%------------------------------------------------------------------------------ % File : Satallax---3.5 % Problem : ALG017^7 : TPTP v9.2.0. Released v5.5.0. % Transfm : none % Format : tptp:raw % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % Computer : n012.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 01:11:53 PM UTC 2025 % Result : Theorem 91.10s 91.17s % Output : Proof 91.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ALG017^7 : TPTP v9.2.0. Released v5.5.0. % 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s % 0.13/0.34 % Computer : n012.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 23:36:08 EDT 2025 % 0.13/0.34 % CPUTime : % 91.10/91.17 % SZS status Theorem % 91.10/91.17 % Mode: mode454:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=3.:SINE_DEPTH=0 % 91.10/91.17 % Inferences: 72 % 91.10/91.17 % SZS output start Proof % 91.10/91.17 thf(ty_mu, type, mu : $tType). % 91.10/91.17 thf(ty_rel_s4, type, rel_s4 : ($i>$i>$o)). % 91.10/91.17 thf(ty_e0, type, e0 : mu). % 91.10/91.17 thf(ty_eigen__1, type, eigen__1 : $i). % 91.10/91.17 thf(ty_eigen__0, type, eigen__0 : $i). % 91.10/91.17 thf(ty_e3, type, e3 : mu). % 91.10/91.17 thf(ty_e2, type, e2 : mu). % 91.10/91.17 thf(ty_e1, type, e1 : mu). % 91.10/91.17 thf(ty_qmltpeq, type, qmltpeq : (mu>mu>$i>$o)). % 91.10/91.17 thf(ty_op, type, op : (mu>mu>mu)). % 91.10/91.17 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])). % 91.10/91.17 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~((((rel_s4 @ eigen__0) @ X1) => ((((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e0) @ e0)) @ e0) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e1) @ e1)) @ e0) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e2) @ e2)) @ e0) @ X2))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e3) @ e3)) @ e0) @ X2)))))))) => (((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e0) @ e0)) @ e1) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e1) @ e1)) @ e1) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e2) @ e2)) @ e1) @ X2))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e3) @ e3)) @ e1) @ X2)))))))) => (((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e0) @ e0)) @ e2) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e1) @ e1)) @ e2) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e2) @ e2)) @ e2) @ X2))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e3) @ e3)) @ e2) @ X2)))))))) => (~(((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e0) @ e0)) @ e3) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e1) @ e1)) @ e3) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e2) @ e2)) @ e3) @ X2))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e3) @ e3)) @ e3) @ X2))))))))))))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e0) @ e0)) @ e0) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e1) @ e1)) @ e0) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e2) @ e2)) @ e0) @ X3))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e3) @ e3)) @ e0) @ X3)))))))) => (((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e0) @ e0)) @ e1) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e1) @ e1)) @ e1) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e2) @ e2)) @ e1) @ X3))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e3) @ e3)) @ e1) @ X3)))))))) => (((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e0) @ e0)) @ e2) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e1) @ e1)) @ e2) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e2) @ e2)) @ e2) @ X3))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e3) @ e3)) @ e2) @ X3)))))))) => (~(((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e0) @ e0)) @ e3) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e1) @ e1)) @ e3) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e2) @ e2)) @ e3) @ X3))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e3) @ e3)) @ e3) @ X3))))))))))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])). % 91.10/91.17 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e0) @ e0)) @ e0) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e1) @ e1)) @ e0) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e2) @ e2)) @ e0) @ X3))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e3) @ e3)) @ e0) @ X3)))))))) => (((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e0) @ e0)) @ e1) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e1) @ e1)) @ e1) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e2) @ e2)) @ e1) @ X3))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e3) @ e3)) @ e1) @ X3)))))))) => (((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e0) @ e0)) @ e2) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e1) @ e1)) @ e2) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e2) @ e2)) @ e2) @ X3))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e3) @ e3)) @ e2) @ X3)))))))) => (~(((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e0) @ e0)) @ e3) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e1) @ e1)) @ e3) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e2) @ e2)) @ e3) @ X3))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e3) @ e3)) @ e3) @ X3))))))))))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (~((((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e0) @ e0)) @ e0) @ X4))) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e1) @ e1)) @ e0) @ X4))) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e2) @ e2)) @ e0) @ X4))) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e3) @ e3)) @ e0) @ X4)))))))) => (((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e0) @ e0)) @ e1) @ X4))) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e1) @ e1)) @ e1) @ X4))) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e2) @ e2)) @ e1) @ X4))) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e3) @ e3)) @ e1) @ X4)))))))) => (((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e0) @ e0)) @ e2) @ X4))) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e1) @ e1)) @ e2) @ X4))) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e2) @ e2)) @ e2) @ X4))) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e3) @ e3)) @ e2) @ X4)))))))) => (~(((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e0) @ e0)) @ e3) @ X4))) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e1) @ e1)) @ e3) @ X4))) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e2) @ e2)) @ e3) @ X4))) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e3) @ e3)) @ e3) @ X4)))))))))))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])). % 91.10/91.17 thf(sP1,plain,sP1 <=> ((((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e0) @ e0)) @ e0) @ X1))) => ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e1) @ e1)) @ e0) @ X1))) => ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e2) @ e2)) @ e0) @ X1))) => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e3) @ e3)) @ e0) @ X1)))))))) => (((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e0) @ e0)) @ e1) @ X1))) => ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e1) @ e1)) @ e1) @ X1))) => ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e2) @ e2)) @ e1) @ X1))) => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e3) @ e3)) @ e1) @ X1)))))))) => (((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e0) @ e0)) @ e2) @ X1))) => ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e1) @ e1)) @ e2) @ X1))) => ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e2) @ e2)) @ e2) @ X1))) => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e3) @ e3)) @ e2) @ X1)))))))) => (~(((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e0) @ e0)) @ e3) @ X1))) => ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e1) @ e1)) @ e3) @ X1))) => ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e2) @ e2)) @ e3) @ X1))) => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e3) @ e3)) @ e3) @ X1))))))))))))) => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (~((((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e0) @ e0)) @ e0) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e1) @ e1)) @ e0) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e2) @ e2)) @ e0) @ X2))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e3) @ e3)) @ e0) @ X2)))))))) => (((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e0) @ e0)) @ e1) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e1) @ e1)) @ e1) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e2) @ e2)) @ e1) @ X2))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e3) @ e3)) @ e1) @ X2)))))))) => (((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e0) @ e0)) @ e2) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e1) @ e1)) @ e2) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e2) @ e2)) @ e2) @ X2))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e3) @ e3)) @ e2) @ X2)))))))) => (~(((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e0) @ e0)) @ e3) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e1) @ e1)) @ e3) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e2) @ e2)) @ e3) @ X2))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e3) @ e3)) @ e3) @ X2)))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP1])])). % 91.10/91.17 thf(sP2,plain,sP2 <=> (![X1:$i]:((rel_s4 @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP2])])). % 91.10/91.17 thf(sP3,plain,sP3 <=> ((rel_s4 @ eigen__1) @ eigen__1),introduced(definition,[new_symbols(definition,[sP3])])). % 91.10/91.17 thf(sP4,plain,sP4 <=> (sP3 => (~((((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e0) @ e0)) @ e0) @ X1))) => ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e1) @ e1)) @ e0) @ X1))) => ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e2) @ e2)) @ e0) @ X1))) => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e3) @ e3)) @ e0) @ X1)))))))) => (((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e0) @ e0)) @ e1) @ X1))) => ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e1) @ e1)) @ e1) @ X1))) => ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e2) @ e2)) @ e1) @ X1))) => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e3) @ e3)) @ e1) @ X1)))))))) => (((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e0) @ e0)) @ e2) @ X1))) => ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e1) @ e1)) @ e2) @ X1))) => ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e2) @ e2)) @ e2) @ X1))) => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e3) @ e3)) @ e2) @ X1)))))))) => (~(((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e0) @ e0)) @ e3) @ X1))) => ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e1) @ e1)) @ e3) @ X1))) => ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e2) @ e2)) @ e3) @ X1))) => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e3) @ e3)) @ e3) @ X1)))))))))))))))),introduced(definition,[new_symbols(definition,[sP4])])). % 91.10/91.17 thf(sP5,plain,sP5 <=> (((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e0) @ e0)) @ e0) @ X1))) => ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e1) @ e1)) @ e0) @ X1))) => ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e2) @ e2)) @ e0) @ X1))) => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e3) @ e3)) @ e0) @ X1)))))))) => (((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e0) @ e0)) @ e1) @ X1))) => ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e1) @ e1)) @ e1) @ X1))) => ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e2) @ e2)) @ e1) @ X1))) => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e3) @ e3)) @ e1) @ X1)))))))) => (((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e0) @ e0)) @ e2) @ X1))) => ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e1) @ e1)) @ e2) @ X1))) => ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e2) @ e2)) @ e2) @ X1))) => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e3) @ e3)) @ e2) @ X1)))))))) => (~(((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e0) @ e0)) @ e3) @ X1))) => ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e1) @ e1)) @ e3) @ X1))) => ((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e2) @ e2)) @ e3) @ X1))) => (~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (((qmltpeq @ ((op @ e3) @ e3)) @ e3) @ X1))))))))))))),introduced(definition,[new_symbols(definition,[sP5])])). % 91.10/91.17 thf(sP6,plain,sP6 <=> (![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => ((((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e0) @ e0)) @ e0) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e1) @ e1)) @ e0) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e2) @ e2)) @ e0) @ X3))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e3) @ e3)) @ e0) @ X3)))))))) => (((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e0) @ e0)) @ e1) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e1) @ e1)) @ e1) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e2) @ e2)) @ e1) @ X3))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e3) @ e3)) @ e1) @ X3)))))))) => (((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e0) @ e0)) @ e2) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e1) @ e1)) @ e2) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e2) @ e2)) @ e2) @ X3))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e3) @ e3)) @ e2) @ X3)))))))) => (~(((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e0) @ e0)) @ e3) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e1) @ e1)) @ e3) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e2) @ e2)) @ e3) @ X3))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e3) @ e3)) @ e3) @ X3))))))))))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (~((((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e0) @ e0)) @ e0) @ X4))) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e1) @ e1)) @ e0) @ X4))) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e2) @ e2)) @ e0) @ X4))) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e3) @ e3)) @ e0) @ X4)))))))) => (((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e0) @ e0)) @ e1) @ X4))) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e1) @ e1)) @ e1) @ X4))) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e2) @ e2)) @ e1) @ X4))) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e3) @ e3)) @ e1) @ X4)))))))) => (((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e0) @ e0)) @ e2) @ X4))) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e1) @ e1)) @ e2) @ X4))) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e2) @ e2)) @ e2) @ X4))) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e3) @ e3)) @ e2) @ X4)))))))) => (~(((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e0) @ e0)) @ e3) @ X4))) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e1) @ e1)) @ e3) @ X4))) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e2) @ e2)) @ e3) @ X4))) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e3) @ e3)) @ e3) @ X4))))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP6])])). % 91.10/91.17 thf(sP7,plain,sP7 <=> (((rel_s4 @ eigen__0) @ eigen__1) => sP1),introduced(definition,[new_symbols(definition,[sP7])])). % 91.10/91.17 thf(sP8,plain,sP8 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (~((((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e0) @ e0)) @ e0) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e1) @ e1)) @ e0) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e2) @ e2)) @ e0) @ X2))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e3) @ e3)) @ e0) @ X2)))))))) => (((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e0) @ e0)) @ e1) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e1) @ e1)) @ e1) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e2) @ e2)) @ e1) @ X2))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e3) @ e3)) @ e1) @ X2)))))))) => (((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e0) @ e0)) @ e2) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e1) @ e1)) @ e2) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e2) @ e2)) @ e2) @ X2))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e3) @ e3)) @ e2) @ X2)))))))) => (~(((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e0) @ e0)) @ e3) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e1) @ e1)) @ e3) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e2) @ e2)) @ e3) @ X2))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e3) @ e3)) @ e3) @ X2))))))))))))))))),introduced(definition,[new_symbols(definition,[sP8])])). % 91.10/91.17 thf(sP9,plain,sP9 <=> (![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => ((((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e0) @ e0)) @ e0) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e1) @ e1)) @ e0) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e2) @ e2)) @ e0) @ X2))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e3) @ e3)) @ e0) @ X2)))))))) => (((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e0) @ e0)) @ e1) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e1) @ e1)) @ e1) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e2) @ e2)) @ e1) @ X2))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e3) @ e3)) @ e1) @ X2)))))))) => (((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e0) @ e0)) @ e2) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e1) @ e1)) @ e2) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e2) @ e2)) @ e2) @ X2))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e3) @ e3)) @ e2) @ X2)))))))) => (~(((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e0) @ e0)) @ e3) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e1) @ e1)) @ e3) @ X2))) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e2) @ e2)) @ e3) @ X2))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((qmltpeq @ ((op @ e3) @ e3)) @ e3) @ X2))))))))))))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e0) @ e0)) @ e0) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e1) @ e1)) @ e0) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e2) @ e2)) @ e0) @ X3))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e3) @ e3)) @ e0) @ X3)))))))) => (((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e0) @ e0)) @ e1) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e1) @ e1)) @ e1) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e2) @ e2)) @ e1) @ X3))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e3) @ e3)) @ e1) @ X3)))))))) => (((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e0) @ e0)) @ e2) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e1) @ e1)) @ e2) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e2) @ e2)) @ e2) @ X3))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e3) @ e3)) @ e2) @ X3)))))))) => (~(((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e0) @ e0)) @ e3) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e1) @ e1)) @ e3) @ X3))) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e2) @ e2)) @ e3) @ X3))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e3) @ e3)) @ e3) @ X3)))))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP9])])). % 91.10/91.17 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))). % 91.10/91.17 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))). % 91.10/91.17 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))). % 91.10/91.17 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))). % 91.10/91.17 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:(((exists_in_world @ X3) @ X2) => ((X1 @ X3) @ X2))))))). % 91.10/91.17 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))). % 91.10/91.17 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))). % 91.10/91.17 thf(def_mvalid,definition,(mvalid = (!!))). % 91.10/91.17 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s4 @ X2) @ X3) => (X1 @ X3))))))). % 91.10/91.17 thf(co1,conjecture,(![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((~(((~((~(((~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e0) @ e0)) @ e0) @ X3))))))) => (~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e1) @ e1)) @ e0) @ X3))))))) => (~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e2) @ e2)) @ e0) @ X3))))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e3) @ e3)) @ e0) @ X3)))))))))))))))))))) => ((~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e0) @ e0)) @ e1) @ X3))))))) => (~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e1) @ e1)) @ e1) @ X3))))))) => (~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e2) @ e2)) @ e1) @ X3))))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e3) @ e3)) @ e1) @ X3)))))))))))))))))))) => ((~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e0) @ e0)) @ e2) @ X3))))))) => (~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e1) @ e1)) @ e2) @ X3))))))) => (~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e2) @ e2)) @ e2) @ X3))))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e3) @ e3)) @ e2) @ X3)))))))))))))))))))) => (~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e0) @ e0)) @ e3) @ X3))))))) => (~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e1) @ e1)) @ e3) @ X3))))))) => (~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e2) @ e2)) @ e3) @ X3))))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e3) @ e3)) @ e3) @ X3))))))))))))))))))))))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (~(((~((~(((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e0) @ e0)) @ e0) @ X4))))))) => (~((~(((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e1) @ e1)) @ e0) @ X4))))))) => (~((~(((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e2) @ e2)) @ e0) @ X4))))))) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e3) @ e3)) @ e0) @ X4)))))))))))))))))))) => ((~((~(((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e0) @ e0)) @ e1) @ X4))))))) => (~((~(((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e1) @ e1)) @ e1) @ X4))))))) => (~((~(((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e2) @ e2)) @ e1) @ X4))))))) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e3) @ e3)) @ e1) @ X4)))))))))))))))))))) => ((~((~(((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e0) @ e0)) @ e2) @ X4))))))) => (~((~(((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e1) @ e1)) @ e2) @ X4))))))) => (~((~(((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e2) @ e2)) @ e2) @ X4))))))) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e3) @ e3)) @ e2) @ X4)))))))))))))))))))) => (~(((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e0) @ e0)) @ e3) @ X4))))))) => (~((~(((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e1) @ e1)) @ e3) @ X4))))))) => (~((~(((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e2) @ e2)) @ e3) @ X4))))))) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e3) @ e3)) @ e3) @ X4)))))))))))))))))))))))))))))))))))). % 91.10/91.17 thf(h1,negated_conjecture,(~(sP6)),inference(assume_negation,[status(cth)],[co1])). % 91.10/91.17 thf(1,plain,(~(sP2) | sP3),inference(all_rule,[status(thm)],[])). % 91.10/91.17 thf(2,plain,(~(sP8) | sP4),inference(all_rule,[status(thm)],[])). % 91.10/91.17 thf(3,plain,((~(sP4) | ~(sP3)) | ~(sP5)),inference(prop_rule,[status(thm)],[])). % 91.10/91.17 thf(4,plain,(sP1 | sP8),inference(prop_rule,[status(thm)],[])). % 91.10/91.17 thf(5,plain,(sP1 | sP5),inference(prop_rule,[status(thm)],[])). % 91.10/91.17 thf(6,plain,(sP7 | ~(sP1)),inference(prop_rule,[status(thm)],[])). % 91.10/91.17 thf(7,plain,(sP9 | ~(sP7)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])). % 91.10/91.17 thf(8,plain,(sP6 | ~(sP9)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])). % 91.10/91.17 thf(a1,axiom,(mreflexive @ rel_s4)). % 91.10/91.17 thf(9,plain,sP2,inference(preprocess,[status(thm)],[a1]). % 91.10/91.17 thf(10,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,h1])). % 91.10/91.17 thf(11,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[10,h0])). % 91.10/91.17 thf(0,theorem,(![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((~(((~((~(((~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e0) @ e0)) @ e0) @ X3))))))) => (~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e1) @ e1)) @ e0) @ X3))))))) => (~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e2) @ e2)) @ e0) @ X3))))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e3) @ e3)) @ e0) @ X3)))))))))))))))))))) => ((~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e0) @ e0)) @ e1) @ X3))))))) => (~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e1) @ e1)) @ e1) @ X3))))))) => (~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e2) @ e2)) @ e1) @ X3))))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e3) @ e3)) @ e1) @ X3)))))))))))))))))))) => ((~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e0) @ e0)) @ e2) @ X3))))))) => (~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e1) @ e1)) @ e2) @ X3))))))) => (~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e2) @ e2)) @ e2) @ X3))))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e3) @ e3)) @ e2) @ X3)))))))))))))))))))) => (~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e0) @ e0)) @ e3) @ X3))))))) => (~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e1) @ e1)) @ e3) @ X3))))))) => (~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e2) @ e2)) @ e3) @ X3))))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((qmltpeq @ ((op @ e3) @ e3)) @ e3) @ X3))))))))))))))))))))))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (~(((~((~(((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e0) @ e0)) @ e0) @ X4))))))) => (~((~(((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e1) @ e1)) @ e0) @ X4))))))) => (~((~(((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e2) @ e2)) @ e0) @ X4))))))) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e3) @ e3)) @ e0) @ X4)))))))))))))))))))) => ((~((~(((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e0) @ e0)) @ e1) @ X4))))))) => (~((~(((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e1) @ e1)) @ e1) @ X4))))))) => (~((~(((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e2) @ e2)) @ e1) @ X4))))))) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e3) @ e3)) @ e1) @ X4)))))))))))))))))))) => ((~((~(((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e0) @ e0)) @ e2) @ X4))))))) => (~((~(((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e1) @ e1)) @ e2) @ X4))))))) => (~((~(((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e2) @ e2)) @ e2) @ X4))))))) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e3) @ e3)) @ e2) @ X4)))))))))))))))))))) => (~(((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e0) @ e0)) @ e3) @ X4))))))) => (~((~(((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e1) @ e1)) @ e3) @ X4))))))) => (~((~(((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e2) @ e2)) @ e3) @ X4))))))) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((qmltpeq @ ((op @ e3) @ e3)) @ e3) @ X4))))))))))))))))))))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[10,h1])). % 91.10/91.17 % SZS output end Proof %------------------------------------------------------------------------------