_symbols(definition,[eigen__24])])). % 70.79/70.93 thf(eigendef_eigen__19, definition, eigen__19 = (eps__0 @ (^[X1:reg]:(~(((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__3))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ france)))))))))), introduced(definition,[new_symbols(definition,[eigen__19])])). % 70.79/70.93 thf(sP1,plain,sP1 <=> ((~(((![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ eigen__2))) => (![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ catalunya)))))) => (~((![X1:reg]:((~((((c @ X1) @ catalunya) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya)))))))))))) => (((c @ X1) @ eigen__2) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ eigen__2))))))))))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 70.79/70.93 thf(sP2,plain,sP2 <=> (![X1:reg]:(((c @ X1) @ eigen__19) => ((c @ X1) @ france))),introduced(definition,[new_symbols(definition,[sP2])])). % 70.79/70.93 thf(sP3,plain,sP3 <=> (![X1:reg]:(((c @ X1) @ france) => ((c @ X1) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP3])])). % 70.79/70.93 thf(sP4,plain,sP4 <=> ((~((((c @ eigen__3) @ paris) => (~((![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__3))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))))) => (((c @ eigen__3) @ eigen__2) => (~((![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__3))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__2))))))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 70.79/70.93 thf(sP5,plain,sP5 <=> (![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(((~(((![X3:reg]:(((c @ X3) @ catalunya) => ((c @ X3) @ spain))) => (![X3:reg]:(((c @ X3) @ spain) => ((c @ X3) @ catalunya)))))) => (![X3:reg]:((~((((c @ X3) @ catalunya) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ catalunya)))))))))))) => (((c @ X3) @ spain) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ spain)))))))))))))))))),introduced(definition,[new_symbols(definition,[sP5])])). % 70.79/70.93 thf(sP6,plain,sP6 <=> (((c @ eigen__5) @ eigen__2) => ((c @ eigen__5) @ france)),introduced(definition,[new_symbols(definition,[sP6])])). % 70.79/70.93 thf(sP7,plain,sP7 <=> (((c @ eigen__7) @ eigen__2) => ((c @ eigen__7) @ catalunya)),introduced(definition,[new_symbols(definition,[sP7])])). % 70.79/70.93 thf(sP8,plain,sP8 <=> (![X1:$i]:(((a @ eigen__0) @ X1) => (![X2:reg]:((~(((~(((~(((![X3:reg]:(((c @ X3) @ france) => ((c @ X3) @ X2))) => (![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france)))))) => (~((![X3:reg]:((~((((c @ X3) @ france) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ france)))))))))))) => (((c @ X3) @ X2) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X2))))))))))))))))) => ((~(((![X3:reg]:(((c @ X3) @ spain) => ((c @ X3) @ X2))) => (![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ spain)))))) => (~((![X3:reg]:((~((((c @ X3) @ spain) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ spain)))))))))))) => (((c @ X3) @ X2) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X2)))))))))))))))))) => (~(((~(((~(((![X3:reg]:(((c @ X3) @ paris) => ((c @ X3) @ X2))) => (![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))) => (~((![X3:reg]:((~((((c @ X3) @ paris) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ paris)))))))))))) => (((c @ X3) @ X2) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X2))))))))))))))))) => ((~(((![X3:reg]:(((c @ X3) @ catalunya) => ((c @ X3) @ X2))) => (![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya)))))) => (~((![X3:reg]:((~((((c @ X3) @ catalunya) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ catalunya)))))))))))) => (((c @ X3) @ X2) => (~((![X4:reg]:((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X3))) => (~((![X5:reg]:(((c @ X5) @ X4) => ((c @ X5) @ X2)))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP8])])). % 70.79/70.93 thf(sP9,plain,sP9 <=> (((c @ eigen__41) @ eigen__19) => ((c @ eigen__41) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP9])])). % 70.79/70.93 thf(sP10,plain,sP10 <=> (![X1:$i]:(((a @ eigen__0) @ X1) => (~(((~(((![X2:reg]:(((c @ X2) @ paris) => ((c @ X2) @ france))) => (![X2:reg]:(((c @ X2) @ france) => ((c @ X2) @ paris)))))) => (~((![X2:reg]:((~((((c @ X2) @ paris) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ paris)))))))))))) => (((c @ X2) @ france) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ france))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP10])])). % 70.79/70.93 thf(sP11,plain,sP11 <=> (![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ spain))),introduced(definition,[new_symbols(definition,[sP11])])). % 70.79/70.93 thf(sP12,plain,sP12 <=> (((c @ eigen__9) @ spain) => ((c @ eigen__9) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP12])])). % 70.79/70.93 thf(sP13,plain,sP13 <=> ((~(((![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ france))) => (![X1:reg]:(((c @ X1) @ france) => ((c @ X1) @ paris)))))) => (~((![X1:reg]:((~((((c @ X1) @ paris) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))))) => (((c @ X1) @ france) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france))))))))))))))),introduced(definition,[new_symbols(definition,[sP13])])). % 70.79/70.93 thf(sP14,plain,sP14 <=> (![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP14])])). % 70.79/70.93 thf(sP15,plain,sP15 <=> (![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ catalunya))),introduced(definition,[new_symbols(definition,[sP15])])). % 70.79/70.93 thf(sP16,plain,sP16 <=> ((c @ eigen__9) @ eigen__2),introduced(definition,[new_symbols(definition,[sP16])])). % 70.79/70.93 thf(sP17,plain,sP17 <=> (((c @ eigen__5) @ eigen__2) => ((c @ eigen__5) @ paris)),introduced(definition,[new_symbols(definition,[sP17])])). % 70.79/70.93 thf(sP18,plain,sP18 <=> (((a @ eigen__0) @ eigen__1) => (~(sP13))),introduced(definition,[new_symbols(definition,[sP18])])). % 70.79/70.93 thf(sP19,plain,sP19 <=> ((c @ eigen__8) @ france),introduced(definition,[new_symbols(definition,[sP19])])). % 70.79/70.93 thf(sP20,plain,sP20 <=> (((c @ eigen__7) @ eigen__2) => ((c @ eigen__7) @ spain)),introduced(definition,[new_symbols(definition,[sP20])])). % 70.79/70.93 thf(sP21,plain,sP21 <=> (((c @ eigen__3) @ paris) => (~((![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__3))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))))))),introduced(definition,[new_symbols(definition,[sP21])])). % 70.79/70.93 thf(sP22,plain,sP22 <=> (![X1:reg]:(((c @ X1) @ eigen__24) => ((c @ X1) @ spain))),introduced(definition,[new_symbols(definition,[sP22])])). % 70.79/70.93 thf(sP23,plain,sP23 <=> ((c @ eigen__4) @ catalunya),introduced(definition,[new_symbols(definition,[sP23])])). % 70.79/70.93 thf(sP24,plain,sP24 <=> (![X1:reg]:((~((((c @ X1) @ catalunya) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya)))))))))))) => (((c @ X1) @ eigen__2) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ eigen__2)))))))))))),introduced(definition,[new_symbols(definition,[sP24])])). % 70.79/70.93 thf(sP25,plain,sP25 <=> ((c @ eigen__5) @ eigen__2),introduced(definition,[new_symbols(definition,[sP25])])). % 70.79/70.93 thf(sP26,plain,sP26 <=> ((c @ eigen__41) @ eigen__19),introduced(definition,[new_symbols(definition,[sP26])])). % 70.79/70.93 thf(sP27,plain,sP27 <=> (((c @ eigen__41) @ france) => ((c @ eigen__41) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP27])])). % 70.79/70.93 thf(sP28,plain,sP28 <=> ((c @ eigen__5) @ paris),introduced(definition,[new_symbols(definition,[sP28])])). % 70.79/70.93 thf(sP29,plain,sP29 <=> (sP23 => ((c @ eigen__4) @ spain)),introduced(definition,[new_symbols(definition,[sP29])])). % 70.79/70.93 thf(sP30,plain,sP30 <=> (((c @ eigen__9) @ catalunya) => ((c @ eigen__9) @ spain)),introduced(definition,[new_symbols(definition,[sP30])])). % 70.79/70.93 thf(sP31,plain,sP31 <=> (((c @ eigen__3) @ eigen__2) => (~((![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__3))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__2)))))))))),introduced(definition,[new_symbols(definition,[sP31])])). % 70.79/70.93 thf(sP32,plain,sP32 <=> (![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ paris))),introduced(definition,[new_symbols(definition,[sP32])])). % 70.79/70.93 thf(sP33,plain,sP33 <=> ((c @ eigen__41) @ france),introduced(definition,[new_symbols(definition,[sP33])])). % 70.79/70.93 thf(sP34,plain,sP34 <=> ((c @ eigen__8) @ eigen__2),introduced(definition,[new_symbols(definition,[sP34])])). % 70.79/70.93 thf(sP35,plain,sP35 <=> ((~((sP23 => (~((![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__4))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya)))))))))))) => (((c @ eigen__4) @ eigen__2) => (~((![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__4))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__2))))))))))),introduced(definition,[new_symbols(definition,[sP35])])). % 70.79/70.93 thf(sP36,plain,sP36 <=> ((![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ eigen__2))) => sP15),introduced(definition,[new_symbols(definition,[sP36])])). % 70.79/70.93 thf(sP37,plain,sP37 <=> (![X1:reg]:(((c @ X1) @ eigen__19) => ((c @ X1) @ eigen__3))),introduced(definition,[new_symbols(definition,[sP37])])). % 70.79/70.93 thf(sP38,plain,sP38 <=> ((c @ eigen__54) @ eigen__2),introduced(definition,[new_symbols(definition,[sP38])])). % 70.79/70.93 thf(sP39,plain,sP39 <=> ((c @ eigen__3) @ paris),introduced(definition,[new_symbols(definition,[sP39])])). % 70.79/70.93 thf(sP40,plain,sP40 <=> (sP37 => (~((![X1:reg]:(((c @ X1) @ eigen__19) => ((c @ X1) @ eigen__2)))))),introduced(definition,[new_symbols(definition,[sP40])])). % 70.79/70.93 thf(sP41,plain,sP41 <=> ((c @ eigen__3) @ france),introduced(definition,[new_symbols(definition,[sP41])])). % 70.79/70.93 thf(sP42,plain,sP42 <=> ((c @ eigen__7) @ eigen__2),introduced(definition,[new_symbols(definition,[sP42])])). % 70.79/70.93 thf(sP43,plain,sP43 <=> ((c @ eigen__54) @ spain),introduced(definition,[new_symbols(definition,[sP43])])). % 70.79/70.93 thf(sP44,plain,sP44 <=> (sP39 => sP41),introduced(definition,[new_symbols(definition,[sP44])])). % 70.79/70.93 thf(sP45,plain,sP45 <=> ((~((sP3 => (![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ france)))))) => (~((![X1:reg]:((~((((c @ X1) @ france) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france)))))))))))) => (((c @ X1) @ eigen__2) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ eigen__2))))))))))))))),introduced(definition,[new_symbols(definition,[sP45])])). % 70.79/70.93 thf(sP46,plain,sP46 <=> ((~((sP14 => sP32))) => (~((![X1:reg]:((~((((c @ X1) @ paris) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))))) => (((c @ X1) @ eigen__2) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ eigen__2))))))))))))))),introduced(definition,[new_symbols(definition,[sP46])])). % 70.79/70.93 thf(sP47,plain,sP47 <=> (![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ spain))),introduced(definition,[new_symbols(definition,[sP47])])). % 70.79/70.93 thf(sP48,plain,sP48 <=> (((c @ eigen__54) @ eigen__24) => sP43),introduced(definition,[new_symbols(definition,[sP48])])). % 70.79/70.93 thf(sP49,plain,sP49 <=> (sP23 => (~((![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__4))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya)))))))))),introduced(definition,[new_symbols(definition,[sP49])])). % 70.79/70.93 thf(sP50,plain,sP50 <=> (![X1:reg]:(((c @ X1) @ paris) => ((c @ X1) @ france))),introduced(definition,[new_symbols(definition,[sP50])])). % 70.79/70.93 thf(sP51,plain,sP51 <=> (![X1:reg]:((~(((~(((~(((![X2:reg]:(((c @ X2) @ france) => ((c @ X2) @ X1))) => (![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ france)))))) => (~((![X2:reg]:((~((((c @ X2) @ france) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ france)))))))))))) => (((c @ X2) @ X1) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X1))))))))))))))))) => ((~(((![X2:reg]:(((c @ X2) @ spain) => ((c @ X2) @ X1))) => (![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain)))))) => (~((![X2:reg]:((~((((c @ X2) @ spain) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ spain)))))))))))) => (((c @ X2) @ X1) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X1)))))))))))))))))) => (~(((~(((~(((![X2:reg]:(((c @ X2) @ paris) => ((c @ X2) @ X1))) => (![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ paris)))))) => (~((![X2:reg]:((~((((c @ X2) @ paris) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ paris)))))))))))) => (((c @ X2) @ X1) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X1))))))))))))))))) => ((~(((![X2:reg]:(((c @ X2) @ catalunya) => ((c @ X2) @ X1))) => (![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ catalunya)))))) => (~((![X2:reg]:((~((((c @ X2) @ catalunya) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ catalunya)))))))))))) => (((c @ X2) @ X1) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X1)))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP51])])). % 70.79/70.93 thf(sP52,plain,sP52 <=> ((c @ eigen__9) @ catalunya),introduced(definition,[new_symbols(definition,[sP52])])). % 70.79/70.93 thf(sP53,plain,sP53 <=> (![X1:reg]:(((c @ X1) @ eigen__19) => ((c @ X1) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP53])])). % 70.79/70.93 thf(sP54,plain,sP54 <=> (![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (~(sP13))))),introduced(definition,[new_symbols(definition,[sP54])])). % 70.79/70.93 thf(sP55,plain,sP55 <=> (sP11 => (![X1:reg]:(((c @ X1) @ spain) => ((c @ X1) @ catalunya)))),introduced(definition,[new_symbols(definition,[sP55])])). % 70.79/70.93 thf(sP56,plain,sP56 <=> ((c @ eigen__54) @ eigen__24),introduced(definition,[new_symbols(definition,[sP56])])). % 70.79/70.93 thf(sP57,plain,sP57 <=> (sP28 => ((c @ eigen__5) @ france)),introduced(definition,[new_symbols(definition,[sP57])])). % 70.79/70.93 thf(sP58,plain,sP58 <=> (((a @ eigen__0) @ eigen__1) => sP51),introduced(definition,[new_symbols(definition,[sP58])])). % 70.79/70.93 thf(sP59,plain,sP59 <=> ((![X1:reg]:(((c @ X1) @ eigen__24) => ((c @ X1) @ eigen__4))) => (~((![X1:reg]:(((c @ X1) @ eigen__24) => ((c @ X1) @ eigen__2)))))),introduced(definition,[new_symbols(definition,[sP59])])). % 70.79/70.93 thf(sP60,plain,sP60 <=> (![X1:reg]:((~((((c @ X1) @ paris) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))))) => (((c @ X1) @ france) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ france)))))))))))),introduced(definition,[new_symbols(definition,[sP60])])). % 70.79/70.93 thf(sP61,plain,sP61 <=> (![X1:reg]:((~((((c @ X1) @ paris) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ paris)))))))))))) => (((c @ X1) @ eigen__2) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ eigen__2)))))))))))),introduced(definition,[new_symbols(definition,[sP61])])). % 70.79/70.93 thf(sP62,plain,sP62 <=> (sP19 => sP34),introduced(definition,[new_symbols(definition,[sP62])])). % 70.79/70.93 thf(sP63,plain,sP63 <=> (![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__4))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__2))))))),introduced(definition,[new_symbols(definition,[sP63])])). % 70.79/70.93 thf(sP64,plain,sP64 <=> ((c @ eigen__8) @ paris),introduced(definition,[new_symbols(definition,[sP64])])). % 70.79/70.93 thf(sP65,plain,sP65 <=> ((~((((c @ eigen__4) @ spain) => (~((![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__4))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain)))))))))))) => (((c @ eigen__4) @ eigen__2) => (~(sP63)))),introduced(definition,[new_symbols(definition,[sP65])])). % 70.79/70.93 thf(sP66,plain,sP66 <=> (![X1:reg]:(((c @ X1) @ catalunya) => ((c @ X1) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP66])])). % 70.79/70.93 thf(sP67,plain,sP67 <=> (sP50 => (![X1:reg]:(((c @ X1) @ france) => ((c @ X1) @ paris)))),introduced(definition,[new_symbols(definition,[sP67])])). % 70.79/70.93 thf(sP68,plain,sP68 <=> (sP3 => (![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ france)))),introduced(definition,[new_symbols(definition,[sP68])])). % 70.79/70.93 thf(sP69,plain,sP69 <=> (![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__3))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ france))))))),introduced(definition,[new_symbols(definition,[sP69])])). % 70.79/70.93 thf(sP70,plain,sP70 <=> ((![X1:reg]:(((c @ X1) @ eigen__24) => ((c @ X1) @ eigen__4))) => (~(sP22))),introduced(definition,[new_symbols(definition,[sP70])])). % 70.79/70.93 thf(sP71,plain,sP71 <=> ((~(sP46)) => sP1),introduced(definition,[new_symbols(definition,[sP71])])). % 70.79/70.93 thf(sP72,plain,sP72 <=> (![X1:reg]:((~((((c @ X1) @ spain) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ spain)))))))))))) => (((c @ X1) @ eigen__2) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ eigen__2)))))))))))),introduced(definition,[new_symbols(definition,[sP72])])). % 70.79/70.93 thf(sP73,plain,sP73 <=> ((~(sP21)) => (sP41 => (~(sP69)))),introduced(definition,[new_symbols(definition,[sP73])])). % 70.79/70.93 thf(sP74,plain,sP74 <=> ((![X1:reg]:(((c @ X1) @ spain) => ((c @ X1) @ eigen__2))) => sP47),introduced(definition,[new_symbols(definition,[sP74])])). % 70.79/70.93 thf(sP75,plain,sP75 <=> (![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => sP51))),introduced(definition,[new_symbols(definition,[sP75])])). % 70.79/70.93 thf(sP76,plain,sP76 <=> (![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__4))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ spain))))))),introduced(definition,[new_symbols(definition,[sP76])])). % 70.79/70.93 thf(sP77,plain,sP77 <=> ((c @ eigen__9) @ spain),introduced(definition,[new_symbols(definition,[sP77])])). % 70.79/70.93 thf(sP78,plain,sP78 <=> (((c @ eigen__7) @ catalunya) => ((c @ eigen__7) @ spain)),introduced(definition,[new_symbols(definition,[sP78])])). % 70.79/70.93 thf(sP79,plain,sP79 <=> (sP64 => sP34),introduced(definition,[new_symbols(definition,[sP79])])). % 70.79/70.93 thf(sP80,plain,sP80 <=> ((c @ eigen__5) @ france),introduced(definition,[new_symbols(definition,[sP80])])). % 70.79/70.93 thf(sP81,plain,sP81 <=> (![X1:$i]:(((a @ eigen__0) @ X1) => (~(((~(sP55)) => (![X2:reg]:((~((((c @ X2) @ catalunya) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ catalunya)))))))))))) => (((c @ X2) @ spain) => (~((![X3:reg]:((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ X2))) => (~((![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ spain))))))))))))))))),introduced(definition,[new_symbols(definition,[sP81])])). % 70.79/70.93 thf(sP82,plain,sP82 <=> (sP64 => sP19),introduced(definition,[new_symbols(definition,[sP82])])). % 70.79/70.93 thf(sP83,plain,sP83 <=> (sP37 => (~(sP2))),introduced(definition,[new_symbols(definition,[sP83])])). % 70.79/70.93 thf(sP84,plain,sP84 <=> ((a @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP84])])). % 70.79/70.93 thf(sP85,plain,sP85 <=> (sP56 => sP38),introduced(definition,[new_symbols(definition,[sP85])])). % 70.79/70.93 thf(sP86,plain,sP86 <=> ((c @ eigen__41) @ eigen__2),introduced(definition,[new_symbols(definition,[sP86])])). % 70.79/70.93 thf(sP87,plain,sP87 <=> (![X1:reg]:(((c @ X1) @ spain) => ((c @ X1) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP87])])). % 70.79/70.93 thf(sP88,plain,sP88 <=> (![X1:reg]:(((c @ X1) @ eigen__24) => ((c @ X1) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP88])])). % 70.79/70.93 thf(sP89,plain,sP89 <=> ((c @ eigen__7) @ spain),introduced(definition,[new_symbols(definition,[sP89])])). % 70.79/70.93 thf(sP90,plain,sP90 <=> (sP43 => sP38),introduced(definition,[new_symbols(definition,[sP90])])). % 70.79/70.93 thf(sP91,plain,sP91 <=> ((~(sP45)) => ((~(sP74)) => (~(sP72)))),introduced(definition,[new_symbols(definition,[sP91])])). % 70.79/70.93 thf(sP92,plain,sP92 <=> ((c @ eigen__7) @ catalunya),introduced(definition,[new_symbols(definition,[sP92])])). % 70.79/70.93 thf(sP93,plain,sP93 <=> ((~(sP91)) => (~(sP71))),introduced(definition,[new_symbols(definition,[sP93])])). % 70.79/70.93 thf(sP94,plain,sP94 <=> (![X1:reg]:(((c @ X1) @ eigen__24) => ((c @ X1) @ eigen__4))),introduced(definition,[new_symbols(definition,[sP94])])). % 70.79/70.93 thf(sP95,plain,sP95 <=> (sP84 => (~(((~(sP55)) => (![X1:reg]:((~((((c @ X1) @ catalunya) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya)))))))))))) => (((c @ X1) @ spain) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ spain)))))))))))))))),introduced(definition,[new_symbols(definition,[sP95])])). % 70.79/70.93 thf(sP96,plain,sP96 <=> (sP41 => (~(sP69))),introduced(definition,[new_symbols(definition,[sP96])])). % 70.79/70.93 thf(sP97,plain,sP97 <=> (![X1:reg]:(((c @ X1) @ eigen__2) => ((c @ X1) @ france))),introduced(definition,[new_symbols(definition,[sP97])])). % 70.79/70.93 thf(sP98,plain,sP98 <=> (![X1:reg]:((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__3))) => (~((![X2:reg]:(((c @ X2) @ X1) => ((c @ X2) @ eigen__2))))))),introduced(definition,[new_symbols(definition,[sP98])])). % 70.79/70.93 thf(sP99,plain,sP99 <=> (sP52 => sP16),introduced(definition,[new_symbols(definition,[sP99])])). % 70.79/70.93 thf(sP100,plain,sP100 <=> (((c @ eigen__4) @ eigen__2) => (~(sP63))),introduced(definition,[new_symbols(definition,[sP100])])). % 70.79/70.93 thf(sP101,plain,sP101 <=> (sP14 => sP32),introduced(definition,[new_symbols(definition,[sP101])])). % 70.79/70.93 thf(sP102,plain,sP102 <=> (((c @ eigen__4) @ spain) => (~(sP76))),introduced(definition,[new_symbols(definition,[sP102])])). % 70.79/70.93 thf(sP103,plain,sP103 <=> ((~(sP55)) => (![X1:reg]:((~((((c @ X1) @ catalunya) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ catalunya)))))))))))) => (((c @ X1) @ spain) => (~((![X2:reg]:((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ X1))) => (~((![X3:reg]:(((c @ X3) @ X2) => ((c @ X3) @ spain))))))))))))),introduced(definition,[new_symbols(definition,[sP103])])). % 70.79/70.93 thf(sP104,plain,sP104 <=> ((~(sP74)) => (~(sP72))),introduced(definition,[new_symbols(definition,[sP104])])). % 70.79/70.93 thf(sP105,plain,sP105 <=> (sP26 => sP33),introduced(definition,[new_symbols(definition,[sP105])])). % 70.79/70.93 thf(sP106,plain,sP106 <=> ((c @ eigen__4) @ spain),introduced(definition,[new_symbols(definition,[sP106])])). % 70.79/70.93 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))). % 70.79/70.93 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))). % 70.79/70.93 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 70.79/70.93 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 70.79/70.93 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 70.79/70.93 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 70.79/70.93 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))). % 70.79/70.93 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))). % 70.79/70.93 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))). % 70.79/70.93 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))). % 70.79/70.93 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))). % 70.79/70.93 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))). % 70.79/70.93 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))). % 70.79/70.93 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))). % 70.79/70.93 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))). % 70.79/70.93 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))). % 70.79/70.93 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))). % 70.79/70.93 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))). % 70.79/70.93 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))). % 70.79/70.93 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))). % 70.79/70.93 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))). % 70.79/70.93 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))). % 70.79/70.93 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))). % 70.79/70.93 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))). % 70.79/70.93 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))). % 70.79/70.93 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))). % 70.79/70.93 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))). % 70.79/70.93 thf(def_mvalid,definition,(mvalid = (!!))). % 70.79/70.93 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))). % 70.79/70.93 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))). % 70.79/70.93 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))). % 70.79/70.93 thf(def_dc,definition,(dc = (^[X1:reg]:(^[X2:reg]:(~(((c @ X1) @ X2))))))). % 70.79/70.93 thf(def_p,definition,(p = (^[X1:reg]:(^[X2:reg]:(![X3:reg]:(((c @ X3) @ X1) => ((c @ X3) @ X2))))))). % 70.79/70.93 thf(def_eq,definition,(eq = (^[X1:reg]:(^[X2:reg]:(~((((p @ X1) @ X2) => (~(((p @ X2) @ X1)))))))))). % 70.79/70.93 thf(def_o,definition,(o = (^[X1:reg]:(^[X2:reg]:(~((![X3:reg]:(((p @ X3) @ X1) => (~(((p @ X3) @ X2))))))))))). % 70.79/70.93 thf(def_po,definition,(po = (^[X1:reg]:(^[X2:reg]:(~(((~((((o @ X1) @ X2) => ((p @ X1) @ X2)))) => ((p @ X2) @ X1)))))))). % 70.79/70.93 thf(def_ec,definition,(ec = (^[X1:reg]:(^[X2:reg]:(~((((c @ X1) @ X2) => ((o @ X1) @ X2)))))))). % 70.79/70.93 thf(def_pp,definition,(pp = (^[X1:reg]:(^[X2:reg]:(~((((p @ X1) @ X2) => ((p @ X2) @ X1)))))))). % 70.79/70.93 thf(def_tpp,definition,(tpp = (^[X1:reg]:(^[X2:reg]:(~((((pp @ X1) @ X2) => (![X3:reg]:(((ec @ X3) @ X1) => (~(((ec @ X3) @ X2)))))))))))). % 70.79/70.93 thf(def_ntpp,definition,(ntpp = (^[X1:reg]:(^[X2:reg]:(~((((pp @ X1) @ X2) => (~((![X3:reg]:(((ec @ X3) @ X1) => (~(((ec @ X3) @ X2)))))))))))))). % 70.79/70.93 thf(con,conjecture,(![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (![X3:reg]:((~(((~(((~(((![X4:reg]:(((c @ X4) @ france) => ((c @ X4) @ X3))) => (![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ france)))))) => (~((![X4:reg]:((~((((c @ X4) @ france) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ france)))))))))))) => (~((~((((c @ X4) @ X3) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3))))))))))))))))))))) => (~((~(((~(((![X4:reg]:(((c @ X4) @ spain) => ((c @ X4) @ X3))) => (![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ spain)))))) => (~((![X4:reg]:((~((((c @ X4) @ spain) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ spain)))))))))))) => (~((~((((c @ X4) @ X3) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3)))))))))))))))))))))))))) => (~(((~(((~(((![X4:reg]:(((c @ X4) @ paris) => ((c @ X4) @ X3))) => (![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ paris)))))) => (~((![X4:reg]:((~((((c @ X4) @ paris) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ paris)))))))))))) => (~((~((((c @ X4) @ X3) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3))))))))))))))))))))) => (~((~(((~(((![X4:reg]:(((c @ X4) @ catalunya) => ((c @ X4) @ X3))) => (![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ catalunya)))))) => (~((![X4:reg]:((~((((c @ X4) @ catalunya) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ catalunya)))))))))))) => (~((~((((c @ X4) @ X3) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3)))))))))))))))))))))))))))))))). % 70.79/70.93 thf(h2,negated_conjecture,(~(sP75)),inference(assume_negation,[status(cth)],[con])). % 70.79/70.93 thf(1,plain,(~(sP50) | sP57),inference(all_rule,[status(thm)],[])). % 70.79/70.93 thf(2,plain,((~(sP57) | ~(sP28)) | sP80),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(3,plain,(~(sP50) | sP82),inference(all_rule,[status(thm)],[])). % 70.79/70.93 thf(4,plain,((~(sP82) | ~(sP64)) | sP19),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(5,plain,(~(sP50) | sP44),inference(all_rule,[status(thm)],[])). % 70.79/70.93 thf(6,plain,((~(sP44) | ~(sP39)) | sP41),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(7,plain,(~(sP11) | sP78),inference(all_rule,[status(thm)],[])). % 70.79/70.93 thf(8,plain,((~(sP78) | ~(sP92)) | sP89),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(9,plain,(~(sP11) | sP30),inference(all_rule,[status(thm)],[])). % 70.79/70.93 thf(10,plain,((~(sP30) | ~(sP52)) | sP77),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(11,plain,(~(sP11) | sP29),inference(all_rule,[status(thm)],[])). % 70.79/70.93 thf(12,plain,((~(sP29) | ~(sP23)) | sP106),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(13,plain,(~(sP87) | sP90),inference(all_rule,[status(thm)],[])). % 70.79/70.93 thf(14,plain,((~(sP90) | ~(sP43)) | sP38),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(15,plain,(~(sP22) | sP48),inference(all_rule,[status(thm)],[])). % 70.79/70.93 thf(16,plain,((~(sP48) | ~(sP56)) | sP43),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(17,plain,(~(sP3) | sP27),inference(all_rule,[status(thm)],[])). % 70.79/70.93 thf(18,plain,((~(sP27) | ~(sP33)) | sP86),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(19,plain,(~(sP2) | sP105),inference(all_rule,[status(thm)],[])). % 70.79/70.93 thf(20,plain,((~(sP105) | ~(sP26)) | sP33),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(21,plain,(~(sP60) | sP73),inference(all_rule,[status(thm)],[])). % 70.79/70.93 thf(22,plain,((~(sP73) | sP21) | sP96),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(23,plain,(sP67 | sP50),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(24,plain,(sP55 | sP11),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(25,plain,(sP85 | ~(sP38)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(26,plain,(sP85 | sP56),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(27,plain,(sP9 | ~(sP86)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(28,plain,(sP9 | sP26),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(29,plain,(sP13 | sP60),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(30,plain,(sP13 | ~(sP67)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(31,plain,(sP103 | ~(sP55)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(32,plain,(sP88 | ~(sP85)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__54])). % 70.79/70.93 thf(33,plain,(sP53 | ~(sP9)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__41])). % 70.79/70.93 thf(34,plain,(~(sP54) | sP10),inference(all_rule,[status(thm)],[])). % 70.79/70.93 thf(35,plain,(~(sP10) | sP18),inference(all_rule,[status(thm)],[])). % 70.79/70.93 thf(36,plain,((~(sP18) | ~(sP84)) | ~(sP13)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(37,plain,(~(sP5) | sP81),inference(all_rule,[status(thm)],[])). % 70.79/70.93 thf(38,plain,(~(sP81) | sP95),inference(all_rule,[status(thm)],[])). % 70.79/70.93 thf(39,plain,((~(sP95) | ~(sP84)) | ~(sP103)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(40,plain,(~(sP63) | sP59),inference(all_rule,[status(thm)],[])). % 70.79/70.93 thf(41,plain,((~(sP59) | ~(sP94)) | ~(sP88)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(42,plain,(~(sP98) | sP40),inference(all_rule,[status(thm)],[])). % 70.79/70.93 thf(43,plain,((~(sP40) | ~(sP37)) | ~(sP53)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(44,plain,(sP70 | sP22),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(45,plain,(sP70 | sP94),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(46,plain,(sP83 | sP2),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(47,plain,(sP83 | sP37),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(48,plain,(sP76 | ~(sP70)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__24])). % 70.79/70.93 thf(49,plain,(sP69 | ~(sP83)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__19])). % 70.79/70.93 thf(50,plain,(~(sP72) | sP65),inference(all_rule,[status(thm)],[])). % 70.79/70.93 thf(51,plain,((~(sP65) | sP102) | sP100),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(52,plain,((~(sP102) | ~(sP106)) | ~(sP76)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(53,plain,(~(sP87) | sP12),inference(all_rule,[status(thm)],[])). % 70.79/70.93 thf(54,plain,((~(sP12) | ~(sP77)) | sP16),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(55,plain,((~(sP96) | ~(sP41)) | ~(sP69)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(56,plain,(~(sP3) | sP62),inference(all_rule,[status(thm)],[])). % 70.79/70.93 thf(57,plain,((~(sP62) | ~(sP19)) | sP34),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(58,plain,(~(sP15) | sP7),inference(all_rule,[status(thm)],[])). % 70.79/70.93 thf(59,plain,((~(sP7) | ~(sP42)) | sP92),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(60,plain,(~(sP32) | sP17),inference(all_rule,[status(thm)],[])). % 70.79/70.93 thf(61,plain,((~(sP17) | ~(sP25)) | sP28),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(62,plain,(sP100 | sP63),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(63,plain,(sP49 | sP23),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(64,plain,(sP99 | ~(sP16)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(65,plain,(sP99 | sP52),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(66,plain,(sP31 | sP98),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(67,plain,(sP21 | sP39),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(68,plain,(sP79 | ~(sP34)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(69,plain,(sP79 | sP64),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(70,plain,(sP20 | ~(sP89)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(71,plain,(sP20 | sP42),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(72,plain,(sP6 | ~(sP80)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(73,plain,(sP6 | sP25),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(74,plain,(sP35 | ~(sP100)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(75,plain,(sP35 | ~(sP49)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(76,plain,(sP66 | ~(sP99)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9])). % 70.79/70.93 thf(77,plain,(sP4 | ~(sP31)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(78,plain,(sP4 | ~(sP21)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(79,plain,(sP14 | ~(sP79)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8])). % 70.79/70.93 thf(80,plain,(sP47 | ~(sP20)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7])). % 70.79/70.93 thf(81,plain,(sP97 | ~(sP6)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5])). % 70.79/70.93 thf(82,plain,(sP24 | ~(sP35)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4])). % 70.79/70.93 thf(83,plain,((~(sP36) | ~(sP66)) | sP15),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(84,plain,(sP61 | ~(sP4)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])). % 70.79/70.93 thf(85,plain,((~(sP101) | ~(sP14)) | sP32),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(86,plain,(sP74 | ~(sP47)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(87,plain,(sP74 | sP87),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(88,plain,(sP68 | ~(sP97)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(89,plain,(sP68 | sP3),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(90,plain,((~(sP1) | sP36) | ~(sP24)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(91,plain,((~(sP46) | sP101) | ~(sP61)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(92,plain,(sP104 | sP72),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(93,plain,(sP104 | ~(sP74)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(94,plain,(sP45 | ~(sP68)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(95,plain,((~(sP71) | sP46) | sP1),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(96,plain,(sP91 | ~(sP104)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(97,plain,(sP91 | ~(sP45)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(98,plain,(sP93 | sP71),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(99,plain,(sP93 | ~(sP91)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(100,plain,(sP51 | ~(sP93)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])). % 70.79/70.93 thf(101,plain,(sP58 | ~(sP51)),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(102,plain,(sP58 | sP84),inference(prop_rule,[status(thm)],[])). % 70.79/70.93 thf(103,plain,(sP8 | ~(sP58)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1])). % 70.79/70.93 thf(104,plain,(sP75 | ~(sP8)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0])). % 70.79/70.93 thf(ax3,axiom,(mvalid @ ((mbox @ a) @ (^[X1:$i]:((ntpp @ paris) @ france))))). % 70.79/70.93 thf(105,plain,sP54,inference(preprocess,[status(thm)],[ax3]). % 70.79/70.93 thf(ax1,axiom,(mvalid @ ((mbox @ a) @ (^[X1:$i]:((tpp @ catalunya) @ spain))))). % 70.79/70.93 thf(106,plain,sP5,inference(preprocess,[status(thm)],[ax1]). % 70.79/70.93 thf(107,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,h2])). % 70.79/70.93 thf(108,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[107,h1])). % 70.79/70.93 thf(109,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[108,h0])). % 70.79/70.93 thf(0,theorem,(![X1:$i]:(![X2:$i]:(((a @ X1) @ X2) => (![X3:reg]:((~(((~(((~(((![X4:reg]:(((c @ X4) @ france) => ((c @ X4) @ X3))) => (![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ france)))))) => (~((![X4:reg]:((~((((c @ X4) @ france) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ france)))))))))))) => (~((~((((c @ X4) @ X3) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3))))))))))))))))))))) => (~((~(((~(((![X4:reg]:(((c @ X4) @ spain) => ((c @ X4) @ X3))) => (![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ spain)))))) => (~((![X4:reg]:((~((((c @ X4) @ spain) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ spain)))))))))))) => (~((~((((c @ X4) @ X3) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3)))))))))))))))))))))))))) => (~(((~(((~(((![X4:reg]:(((c @ X4) @ paris) => ((c @ X4) @ X3))) => (![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ paris)))))) => (~((![X4:reg]:((~((((c @ X4) @ paris) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ paris)))))))))))) => (~((~((((c @ X4) @ X3) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3))))))))))))))))))))) => (~((~(((~(((![X4:reg]:(((c @ X4) @ catalunya) => ((c @ X4) @ X3))) => (![X4:reg]:(((c @ X4) @ X3) => ((c @ X4) @ catalunya)))))) => (~((![X4:reg]:((~((((c @ X4) @ catalunya) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ catalunya)))))))))))) => (~((~((((c @ X4) @ X3) => (~((![X5:reg]:((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X4))) => (~((![X6:reg]:(((c @ X6) @ X5) => ((c @ X6) @ X3))))))))))))))))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h2])],[107,h2])). % 70.79/70.93 % SZS output end Proof %------------------------------------------------------------------------------