%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : ALG111+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % 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 : 600s % DateTime : Thu Jul 14 18:29:27 EDT 2022 % Result : Theorem 19.63s 19.82s % Output : Proof 19.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : ALG111+1 : TPTP v8.1.0. Released v2.7.0. % 0.11/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n017.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Thu Jun 9 01:36:18 EDT 2022 % 0.12/0.33 % CPUTime : % 19.63/19.82 (* PROOF-FOUND *) % 19.63/19.82 % SZS status Theorem % 19.63/19.82 (* BEGIN-PROOF *) % 19.63/19.82 % SZS output start Proof % 19.63/19.82 Theorem co1 : ((((h1 (op1 (e10) (e10))) = (op2 (h1 (e10)) (h1 (e10))))/\(((h1 (op1 (e10) (e11))) = (op2 (h1 (e10)) (h1 (e11))))/\(((h1 (op1 (e10) (e12))) = (op2 (h1 (e10)) (h1 (e12))))/\(((h1 (op1 (e10) (e13))) = (op2 (h1 (e10)) (h1 (e13))))/\(((h1 (op1 (e11) (e10))) = (op2 (h1 (e11)) (h1 (e10))))/\(((h1 (op1 (e11) (e11))) = (op2 (h1 (e11)) (h1 (e11))))/\(((h1 (op1 (e11) (e12))) = (op2 (h1 (e11)) (h1 (e12))))/\(((h1 (op1 (e11) (e13))) = (op2 (h1 (e11)) (h1 (e13))))/\(((h1 (op1 (e12) (e10))) = (op2 (h1 (e12)) (h1 (e10))))/\(((h1 (op1 (e12) (e11))) = (op2 (h1 (e12)) (h1 (e11))))/\(((h1 (op1 (e12) (e12))) = (op2 (h1 (e12)) (h1 (e12))))/\(((h1 (op1 (e12) (e13))) = (op2 (h1 (e12)) (h1 (e13))))/\(((h1 (op1 (e13) (e10))) = (op2 (h1 (e13)) (h1 (e10))))/\(((h1 (op1 (e13) (e11))) = (op2 (h1 (e13)) (h1 (e11))))/\(((h1 (op1 (e13) (e12))) = (op2 (h1 (e13)) (h1 (e12))))/\(((h1 (op1 (e13) (e13))) = (op2 (h1 (e13)) (h1 (e13))))/\((((h1 (e10)) = (e20))\/(((h1 (e11)) = (e20))\/(((h1 (e12)) = (e20))\/((h1 (e13)) = (e20)))))/\((((h1 (e10)) = (e21))\/(((h1 (e11)) = (e21))\/(((h1 (e12)) = (e21))\/((h1 (e13)) = (e21)))))/\((((h1 (e10)) = (e22))\/(((h1 (e11)) = (e22))\/(((h1 (e12)) = (e22))\/((h1 (e13)) = (e22)))))/\(((h1 (e10)) = (e23))\/(((h1 (e11)) = (e23))\/(((h1 (e12)) = (e23))\/((h1 (e13)) = (e23))))))))))))))))))))))))\/((((h2 (op1 (e10) (e10))) = (op2 (h2 (e10)) (h2 (e10))))/\(((h2 (op1 (e10) (e11))) = (op2 (h2 (e10)) (h2 (e11))))/\(((h2 (op1 (e10) (e12))) = (op2 (h2 (e10)) (h2 (e12))))/\(((h2 (op1 (e10) (e13))) = (op2 (h2 (e10)) (h2 (e13))))/\(((h2 (op1 (e11) (e10))) = (op2 (h2 (e11)) (h2 (e10))))/\(((h2 (op1 (e11) (e11))) = (op2 (h2 (e11)) (h2 (e11))))/\(((h2 (op1 (e11) (e12))) = (op2 (h2 (e11)) (h2 (e12))))/\(((h2 (op1 (e11) (e13))) = (op2 (h2 (e11)) (h2 (e13))))/\(((h2 (op1 (e12) (e10))) = (op2 (h2 (e12)) (h2 (e10))))/\(((h2 (op1 (e12) (e11))) = (op2 (h2 (e12)) (h2 (e11))))/\(((h2 (op1 (e12) (e12))) = (op2 (h2 (e12)) (h2 (e12))))/\(((h2 (op1 (e12) (e13))) = (op2 (h2 (e12)) (h2 (e13))))/\(((h2 (op1 (e13) (e10))) = (op2 (h2 (e13)) (h2 (e10))))/\(((h2 (op1 (e13) (e11))) = (op2 (h2 (e13)) (h2 (e11))))/\(((h2 (op1 (e13) (e12))) = (op2 (h2 (e13)) (h2 (e12))))/\(((h2 (op1 (e13) (e13))) = (op2 (h2 (e13)) (h2 (e13))))/\((((h2 (e10)) = (e20))\/(((h2 (e11)) = (e20))\/(((h2 (e12)) = (e20))\/((h2 (e13)) = (e20)))))/\((((h2 (e10)) = (e21))\/(((h2 (e11)) = (e21))\/(((h2 (e12)) = (e21))\/((h2 (e13)) = (e21)))))/\((((h2 (e10)) = (e22))\/(((h2 (e11)) = (e22))\/(((h2 (e12)) = (e22))\/((h2 (e13)) = (e22)))))/\(((h2 (e10)) = (e23))\/(((h2 (e11)) = (e23))\/(((h2 (e12)) = (e23))\/((h2 (e13)) = (e23))))))))))))))))))))))))\/((((h3 (op1 (e10) (e10))) = (op2 (h3 (e10)) (h3 (e10))))/\(((h3 (op1 (e10) (e11))) = (op2 (h3 (e10)) (h3 (e11))))/\(((h3 (op1 (e10) (e12))) = (op2 (h3 (e10)) (h3 (e12))))/\(((h3 (op1 (e10) (e13))) = (op2 (h3 (e10)) (h3 (e13))))/\(((h3 (op1 (e11) (e10))) = (op2 (h3 (e11)) (h3 (e10))))/\(((h3 (op1 (e11) (e11))) = (op2 (h3 (e11)) (h3 (e11))))/\(((h3 (op1 (e11) (e12))) = (op2 (h3 (e11)) (h3 (e12))))/\(((h3 (op1 (e11) (e13))) = (op2 (h3 (e11)) (h3 (e13))))/\(((h3 (op1 (e12) (e10))) = (op2 (h3 (e12)) (h3 (e10))))/\(((h3 (op1 (e12) (e11))) = (op2 (h3 (e12)) (h3 (e11))))/\(((h3 (op1 (e12) (e12))) = (op2 (h3 (e12)) (h3 (e12))))/\(((h3 (op1 (e12) (e13))) = (op2 (h3 (e12)) (h3 (e13))))/\(((h3 (op1 (e13) (e10))) = (op2 (h3 (e13)) (h3 (e10))))/\(((h3 (op1 (e13) (e11))) = (op2 (h3 (e13)) (h3 (e11))))/\(((h3 (op1 (e13) (e12))) = (op2 (h3 (e13)) (h3 (e12))))/\(((h3 (op1 (e13) (e13))) = (op2 (h3 (e13)) (h3 (e13))))/\((((h3 (e10)) = (e20))\/(((h3 (e11)) = (e20))\/(((h3 (e12)) = (e20))\/((h3 (e13)) = (e20)))))/\((((h3 (e10)) = (e21))\/(((h3 (e11)) = (e21))\/(((h3 (e12)) = (e21))\/((h3 (e13)) = (e21)))))/\((((h3 (e10)) = (e22))\/(((h3 (e11)) = (e22))\/(((h3 (e12)) = (e22))\/((h3 (e13)) = (e22)))))/\(((h3 (e10)) = (e23))\/(((h3 (e11)) = (e23))\/(((h3 (e12)) = (e23))\/((h3 (e13)) = (e23))))))))))))))))))))))))\/(((h4 (op1 (e10) (e10))) = (op2 (h4 (e10)) (h4 (e10))))/\(((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))/\(((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))/\(((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))/\(((h4 (op1 (e11) (e10))) = (op2 (h4 (e11)) (h4 (e10))))/\(((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))/\(((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))/\(((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))/\(((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))/\(((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))/\(((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))/\(((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))/\(((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))/\(((h4 (op1 (e13) (e11))) = (op2 (h4 (e13)) (h4 (e11))))/\(((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))/\(((h4 (op1 (e13) (e13))) = (op2 (h4 (e13)) (h4 (e13))))/\((((h4 (e10)) = (e20))\/(((h4 (e11)) = (e20))\/(((h4 (e12)) = (e20))\/((h4 (e13)) = (e20)))))/\((((h4 (e10)) = (e21))\/(((h4 (e11)) = (e21))\/(((h4 (e12)) = (e21))\/((h4 (e13)) = (e21)))))/\((((h4 (e10)) = (e22))\/(((h4 (e11)) = (e22))\/(((h4 (e12)) = (e22))\/((h4 (e13)) = (e22)))))/\(((h4 (e10)) = (e23))\/(((h4 (e11)) = (e23))\/(((h4 (e12)) = (e23))\/((h4 (e13)) = (e23))))))))))))))))))))))))))). % 19.63/19.82 Proof. % 19.63/19.82 assert (zenon_L1_ : (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> (~((op2 (e20) (e20)) = (e20))) -> (~((op2 (e20) (e21)) = (e20))) -> (~((op2 (e20) (e22)) = (e20))) -> (~((op2 (e20) (e23)) = (e20))) -> False). % 19.63/19.82 do 0 intro. intros zenon_H12 zenon_H13 zenon_H14 zenon_H15 zenon_H16. % 19.63/19.82 apply (zenon_or_s _ _ zenon_H12); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ]. % 19.63/19.82 exact (zenon_H13 zenon_H18). % 19.63/19.82 apply (zenon_or_s _ _ zenon_H17); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ]. % 19.63/19.82 exact (zenon_H14 zenon_H1a). % 19.63/19.82 apply (zenon_or_s _ _ zenon_H19); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ]. % 19.63/19.82 exact (zenon_H15 zenon_H1c). % 19.63/19.82 exact (zenon_H16 zenon_H1b). % 19.63/19.82 (* end of lemma zenon_L1_ *) % 19.63/19.82 assert (zenon_L2_ : (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e23) (e20)) = (e23))) -> (~((op2 (e23) (e21)) = (e23))) -> (~((op2 (e23) (e22)) = (e23))) -> (~((op2 (e23) (e23)) = (e23))) -> False). % 19.63/19.82 do 0 intro. intros zenon_H1d zenon_H1e zenon_H1f zenon_H20 zenon_H21. % 19.63/19.82 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 19.63/19.82 exact (zenon_H1e zenon_H23). % 19.63/19.82 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 19.63/19.82 exact (zenon_H1f zenon_H25). % 19.63/19.82 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 19.63/19.82 exact (zenon_H20 zenon_H27). % 19.63/19.82 exact (zenon_H21 zenon_H26). % 19.63/19.82 (* end of lemma zenon_L2_ *) % 19.63/19.82 assert (zenon_L3_ : ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (~((op2 (e23) (e20)) = (e23))) -> (~((op2 (e23) (e21)) = (e23))) -> (~((op2 (e23) (e22)) = (e23))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> False). % 19.63/19.82 do 0 intro. intros zenon_H28 zenon_H1e zenon_H1f zenon_H20 zenon_H1d. % 19.63/19.82 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H21 | zenon_intro zenon_H21 ]. % 19.63/19.82 apply (zenon_L2_); trivial. % 19.63/19.82 apply (zenon_L2_); trivial. % 19.63/19.82 (* end of lemma zenon_L3_ *) % 19.63/19.82 assert (zenon_L4_ : (~((e23) = (e23))) -> False). % 19.63/19.82 do 0 intro. intros zenon_H29. % 19.63/19.82 apply zenon_H29. apply refl_equal. % 19.63/19.82 (* end of lemma zenon_L4_ *) % 19.63/19.82 assert (zenon_L5_ : (~((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> False). % 19.63/19.82 do 0 intro. intros zenon_H2a zenon_H2b. % 19.63/19.82 cut (((op2 (e23) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H2c]. % 19.63/19.82 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 19.63/19.82 congruence. % 19.63/19.82 apply zenon_H29. apply refl_equal. % 19.63/19.82 apply zenon_H2c. apply sym_equal. exact zenon_H2b. % 19.63/19.82 (* end of lemma zenon_L5_ *) % 19.63/19.82 assert (zenon_L6_ : (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((op2 (e21) (e21)) = (e22))) -> (~((op2 (e21) (e21)) = (e23))) -> False). % 19.63/19.82 do 0 intro. intros zenon_H2d zenon_H2b zenon_H2e zenon_H2f zenon_H30 zenon_H31 zenon_H32. % 19.63/19.82 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 19.63/19.82 cut (((e20) = (op2 (e23) (op2 (e23) (e23)))) = ((op2 (e21) (e21)) = (op2 (e23) (e21)))). % 19.63/19.82 intro zenon_D_pnotp. % 19.63/19.82 apply zenon_H2f. % 19.63/19.82 rewrite <- zenon_D_pnotp. % 19.63/19.82 exact zenon_H2e. % 19.63/19.82 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 19.63/19.82 cut (((e20) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H35]. % 19.63/19.82 congruence. % 19.63/19.82 elim (classic ((op2 (e21) (e21)) = (op2 (e21) (e21)))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 19.63/19.82 cut (((op2 (e21) (e21)) = (op2 (e21) (e21))) = ((e20) = (op2 (e21) (e21)))). % 19.63/19.82 intro zenon_D_pnotp. % 19.63/19.82 apply zenon_H35. % 19.63/19.82 rewrite <- zenon_D_pnotp. % 19.63/19.82 exact zenon_H36. % 19.63/19.82 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 19.63/19.82 cut (((op2 (e21) (e21)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 19.63/19.82 congruence. % 19.63/19.82 exact (zenon_H38 zenon_H34). % 19.63/19.82 apply zenon_H37. apply refl_equal. % 19.63/19.82 apply zenon_H37. apply refl_equal. % 19.63/19.82 apply (zenon_L5_); trivial. % 19.63/19.82 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 19.63/19.82 exact (zenon_H30 zenon_H3a). % 19.63/19.82 apply (zenon_or_s _ _ zenon_H39); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 19.63/19.82 exact (zenon_H31 zenon_H3c). % 19.63/19.82 exact (zenon_H32 zenon_H3b). % 19.63/19.82 (* end of lemma zenon_L6_ *) % 19.63/19.82 assert (zenon_L7_ : ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((op2 (e21) (e21)) = (e23))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e23) (e21)) = (e23))) -> (~((op2 (e23) (e20)) = (e23))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> False). % 19.63/19.82 do 0 intro. intros zenon_H3d zenon_H2f zenon_H2e zenon_H2b zenon_H30 zenon_H32 zenon_H2d zenon_H1d zenon_H1f zenon_H1e zenon_H28. % 19.63/19.82 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H20 | zenon_intro zenon_H31 ]. % 19.63/19.82 apply (zenon_L3_); trivial. % 19.63/19.82 apply (zenon_L6_); trivial. % 19.63/19.82 (* end of lemma zenon_L7_ *) % 19.63/19.82 assert (zenon_L8_ : (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e20))) -> (~((op2 (e20) (e20)) = (e21))) -> (~((op2 (e20) (e20)) = (e22))) -> (~((op2 (e20) (e20)) = (e23))) -> False). % 19.63/19.82 do 0 intro. intros zenon_H3e zenon_H13 zenon_H3f zenon_H40 zenon_H41. % 19.63/19.82 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H18 | zenon_intro zenon_H42 ]. % 19.63/19.82 exact (zenon_H13 zenon_H18). % 19.63/19.82 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ]. % 19.63/19.82 exact (zenon_H3f zenon_H44). % 19.63/19.82 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H46 | zenon_intro zenon_H45 ]. % 19.63/19.82 exact (zenon_H40 zenon_H46). % 19.63/19.82 exact (zenon_H41 zenon_H45). % 19.63/19.82 (* end of lemma zenon_L8_ *) % 19.63/19.82 assert (zenon_L9_ : ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (~((op2 (e23) (e20)) = (e23))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e23))) -> (~((op2 (e20) (e20)) = (e21))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> False). % 19.63/19.82 do 0 intro. intros zenon_H47 zenon_H2b zenon_H28 zenon_H1e zenon_H1d zenon_H3e zenon_H41 zenon_H3f zenon_H13 zenon_H48. % 19.63/19.82 apply (zenon_or_s _ _ zenon_H47); [ zenon_intro zenon_H1f | zenon_intro zenon_H2c ]. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H20 | zenon_intro zenon_H40 ]. % 19.63/19.83 apply (zenon_L3_); trivial. % 19.63/19.83 apply (zenon_L8_); trivial. % 19.63/19.83 apply zenon_H2c. apply sym_equal. exact zenon_H2b. % 19.63/19.83 (* end of lemma zenon_L9_ *) % 19.63/19.83 assert (zenon_L10_ : (~((op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23))) = (op2 (e20) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H49 zenon_H2b zenon_H2e. % 19.63/19.83 cut (((op2 (e23) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H2c]. % 19.63/19.83 cut (((op2 (e23) (op2 (e23) (e23))) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 19.63/19.83 congruence. % 19.63/19.83 apply zenon_H4a. apply sym_equal. exact zenon_H2e. % 19.63/19.83 apply zenon_H2c. apply sym_equal. exact zenon_H2b. % 19.63/19.83 (* end of lemma zenon_L10_ *) % 19.63/19.83 assert (zenon_L11_ : (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (~((op2 (e21) (e21)) = (e20))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (e23))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H2d zenon_H38 zenon_H30 zenon_H4b zenon_H2e zenon_H2b zenon_H4c zenon_H32. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 19.63/19.83 exact (zenon_H38 zenon_H34). % 19.63/19.83 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 19.63/19.83 exact (zenon_H30 zenon_H3a). % 19.63/19.83 apply (zenon_or_s _ _ zenon_H39); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 19.63/19.83 elim (classic ((op2 (e21) (e21)) = (op2 (e21) (e21)))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 19.63/19.83 cut (((op2 (e21) (e21)) = (op2 (e21) (e21))) = ((op2 (e20) (e21)) = (op2 (e21) (e21)))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_H4b. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H36. % 19.63/19.83 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 19.63/19.83 cut (((op2 (e21) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 19.63/19.83 congruence. % 19.63/19.83 cut (((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) = ((op2 (e21) (e21)) = (op2 (e20) (e21)))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_H4d. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H4c. % 19.63/19.83 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23))) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 19.63/19.83 cut (((e22) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 19.63/19.83 congruence. % 19.63/19.83 elim (classic ((op2 (e21) (e21)) = (op2 (e21) (e21)))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 19.63/19.83 cut (((op2 (e21) (e21)) = (op2 (e21) (e21))) = ((e22) = (op2 (e21) (e21)))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_H4e. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H36. % 19.63/19.83 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 19.63/19.83 cut (((op2 (e21) (e21)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 19.63/19.83 congruence. % 19.63/19.83 exact (zenon_H31 zenon_H3c). % 19.63/19.83 apply zenon_H37. apply refl_equal. % 19.63/19.83 apply zenon_H37. apply refl_equal. % 19.63/19.83 apply (zenon_L10_); trivial. % 19.63/19.83 apply zenon_H37. apply refl_equal. % 19.63/19.83 apply zenon_H37. apply refl_equal. % 19.63/19.83 exact (zenon_H32 zenon_H3b). % 19.63/19.83 (* end of lemma zenon_L11_ *) % 19.63/19.83 assert (zenon_L12_ : ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (~((op2 (e21) (e21)) = (e20))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (e23))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H4f zenon_H38 zenon_H4b zenon_H4c zenon_H2e zenon_H2b zenon_H32 zenon_H2d. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H30 | zenon_intro zenon_H30 ]. % 19.63/19.83 apply (zenon_L11_); trivial. % 19.63/19.83 apply (zenon_L11_); trivial. % 19.63/19.83 (* end of lemma zenon_L12_ *) % 19.63/19.83 assert (zenon_L13_ : ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((op2 (e21) (e21)) = (e23))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e23))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H50 zenon_H4c zenon_H4b zenon_H4f zenon_H3d zenon_H2f zenon_H2e zenon_H2b zenon_H30 zenon_H32 zenon_H2d zenon_H1d zenon_H28 zenon_H47 zenon_H3e zenon_H41 zenon_H13 zenon_H48 zenon_H51. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H1e | zenon_intro zenon_H38 ]. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H1f | zenon_intro zenon_H3f ]. % 19.63/19.83 apply (zenon_L7_); trivial. % 19.63/19.83 apply (zenon_L9_); trivial. % 19.63/19.83 apply (zenon_L12_); trivial. % 19.63/19.83 (* end of lemma zenon_L13_ *) % 19.63/19.83 assert (zenon_L14_ : ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e23))) -> (~((op2 (e20) (e20)) = (e21))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e21) (e21)) = (e21))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e20)) = (e20))) -> (~((op2 (e20) (e21)) = (e20))) -> (~((op2 (e20) (e22)) = (e20))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H52 zenon_H47 zenon_H2b zenon_H28 zenon_H1d zenon_H3e zenon_H41 zenon_H3f zenon_H48 zenon_H2d zenon_H2e zenon_H4c zenon_H4b zenon_H30 zenon_H50 zenon_H13 zenon_H14 zenon_H15 zenon_H12. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H16 | zenon_intro zenon_H32 ]. % 19.63/19.83 apply (zenon_L1_); trivial. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H1e | zenon_intro zenon_H38 ]. % 19.63/19.83 apply (zenon_L9_); trivial. % 19.63/19.83 apply (zenon_L11_); trivial. % 19.63/19.83 (* end of lemma zenon_L14_ *) % 19.63/19.83 assert (zenon_L15_ : ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (~((op2 (e20) (e20)) = (e21))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> (~((op2 (e20) (e20)) = (e20))) -> (~((op2 (e20) (e21)) = (e20))) -> (~((op2 (e20) (e22)) = (e20))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H53 zenon_H50 zenon_H30 zenon_H4b zenon_H4c zenon_H2e zenon_H2d zenon_H48 zenon_H3f zenon_H3e zenon_H1d zenon_H28 zenon_H2b zenon_H47 zenon_H52 zenon_H13 zenon_H14 zenon_H15 zenon_H12. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H16 | zenon_intro zenon_H41 ]. % 19.63/19.83 apply (zenon_L1_); trivial. % 19.63/19.83 apply (zenon_L14_); trivial. % 19.63/19.83 (* end of lemma zenon_L15_ *) % 19.63/19.83 assert (zenon_L16_ : ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> (~((op2 (e20) (e22)) = (e20))) -> (~((op2 (e20) (e21)) = (e20))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e21))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H4f zenon_H12 zenon_H15 zenon_H14 zenon_H13 zenon_H52 zenon_H47 zenon_H2b zenon_H28 zenon_H1d zenon_H3e zenon_H3f zenon_H48 zenon_H2d zenon_H2e zenon_H4c zenon_H4b zenon_H50 zenon_H53. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H30 | zenon_intro zenon_H30 ]. % 19.63/19.83 apply (zenon_L15_); trivial. % 19.63/19.83 apply (zenon_L15_); trivial. % 19.63/19.83 (* end of lemma zenon_L16_ *) % 19.63/19.83 assert (zenon_L17_ : ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e20)) = (e20))) -> (~((op2 (e20) (e21)) = (e20))) -> (~((op2 (e20) (e22)) = (e20))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H54 zenon_H53 zenon_H52 zenon_H51 zenon_H48 zenon_H3e zenon_H47 zenon_H28 zenon_H1d zenon_H2d zenon_H2b zenon_H2e zenon_H2f zenon_H3d zenon_H4f zenon_H4b zenon_H4c zenon_H50 zenon_H13 zenon_H14 zenon_H15 zenon_H12. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H16 | zenon_intro zenon_H41 ]. % 19.63/19.83 apply (zenon_L1_); trivial. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H16 | zenon_intro zenon_H32 ]. % 19.63/19.83 apply (zenon_L1_); trivial. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H30 | zenon_intro zenon_H3f ]. % 19.63/19.83 apply (zenon_L13_); trivial. % 19.63/19.83 apply (zenon_L16_); trivial. % 19.63/19.83 (* end of lemma zenon_L17_ *) % 19.63/19.83 assert (zenon_L18_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (e10))) -> (~((op1 (e10) (e11)) = (e10))) -> (~((op1 (e10) (e12)) = (e10))) -> (~((op1 (e10) (e13)) = (e10))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H55 zenon_H56 zenon_H57 zenon_H58 zenon_H59. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H55); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 19.63/19.83 exact (zenon_H56 zenon_H5b). % 19.63/19.83 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H5d | zenon_intro zenon_H5c ]. % 19.63/19.83 exact (zenon_H57 zenon_H5d). % 19.63/19.83 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ]. % 19.63/19.83 exact (zenon_H58 zenon_H5f). % 19.63/19.83 exact (zenon_H59 zenon_H5e). % 19.63/19.83 (* end of lemma zenon_L18_ *) % 19.63/19.83 assert (zenon_L19_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (e13))) -> (~((op1 (e13) (e11)) = (e13))) -> (~((op1 (e13) (e12)) = (e13))) -> (~((op1 (e13) (e13)) = (e13))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H60 zenon_H61 zenon_H62 zenon_H63 zenon_H64. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H60); [ zenon_intro zenon_H66 | zenon_intro zenon_H65 ]. % 19.63/19.83 exact (zenon_H61 zenon_H66). % 19.63/19.83 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H68 | zenon_intro zenon_H67 ]. % 19.63/19.83 exact (zenon_H62 zenon_H68). % 19.63/19.83 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H6a | zenon_intro zenon_H69 ]. % 19.63/19.83 exact (zenon_H63 zenon_H6a). % 19.63/19.83 exact (zenon_H64 zenon_H69). % 19.63/19.83 (* end of lemma zenon_L19_ *) % 19.63/19.83 assert (zenon_L20_ : ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (~((op1 (e13) (e10)) = (e13))) -> (~((op1 (e13) (e11)) = (e13))) -> (~((op1 (e13) (e12)) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H6b zenon_H61 zenon_H62 zenon_H63 zenon_H60. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H64 | zenon_intro zenon_H64 ]. % 19.63/19.83 apply (zenon_L19_); trivial. % 19.63/19.83 apply (zenon_L19_); trivial. % 19.63/19.83 (* end of lemma zenon_L20_ *) % 19.63/19.83 assert (zenon_L21_ : (~((e13) = (e13))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H6c. % 19.63/19.83 apply zenon_H6c. apply refl_equal. % 19.63/19.83 (* end of lemma zenon_L21_ *) % 19.63/19.83 assert (zenon_L22_ : (~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H6d zenon_H6e. % 19.63/19.83 cut (((op1 (e13) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 19.63/19.83 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 19.63/19.83 congruence. % 19.63/19.83 apply zenon_H6c. apply refl_equal. % 19.63/19.83 apply zenon_H6f. apply sym_equal. exact zenon_H6e. % 19.63/19.83 (* end of lemma zenon_L22_ *) % 19.63/19.83 assert (zenon_L23_ : (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (e11))) -> (~((op1 (e11) (e11)) = (e12))) -> (~((op1 (e11) (e11)) = (e13))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H73 zenon_H74 zenon_H75. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H70); [ zenon_intro zenon_H77 | zenon_intro zenon_H76 ]. % 19.63/19.83 cut (((e10) = (op1 (e13) (op1 (e13) (e13)))) = ((op1 (e11) (e11)) = (op1 (e13) (e11)))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_H72. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H71. % 19.63/19.83 cut (((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 19.63/19.83 cut (((e10) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H78]. % 19.63/19.83 congruence. % 19.63/19.83 elim (classic ((op1 (e11) (e11)) = (op1 (e11) (e11)))); [ zenon_intro zenon_H79 | zenon_intro zenon_H7a ]. % 19.63/19.83 cut (((op1 (e11) (e11)) = (op1 (e11) (e11))) = ((e10) = (op1 (e11) (e11)))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_H78. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H79. % 19.63/19.83 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 19.63/19.83 cut (((op1 (e11) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 19.63/19.83 congruence. % 19.63/19.83 exact (zenon_H7b zenon_H77). % 19.63/19.83 apply zenon_H7a. apply refl_equal. % 19.63/19.83 apply zenon_H7a. apply refl_equal. % 19.63/19.83 apply (zenon_L22_); trivial. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H76); [ zenon_intro zenon_H7d | zenon_intro zenon_H7c ]. % 19.63/19.83 exact (zenon_H73 zenon_H7d). % 19.63/19.83 apply (zenon_or_s _ _ zenon_H7c); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ]. % 19.63/19.83 exact (zenon_H74 zenon_H7f). % 19.63/19.83 exact (zenon_H75 zenon_H7e). % 19.63/19.83 (* end of lemma zenon_L23_ *) % 19.63/19.83 assert (zenon_L24_ : ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (e11))) -> (~((op1 (e11) (e11)) = (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (e13))) -> (~((op1 (e13) (e10)) = (e13))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H73 zenon_H75 zenon_H70 zenon_H60 zenon_H62 zenon_H61 zenon_H6b. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H80); [ zenon_intro zenon_H63 | zenon_intro zenon_H74 ]. % 19.63/19.83 apply (zenon_L20_); trivial. % 19.63/19.83 apply (zenon_L23_); trivial. % 19.63/19.83 (* end of lemma zenon_L24_ *) % 19.63/19.83 assert (zenon_L25_ : (~((e11) = (e11))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H81. % 19.63/19.83 apply zenon_H81. apply refl_equal. % 19.63/19.83 (* end of lemma zenon_L25_ *) % 19.63/19.83 assert (zenon_L26_ : ((op1 (e10) (e11)) = (e11)) -> ((op1 (e10) (e11)) = (e12)) -> (~((e11) = (e12))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H82 zenon_H83 zenon_H84. % 19.63/19.83 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H85 | zenon_intro zenon_H86 ]. % 19.63/19.83 cut (((e12) = (e12)) = ((e11) = (e12))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_H84. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H85. % 19.63/19.83 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 19.63/19.83 cut (((e12) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 19.63/19.83 congruence. % 19.63/19.83 cut (((op1 (e10) (e11)) = (e11)) = ((e12) = (e11))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_H87. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H82. % 19.63/19.83 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 19.63/19.83 cut (((op1 (e10) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 19.63/19.83 congruence. % 19.63/19.83 exact (zenon_H88 zenon_H83). % 19.63/19.83 apply zenon_H81. apply refl_equal. % 19.63/19.83 apply zenon_H86. apply refl_equal. % 19.63/19.83 apply zenon_H86. apply refl_equal. % 19.63/19.83 (* end of lemma zenon_L26_ *) % 19.63/19.83 assert (zenon_L27_ : (~((op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13))) = (op1 (e10) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H89 zenon_H6e zenon_H71. % 19.63/19.83 cut (((op1 (e13) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 19.63/19.83 cut (((op1 (e13) (op1 (e13) (e13))) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H8a]. % 19.63/19.83 congruence. % 19.63/19.83 apply zenon_H8a. apply sym_equal. exact zenon_H71. % 19.63/19.83 apply zenon_H6f. apply sym_equal. exact zenon_H6e. % 19.63/19.83 (* end of lemma zenon_L27_ *) % 19.63/19.83 assert (zenon_L28_ : ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> ((op1 (e10) (e12)) = (e12)) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H8b zenon_H8c zenon_H6e zenon_H71 zenon_H8d. % 19.63/19.83 elim (classic ((op1 (e10) (e12)) = (op1 (e10) (e12)))); [ zenon_intro zenon_H8e | zenon_intro zenon_H8f ]. % 19.63/19.83 cut (((op1 (e10) (e12)) = (op1 (e10) (e12))) = ((op1 (e10) (e11)) = (op1 (e10) (e12)))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_H8d. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H8e. % 19.63/19.83 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 19.63/19.83 cut (((op1 (e10) (e12)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H90]. % 19.63/19.83 congruence. % 19.63/19.83 cut (((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) = ((op1 (e10) (e12)) = (op1 (e10) (e11)))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_H90. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H8b. % 19.63/19.83 cut (((op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13))) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 19.63/19.83 cut (((e12) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H91]. % 19.63/19.83 congruence. % 19.63/19.83 elim (classic ((op1 (e10) (e12)) = (op1 (e10) (e12)))); [ zenon_intro zenon_H8e | zenon_intro zenon_H8f ]. % 19.63/19.83 cut (((op1 (e10) (e12)) = (op1 (e10) (e12))) = ((e12) = (op1 (e10) (e12)))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_H91. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H8e. % 19.63/19.83 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 19.63/19.83 cut (((op1 (e10) (e12)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H92]. % 19.63/19.83 congruence. % 19.63/19.83 exact (zenon_H92 zenon_H8c). % 19.63/19.83 apply zenon_H8f. apply refl_equal. % 19.63/19.83 apply zenon_H8f. apply refl_equal. % 19.63/19.83 apply (zenon_L27_); trivial. % 19.63/19.83 apply zenon_H8f. apply refl_equal. % 19.63/19.83 apply zenon_H8f. apply refl_equal. % 19.63/19.83 (* end of lemma zenon_L28_ *) % 19.63/19.83 assert (zenon_L29_ : ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H8b zenon_H93 zenon_H6e zenon_H71 zenon_H94. % 19.63/19.83 elim (classic ((op1 (e10) (e13)) = (op1 (e10) (e13)))); [ zenon_intro zenon_H95 | zenon_intro zenon_H96 ]. % 19.63/19.83 cut (((op1 (e10) (e13)) = (op1 (e10) (e13))) = ((op1 (e10) (e11)) = (op1 (e10) (e13)))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_H94. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H95. % 19.63/19.83 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 19.63/19.83 cut (((op1 (e10) (e13)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 19.63/19.83 congruence. % 19.63/19.83 cut (((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) = ((op1 (e10) (e13)) = (op1 (e10) (e11)))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_H97. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H8b. % 19.63/19.83 cut (((op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13))) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 19.63/19.83 cut (((e12) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 19.63/19.83 congruence. % 19.63/19.83 elim (classic ((op1 (e10) (e13)) = (op1 (e10) (e13)))); [ zenon_intro zenon_H95 | zenon_intro zenon_H96 ]. % 19.63/19.83 cut (((op1 (e10) (e13)) = (op1 (e10) (e13))) = ((e12) = (op1 (e10) (e13)))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_H98. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H95. % 19.63/19.83 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 19.63/19.83 cut (((op1 (e10) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 19.63/19.83 congruence. % 19.63/19.83 exact (zenon_H99 zenon_H93). % 19.63/19.83 apply zenon_H96. apply refl_equal. % 19.63/19.83 apply zenon_H96. apply refl_equal. % 19.63/19.83 apply (zenon_L27_); trivial. % 19.63/19.83 apply zenon_H96. apply refl_equal. % 19.63/19.83 apply zenon_H96. apply refl_equal. % 19.63/19.83 (* end of lemma zenon_L29_ *) % 19.63/19.83 assert (zenon_L30_ : (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (e12))) -> (~((e11) = (e12))) -> ((op1 (e10) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H9a zenon_H9b zenon_H84 zenon_H82 zenon_H8d zenon_H8b zenon_H6e zenon_H71 zenon_H94. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H9a); [ zenon_intro zenon_H9d | zenon_intro zenon_H9c ]. % 19.63/19.83 exact (zenon_H9b zenon_H9d). % 19.63/19.83 apply (zenon_or_s _ _ zenon_H9c); [ zenon_intro zenon_H83 | zenon_intro zenon_H9e ]. % 19.63/19.83 apply (zenon_L26_); trivial. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H9e); [ zenon_intro zenon_H8c | zenon_intro zenon_H93 ]. % 19.63/19.83 apply (zenon_L28_); trivial. % 19.63/19.83 apply (zenon_L29_); trivial. % 19.63/19.83 (* end of lemma zenon_L30_ *) % 19.63/19.83 assert (zenon_L31_ : (~((e10) = (e10))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H9f. % 19.63/19.83 apply zenon_H9f. apply refl_equal. % 19.63/19.83 (* end of lemma zenon_L31_ *) % 19.63/19.83 assert (zenon_L32_ : ((op1 (e10) (e12)) = (e10)) -> ((op1 (e10) (e12)) = (e11)) -> (~((e10) = (e11))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H5f zenon_Ha0 zenon_Ha1. % 19.63/19.83 elim (classic ((e11) = (e11))); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H81 ]. % 19.63/19.83 cut (((e11) = (e11)) = ((e10) = (e11))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_Ha1. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_Ha2. % 19.63/19.83 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 19.63/19.83 cut (((e11) = (e10))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 19.63/19.83 congruence. % 19.63/19.83 cut (((op1 (e10) (e12)) = (e10)) = ((e11) = (e10))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_Ha3. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H5f. % 19.63/19.83 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H9f]. % 19.63/19.83 cut (((op1 (e10) (e12)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 19.63/19.83 congruence. % 19.63/19.83 exact (zenon_Ha4 zenon_Ha0). % 19.63/19.83 apply zenon_H9f. apply refl_equal. % 19.63/19.83 apply zenon_H81. apply refl_equal. % 19.63/19.83 apply zenon_H81. apply refl_equal. % 19.63/19.83 (* end of lemma zenon_L32_ *) % 19.63/19.83 assert (zenon_L33_ : (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e10) (e13)) = (e11)) -> False). % 19.63/19.83 do 0 intro. intros zenon_Ha5 zenon_H6e zenon_Ha6. % 19.63/19.83 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e10) (e13)) = (op1 (e13) (e13)))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_Ha5. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H6e. % 19.63/19.83 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 19.63/19.83 cut (((e11) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 19.63/19.83 congruence. % 19.63/19.83 elim (classic ((op1 (e10) (e13)) = (op1 (e10) (e13)))); [ zenon_intro zenon_H95 | zenon_intro zenon_H96 ]. % 19.63/19.83 cut (((op1 (e10) (e13)) = (op1 (e10) (e13))) = ((e11) = (op1 (e10) (e13)))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_Ha8. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H95. % 19.63/19.83 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 19.63/19.83 cut (((op1 (e10) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 19.63/19.83 congruence. % 19.63/19.83 exact (zenon_Ha9 zenon_Ha6). % 19.63/19.83 apply zenon_H96. apply refl_equal. % 19.63/19.83 apply zenon_H96. apply refl_equal. % 19.63/19.83 apply zenon_Ha7. apply refl_equal. % 19.63/19.83 (* end of lemma zenon_L33_ *) % 19.63/19.83 assert (zenon_L34_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (e10))) -> (~((op1 (e10) (e11)) = (e10))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (e12))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e10)) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (e10))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H55 zenon_H56 zenon_H57 zenon_H6e zenon_Ha5 zenon_Ha1 zenon_H9a zenon_H9b zenon_H84 zenon_H8d zenon_H8b zenon_H71 zenon_H94 zenon_Haa zenon_Hab zenon_H59. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H55); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 19.63/19.83 exact (zenon_H56 zenon_H5b). % 19.63/19.83 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H5d | zenon_intro zenon_H5c ]. % 19.63/19.83 exact (zenon_H57 zenon_H5d). % 19.63/19.83 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ]. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_Had | zenon_intro zenon_Hac ]. % 19.63/19.83 exact (zenon_Haa zenon_Had). % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H82 | zenon_intro zenon_Hae ]. % 19.63/19.83 apply (zenon_L30_); trivial. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_Ha0 | zenon_intro zenon_Ha6 ]. % 19.63/19.83 apply (zenon_L32_); trivial. % 19.63/19.83 apply (zenon_L33_); trivial. % 19.63/19.83 exact (zenon_H59 zenon_H5e). % 19.63/19.83 (* end of lemma zenon_L34_ *) % 19.63/19.83 assert (zenon_L35_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (~((op1 (e10) (e10)) = (e10))) -> (~((op1 (e10) (e10)) = (e11))) -> (~((op1 (e10) (e10)) = (e12))) -> (~((op1 (e10) (e10)) = (e13))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Haf zenon_H56 zenon_Haa zenon_H9b zenon_Hb0. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_H5b | zenon_intro zenon_Hb1 ]. % 19.63/19.83 exact (zenon_H56 zenon_H5b). % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Had | zenon_intro zenon_Hb2 ]. % 19.63/19.83 exact (zenon_Haa zenon_Had). % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H9d | zenon_intro zenon_Hb3 ]. % 19.63/19.83 exact (zenon_H9b zenon_H9d). % 19.63/19.83 exact (zenon_Hb0 zenon_Hb3). % 19.63/19.83 (* end of lemma zenon_L35_ *) % 19.63/19.83 assert (zenon_L36_ : ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (~((op1 (e10) (e10)) = (e10))) -> (~((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e10)) = (e12))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (e11))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hb4 zenon_Haf zenon_H56 zenon_H57 zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H9b zenon_H84 zenon_H8d zenon_H8b zenon_H71 zenon_H6e zenon_H94 zenon_H9a zenon_Haa zenon_H55. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_H59 | zenon_intro zenon_Hb0 ]. % 19.63/19.83 apply (zenon_L34_); trivial. % 19.63/19.83 apply (zenon_L35_); trivial. % 19.63/19.83 (* end of lemma zenon_L36_ *) % 19.63/19.83 assert (zenon_L37_ : ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e13)) = (e13))) -> (~((op1 (e13) (e10)) = (e13))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (~((op1 (e10) (e10)) = (e10))) -> (~((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (e11))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hb5 zenon_H60 zenon_H64 zenon_H61 zenon_Hb4 zenon_Haf zenon_H56 zenon_H57 zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H71 zenon_H6e zenon_H94 zenon_H9a zenon_Haa zenon_H55 zenon_Hb6. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H62 | zenon_intro zenon_H6f ]. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H63 | zenon_intro zenon_H9b ]. % 19.63/19.83 apply (zenon_L19_); trivial. % 19.63/19.83 apply (zenon_L36_); trivial. % 19.63/19.83 apply zenon_H6f. apply sym_equal. exact zenon_H6e. % 19.63/19.83 (* end of lemma zenon_L37_ *) % 19.63/19.83 assert (zenon_L38_ : ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e11)) = (e10))) -> (~((op1 (e10) (e10)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (~((op1 (e13) (e13)) = (e13))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (~((op1 (e13) (e10)) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e11) (e11)) = (e13))) -> (~((op1 (e11) (e11)) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hb7 zenon_Hb6 zenon_H55 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_H57 zenon_H56 zenon_Haf zenon_Hb4 zenon_H64 zenon_Hb5 zenon_H6b zenon_H61 zenon_H60 zenon_H70 zenon_H75 zenon_H73 zenon_H6e zenon_H71 zenon_H72 zenon_H80. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H62 | zenon_intro zenon_Haa ]. % 19.63/19.83 apply (zenon_L24_); trivial. % 19.63/19.83 apply (zenon_L37_); trivial. % 19.63/19.83 (* end of lemma zenon_L38_ *) % 19.63/19.83 assert (zenon_L39_ : (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e11) (e11)) = (e10))) -> (~((op1 (e11) (e11)) = (e11))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (e13))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H70 zenon_H7b zenon_H73 zenon_Hb8 zenon_H71 zenon_H6e zenon_H8b zenon_H75. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H70); [ zenon_intro zenon_H77 | zenon_intro zenon_H76 ]. % 19.63/19.83 exact (zenon_H7b zenon_H77). % 19.63/19.83 apply (zenon_or_s _ _ zenon_H76); [ zenon_intro zenon_H7d | zenon_intro zenon_H7c ]. % 19.63/19.83 exact (zenon_H73 zenon_H7d). % 19.63/19.83 apply (zenon_or_s _ _ zenon_H7c); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ]. % 19.63/19.83 elim (classic ((op1 (e11) (e11)) = (op1 (e11) (e11)))); [ zenon_intro zenon_H79 | zenon_intro zenon_H7a ]. % 19.63/19.83 cut (((op1 (e11) (e11)) = (op1 (e11) (e11))) = ((op1 (e10) (e11)) = (op1 (e11) (e11)))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_Hb8. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H79. % 19.63/19.83 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 19.63/19.83 cut (((op1 (e11) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hb9]. % 19.63/19.83 congruence. % 19.63/19.83 cut (((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) = ((op1 (e11) (e11)) = (op1 (e10) (e11)))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_Hb9. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H8b. % 19.63/19.83 cut (((op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13))) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 19.63/19.83 cut (((e12) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hba]. % 19.63/19.83 congruence. % 19.63/19.83 elim (classic ((op1 (e11) (e11)) = (op1 (e11) (e11)))); [ zenon_intro zenon_H79 | zenon_intro zenon_H7a ]. % 19.63/19.83 cut (((op1 (e11) (e11)) = (op1 (e11) (e11))) = ((e12) = (op1 (e11) (e11)))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_Hba. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H79. % 19.63/19.83 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 19.63/19.83 cut (((op1 (e11) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H74]. % 19.63/19.83 congruence. % 19.63/19.83 exact (zenon_H74 zenon_H7f). % 19.63/19.83 apply zenon_H7a. apply refl_equal. % 19.63/19.83 apply zenon_H7a. apply refl_equal. % 19.63/19.83 apply (zenon_L27_); trivial. % 19.63/19.83 apply zenon_H7a. apply refl_equal. % 19.63/19.83 apply zenon_H7a. apply refl_equal. % 19.63/19.83 exact (zenon_H75 zenon_H7e). % 19.63/19.83 (* end of lemma zenon_L39_ *) % 19.63/19.83 assert (zenon_L40_ : ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> (~((op1 (e11) (e11)) = (e11))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (e11))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e11)) = (e10))) -> (~((op1 (e10) (e10)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (~((op1 (e13) (e13)) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hbb zenon_H73 zenon_Hb8 zenon_H75 zenon_H70 zenon_Hb6 zenon_H55 zenon_Haa zenon_H9a zenon_H94 zenon_H6e zenon_H71 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_H57 zenon_H56 zenon_Haf zenon_Hb4 zenon_H64 zenon_H60 zenon_Hb5. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_H61 | zenon_intro zenon_H7b ]. % 19.63/19.83 apply (zenon_L37_); trivial. % 19.63/19.83 apply (zenon_L39_); trivial. % 19.63/19.83 (* end of lemma zenon_L40_ *) % 19.63/19.83 assert (zenon_L41_ : ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (e11))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e11) (e11)) = (e13))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (e11))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> (~((op1 (e10) (e10)) = (e10))) -> (~((op1 (e10) (e11)) = (e10))) -> (~((op1 (e10) (e12)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hbc zenon_Hb5 zenon_H60 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H71 zenon_H6e zenon_H94 zenon_H9a zenon_Haa zenon_Hb6 zenon_H70 zenon_H75 zenon_Hb8 zenon_H73 zenon_Hbb zenon_H56 zenon_H57 zenon_H58 zenon_H55. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_H59 | zenon_intro zenon_H64 ]. % 19.63/19.83 apply (zenon_L18_); trivial. % 19.63/19.83 apply (zenon_L40_); trivial. % 19.63/19.83 (* end of lemma zenon_L41_ *) % 19.63/19.83 assert (zenon_L42_ : ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e12)) = (e10))) -> (~((op1 (e10) (e11)) = (e10))) -> (~((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e10)) = (e11))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hbd zenon_H55 zenon_H58 zenon_H57 zenon_H56 zenon_Hbb zenon_Hb8 zenon_H75 zenon_H70 zenon_Hb6 zenon_Haa zenon_H9a zenon_H94 zenon_H6e zenon_H71 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_H60 zenon_Hb5 zenon_Hbc. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H73 | zenon_intro zenon_H73 ]. % 19.63/19.83 apply (zenon_L41_); trivial. % 19.63/19.83 apply (zenon_L41_); trivial. % 19.63/19.83 (* end of lemma zenon_L42_ *) % 19.63/19.83 assert (zenon_L43_ : ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (e10))) -> (~((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e10)) = (e11))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hbe zenon_H55 zenon_H57 zenon_H56 zenon_Hbd zenon_Hbb zenon_Hb8 zenon_H70 zenon_Hb6 zenon_Haa zenon_H9a zenon_H94 zenon_H6e zenon_H71 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_H60 zenon_Hb5 zenon_Hbc zenon_Hbf. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H58 | zenon_intro zenon_H9b ]. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H59 | zenon_intro zenon_H75 ]. % 19.63/19.83 apply (zenon_L18_); trivial. % 19.63/19.83 apply (zenon_L42_); trivial. % 19.63/19.83 apply (zenon_L36_); trivial. % 19.63/19.83 (* end of lemma zenon_L43_ *) % 19.63/19.83 assert (zenon_L44_ : ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> (~((op1 (e10) (e10)) = (e10))) -> (~((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e11) (e11)) = (e10))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hb5 zenon_H60 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H94 zenon_H9a zenon_Hb6 zenon_Hbb zenon_Hbd zenon_H56 zenon_H57 zenon_H55 zenon_Hbe zenon_H7b zenon_Hb8 zenon_H8b zenon_H71 zenon_H6e zenon_H75 zenon_H70. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H73 | zenon_intro zenon_Haa ]. % 19.63/19.83 apply (zenon_L39_); trivial. % 19.63/19.83 apply (zenon_L43_); trivial. % 19.63/19.83 (* end of lemma zenon_L44_ *) % 19.63/19.83 assert (zenon_L45_ : ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (e10))) -> (~((op1 (e10) (e11)) = (e10))) -> (~((op1 (e10) (e12)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H56 zenon_H57 zenon_H58 zenon_H55. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H59 | zenon_intro zenon_H75 ]. % 19.63/19.83 apply (zenon_L18_); trivial. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_H59 | zenon_intro zenon_H64 ]. % 19.63/19.83 apply (zenon_L18_); trivial. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H73 | zenon_intro zenon_Haa ]. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_H61 | zenon_intro zenon_H7b ]. % 19.63/19.83 apply (zenon_L38_); trivial. % 19.63/19.83 apply (zenon_L44_); trivial. % 19.63/19.83 apply (zenon_L42_); trivial. % 19.63/19.83 (* end of lemma zenon_L45_ *) % 19.63/19.83 assert (zenon_L46_ : ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e11)) = (e10))) -> (~((op1 (e10) (e10)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (~((op1 (e11) (e11)) = (e10))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hc0 zenon_H55 zenon_H9a zenon_H94 zenon_H8d zenon_H84 zenon_H9b zenon_Ha1 zenon_Ha5 zenon_Hab zenon_H57 zenon_H56 zenon_Haf zenon_Hb4 zenon_H7b zenon_Hb8 zenon_H8b zenon_H71 zenon_H6e zenon_H75 zenon_H70. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H73 | zenon_intro zenon_Haa ]. % 19.63/19.83 apply (zenon_L39_); trivial. % 19.63/19.83 apply (zenon_L36_); trivial. % 19.63/19.83 (* end of lemma zenon_L46_ *) % 19.63/19.83 assert (zenon_L47_ : ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> (~((op1 (e10) (e12)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e11)) = (e10))) -> (~((op1 (e10) (e10)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (~((op1 (e13) (e13)) = (e13))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e11) (e11)) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> (~((op1 (e10) (e10)) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hbc zenon_H58 zenon_Hbd zenon_Hb7 zenon_Hb6 zenon_H55 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_H57 zenon_H56 zenon_Haf zenon_Hb4 zenon_H64 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H75 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_H9b zenon_Hb8 zenon_Hbb. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H73 | zenon_intro zenon_Haa ]. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_H61 | zenon_intro zenon_H7b ]. % 19.63/19.83 apply (zenon_L38_); trivial. % 19.63/19.83 apply (zenon_L46_); trivial. % 19.63/19.83 apply (zenon_L42_); trivial. % 19.63/19.83 (* end of lemma zenon_L47_ *) % 19.63/19.83 assert (zenon_L48_ : ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> (~((op1 (e10) (e10)) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> (~((op1 (e10) (e10)) = (e10))) -> (~((op1 (e10) (e11)) = (e10))) -> (~((op1 (e10) (e12)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hbf zenon_Hbc zenon_Hbd zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_H9b zenon_Hb8 zenon_Hbb zenon_H56 zenon_H57 zenon_H58 zenon_H55. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H59 | zenon_intro zenon_H75 ]. % 19.63/19.83 apply (zenon_L18_); trivial. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_H59 | zenon_intro zenon_H64 ]. % 19.63/19.83 apply (zenon_L18_); trivial. % 19.63/19.83 apply (zenon_L47_); trivial. % 19.63/19.83 (* end of lemma zenon_L48_ *) % 19.63/19.83 assert (zenon_L49_ : (~((h4 (e10)) = (e20))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hc1 zenon_Hc2 zenon_H2e. % 19.63/19.83 cut (((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) = ((h4 (e10)) = (e20))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_Hc1. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_Hc2. % 19.63/19.83 cut (((op2 (e23) (op2 (e23) (e23))) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 19.63/19.83 cut (((h4 (e10)) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 19.63/19.83 congruence. % 19.63/19.83 apply zenon_Hc3. apply refl_equal. % 19.63/19.83 apply zenon_H4a. apply sym_equal. exact zenon_H2e. % 19.63/19.83 (* end of lemma zenon_L49_ *) % 19.63/19.83 assert (zenon_L50_ : (~((e21) = (e21))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hc4. % 19.63/19.83 apply zenon_Hc4. apply refl_equal. % 19.63/19.83 (* end of lemma zenon_L50_ *) % 19.63/19.83 assert (zenon_L51_ : ((op2 (e20) (e21)) = (e21)) -> ((op2 (e20) (e21)) = (e22)) -> (~((e21) = (e22))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hc5 zenon_Hc6 zenon_Hc7. % 19.63/19.83 elim (classic ((e22) = (e22))); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hc9 ]. % 19.63/19.83 cut (((e22) = (e22)) = ((e21) = (e22))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_Hc7. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_Hc8. % 19.63/19.83 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_Hc9]. % 19.63/19.83 cut (((e22) = (e21))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 19.63/19.83 congruence. % 19.63/19.83 cut (((op2 (e20) (e21)) = (e21)) = ((e22) = (e21))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_Hca. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_Hc5. % 19.63/19.83 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_Hc4]. % 19.63/19.83 cut (((op2 (e20) (e21)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 19.63/19.83 congruence. % 19.63/19.83 exact (zenon_Hcb zenon_Hc6). % 19.63/19.83 apply zenon_Hc4. apply refl_equal. % 19.63/19.83 apply zenon_Hc9. apply refl_equal. % 19.63/19.83 apply zenon_Hc9. apply refl_equal. % 19.63/19.83 (* end of lemma zenon_L51_ *) % 19.63/19.83 assert (zenon_L52_ : ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((op2 (e20) (e22)) = (e22)) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e22)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H4c zenon_Hcc zenon_H2b zenon_H2e zenon_Hcd. % 19.63/19.83 elim (classic ((op2 (e20) (e22)) = (op2 (e20) (e22)))); [ zenon_intro zenon_Hce | zenon_intro zenon_Hcf ]. % 19.63/19.83 cut (((op2 (e20) (e22)) = (op2 (e20) (e22))) = ((op2 (e20) (e21)) = (op2 (e20) (e22)))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_Hcd. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_Hce. % 19.63/19.83 cut (((op2 (e20) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 19.63/19.83 cut (((op2 (e20) (e22)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Hd0]. % 19.63/19.83 congruence. % 19.63/19.83 cut (((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) = ((op2 (e20) (e22)) = (op2 (e20) (e21)))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_Hd0. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H4c. % 19.63/19.83 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23))) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 19.63/19.83 cut (((e22) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 19.63/19.83 congruence. % 19.63/19.83 elim (classic ((op2 (e20) (e22)) = (op2 (e20) (e22)))); [ zenon_intro zenon_Hce | zenon_intro zenon_Hcf ]. % 19.63/19.83 cut (((op2 (e20) (e22)) = (op2 (e20) (e22))) = ((e22) = (op2 (e20) (e22)))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_Hd1. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_Hce. % 19.63/19.83 cut (((op2 (e20) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 19.63/19.83 cut (((op2 (e20) (e22)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_Hd2]. % 19.63/19.83 congruence. % 19.63/19.83 exact (zenon_Hd2 zenon_Hcc). % 19.63/19.83 apply zenon_Hcf. apply refl_equal. % 19.63/19.83 apply zenon_Hcf. apply refl_equal. % 19.63/19.83 apply (zenon_L10_); trivial. % 19.63/19.83 apply zenon_Hcf. apply refl_equal. % 19.63/19.83 apply zenon_Hcf. apply refl_equal. % 19.63/19.83 (* end of lemma zenon_L52_ *) % 19.63/19.83 assert (zenon_L53_ : ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H4c zenon_Hd3 zenon_H2b zenon_H2e zenon_Hd4. % 19.63/19.83 elim (classic ((op2 (e20) (e23)) = (op2 (e20) (e23)))); [ zenon_intro zenon_Hd5 | zenon_intro zenon_Hd6 ]. % 19.63/19.83 cut (((op2 (e20) (e23)) = (op2 (e20) (e23))) = ((op2 (e20) (e21)) = (op2 (e20) (e23)))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_Hd4. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_Hd5. % 19.63/19.83 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hd6]. % 19.63/19.83 cut (((op2 (e20) (e23)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 19.63/19.83 congruence. % 19.63/19.83 cut (((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) = ((op2 (e20) (e23)) = (op2 (e20) (e21)))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_Hd7. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H4c. % 19.63/19.83 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23))) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 19.63/19.83 cut (((e22) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hd8]. % 19.63/19.83 congruence. % 19.63/19.83 elim (classic ((op2 (e20) (e23)) = (op2 (e20) (e23)))); [ zenon_intro zenon_Hd5 | zenon_intro zenon_Hd6 ]. % 19.63/19.83 cut (((op2 (e20) (e23)) = (op2 (e20) (e23))) = ((e22) = (op2 (e20) (e23)))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_Hd8. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_Hd5. % 19.63/19.83 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hd6]. % 19.63/19.83 cut (((op2 (e20) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 19.63/19.83 congruence. % 19.63/19.83 exact (zenon_Hd9 zenon_Hd3). % 19.63/19.83 apply zenon_Hd6. apply refl_equal. % 19.63/19.83 apply zenon_Hd6. apply refl_equal. % 19.63/19.83 apply (zenon_L10_); trivial. % 19.63/19.83 apply zenon_Hd6. apply refl_equal. % 19.63/19.83 apply zenon_Hd6. apply refl_equal. % 19.63/19.83 (* end of lemma zenon_L53_ *) % 19.63/19.83 assert (zenon_L54_ : (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (e22))) -> (~((e21) = (e22))) -> ((op2 (e20) (e21)) = (e21)) -> (~((op2 (e20) (e21)) = (op2 (e20) (e22)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hda zenon_H40 zenon_Hc7 zenon_Hc5 zenon_Hcd zenon_H4c zenon_H2b zenon_H2e zenon_Hd4. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H46 | zenon_intro zenon_Hdb ]. % 19.63/19.83 exact (zenon_H40 zenon_H46). % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hdc ]. % 19.63/19.83 apply (zenon_L51_); trivial. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hd3 ]. % 19.63/19.83 apply (zenon_L52_); trivial. % 19.63/19.83 apply (zenon_L53_); trivial. % 19.63/19.83 (* end of lemma zenon_L54_ *) % 19.63/19.83 assert (zenon_L55_ : (~((e20) = (e20))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hdd. % 19.63/19.83 apply zenon_Hdd. apply refl_equal. % 19.63/19.83 (* end of lemma zenon_L55_ *) % 19.63/19.83 assert (zenon_L56_ : ((op2 (e20) (e22)) = (e20)) -> ((op2 (e20) (e22)) = (e21)) -> (~((e20) = (e21))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H1c zenon_Hde zenon_Hdf. % 19.63/19.83 elim (classic ((e21) = (e21))); [ zenon_intro zenon_He0 | zenon_intro zenon_Hc4 ]. % 19.63/19.83 cut (((e21) = (e21)) = ((e20) = (e21))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_Hdf. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_He0. % 19.63/19.83 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_Hc4]. % 19.63/19.83 cut (((e21) = (e20))); [idtac | apply NNPP; zenon_intro zenon_He1]. % 19.63/19.83 congruence. % 19.63/19.83 cut (((op2 (e20) (e22)) = (e20)) = ((e21) = (e20))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_He1. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H1c. % 19.63/19.83 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_Hdd]. % 19.63/19.83 cut (((op2 (e20) (e22)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_He2]. % 19.63/19.83 congruence. % 19.63/19.83 exact (zenon_He2 zenon_Hde). % 19.63/19.83 apply zenon_Hdd. apply refl_equal. % 19.63/19.83 apply zenon_Hc4. apply refl_equal. % 19.63/19.83 apply zenon_Hc4. apply refl_equal. % 19.63/19.83 (* end of lemma zenon_L56_ *) % 19.63/19.83 assert (zenon_L57_ : (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e20) (e23)) = (e21)) -> False). % 19.63/19.83 do 0 intro. intros zenon_He3 zenon_H2b zenon_He4. % 19.63/19.83 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e20) (e23)) = (op2 (e23) (e23)))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_He3. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H2b. % 19.63/19.83 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_He5]. % 19.63/19.83 cut (((e21) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_He6]. % 19.63/19.83 congruence. % 19.63/19.83 elim (classic ((op2 (e20) (e23)) = (op2 (e20) (e23)))); [ zenon_intro zenon_Hd5 | zenon_intro zenon_Hd6 ]. % 19.63/19.83 cut (((op2 (e20) (e23)) = (op2 (e20) (e23))) = ((e21) = (op2 (e20) (e23)))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_He6. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_Hd5. % 19.63/19.83 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hd6]. % 19.63/19.83 cut (((op2 (e20) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_He7]. % 19.63/19.83 congruence. % 19.63/19.83 exact (zenon_He7 zenon_He4). % 19.63/19.83 apply zenon_Hd6. apply refl_equal. % 19.63/19.83 apply zenon_Hd6. apply refl_equal. % 19.63/19.83 apply zenon_He5. apply refl_equal. % 19.63/19.83 (* end of lemma zenon_L57_ *) % 19.63/19.83 assert (zenon_L58_ : ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (e10))) -> (~((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (e11))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (e11))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hbe zenon_H55 zenon_H57 zenon_H56 zenon_Hbc zenon_Hb5 zenon_H60 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H71 zenon_H6e zenon_H94 zenon_H9a zenon_Haa zenon_Hb6 zenon_H70 zenon_Hb8 zenon_H73 zenon_Hbb zenon_Hbf. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H58 | zenon_intro zenon_H9b ]. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H59 | zenon_intro zenon_H75 ]. % 19.63/19.83 apply (zenon_L18_); trivial. % 19.63/19.83 apply (zenon_L41_); trivial. % 19.63/19.83 apply (zenon_L36_); trivial. % 19.63/19.83 (* end of lemma zenon_L58_ *) % 19.63/19.83 assert (zenon_L59_ : ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (~((op1 (e13) (e10)) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (e10))) -> (~((op1 (e10) (e10)) = (e11))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e11)) = (e10))) -> (~((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hb5 zenon_H6b zenon_H61 zenon_H60 zenon_H55 zenon_H59 zenon_Haa zenon_H9a zenon_H94 zenon_H6e zenon_H71 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_H57 zenon_H56 zenon_Hb6. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H62 | zenon_intro zenon_H6f ]. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H63 | zenon_intro zenon_H9b ]. % 19.63/19.83 apply (zenon_L20_); trivial. % 19.63/19.83 apply (zenon_L34_); trivial. % 19.63/19.83 apply zenon_H6f. apply sym_equal. exact zenon_H6e. % 19.63/19.83 (* end of lemma zenon_L59_ *) % 19.63/19.83 assert (zenon_L60_ : (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e12) (e12)) = (e10))) -> (~((op1 (e12) (e12)) = (e11))) -> (~((op1 (e12) (e12)) = (e12))) -> (~((op1 (e12) (e12)) = (e13))) -> False). % 19.63/19.83 do 0 intro. intros zenon_He8 zenon_He9 zenon_Hea zenon_Heb zenon_Hec. % 19.63/19.83 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hee | zenon_intro zenon_Hed ]. % 19.63/19.83 exact (zenon_He9 zenon_Hee). % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hef ]. % 19.63/19.83 exact (zenon_Hea zenon_Hf0). % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hef); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf1 ]. % 19.63/19.83 exact (zenon_Heb zenon_Hf2). % 19.63/19.83 exact (zenon_Hec zenon_Hf1). % 19.63/19.83 (* end of lemma zenon_L60_ *) % 19.63/19.83 assert (zenon_L61_ : ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (~((op1 (e12) (e12)) = (e11))) -> (~((op1 (e12) (e12)) = (e12))) -> (~((op1 (e12) (e12)) = (e13))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e10)) = (e10))) -> (~((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (e11))) -> (~((op1 (e10) (e13)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hf3 zenon_Hea zenon_Heb zenon_Hec zenon_He8 zenon_Hb6 zenon_H56 zenon_H57 zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H71 zenon_H6e zenon_H94 zenon_H9a zenon_Haa zenon_H59 zenon_H55 zenon_H60 zenon_H6b zenon_Hb5. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_H61 | zenon_intro zenon_He9 ]. % 19.63/19.83 apply (zenon_L59_); trivial. % 19.63/19.83 apply (zenon_L60_); trivial. % 19.63/19.83 (* end of lemma zenon_L61_ *) % 19.63/19.83 assert (zenon_L62_ : ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (~((op1 (e12) (e12)) = (e11))) -> (~((op1 (e12) (e12)) = (e12))) -> (~((op1 (e12) (e12)) = (e13))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (e11))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e11)) = (e10))) -> (~((op1 (e10) (e10)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (~((op1 (e13) (e13)) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hf3 zenon_Hea zenon_Heb zenon_Hec zenon_He8 zenon_Hb6 zenon_H55 zenon_Haa zenon_H9a zenon_H94 zenon_H6e zenon_H71 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_H57 zenon_H56 zenon_Haf zenon_Hb4 zenon_H64 zenon_H60 zenon_Hb5. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_H61 | zenon_intro zenon_He9 ]. % 19.63/19.83 apply (zenon_L37_); trivial. % 19.63/19.83 apply (zenon_L60_); trivial. % 19.63/19.83 (* end of lemma zenon_L62_ *) % 19.63/19.83 assert (zenon_L63_ : ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e10)) = (e13))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e13)) = (e13))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (~((op1 (e10) (e10)) = (e10))) -> (~((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (e11))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e12) (e12)) = (e13))) -> (~((op1 (e12) (e12)) = (e11))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hf4 zenon_Hb0 zenon_Hb5 zenon_H60 zenon_H64 zenon_Hb4 zenon_Haf zenon_H56 zenon_H57 zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H71 zenon_H6e zenon_H94 zenon_H9a zenon_Haa zenon_H55 zenon_Hb6 zenon_He8 zenon_Hec zenon_Hea zenon_Hf3. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Heb | zenon_intro zenon_H9b ]. % 19.63/19.83 apply (zenon_L62_); trivial. % 19.63/19.83 apply (zenon_L35_); trivial. % 19.63/19.83 (* end of lemma zenon_L63_ *) % 19.63/19.83 assert (zenon_L64_ : ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> (~((op1 (e11) (e11)) = (e11))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e10)) = (e11))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> (~((op1 (e10) (e10)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_H6b zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hbf zenon_Hbb zenon_H73 zenon_Hb8 zenon_H70 zenon_Hb6 zenon_Haa zenon_H9a zenon_H94 zenon_H6e zenon_H71 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_H60 zenon_Hb5 zenon_Hbc zenon_H56 zenon_H55 zenon_Hbe. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_H57 | zenon_intro zenon_Hea ]. % 19.63/19.83 apply (zenon_L58_); trivial. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hf7); [ zenon_intro zenon_H57 | zenon_intro zenon_H6f ]. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H58 | zenon_intro zenon_H9b ]. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_H59 | zenon_intro zenon_Hb0 ]. % 19.63/19.83 apply (zenon_L18_); trivial. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_H59 | zenon_intro zenon_Hec ]. % 19.63/19.83 apply (zenon_L18_); trivial. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_H59 | zenon_intro zenon_H64 ]. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Heb | zenon_intro zenon_H9b ]. % 19.63/19.83 apply (zenon_L61_); trivial. % 19.63/19.83 apply (zenon_L36_); trivial. % 19.63/19.83 apply (zenon_L63_); trivial. % 19.63/19.83 apply (zenon_L36_); trivial. % 19.63/19.83 apply zenon_H6f. apply sym_equal. exact zenon_H6e. % 19.63/19.83 (* end of lemma zenon_L64_ *) % 19.63/19.83 assert (zenon_L65_ : ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (e11))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> (~((op1 (e10) (e10)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_H6b zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_Hbf zenon_Hbc zenon_Hb5 zenon_H60 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H71 zenon_H6e zenon_H94 zenon_H9a zenon_Haa zenon_Hb6 zenon_H70 zenon_Hb8 zenon_Hbb zenon_Hbd zenon_H56 zenon_H55 zenon_Hbe. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H57 | zenon_intro zenon_H73 ]. % 19.63/19.83 apply (zenon_L43_); trivial. % 19.63/19.83 apply (zenon_L64_); trivial. % 19.63/19.83 (* end of lemma zenon_L65_ *) % 19.63/19.83 assert (zenon_L66_ : ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (e12))) -> (~((op1 (e11) (e11)) = (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hc0 zenon_Hbe zenon_H55 zenon_H56 zenon_Hbd zenon_Hbb zenon_Hb8 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_H60 zenon_Hb5 zenon_Hbc zenon_Hbf zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_H6b zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_H72 zenon_H71 zenon_H6e zenon_H74 zenon_H75 zenon_H70. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H73 | zenon_intro zenon_Haa ]. % 19.63/19.83 apply (zenon_L23_); trivial. % 19.63/19.83 apply (zenon_L65_); trivial. % 19.63/19.83 (* end of lemma zenon_L66_ *) % 19.63/19.83 assert (zenon_L67_ : ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (e20))) -> (~((h4 (op1 (e10) (e10))) = (op2 (h4 (e10)) (h4 (e10))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e22)))) -> (~((e21) = (e22))) -> (~((op2 (e20) (e20)) = (e22))) -> (~((e20) = (e21))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op2 (e20) (e21)) = (e20))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H56 zenon_H55 zenon_Hfa zenon_H12 zenon_H16 zenon_Hfb zenon_Hfc zenon_H2e zenon_Hc2 zenon_H2b zenon_Hda zenon_Hd4 zenon_H4c zenon_Hcd zenon_Hc7 zenon_H40 zenon_Hdf zenon_He3 zenon_Hfd zenon_H14 zenon_H13 zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H57 | zenon_intro zenon_Haa ]. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H58 | zenon_intro zenon_H9b ]. % 19.63/19.83 apply (zenon_L45_); trivial. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H58 | zenon_intro zenon_H74 ]. % 19.63/19.83 apply (zenon_L48_); trivial. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H59 | zenon_intro zenon_H75 ]. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H12); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ]. % 19.63/19.83 exact (zenon_H13 zenon_H18). % 19.63/19.83 apply (zenon_or_s _ _ zenon_H17); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ]. % 19.63/19.83 exact (zenon_H14 zenon_H1a). % 19.63/19.83 apply (zenon_or_s _ _ zenon_H19); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ]. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_H44 | zenon_intro zenon_Hfe ]. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H55); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 19.63/19.83 exact (zenon_H56 zenon_H5b). % 19.63/19.83 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H5d | zenon_intro zenon_H5c ]. % 19.63/19.83 exact (zenon_H57 zenon_H5d). % 19.63/19.83 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ]. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_Had | zenon_intro zenon_Hac ]. % 19.63/19.83 cut (((h4 (e11)) = (op2 (e23) (e23))) = ((h4 (op1 (e10) (e10))) = (op2 (h4 (e10)) (h4 (e10))))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_Hfb. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_Hfc. % 19.63/19.83 cut (((op2 (e23) (e23)) = (op2 (h4 (e10)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_Hff]. % 19.63/19.83 cut (((h4 (e11)) = (h4 (op1 (e10) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H100]. % 19.63/19.83 congruence. % 19.63/19.83 elim (classic ((h4 (op1 (e10) (e10))) = (h4 (op1 (e10) (e10))))); [ zenon_intro zenon_H101 | zenon_intro zenon_H102 ]. % 19.63/19.83 cut (((h4 (op1 (e10) (e10))) = (h4 (op1 (e10) (e10)))) = ((h4 (e11)) = (h4 (op1 (e10) (e10))))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_H100. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H101. % 19.63/19.83 cut (((h4 (op1 (e10) (e10))) = (h4 (op1 (e10) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H102]. % 19.63/19.83 cut (((h4 (op1 (e10) (e10))) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H103]. % 19.63/19.83 congruence. % 19.63/19.83 cut (((op1 (e10) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 19.63/19.83 congruence. % 19.63/19.83 exact (zenon_Haa zenon_Had). % 19.63/19.83 apply zenon_H102. apply refl_equal. % 19.63/19.83 apply zenon_H102. apply refl_equal. % 19.63/19.83 elim (classic ((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10))))); [ zenon_intro zenon_H104 | zenon_intro zenon_H105 ]. % 19.63/19.83 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10)))) = ((op2 (e23) (e23)) = (op2 (h4 (e10)) (h4 (e10))))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_Hff. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H104. % 19.63/19.83 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H105]. % 19.63/19.83 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H106]. % 19.63/19.83 congruence. % 19.63/19.83 cut (((op2 (e20) (e20)) = (e21)) = ((op2 (h4 (e10)) (h4 (e10))) = (op2 (e23) (e23)))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_H106. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H44. % 19.63/19.83 cut (((e21) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 19.63/19.83 cut (((op2 (e20) (e20)) = (op2 (h4 (e10)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H108]. % 19.63/19.83 congruence. % 19.63/19.83 elim (classic ((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10))))); [ zenon_intro zenon_H104 | zenon_intro zenon_H105 ]. % 19.63/19.83 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10)))) = ((op2 (e20) (e20)) = (op2 (h4 (e10)) (h4 (e10))))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_H108. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H104. % 19.63/19.83 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H105]. % 19.63/19.83 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H109]. % 19.63/19.83 congruence. % 19.63/19.83 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_Hc1]. % 19.63/19.83 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_Hc1]. % 19.63/19.83 congruence. % 19.63/19.83 apply (zenon_L49_); trivial. % 19.63/19.83 apply (zenon_L49_); trivial. % 19.63/19.83 apply zenon_H105. apply refl_equal. % 19.63/19.83 apply zenon_H105. apply refl_equal. % 19.63/19.83 exact (zenon_H107 zenon_H2b). % 19.63/19.83 apply zenon_H105. apply refl_equal. % 19.63/19.83 apply zenon_H105. apply refl_equal. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H82 | zenon_intro zenon_Hae ]. % 19.63/19.83 apply (zenon_L30_); trivial. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_Ha0 | zenon_intro zenon_Ha6 ]. % 19.63/19.83 apply (zenon_L32_); trivial. % 19.63/19.83 apply (zenon_L33_); trivial. % 19.63/19.83 exact (zenon_H59 zenon_H5e). % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_Hc5 | zenon_intro zenon_H10a ]. % 19.63/19.83 apply (zenon_L54_); trivial. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hde | zenon_intro zenon_He4 ]. % 19.63/19.83 apply (zenon_L56_); trivial. % 19.63/19.83 apply (zenon_L57_); trivial. % 19.63/19.83 exact (zenon_H16 zenon_H1b). % 19.63/19.83 apply (zenon_L66_); trivial. % 19.63/19.83 apply (zenon_L65_); trivial. % 19.63/19.83 (* end of lemma zenon_L67_ *) % 19.63/19.83 assert (zenon_L68_ : ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> (~((op2 (e20) (e20)) = (e20))) -> (~((op2 (e20) (e21)) = (e20))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((e20) = (e21))) -> (~((op2 (e20) (e20)) = (e22))) -> (~((e21) = (e22))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e22)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (~((h4 (op1 (e10) (e10))) = (op2 (h4 (e10)) (h4 (e10))))) -> (~((op2 (e20) (e23)) = (e20))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H10b zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H13 zenon_H14 zenon_Hfd zenon_He3 zenon_Hdf zenon_H40 zenon_Hc7 zenon_Hcd zenon_H4c zenon_Hd4 zenon_Hda zenon_H2b zenon_Hc2 zenon_H2e zenon_Hfc zenon_Hfb zenon_H16 zenon_H12 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H56 | zenon_intro zenon_H56 ]. % 19.63/19.83 apply (zenon_L67_); trivial. % 19.63/19.83 apply (zenon_L67_); trivial. % 19.63/19.83 (* end of lemma zenon_L68_ *) % 19.63/19.83 assert (zenon_L69_ : ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> (~((op2 (e20) (e20)) = (e22))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (~((op2 (e20) (e20)) = (e20))) -> (~((op2 (e20) (e20)) = (e23))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (~((op2 (e21) (e21)) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H54 zenon_H40 zenon_H51 zenon_H48 zenon_H13 zenon_H41 zenon_H3e zenon_H47 zenon_H28 zenon_H1d zenon_H2d zenon_H32 zenon_H2b zenon_H2e zenon_H2f zenon_H3d zenon_H4f zenon_H4b zenon_H4c zenon_H50. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H30 | zenon_intro zenon_H3f ]. % 19.63/19.83 apply (zenon_L13_); trivial. % 19.63/19.83 apply (zenon_L8_); trivial. % 19.63/19.83 (* end of lemma zenon_L69_ *) % 19.63/19.83 assert (zenon_L70_ : ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((h4 (op1 (e10) (e10))) = (op2 (h4 (e10)) (h4 (e10))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e22)))) -> (~((e21) = (e22))) -> (~((e20) = (e21))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e20) (e20)) = (e22)))) -> False). % 19.63/19.83 do 0 intro. intros zenon_H10c zenon_H10d zenon_H54 zenon_H53 zenon_H52 zenon_H51 zenon_H48 zenon_H3e zenon_H47 zenon_H28 zenon_H1d zenon_H2d zenon_H2b zenon_H2e zenon_H2f zenon_H3d zenon_H4f zenon_H4b zenon_H4c zenon_H50 zenon_H13 zenon_H12 zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_Hfb zenon_Hfc zenon_Hc2 zenon_Hda zenon_Hd4 zenon_Hcd zenon_Hc7 zenon_Hdf zenon_He3 zenon_Hfd zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_H10b zenon_H10e. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3f ]. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.63/19.83 apply (zenon_L17_); trivial. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H16 | zenon_intro zenon_H41 ]. % 19.63/19.83 apply (zenon_L68_); trivial. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H16 | zenon_intro zenon_H32 ]. % 19.63/19.83 apply (zenon_L68_); trivial. % 19.63/19.83 apply (zenon_L69_); trivial. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H14 | zenon_intro zenon_H2c ]. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.63/19.83 apply (zenon_L17_); trivial. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H16 | zenon_intro zenon_H41 ]. % 19.63/19.83 apply (zenon_L68_); trivial. % 19.63/19.83 apply (zenon_L8_); trivial. % 19.63/19.83 apply zenon_H2c. apply sym_equal. exact zenon_H2b. % 19.63/19.83 (* end of lemma zenon_L70_ *) % 19.63/19.83 assert (zenon_L71_ : ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))) -> False). % 19.63/19.83 do 0 intro. intros zenon_Hf9 zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H56 zenon_H55 zenon_Hfc zenon_Hc2 zenon_H10f zenon_H110. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H57 | zenon_intro zenon_Haa ]. % 19.63/19.83 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H58 | zenon_intro zenon_H9b ]. % 19.63/19.83 apply (zenon_L45_); trivial. % 19.63/19.83 apply (zenon_or_s _ _ zenon_H9a); [ zenon_intro zenon_H9d | zenon_intro zenon_H9c ]. % 19.63/19.83 exact (zenon_H9b zenon_H9d). % 19.63/19.83 apply (zenon_or_s _ _ zenon_H9c); [ zenon_intro zenon_H83 | zenon_intro zenon_H9e ]. % 19.63/19.83 cut (((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) = ((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_H110. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H10f. % 19.63/19.83 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23))) = (op2 (h4 (e10)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 19.63/19.83 cut (((h4 (e12)) = (h4 (op1 (e10) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 19.63/19.83 congruence. % 19.63/19.83 elim (classic ((h4 (op1 (e10) (e11))) = (h4 (op1 (e10) (e11))))); [ zenon_intro zenon_H113 | zenon_intro zenon_H114 ]. % 19.63/19.83 cut (((h4 (op1 (e10) (e11))) = (h4 (op1 (e10) (e11)))) = ((h4 (e12)) = (h4 (op1 (e10) (e11))))). % 19.63/19.83 intro zenon_D_pnotp. % 19.63/19.83 apply zenon_H112. % 19.63/19.83 rewrite <- zenon_D_pnotp. % 19.63/19.83 exact zenon_H113. % 19.63/19.83 cut (((h4 (op1 (e10) (e11))) = (h4 (op1 (e10) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H114]. % 19.63/19.83 cut (((h4 (op1 (e10) (e11))) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H115]. % 19.63/19.83 congruence. % 19.63/19.83 cut (((op1 (e10) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 19.63/19.83 congruence. % 19.63/19.83 exact (zenon_H88 zenon_H83). % 19.63/19.83 apply zenon_H114. apply refl_equal. % 19.63/19.83 apply zenon_H114. apply refl_equal. % 19.63/19.83 cut (((op2 (e23) (e23)) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 19.63/19.84 cut (((op2 (e23) (op2 (e23) (e23))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H117]. % 19.63/19.84 congruence. % 19.63/19.84 apply zenon_H117. apply sym_equal. exact zenon_Hc2. % 19.63/19.84 apply zenon_H116. apply sym_equal. exact zenon_Hfc. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H9e); [ zenon_intro zenon_H8c | zenon_intro zenon_H93 ]. % 19.63/19.84 apply (zenon_L28_); trivial. % 19.63/19.84 apply (zenon_L29_); trivial. % 19.63/19.84 apply (zenon_L65_); trivial. % 19.63/19.84 (* end of lemma zenon_L71_ *) % 19.63/19.84 assert (zenon_L72_ : ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> (~((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> False). % 19.63/19.84 do 0 intro. intros zenon_H10b zenon_H110 zenon_H10f zenon_Hc2 zenon_Hfc zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_Hf9. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H56 | zenon_intro zenon_H56 ]. % 19.63/19.84 apply (zenon_L71_); trivial. % 19.63/19.84 apply (zenon_L71_); trivial. % 19.63/19.84 (* end of lemma zenon_L72_ *) % 19.63/19.84 assert (zenon_L73_ : (~((h4 (e12)) = (e22))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> False). % 19.63/19.84 do 0 intro. intros zenon_H118 zenon_H10f zenon_H4c. % 19.63/19.84 cut (((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) = ((h4 (e12)) = (e22))). % 19.63/19.84 intro zenon_D_pnotp. % 19.63/19.84 apply zenon_H118. % 19.63/19.84 rewrite <- zenon_D_pnotp. % 19.63/19.84 exact zenon_H10f. % 19.63/19.84 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23))) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 19.63/19.84 cut (((h4 (e12)) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H11a]. % 19.63/19.84 congruence. % 19.63/19.84 apply zenon_H11a. apply refl_equal. % 19.63/19.84 apply zenon_H119. apply sym_equal. exact zenon_H4c. % 19.63/19.84 (* end of lemma zenon_L73_ *) % 19.63/19.84 assert (zenon_L74_ : ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (e20))) -> (~((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (e20))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> False). % 19.63/19.84 do 0 intro. intros zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H56 zenon_H55 zenon_Hfa zenon_H12 zenon_H16 zenon_H11b zenon_H4c zenon_H10f zenon_H2e zenon_Hc2 zenon_H14 zenon_H13 zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8. % 19.63/19.84 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H57 | zenon_intro zenon_Haa ]. % 19.63/19.84 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H58 | zenon_intro zenon_H9b ]. % 19.63/19.84 apply (zenon_L45_); trivial. % 19.63/19.84 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H58 | zenon_intro zenon_H74 ]. % 19.63/19.84 apply (zenon_L48_); trivial. % 19.63/19.84 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H59 | zenon_intro zenon_H75 ]. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H12); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ]. % 19.63/19.84 exact (zenon_H13 zenon_H18). % 19.63/19.84 apply (zenon_or_s _ _ zenon_H17); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ]. % 19.63/19.84 exact (zenon_H14 zenon_H1a). % 19.63/19.84 apply (zenon_or_s _ _ zenon_H19); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ]. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H55); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 19.63/19.84 exact (zenon_H56 zenon_H5b). % 19.63/19.84 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H5d | zenon_intro zenon_H5c ]. % 19.63/19.84 exact (zenon_H57 zenon_H5d). % 19.63/19.84 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ]. % 19.63/19.84 cut (((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) = ((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))). % 19.63/19.84 intro zenon_D_pnotp. % 19.63/19.84 apply zenon_H11b. % 19.63/19.84 rewrite <- zenon_D_pnotp. % 19.63/19.84 exact zenon_Hc2. % 19.63/19.84 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (h4 (e10)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 19.63/19.84 cut (((h4 (e10)) = (h4 (op1 (e10) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H11d]. % 19.63/19.84 congruence. % 19.63/19.84 elim (classic ((h4 (op1 (e10) (e12))) = (h4 (op1 (e10) (e12))))); [ zenon_intro zenon_H11e | zenon_intro zenon_H11f ]. % 19.63/19.84 cut (((h4 (op1 (e10) (e12))) = (h4 (op1 (e10) (e12)))) = ((h4 (e10)) = (h4 (op1 (e10) (e12))))). % 19.63/19.84 intro zenon_D_pnotp. % 19.63/19.84 apply zenon_H11d. % 19.63/19.84 rewrite <- zenon_D_pnotp. % 19.63/19.84 exact zenon_H11e. % 19.63/19.84 cut (((h4 (op1 (e10) (e12))) = (h4 (op1 (e10) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H11f]. % 19.63/19.84 cut (((h4 (op1 (e10) (e12))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H120]. % 19.63/19.84 congruence. % 19.63/19.84 cut (((op1 (e10) (e12)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 19.63/19.84 congruence. % 19.63/19.84 exact (zenon_H58 zenon_H5f). % 19.63/19.84 apply zenon_H11f. apply refl_equal. % 19.63/19.84 apply zenon_H11f. apply refl_equal. % 19.63/19.84 elim (classic ((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12))))); [ zenon_intro zenon_H121 | zenon_intro zenon_H122 ]. % 19.63/19.84 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12)))) = ((op2 (e23) (op2 (e23) (e23))) = (op2 (h4 (e10)) (h4 (e12))))). % 19.63/19.84 intro zenon_D_pnotp. % 19.63/19.84 apply zenon_H11c. % 19.63/19.84 rewrite <- zenon_D_pnotp. % 19.63/19.84 exact zenon_H121. % 19.63/19.84 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H122]. % 19.63/19.84 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H123]. % 19.63/19.84 congruence. % 19.63/19.84 cut (((op2 (e20) (e22)) = (e20)) = ((op2 (h4 (e10)) (h4 (e12))) = (op2 (e23) (op2 (e23) (e23))))). % 19.63/19.84 intro zenon_D_pnotp. % 19.63/19.84 apply zenon_H123. % 19.63/19.84 rewrite <- zenon_D_pnotp. % 19.63/19.84 exact zenon_H1c. % 19.63/19.84 cut (((e20) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H124]. % 19.63/19.84 cut (((op2 (e20) (e22)) = (op2 (h4 (e10)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H125]. % 19.63/19.84 congruence. % 19.63/19.84 elim (classic ((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12))))); [ zenon_intro zenon_H121 | zenon_intro zenon_H122 ]. % 19.63/19.84 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12)))) = ((op2 (e20) (e22)) = (op2 (h4 (e10)) (h4 (e12))))). % 19.63/19.84 intro zenon_D_pnotp. % 19.63/19.84 apply zenon_H125. % 19.63/19.84 rewrite <- zenon_D_pnotp. % 19.63/19.84 exact zenon_H121. % 19.63/19.84 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H122]. % 19.63/19.84 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H126]. % 19.63/19.84 congruence. % 19.63/19.84 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H118]. % 19.63/19.84 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_Hc1]. % 19.63/19.84 congruence. % 19.63/19.84 apply (zenon_L49_); trivial. % 19.63/19.84 apply (zenon_L73_); trivial. % 19.63/19.84 apply zenon_H122. apply refl_equal. % 19.63/19.84 apply zenon_H122. apply refl_equal. % 19.63/19.84 exact (zenon_H124 zenon_H2e). % 19.63/19.84 apply zenon_H122. apply refl_equal. % 19.63/19.84 apply zenon_H122. apply refl_equal. % 19.63/19.84 exact (zenon_H59 zenon_H5e). % 19.63/19.84 exact (zenon_H16 zenon_H1b). % 19.63/19.84 apply (zenon_L66_); trivial. % 19.63/19.84 apply (zenon_L65_); trivial. % 19.63/19.84 (* end of lemma zenon_L74_ *) % 19.63/19.84 assert (zenon_L75_ : ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> (~((op2 (e20) (e20)) = (e20))) -> (~((op2 (e20) (e21)) = (e20))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))) -> (~((op2 (e20) (e23)) = (e20))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> False). % 19.63/19.84 do 0 intro. intros zenon_H10b zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H13 zenon_H14 zenon_Hc2 zenon_H2e zenon_H10f zenon_H4c zenon_H11b zenon_H16 zenon_H12 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H56 | zenon_intro zenon_H56 ]. % 19.63/19.84 apply (zenon_L74_); trivial. % 19.63/19.84 apply (zenon_L74_); trivial. % 19.63/19.84 (* end of lemma zenon_L75_ *) % 19.63/19.84 assert (zenon_L76_ : ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> (~((op2 (e20) (e20)) = (e21))) -> (~((op2 (e20) (e20)) = (e22))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> (~((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (e20))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> False). % 19.63/19.84 do 0 intro. intros zenon_H53 zenon_H3f zenon_H40 zenon_H3e zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_H12 zenon_H11b zenon_H4c zenon_H10f zenon_H2e zenon_Hc2 zenon_H14 zenon_H13 zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_H10b. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H16 | zenon_intro zenon_H41 ]. % 19.63/19.84 apply (zenon_L75_); trivial. % 19.63/19.84 apply (zenon_L8_); trivial. % 19.63/19.84 (* end of lemma zenon_L76_ *) % 19.63/19.84 assert (zenon_L77_ : ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e20) (e20)) = (e22)))) -> False). % 19.63/19.84 do 0 intro. intros zenon_H10c zenon_H10d zenon_H127 zenon_H54 zenon_H53 zenon_H52 zenon_H51 zenon_H48 zenon_H3e zenon_H47 zenon_H28 zenon_H1d zenon_H2d zenon_H2b zenon_H2e zenon_H2f zenon_H3d zenon_H4f zenon_H4b zenon_H4c zenon_H50 zenon_H13 zenon_H12 zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_H11b zenon_H10f zenon_Hc2 zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_H10b zenon_H10e. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3f ]. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.63/19.84 apply (zenon_L17_); trivial. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H16 | zenon_intro zenon_H41 ]. % 19.63/19.84 apply (zenon_L75_); trivial. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H16 | zenon_intro zenon_H32 ]. % 19.63/19.84 apply (zenon_L75_); trivial. % 19.63/19.84 apply (zenon_L69_); trivial. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H14 | zenon_intro zenon_H30 ]. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.63/19.84 apply (zenon_L16_); trivial. % 19.63/19.84 apply (zenon_L76_); trivial. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H14 | zenon_intro zenon_H2c ]. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.63/19.84 apply (zenon_L15_); trivial. % 19.63/19.84 apply (zenon_L76_); trivial. % 19.63/19.84 apply zenon_H2c. apply sym_equal. exact zenon_H2b. % 19.63/19.84 (* end of lemma zenon_L77_ *) % 19.63/19.84 assert (zenon_L78_ : ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> (~((op2 (e20) (e20)) = (e22))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> (~((op2 (e20) (e20)) = (e20))) -> (~((op2 (e20) (e21)) = (e20))) -> (~((op2 (e20) (e22)) = (e20))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> False). % 19.63/19.84 do 0 intro. intros zenon_H53 zenon_H54 zenon_H40 zenon_H51 zenon_H48 zenon_H3e zenon_H47 zenon_H28 zenon_H1d zenon_H2d zenon_H2b zenon_H2e zenon_H2f zenon_H3d zenon_H4f zenon_H4b zenon_H4c zenon_H50 zenon_H52 zenon_H13 zenon_H14 zenon_H15 zenon_H12. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H16 | zenon_intro zenon_H41 ]. % 19.63/19.84 apply (zenon_L1_); trivial. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H16 | zenon_intro zenon_H32 ]. % 19.63/19.84 apply (zenon_L1_); trivial. % 19.63/19.84 apply (zenon_L69_); trivial. % 19.63/19.84 (* end of lemma zenon_L78_ *) % 19.63/19.84 assert (zenon_L79_ : (~((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))) -> ((op1 (e10) (e13)) = (e13)) -> ((op2 (e20) (e23)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> False). % 19.63/19.84 do 0 intro. intros zenon_H128 zenon_H129 zenon_H12a zenon_Hc2 zenon_H2e zenon_H12b. % 19.63/19.84 cut (((h4 (e13)) = (e23)) = ((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))). % 19.63/19.84 intro zenon_D_pnotp. % 19.63/19.84 apply zenon_H128. % 19.63/19.84 rewrite <- zenon_D_pnotp. % 19.63/19.84 exact zenon_H12b. % 19.63/19.84 cut (((e23) = (op2 (h4 (e10)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H12c]. % 19.63/19.84 cut (((h4 (e13)) = (h4 (op1 (e10) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 19.63/19.84 congruence. % 19.63/19.84 elim (classic ((h4 (op1 (e10) (e13))) = (h4 (op1 (e10) (e13))))); [ zenon_intro zenon_H12e | zenon_intro zenon_H12f ]. % 19.63/19.84 cut (((h4 (op1 (e10) (e13))) = (h4 (op1 (e10) (e13)))) = ((h4 (e13)) = (h4 (op1 (e10) (e13))))). % 19.63/19.84 intro zenon_D_pnotp. % 19.63/19.84 apply zenon_H12d. % 19.63/19.84 rewrite <- zenon_D_pnotp. % 19.63/19.84 exact zenon_H12e. % 19.63/19.84 cut (((h4 (op1 (e10) (e13))) = (h4 (op1 (e10) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H12f]. % 19.63/19.84 cut (((h4 (op1 (e10) (e13))) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H130]. % 19.63/19.84 congruence. % 19.63/19.84 cut (((op1 (e10) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H131]. % 19.63/19.84 congruence. % 19.63/19.84 exact (zenon_H131 zenon_H129). % 19.63/19.84 apply zenon_H12f. apply refl_equal. % 19.63/19.84 apply zenon_H12f. apply refl_equal. % 19.63/19.84 elim (classic ((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13))))); [ zenon_intro zenon_H132 | zenon_intro zenon_H133 ]. % 19.63/19.84 cut (((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13)))) = ((e23) = (op2 (h4 (e10)) (h4 (e13))))). % 19.63/19.84 intro zenon_D_pnotp. % 19.63/19.84 apply zenon_H12c. % 19.63/19.84 rewrite <- zenon_D_pnotp. % 19.63/19.84 exact zenon_H132. % 19.63/19.84 cut (((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H133]. % 19.63/19.84 cut (((op2 (h4 (e10)) (h4 (e13))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 19.63/19.84 congruence. % 19.63/19.84 cut (((op2 (e20) (e23)) = (e23)) = ((op2 (h4 (e10)) (h4 (e13))) = (e23))). % 19.63/19.84 intro zenon_D_pnotp. % 19.63/19.84 apply zenon_H134. % 19.63/19.84 rewrite <- zenon_D_pnotp. % 19.63/19.84 exact zenon_H12a. % 19.63/19.84 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 19.63/19.84 cut (((op2 (e20) (e23)) = (op2 (h4 (e10)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H135]. % 19.63/19.84 congruence. % 19.63/19.84 elim (classic ((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13))))); [ zenon_intro zenon_H132 | zenon_intro zenon_H133 ]. % 19.63/19.84 cut (((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13)))) = ((op2 (e20) (e23)) = (op2 (h4 (e10)) (h4 (e13))))). % 19.63/19.84 intro zenon_D_pnotp. % 19.63/19.84 apply zenon_H135. % 19.63/19.84 rewrite <- zenon_D_pnotp. % 19.63/19.84 exact zenon_H132. % 19.63/19.84 cut (((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H133]. % 19.63/19.84 cut (((op2 (h4 (e10)) (h4 (e13))) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 19.63/19.84 congruence. % 19.63/19.84 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 19.63/19.84 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_Hc1]. % 19.63/19.84 congruence. % 19.63/19.84 apply (zenon_L49_); trivial. % 19.63/19.84 exact (zenon_H137 zenon_H12b). % 19.63/19.84 apply zenon_H133. apply refl_equal. % 19.63/19.84 apply zenon_H133. apply refl_equal. % 19.63/19.84 apply zenon_H29. apply refl_equal. % 19.63/19.84 apply zenon_H133. apply refl_equal. % 19.63/19.84 apply zenon_H133. apply refl_equal. % 19.63/19.84 (* end of lemma zenon_L79_ *) % 19.63/19.84 assert (zenon_L80_ : (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e13)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> False). % 19.63/19.84 do 0 intro. intros zenon_H138 zenon_H129 zenon_H139. % 19.63/19.84 cut (((op1 (e10) (e13)) = (e13)) = ((op1 (e10) (e13)) = (op1 (e11) (e13)))). % 19.63/19.84 intro zenon_D_pnotp. % 19.63/19.84 apply zenon_H138. % 19.63/19.84 rewrite <- zenon_D_pnotp. % 19.63/19.84 exact zenon_H129. % 19.63/19.84 cut (((e13) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H13a]. % 19.63/19.84 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 19.63/19.84 congruence. % 19.63/19.84 apply zenon_H96. apply refl_equal. % 19.63/19.84 apply zenon_H13a. apply sym_equal. exact zenon_H139. % 19.63/19.84 (* end of lemma zenon_L80_ *) % 19.63/19.84 assert (zenon_L81_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (e10))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> False). % 19.63/19.84 do 0 intro. intros zenon_H13b zenon_H59 zenon_Ha5 zenon_H94 zenon_H71 zenon_H6e zenon_H8b zenon_H138 zenon_H139. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H5e | zenon_intro zenon_H13c ]. % 19.63/19.84 exact (zenon_H59 zenon_H5e). % 19.63/19.84 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H13d ]. % 19.63/19.84 apply (zenon_L33_); trivial. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H93 | zenon_intro zenon_H129 ]. % 19.63/19.84 apply (zenon_L29_); trivial. % 19.63/19.84 apply (zenon_L80_); trivial. % 19.63/19.84 (* end of lemma zenon_L81_ *) % 19.63/19.84 assert (zenon_L82_ : (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e13)) -> ((op1 (e12) (e13)) = (e13)) -> False). % 19.63/19.84 do 0 intro. intros zenon_H13e zenon_H129 zenon_H13f. % 19.63/19.84 cut (((op1 (e10) (e13)) = (e13)) = ((op1 (e10) (e13)) = (op1 (e12) (e13)))). % 19.63/19.84 intro zenon_D_pnotp. % 19.63/19.84 apply zenon_H13e. % 19.63/19.84 rewrite <- zenon_D_pnotp. % 19.63/19.84 exact zenon_H129. % 19.63/19.84 cut (((e13) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H140]. % 19.63/19.84 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 19.63/19.84 congruence. % 19.63/19.84 apply zenon_H96. apply refl_equal. % 19.63/19.84 apply zenon_H140. apply sym_equal. exact zenon_H13f. % 19.63/19.84 (* end of lemma zenon_L82_ *) % 19.63/19.84 assert (zenon_L83_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (e10))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> False). % 19.63/19.84 do 0 intro. intros zenon_H13b zenon_H59 zenon_Ha5 zenon_H94 zenon_H71 zenon_H6e zenon_H8b zenon_H13e zenon_H13f. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H5e | zenon_intro zenon_H13c ]. % 19.63/19.84 exact (zenon_H59 zenon_H5e). % 19.63/19.84 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H13d ]. % 19.63/19.84 apply (zenon_L33_); trivial. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H93 | zenon_intro zenon_H129 ]. % 19.63/19.84 apply (zenon_L29_); trivial. % 19.63/19.84 apply (zenon_L82_); trivial. % 19.63/19.84 (* end of lemma zenon_L83_ *) % 19.63/19.84 assert (zenon_L84_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((h4 (e13)) = (e23)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e23)) -> (~((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (e10))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e13)) = (e13))) -> False). % 19.63/19.84 do 0 intro. intros zenon_H141 zenon_H12b zenon_H2e zenon_Hc2 zenon_H12a zenon_H128 zenon_H138 zenon_H13e zenon_H8b zenon_H6e zenon_H71 zenon_H94 zenon_Ha5 zenon_H59 zenon_H13b zenon_H64. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H129 | zenon_intro zenon_H142 ]. % 19.63/19.84 apply (zenon_L79_); trivial. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H139 | zenon_intro zenon_H143 ]. % 19.63/19.84 apply (zenon_L81_); trivial. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H13f | zenon_intro zenon_H69 ]. % 19.63/19.84 apply (zenon_L83_); trivial. % 19.63/19.84 exact (zenon_H64 zenon_H69). % 19.63/19.84 (* end of lemma zenon_L84_ *) % 19.63/19.84 assert (zenon_L85_ : (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((op2 (e20) (e23)) = (e23)) -> ((op2 (e21) (e23)) = (e23)) -> False). % 19.63/19.84 do 0 intro. intros zenon_H144 zenon_H12a zenon_H145. % 19.63/19.84 cut (((op2 (e20) (e23)) = (e23)) = ((op2 (e20) (e23)) = (op2 (e21) (e23)))). % 19.63/19.84 intro zenon_D_pnotp. % 19.63/19.84 apply zenon_H144. % 19.63/19.84 rewrite <- zenon_D_pnotp. % 19.63/19.84 exact zenon_H12a. % 19.63/19.84 cut (((e23) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 19.63/19.84 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hd6]. % 19.63/19.84 congruence. % 19.63/19.84 apply zenon_Hd6. apply refl_equal. % 19.63/19.84 apply zenon_H146. apply sym_equal. exact zenon_H145. % 19.63/19.84 (* end of lemma zenon_L85_ *) % 19.63/19.84 assert (zenon_L86_ : (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (e20))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((op2 (e21) (e23)) = (e23)) -> False). % 19.63/19.84 do 0 intro. intros zenon_H147 zenon_H16 zenon_He3 zenon_Hd4 zenon_H2e zenon_H2b zenon_H4c zenon_H144 zenon_H145. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H1b | zenon_intro zenon_H148 ]. % 19.63/19.84 exact (zenon_H16 zenon_H1b). % 19.63/19.84 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_He4 | zenon_intro zenon_H149 ]. % 19.63/19.84 apply (zenon_L57_); trivial. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H12a ]. % 19.63/19.84 apply (zenon_L53_); trivial. % 19.63/19.84 apply (zenon_L85_); trivial. % 19.63/19.84 (* end of lemma zenon_L86_ *) % 19.63/19.84 assert (zenon_L87_ : (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e23)) -> ((op2 (e22) (e23)) = (e23)) -> False). % 19.63/19.84 do 0 intro. intros zenon_H14a zenon_H12a zenon_H14b. % 19.63/19.84 cut (((op2 (e20) (e23)) = (e23)) = ((op2 (e20) (e23)) = (op2 (e22) (e23)))). % 19.63/19.84 intro zenon_D_pnotp. % 19.63/19.84 apply zenon_H14a. % 19.63/19.84 rewrite <- zenon_D_pnotp. % 19.63/19.84 exact zenon_H12a. % 19.63/19.84 cut (((e23) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H14c]. % 19.63/19.84 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hd6]. % 19.63/19.84 congruence. % 19.63/19.84 apply zenon_Hd6. apply refl_equal. % 19.63/19.84 apply zenon_H14c. apply sym_equal. exact zenon_H14b. % 19.63/19.84 (* end of lemma zenon_L87_ *) % 19.63/19.84 assert (zenon_L88_ : (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (e20))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> False). % 19.63/19.84 do 0 intro. intros zenon_H147 zenon_H16 zenon_He3 zenon_Hd4 zenon_H2e zenon_H2b zenon_H4c zenon_H14a zenon_H14b. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H1b | zenon_intro zenon_H148 ]. % 19.63/19.84 exact (zenon_H16 zenon_H1b). % 19.63/19.84 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_He4 | zenon_intro zenon_H149 ]. % 19.63/19.84 apply (zenon_L57_); trivial. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H12a ]. % 19.63/19.84 apply (zenon_L53_); trivial. % 19.63/19.84 apply (zenon_L87_); trivial. % 19.63/19.84 (* end of lemma zenon_L88_ *) % 19.63/19.84 assert (zenon_L89_ : ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e23) (e23)) = (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (e20))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (~((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))) -> ((h4 (e13)) = (e23)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> False). % 19.63/19.84 do 0 intro. intros zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H56 zenon_H55 zenon_Hfa zenon_H14d zenon_H21 zenon_H14a zenon_H16 zenon_He3 zenon_H2b zenon_Hd4 zenon_H4c zenon_H144 zenon_H147 zenon_H128 zenon_H12b zenon_H2e zenon_Hc2 zenon_H13b zenon_H138 zenon_H13e zenon_H141 zenon_H14e zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8. % 19.63/19.84 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H57 | zenon_intro zenon_Haa ]. % 19.63/19.84 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H58 | zenon_intro zenon_H9b ]. % 19.63/19.84 apply (zenon_L45_); trivial. % 19.63/19.84 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H58 | zenon_intro zenon_H74 ]. % 19.63/19.84 apply (zenon_L48_); trivial. % 19.63/19.84 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H59 | zenon_intro zenon_H75 ]. % 19.63/19.84 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H73 | zenon_intro zenon_Haa ]. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H64 | zenon_intro zenon_H75 ]. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H12a | zenon_intro zenon_H14f ]. % 19.63/19.84 apply (zenon_L84_); trivial. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H145 | zenon_intro zenon_H150 ]. % 19.63/19.84 apply (zenon_L86_); trivial. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H14b | zenon_intro zenon_H26 ]. % 19.63/19.84 apply (zenon_L88_); trivial. % 19.63/19.84 exact (zenon_H21 zenon_H26). % 19.63/19.84 apply (zenon_L23_); trivial. % 19.63/19.84 apply (zenon_L34_); trivial. % 19.63/19.84 apply (zenon_L66_); trivial. % 19.63/19.84 apply (zenon_L65_); trivial. % 19.63/19.84 (* end of lemma zenon_L89_ *) % 19.63/19.84 assert (zenon_L90_ : ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e21) (e21)) = (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((op2 (e21) (e21)) = (e22))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (e20))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (~((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))) -> ((h4 (e13)) = (e23)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> False). % 19.63/19.84 do 0 intro. intros zenon_H151 zenon_H2f zenon_H30 zenon_H31 zenon_H2d zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_H14d zenon_H14a zenon_H16 zenon_He3 zenon_H2b zenon_Hd4 zenon_H4c zenon_H144 zenon_H147 zenon_H128 zenon_H12b zenon_H2e zenon_Hc2 zenon_H13b zenon_H138 zenon_H13e zenon_H141 zenon_H14e zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_H10b. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H21 | zenon_intro zenon_H32 ]. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H56 | zenon_intro zenon_H56 ]. % 19.63/19.84 apply (zenon_L89_); trivial. % 19.63/19.84 apply (zenon_L89_); trivial. % 19.63/19.84 apply (zenon_L6_); trivial. % 19.63/19.84 (* end of lemma zenon_L90_ *) % 19.63/19.84 assert (zenon_L91_ : ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> (~((op2 (e20) (e20)) = (e20))) -> (~((op2 (e20) (e20)) = (e21))) -> (~((op2 (e20) (e20)) = (e22))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (~((op2 (e21) (e21)) = (e22))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e21) (e21)) = (e23)))) -> False). % 19.63/19.84 do 0 intro. intros zenon_H53 zenon_H13 zenon_H3f zenon_H40 zenon_H3e zenon_H10b zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H14e zenon_H141 zenon_H13e zenon_H138 zenon_H13b zenon_Hc2 zenon_H2e zenon_H12b zenon_H128 zenon_H147 zenon_H144 zenon_H4c zenon_Hd4 zenon_H2b zenon_He3 zenon_H14a zenon_H14d zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9 zenon_H2d zenon_H31 zenon_H30 zenon_H2f zenon_H151. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H16 | zenon_intro zenon_H41 ]. % 19.63/19.84 apply (zenon_L90_); trivial. % 19.63/19.84 apply (zenon_L8_); trivial. % 19.63/19.84 (* end of lemma zenon_L91_ *) % 19.63/19.84 assert (zenon_L92_ : ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e21) (e21)) = (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (e22))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (~((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))) -> ((h4 (e13)) = (e23)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e22))) -> (~((op2 (e20) (e20)) = (e21))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> False). % 19.63/19.84 do 0 intro. intros zenon_H4f zenon_H151 zenon_H2f zenon_H31 zenon_H2d zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_H14d zenon_H14a zenon_He3 zenon_H2b zenon_Hd4 zenon_H4c zenon_H144 zenon_H147 zenon_H128 zenon_H12b zenon_H2e zenon_Hc2 zenon_H13b zenon_H138 zenon_H13e zenon_H141 zenon_H14e zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_H10b zenon_H3e zenon_H40 zenon_H3f zenon_H13 zenon_H53. % 19.63/19.84 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H30 | zenon_intro zenon_H30 ]. % 19.63/19.84 apply (zenon_L91_); trivial. % 19.63/19.84 apply (zenon_L91_); trivial. % 19.63/19.84 (* end of lemma zenon_L92_ *) % 19.63/19.84 assert (zenon_L93_ : ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> (~((op2 (e20) (e20)) = (e20))) -> (~((op2 (e20) (e20)) = (e22))) -> (~((op2 (e20) (e20)) = (e23))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (e20))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (~((op2 (e21) (e21)) = (e22))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e21) (e21)) = (e23)))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H54 zenon_H13 zenon_H40 zenon_H41 zenon_H3e zenon_H10b zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H14e zenon_H141 zenon_H13e zenon_H138 zenon_H13b zenon_Hc2 zenon_H2e zenon_H12b zenon_H128 zenon_H147 zenon_H144 zenon_H4c zenon_Hd4 zenon_H2b zenon_He3 zenon_H16 zenon_H14a zenon_H14d zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9 zenon_H2d zenon_H31 zenon_H2f zenon_H151. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H30 | zenon_intro zenon_H3f ]. % 19.63/19.85 apply (zenon_L90_); trivial. % 19.63/19.85 apply (zenon_L8_); trivial. % 19.63/19.85 (* end of lemma zenon_L93_ *) % 19.63/19.85 assert (zenon_L94_ : ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e20) (e20)) = (e22)))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H10c zenon_H10d zenon_H127 zenon_H54 zenon_H53 zenon_H52 zenon_H51 zenon_H48 zenon_H3e zenon_H47 zenon_H28 zenon_H1d zenon_H2d zenon_H2b zenon_H2e zenon_H2f zenon_H3d zenon_H4f zenon_H4b zenon_H4c zenon_H50 zenon_H13 zenon_H12 zenon_H152 zenon_H10b zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H14e zenon_H141 zenon_H13e zenon_H138 zenon_H13b zenon_Hc2 zenon_H12b zenon_H128 zenon_H147 zenon_H144 zenon_Hd4 zenon_He3 zenon_H14a zenon_H14d zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9 zenon_H151 zenon_H10e. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3f ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.63/19.85 apply (zenon_L17_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H15 | zenon_intro zenon_H31 ]. % 19.63/19.85 apply (zenon_L78_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H16 | zenon_intro zenon_H41 ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H30 | zenon_intro zenon_H3f ]. % 19.63/19.85 apply (zenon_L90_); trivial. % 19.63/19.85 apply (zenon_L92_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H16 | zenon_intro zenon_H32 ]. % 19.63/19.85 apply (zenon_L93_); trivial. % 19.63/19.85 apply (zenon_L69_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H14 | zenon_intro zenon_H30 ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.63/19.85 apply (zenon_L16_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H15 | zenon_intro zenon_H31 ]. % 19.63/19.85 apply (zenon_L78_); trivial. % 19.63/19.85 apply (zenon_L92_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H14 | zenon_intro zenon_H2c ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.63/19.85 apply (zenon_L17_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H15 | zenon_intro zenon_H31 ]. % 19.63/19.85 apply (zenon_L78_); trivial. % 19.63/19.85 apply (zenon_L91_); trivial. % 19.63/19.85 apply zenon_H2c. apply sym_equal. exact zenon_H2b. % 19.63/19.85 (* end of lemma zenon_L94_ *) % 19.63/19.85 assert (zenon_L95_ : (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (~((op2 (e21) (e21)) = (e22))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> (~((op2 (e20) (e20)) = (e20))) -> (~((op2 (e20) (e21)) = (e20))) -> (~((op2 (e20) (e22)) = (e20))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H2d zenon_H31 zenon_H2b zenon_H2e zenon_H2f zenon_H4f zenon_H52 zenon_H47 zenon_H28 zenon_H1d zenon_H3e zenon_H48 zenon_H4c zenon_H4b zenon_H50 zenon_H53 zenon_H54 zenon_H13 zenon_H14 zenon_H15 zenon_H12. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H16 | zenon_intro zenon_H32 ]. % 19.63/19.85 apply (zenon_L1_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H30 | zenon_intro zenon_H3f ]. % 19.63/19.85 apply (zenon_L6_); trivial. % 19.63/19.85 apply (zenon_L16_); trivial. % 19.63/19.85 (* end of lemma zenon_L95_ *) % 19.63/19.85 assert (zenon_L96_ : (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e11) (e11)) = (e12))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> (~((op1 (e10) (e10)) = (e10))) -> (~((op1 (e10) (e11)) = (e10))) -> (~((op1 (e10) (e12)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H70 zenon_H74 zenon_H6e zenon_H71 zenon_H72 zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_H6b zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_Hbf zenon_Hbc zenon_Hb5 zenon_H60 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb8 zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hc0 zenon_H56 zenon_H57 zenon_H58 zenon_H55. % 19.63/19.85 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H59 | zenon_intro zenon_H75 ]. % 19.63/19.85 apply (zenon_L18_); trivial. % 19.63/19.85 apply (zenon_L66_); trivial. % 19.63/19.85 (* end of lemma zenon_L96_ *) % 19.63/19.85 assert (zenon_L97_ : (~((h4 (e11)) = (e21))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H153 zenon_Hfc zenon_H2b. % 19.63/19.85 cut (((h4 (e11)) = (op2 (e23) (e23))) = ((h4 (e11)) = (e21))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H153. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_Hfc. % 19.63/19.85 cut (((op2 (e23) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H2c]. % 19.63/19.85 cut (((h4 (e11)) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H154]. % 19.63/19.85 congruence. % 19.63/19.85 apply zenon_H154. apply refl_equal. % 19.63/19.85 apply zenon_H2c. apply sym_equal. exact zenon_H2b. % 19.63/19.85 (* end of lemma zenon_L97_ *) % 19.63/19.85 assert (zenon_L98_ : (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((e10) = (e12))) -> ((op1 (e12) (e10)) = (e10)) -> (~((op1 (e12) (e11)) = (e12))) -> (~((op1 (e12) (e12)) = (e12))) -> (~((op1 (e12) (e13)) = (e12))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H155 zenon_H156 zenon_H157 zenon_H158 zenon_Heb zenon_H159. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H15b | zenon_intro zenon_H15a ]. % 19.63/19.85 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H85 | zenon_intro zenon_H86 ]. % 19.63/19.85 cut (((e12) = (e12)) = ((e10) = (e12))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H156. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H85. % 19.63/19.85 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 19.63/19.85 cut (((e12) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H15c]. % 19.63/19.85 congruence. % 19.63/19.85 cut (((op1 (e12) (e10)) = (e10)) = ((e12) = (e10))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H15c. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H157. % 19.63/19.85 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H9f]. % 19.63/19.85 cut (((op1 (e12) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H15d]. % 19.63/19.85 congruence. % 19.63/19.85 exact (zenon_H15d zenon_H15b). % 19.63/19.85 apply zenon_H9f. apply refl_equal. % 19.63/19.85 apply zenon_H86. apply refl_equal. % 19.63/19.85 apply zenon_H86. apply refl_equal. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 19.63/19.85 exact (zenon_H158 zenon_H15f). % 19.63/19.85 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H160 ]. % 19.63/19.85 exact (zenon_Heb zenon_Hf2). % 19.63/19.85 exact (zenon_H159 zenon_H160). % 19.63/19.85 (* end of lemma zenon_L98_ *) % 19.63/19.85 assert (zenon_L99_ : (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e10)) -> ((e11) = (op1 (e13) (e13))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H161 zenon_H71 zenon_H162 zenon_H6e. % 19.63/19.85 cut (((e10) = (op1 (e13) (op1 (e13) (e13)))) = ((op1 (e13) (e10)) = (op1 (e13) (e11)))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H161. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H71. % 19.63/19.85 cut (((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 19.63/19.85 cut (((e10) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H163]. % 19.63/19.85 congruence. % 19.63/19.85 elim (classic ((op1 (e13) (e10)) = (op1 (e13) (e10)))); [ zenon_intro zenon_H164 | zenon_intro zenon_H165 ]. % 19.63/19.85 cut (((op1 (e13) (e10)) = (op1 (e13) (e10))) = ((e10) = (op1 (e13) (e10)))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H163. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H164. % 19.63/19.85 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H165]. % 19.63/19.85 cut (((op1 (e13) (e10)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H166]. % 19.63/19.85 congruence. % 19.63/19.85 exact (zenon_H166 zenon_H162). % 19.63/19.85 apply zenon_H165. apply refl_equal. % 19.63/19.85 apply zenon_H165. apply refl_equal. % 19.63/19.85 apply (zenon_L22_); trivial. % 19.63/19.85 (* end of lemma zenon_L99_ *) % 19.63/19.85 assert (zenon_L100_ : (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((e20) = (e22))) -> ((op2 (e22) (e20)) = (e20)) -> (~((op2 (e22) (e21)) = (e22))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e23)) = (e22))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H167 zenon_H168 zenon_H169 zenon_H16a zenon_H16b zenon_H16c. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_H16e | zenon_intro zenon_H16d ]. % 19.63/19.85 elim (classic ((e22) = (e22))); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hc9 ]. % 19.63/19.85 cut (((e22) = (e22)) = ((e20) = (e22))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H168. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_Hc8. % 19.63/19.85 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_Hc9]. % 19.63/19.85 cut (((e22) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H16f]. % 19.63/19.85 congruence. % 19.63/19.85 cut (((op2 (e22) (e20)) = (e20)) = ((e22) = (e20))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H16f. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H169. % 19.63/19.85 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_Hdd]. % 19.63/19.85 cut (((op2 (e22) (e20)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H170]. % 19.63/19.85 congruence. % 19.63/19.85 exact (zenon_H170 zenon_H16e). % 19.63/19.85 apply zenon_Hdd. apply refl_equal. % 19.63/19.85 apply zenon_Hc9. apply refl_equal. % 19.63/19.85 apply zenon_Hc9. apply refl_equal. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H172 | zenon_intro zenon_H171 ]. % 19.63/19.85 exact (zenon_H16a zenon_H172). % 19.63/19.85 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H174 | zenon_intro zenon_H173 ]. % 19.63/19.85 exact (zenon_H16b zenon_H174). % 19.63/19.85 exact (zenon_H16c zenon_H173). % 19.63/19.85 (* end of lemma zenon_L100_ *) % 19.63/19.85 assert (zenon_L101_ : (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e20)) -> ((e21) = (op2 (e23) (e23))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H175 zenon_H2e zenon_H176 zenon_H2b. % 19.63/19.85 cut (((e20) = (op2 (e23) (op2 (e23) (e23)))) = ((op2 (e23) (e20)) = (op2 (e23) (e21)))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H175. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H2e. % 19.63/19.85 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 19.63/19.85 cut (((e20) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H177]. % 19.63/19.85 congruence. % 19.63/19.85 elim (classic ((op2 (e23) (e20)) = (op2 (e23) (e20)))); [ zenon_intro zenon_H178 | zenon_intro zenon_H179 ]. % 19.63/19.85 cut (((op2 (e23) (e20)) = (op2 (e23) (e20))) = ((e20) = (op2 (e23) (e20)))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H177. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H178. % 19.63/19.85 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H179]. % 19.63/19.85 cut (((op2 (e23) (e20)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H17a]. % 19.63/19.85 congruence. % 19.63/19.85 exact (zenon_H17a zenon_H176). % 19.63/19.85 apply zenon_H179. apply refl_equal. % 19.63/19.85 apply zenon_H179. apply refl_equal. % 19.63/19.85 apply (zenon_L5_); trivial. % 19.63/19.85 (* end of lemma zenon_L101_ *) % 19.63/19.85 assert (zenon_L102_ : ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e22))) -> (~((op2 (e22) (e21)) = (e22))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e23)) = (e22))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((h4 (op1 (e11) (e10))) = (op2 (h4 (e11)) (h4 (e10))))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> False). % 19.63/19.85 do 0 intro. intros zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H56 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H17b zenon_H17c zenon_H175 zenon_H168 zenon_H16a zenon_H16b zenon_H16c zenon_H167 zenon_H17d zenon_H2e zenon_Hc2 zenon_H2b zenon_Hfc zenon_H155 zenon_H156 zenon_H161 zenon_H17e zenon_H13 zenon_H17f zenon_H180. % 19.63/19.85 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H57 | zenon_intro zenon_Haa ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H58 | zenon_intro zenon_H9b ]. % 19.63/19.85 apply (zenon_L45_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H58 | zenon_intro zenon_H74 ]. % 19.63/19.85 apply (zenon_L48_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H58 | zenon_intro zenon_Heb ]. % 19.63/19.85 apply (zenon_L96_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H17b); [ zenon_intro zenon_H158 | zenon_intro zenon_Haa ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H159 | zenon_intro zenon_H75 ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H17c); [ zenon_intro zenon_H18 | zenon_intro zenon_H181 ]. % 19.63/19.85 exact (zenon_H13 zenon_H18). % 19.63/19.85 apply (zenon_or_s _ _ zenon_H181); [ zenon_intro zenon_H183 | zenon_intro zenon_H182 ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H5b | zenon_intro zenon_H184 ]. % 19.63/19.85 exact (zenon_H56 zenon_H5b). % 19.63/19.85 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_H186 | zenon_intro zenon_H185 ]. % 19.63/19.85 cut (((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) = ((h4 (op1 (e11) (e10))) = (op2 (h4 (e11)) (h4 (e10))))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H17d. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_Hc2. % 19.63/19.85 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (h4 (e11)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 19.63/19.85 cut (((h4 (e10)) = (h4 (op1 (e11) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H188]. % 19.63/19.85 congruence. % 19.63/19.85 elim (classic ((h4 (op1 (e11) (e10))) = (h4 (op1 (e11) (e10))))); [ zenon_intro zenon_H189 | zenon_intro zenon_H18a ]. % 19.63/19.85 cut (((h4 (op1 (e11) (e10))) = (h4 (op1 (e11) (e10)))) = ((h4 (e10)) = (h4 (op1 (e11) (e10))))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H188. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H189. % 19.63/19.85 cut (((h4 (op1 (e11) (e10))) = (h4 (op1 (e11) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H18a]. % 19.63/19.85 cut (((h4 (op1 (e11) (e10))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H18b]. % 19.63/19.85 congruence. % 19.63/19.85 cut (((op1 (e11) (e10)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H18c]. % 19.63/19.85 congruence. % 19.63/19.85 exact (zenon_H18c zenon_H186). % 19.63/19.85 apply zenon_H18a. apply refl_equal. % 19.63/19.85 apply zenon_H18a. apply refl_equal. % 19.63/19.85 elim (classic ((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10))))); [ zenon_intro zenon_H18d | zenon_intro zenon_H18e ]. % 19.63/19.85 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10)))) = ((op2 (e23) (op2 (e23) (e23))) = (op2 (h4 (e11)) (h4 (e10))))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H187. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H18d. % 19.63/19.85 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H18e]. % 19.63/19.85 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 19.63/19.85 congruence. % 19.63/19.85 cut (((op2 (e21) (e20)) = (e20)) = ((op2 (h4 (e11)) (h4 (e10))) = (op2 (e23) (op2 (e23) (e23))))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H18f. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H183. % 19.63/19.85 cut (((e20) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H124]. % 19.63/19.85 cut (((op2 (e21) (e20)) = (op2 (h4 (e11)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H190]. % 19.63/19.85 congruence. % 19.63/19.85 elim (classic ((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10))))); [ zenon_intro zenon_H18d | zenon_intro zenon_H18e ]. % 19.63/19.85 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10)))) = ((op2 (e21) (e20)) = (op2 (h4 (e11)) (h4 (e10))))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H190. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H18d. % 19.63/19.85 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H18e]. % 19.63/19.85 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H191]. % 19.63/19.85 congruence. % 19.63/19.85 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_Hc1]. % 19.63/19.85 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H153]. % 19.63/19.85 congruence. % 19.63/19.85 apply (zenon_L97_); trivial. % 19.63/19.85 apply (zenon_L49_); trivial. % 19.63/19.85 apply zenon_H18e. apply refl_equal. % 19.63/19.85 apply zenon_H18e. apply refl_equal. % 19.63/19.85 exact (zenon_H124 zenon_H2e). % 19.63/19.85 apply zenon_H18e. apply refl_equal. % 19.63/19.85 apply zenon_H18e. apply refl_equal. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H157 | zenon_intro zenon_H162 ]. % 19.63/19.85 apply (zenon_L98_); trivial. % 19.63/19.85 apply (zenon_L99_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H169 | zenon_intro zenon_H176 ]. % 19.63/19.85 apply (zenon_L100_); trivial. % 19.63/19.85 apply (zenon_L101_); trivial. % 19.63/19.85 apply (zenon_L66_); trivial. % 19.63/19.85 apply (zenon_L65_); trivial. % 19.63/19.85 apply (zenon_L65_); trivial. % 19.63/19.85 (* end of lemma zenon_L102_ *) % 19.63/19.85 assert (zenon_L103_ : ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e11) (e10))) = (op2 (h4 (e11)) (h4 (e10))))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e22) (e23)) = (e22))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e21)) = (e22))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H10b zenon_H180 zenon_H17f zenon_H13 zenon_H17e zenon_H161 zenon_H156 zenon_H155 zenon_Hfc zenon_H2b zenon_Hc2 zenon_H2e zenon_H17d zenon_H167 zenon_H16c zenon_H16b zenon_H16a zenon_H168 zenon_H175 zenon_H17c zenon_H17b zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H56 | zenon_intro zenon_H56 ]. % 19.63/19.85 apply (zenon_L102_); trivial. % 19.63/19.85 apply (zenon_L102_); trivial. % 19.63/19.85 (* end of lemma zenon_L103_ *) % 19.63/19.85 assert (zenon_L104_ : ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e23))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> (~((op2 (e20) (e20)) = (e22))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e22))) -> (~((op2 (e22) (e21)) = (e22))) -> (~((op2 (e22) (e22)) = (e22))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((h4 (op1 (e11) (e10))) = (op2 (h4 (e11)) (h4 (e10))))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H192 zenon_H50 zenon_H4c zenon_H4b zenon_H4f zenon_H3d zenon_H2f zenon_H2d zenon_H1d zenon_H28 zenon_H47 zenon_H3e zenon_H41 zenon_H48 zenon_H51 zenon_H40 zenon_H54 zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H17b zenon_H17c zenon_H175 zenon_H168 zenon_H16a zenon_H16b zenon_H167 zenon_H17d zenon_H2e zenon_Hc2 zenon_H2b zenon_Hfc zenon_H155 zenon_H156 zenon_H161 zenon_H17e zenon_H13 zenon_H17f zenon_H180 zenon_H10b. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H16c | zenon_intro zenon_H32 ]. % 19.63/19.85 apply (zenon_L103_); trivial. % 19.63/19.85 apply (zenon_L69_); trivial. % 19.63/19.85 (* end of lemma zenon_L104_ *) % 19.63/19.85 assert (zenon_L105_ : ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e11) (e10))) = (op2 (h4 (e11)) (h4 (e10))))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e22))) -> (~((op2 (e20) (e20)) = (e21))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H193 zenon_H10b zenon_H180 zenon_H17f zenon_H13 zenon_H17e zenon_H161 zenon_H156 zenon_H155 zenon_Hfc zenon_H2b zenon_Hc2 zenon_H2e zenon_H17d zenon_H167 zenon_H16b zenon_H168 zenon_H175 zenon_H17c zenon_H17b zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9 zenon_H3e zenon_H40 zenon_H3f zenon_H194. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H16a | zenon_intro zenon_H2c ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H16c | zenon_intro zenon_H41 ]. % 19.63/19.85 apply (zenon_L103_); trivial. % 19.63/19.85 apply (zenon_L8_); trivial. % 19.63/19.85 apply zenon_H2c. apply sym_equal. exact zenon_H2b. % 19.63/19.85 (* end of lemma zenon_L105_ *) % 19.63/19.85 assert (zenon_L106_ : ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e11) (e10))) = (op2 (h4 (e11)) (h4 (e10))))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> (~((op2 (e20) (e20)) = (e21))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e22) (e22)) = (e22)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e20) (e20)) = (e22)))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H10d zenon_H54 zenon_H53 zenon_H52 zenon_H51 zenon_H48 zenon_H3e zenon_H47 zenon_H28 zenon_H1d zenon_H2d zenon_H2b zenon_H2e zenon_H2f zenon_H3d zenon_H4f zenon_H4b zenon_H4c zenon_H50 zenon_H13 zenon_H12 zenon_H152 zenon_H193 zenon_H10b zenon_H180 zenon_H17f zenon_H17e zenon_H161 zenon_H156 zenon_H155 zenon_Hfc zenon_Hc2 zenon_H17d zenon_H167 zenon_H168 zenon_H175 zenon_H17c zenon_H17b zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9 zenon_H3f zenon_H194 zenon_H195 zenon_H10e. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H14 | zenon_intro zenon_H2c ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.63/19.85 apply (zenon_L17_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H15 | zenon_intro zenon_H31 ]. % 19.63/19.85 apply (zenon_L78_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H15 | zenon_intro zenon_H16b ]. % 19.63/19.85 apply (zenon_L95_); trivial. % 19.63/19.85 apply (zenon_L105_); trivial. % 19.63/19.85 apply zenon_H2c. apply sym_equal. exact zenon_H2b. % 19.63/19.85 (* end of lemma zenon_L106_ *) % 19.63/19.85 assert (zenon_L107_ : ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e20) (e20)) = (e22)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e22) (e22)) = (e22)))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e11) (e10))) = (op2 (h4 (e11)) (h4 (e10))))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H10c zenon_H54 zenon_H53 zenon_H52 zenon_H51 zenon_H48 zenon_H3e zenon_H47 zenon_H28 zenon_H1d zenon_H2d zenon_H2b zenon_H2e zenon_H2f zenon_H3d zenon_H4f zenon_H4b zenon_H4c zenon_H50 zenon_H13 zenon_H12 zenon_H196 zenon_H10e zenon_H195 zenon_H193 zenon_H152 zenon_H10d zenon_H10b zenon_H180 zenon_H17f zenon_H17e zenon_H161 zenon_H156 zenon_H155 zenon_Hfc zenon_Hc2 zenon_H17d zenon_H167 zenon_H168 zenon_H175 zenon_H17c zenon_H17b zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9 zenon_H192 zenon_H194. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3f ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.63/19.85 apply (zenon_L17_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H15 | zenon_intro zenon_H31 ]. % 19.63/19.85 apply (zenon_L78_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H15 | zenon_intro zenon_H16b ]. % 19.63/19.85 apply (zenon_L95_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H196); [ zenon_intro zenon_H16a | zenon_intro zenon_H3f ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H16c | zenon_intro zenon_H41 ]. % 19.63/19.85 apply (zenon_L103_); trivial. % 19.63/19.85 apply (zenon_L104_); trivial. % 19.63/19.85 apply (zenon_L106_); trivial. % 19.63/19.85 apply (zenon_L106_); trivial. % 19.63/19.85 (* end of lemma zenon_L107_ *) % 19.63/19.85 assert (zenon_L108_ : ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((op2 (e21) (e21)) = (e22))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (~((op2 (e22) (e20)) = (e22))) -> (~((op2 (e22) (e21)) = (e22))) -> (~((op2 (e22) (e22)) = (e22))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H192 zenon_H2f zenon_H2e zenon_H2b zenon_H30 zenon_H31 zenon_H2d zenon_H170 zenon_H16a zenon_H16b zenon_H167. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H16c | zenon_intro zenon_H32 ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_H16e | zenon_intro zenon_H16d ]. % 19.63/19.85 exact (zenon_H170 zenon_H16e). % 19.63/19.85 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H172 | zenon_intro zenon_H171 ]. % 19.63/19.85 exact (zenon_H16a zenon_H172). % 19.63/19.85 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H174 | zenon_intro zenon_H173 ]. % 19.63/19.85 exact (zenon_H16b zenon_H174). % 19.63/19.85 exact (zenon_H16c zenon_H173). % 19.63/19.85 apply (zenon_L6_); trivial. % 19.63/19.85 (* end of lemma zenon_L108_ *) % 19.63/19.85 assert (zenon_L109_ : ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e20)) = (e22))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (~((op2 (e21) (e21)) = (e22))) -> (~((op2 (e21) (e21)) = (e21))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H193 zenon_H167 zenon_H16b zenon_H170 zenon_H2d zenon_H31 zenon_H30 zenon_H2b zenon_H2e zenon_H2f zenon_H192. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H16a | zenon_intro zenon_H2c ]. % 19.63/19.85 apply (zenon_L108_); trivial. % 19.63/19.85 apply zenon_H2c. apply sym_equal. exact zenon_H2b. % 19.63/19.85 (* end of lemma zenon_L109_ *) % 19.63/19.85 assert (zenon_L110_ : ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e12)) = (e12))) -> (~((op1 (e12) (e10)) = (e12))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e11) (e11)) = (e12))) -> (~((op1 (e11) (e11)) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H17b zenon_Hbe zenon_H55 zenon_H56 zenon_Hbc zenon_Hb5 zenon_H60 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb8 zenon_Hbb zenon_Hbf zenon_Hf7 zenon_Hf3 zenon_He8 zenon_H6b zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H155 zenon_Heb zenon_H15d zenon_H70 zenon_H74 zenon_H73 zenon_H6e zenon_H71 zenon_H72 zenon_H17f. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H17b); [ zenon_intro zenon_H158 | zenon_intro zenon_Haa ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H159 | zenon_intro zenon_H75 ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H15b | zenon_intro zenon_H15a ]. % 19.63/19.85 exact (zenon_H15d zenon_H15b). % 19.63/19.85 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 19.63/19.85 exact (zenon_H158 zenon_H15f). % 19.63/19.85 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H160 ]. % 19.63/19.85 exact (zenon_Heb zenon_Hf2). % 19.63/19.85 exact (zenon_H159 zenon_H160). % 19.63/19.85 apply (zenon_L23_); trivial. % 19.63/19.85 apply (zenon_L64_); trivial. % 19.63/19.85 (* end of lemma zenon_L110_ *) % 19.63/19.85 assert (zenon_L111_ : (~((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))) -> ((h4 (e13)) = (e23)) -> ((op1 (e11) (e11)) = (e13)) -> ((op2 (e21) (e21)) = (e23)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H197 zenon_H12b zenon_H7e zenon_H3b zenon_Hfc zenon_H2b. % 19.63/19.85 cut (((h4 (e13)) = (e23)) = ((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H197. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H12b. % 19.63/19.85 cut (((e23) = (op2 (h4 (e11)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H198]. % 19.63/19.85 cut (((h4 (e13)) = (h4 (op1 (e11) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 19.63/19.85 congruence. % 19.63/19.85 elim (classic ((h4 (op1 (e11) (e11))) = (h4 (op1 (e11) (e11))))); [ zenon_intro zenon_H19a | zenon_intro zenon_H19b ]. % 19.63/19.85 cut (((h4 (op1 (e11) (e11))) = (h4 (op1 (e11) (e11)))) = ((h4 (e13)) = (h4 (op1 (e11) (e11))))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H199. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H19a. % 19.63/19.85 cut (((h4 (op1 (e11) (e11))) = (h4 (op1 (e11) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H19b]. % 19.63/19.85 cut (((h4 (op1 (e11) (e11))) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 19.63/19.85 congruence. % 19.63/19.85 cut (((op1 (e11) (e11)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H75]. % 19.63/19.85 congruence. % 19.63/19.85 exact (zenon_H75 zenon_H7e). % 19.63/19.85 apply zenon_H19b. apply refl_equal. % 19.63/19.85 apply zenon_H19b. apply refl_equal. % 19.63/19.85 elim (classic ((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11))))); [ zenon_intro zenon_H19d | zenon_intro zenon_H19e ]. % 19.63/19.85 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11)))) = ((e23) = (op2 (h4 (e11)) (h4 (e11))))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H198. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H19d. % 19.63/19.85 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H19e]. % 19.63/19.85 cut (((op2 (h4 (e11)) (h4 (e11))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 19.63/19.85 congruence. % 19.63/19.85 cut (((op2 (e21) (e21)) = (e23)) = ((op2 (h4 (e11)) (h4 (e11))) = (e23))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H19f. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H3b. % 19.63/19.85 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 19.63/19.85 cut (((op2 (e21) (e21)) = (op2 (h4 (e11)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 19.63/19.85 congruence. % 19.63/19.85 elim (classic ((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11))))); [ zenon_intro zenon_H19d | zenon_intro zenon_H19e ]. % 19.63/19.85 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11)))) = ((op2 (e21) (e21)) = (op2 (h4 (e11)) (h4 (e11))))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H1a0. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H19d. % 19.63/19.85 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H19e]. % 19.63/19.85 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 19.63/19.85 congruence. % 19.63/19.85 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H153]. % 19.63/19.85 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H153]. % 19.63/19.85 congruence. % 19.63/19.85 apply (zenon_L97_); trivial. % 19.63/19.85 apply (zenon_L97_); trivial. % 19.63/19.85 apply zenon_H19e. apply refl_equal. % 19.63/19.85 apply zenon_H19e. apply refl_equal. % 19.63/19.85 apply zenon_H29. apply refl_equal. % 19.63/19.85 apply zenon_H19e. apply refl_equal. % 19.63/19.85 apply zenon_H19e. apply refl_equal. % 19.63/19.85 (* end of lemma zenon_L111_ *) % 19.63/19.85 assert (zenon_L112_ : (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e11) (e11)) = (e10))) -> (~((op1 (e11) (e11)) = (e11))) -> (~((op1 (e11) (e11)) = (e12))) -> (~((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e21) (e21)) = (e23)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H70 zenon_H7b zenon_H73 zenon_H74 zenon_H197 zenon_H12b zenon_H3b zenon_Hfc zenon_H2b. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H70); [ zenon_intro zenon_H77 | zenon_intro zenon_H76 ]. % 19.63/19.85 exact (zenon_H7b zenon_H77). % 19.63/19.85 apply (zenon_or_s _ _ zenon_H76); [ zenon_intro zenon_H7d | zenon_intro zenon_H7c ]. % 19.63/19.85 exact (zenon_H73 zenon_H7d). % 19.63/19.85 apply (zenon_or_s _ _ zenon_H7c); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ]. % 19.63/19.85 exact (zenon_H74 zenon_H7f). % 19.63/19.85 apply (zenon_L111_); trivial. % 19.63/19.85 (* end of lemma zenon_L112_ *) % 19.63/19.85 assert (zenon_L113_ : (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (~((op2 (e21) (e21)) = (e20))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((op2 (e21) (e21)) = (e22))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e11) (e11)) = (e10))) -> (~((op1 (e11) (e11)) = (e11))) -> (~((op1 (e11) (e11)) = (e12))) -> (~((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H2d zenon_H38 zenon_H30 zenon_H31 zenon_H70 zenon_H7b zenon_H73 zenon_H74 zenon_H197 zenon_H12b zenon_Hfc zenon_H2b. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 19.63/19.85 exact (zenon_H38 zenon_H34). % 19.63/19.85 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 19.63/19.85 exact (zenon_H30 zenon_H3a). % 19.63/19.85 apply (zenon_or_s _ _ zenon_H39); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 19.63/19.85 exact (zenon_H31 zenon_H3c). % 19.63/19.85 apply (zenon_L112_); trivial. % 19.63/19.85 (* end of lemma zenon_L113_ *) % 19.63/19.85 assert (zenon_L114_ : ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (~((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))) -> ((h4 (e13)) = (e23)) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (e22))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((op2 (e21) (e21)) = (e20))) -> ((~((op1 (e12) (e10)) = (e12)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> False). % 19.63/19.85 do 0 intro. intros zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H56 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H17b zenon_H155 zenon_H17f zenon_H2d zenon_H197 zenon_H12b zenon_H2b zenon_Hfc zenon_H31 zenon_H30 zenon_H38 zenon_H1a2 zenon_H180. % 19.63/19.85 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H57 | zenon_intro zenon_Haa ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H58 | zenon_intro zenon_H9b ]. % 19.63/19.85 apply (zenon_L45_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H58 | zenon_intro zenon_H74 ]. % 19.63/19.85 apply (zenon_L48_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H58 | zenon_intro zenon_Heb ]. % 19.63/19.85 apply (zenon_L96_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H73 | zenon_intro zenon_Haa ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H15d | zenon_intro zenon_H7b ]. % 19.63/19.85 apply (zenon_L110_); trivial. % 19.63/19.85 apply (zenon_L113_); trivial. % 19.63/19.85 apply (zenon_L43_); trivial. % 19.63/19.85 apply (zenon_L65_); trivial. % 19.63/19.85 (* end of lemma zenon_L114_ *) % 19.63/19.85 assert (zenon_L115_ : ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e12) (e10)) = (e12)))\/(~((op1 (e11) (e11)) = (e10)))) -> (~((op2 (e21) (e21)) = (e20))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((op2 (e21) (e21)) = (e22))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H10b zenon_H180 zenon_H1a2 zenon_H38 zenon_H30 zenon_H31 zenon_Hfc zenon_H2b zenon_H12b zenon_H197 zenon_H2d zenon_H17f zenon_H155 zenon_H17b zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H56 | zenon_intro zenon_H56 ]. % 19.63/19.85 apply (zenon_L114_); trivial. % 19.63/19.85 apply (zenon_L114_); trivial. % 19.63/19.85 (* end of lemma zenon_L115_ *) % 19.63/19.85 assert (zenon_L116_ : ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e22) (e22)) = (e22)))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (e21))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e12) (e10)) = (e12)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op2 (e22) (e20)) = (e22)))\/(~((op2 (e21) (e21)) = (e20)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> (~((op2 (e20) (e21)) = (e20))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (e22))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H195 zenon_H193 zenon_H167 zenon_H30 zenon_H192 zenon_H10b zenon_H180 zenon_H1a2 zenon_Hfc zenon_H12b zenon_H197 zenon_H17f zenon_H155 zenon_H17b zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9 zenon_H1a3 zenon_H12 zenon_H14 zenon_H13 zenon_H54 zenon_H53 zenon_H50 zenon_H4b zenon_H4c zenon_H48 zenon_H3e zenon_H1d zenon_H28 zenon_H47 zenon_H52 zenon_H4f zenon_H2f zenon_H2e zenon_H2b zenon_H31 zenon_H2d. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H15 | zenon_intro zenon_H16b ]. % 19.63/19.85 apply (zenon_L95_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H170 | zenon_intro zenon_H38 ]. % 19.63/19.85 apply (zenon_L109_); trivial. % 19.63/19.85 apply (zenon_L115_); trivial. % 19.63/19.85 (* end of lemma zenon_L116_ *) % 19.63/19.85 assert (zenon_L117_ : ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e22) (e22)) = (e22)))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e12) (e10)) = (e12)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op2 (e22) (e20)) = (e22)))\/(~((op2 (e21) (e21)) = (e20)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> (~((op2 (e20) (e21)) = (e20))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> (~((op2 (e20) (e20)) = (e22))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H152 zenon_H195 zenon_H193 zenon_H167 zenon_H192 zenon_H10b zenon_H180 zenon_H1a2 zenon_Hfc zenon_H12b zenon_H197 zenon_H17f zenon_H155 zenon_H17b zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9 zenon_H1a3 zenon_H12 zenon_H14 zenon_H13 zenon_H52 zenon_H50 zenon_H4c zenon_H4b zenon_H4f zenon_H3d zenon_H2f zenon_H2e zenon_H2b zenon_H2d zenon_H1d zenon_H28 zenon_H47 zenon_H3e zenon_H48 zenon_H51 zenon_H40 zenon_H54 zenon_H53. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H15 | zenon_intro zenon_H31 ]. % 19.63/19.85 apply (zenon_L78_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H30 | zenon_intro zenon_H30 ]. % 19.63/19.85 apply (zenon_L116_); trivial. % 19.63/19.85 apply (zenon_L116_); trivial. % 19.63/19.85 (* end of lemma zenon_L117_ *) % 19.63/19.85 assert (zenon_L118_ : ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e22) (e22)) = (e22)))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e12) (e10)) = (e12)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op2 (e22) (e20)) = (e22)))\/(~((op2 (e21) (e21)) = (e20)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e20) (e20)) = (e22)))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H10c zenon_H10d zenon_H127 zenon_H54 zenon_H53 zenon_H52 zenon_H51 zenon_H48 zenon_H3e zenon_H47 zenon_H28 zenon_H1d zenon_H2d zenon_H2b zenon_H2e zenon_H2f zenon_H3d zenon_H4f zenon_H4b zenon_H4c zenon_H50 zenon_H13 zenon_H12 zenon_H152 zenon_H195 zenon_H193 zenon_H167 zenon_H192 zenon_H10b zenon_H180 zenon_H1a2 zenon_Hfc zenon_H12b zenon_H197 zenon_H17f zenon_H155 zenon_H17b zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9 zenon_H1a3 zenon_H10e. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3f ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.63/19.85 apply (zenon_L17_); trivial. % 19.63/19.85 apply (zenon_L117_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H14 | zenon_intro zenon_H30 ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.63/19.85 apply (zenon_L16_); trivial. % 19.63/19.85 apply (zenon_L117_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H14 | zenon_intro zenon_H2c ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.63/19.85 apply (zenon_L17_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H15 | zenon_intro zenon_H31 ]. % 19.63/19.85 apply (zenon_L78_); trivial. % 19.63/19.85 apply (zenon_L116_); trivial. % 19.63/19.85 apply zenon_H2c. apply sym_equal. exact zenon_H2b. % 19.63/19.85 (* end of lemma zenon_L118_ *) % 19.63/19.85 assert (zenon_L119_ : ((op2 (e21) (e20)) = (e20)) -> ((op2 (e21) (e20)) = (e21)) -> (~((e20) = (e21))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H183 zenon_H1a4 zenon_Hdf. % 19.63/19.85 elim (classic ((e21) = (e21))); [ zenon_intro zenon_He0 | zenon_intro zenon_Hc4 ]. % 19.63/19.85 cut (((e21) = (e21)) = ((e20) = (e21))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_Hdf. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_He0. % 19.63/19.85 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_Hc4]. % 19.63/19.85 cut (((e21) = (e20))); [idtac | apply NNPP; zenon_intro zenon_He1]. % 19.63/19.85 congruence. % 19.63/19.85 cut (((op2 (e21) (e20)) = (e20)) = ((e21) = (e20))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_He1. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H183. % 19.63/19.85 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_Hdd]. % 19.63/19.85 cut (((op2 (e21) (e20)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1a5]. % 19.63/19.85 congruence. % 19.63/19.85 exact (zenon_H1a5 zenon_H1a4). % 19.63/19.85 apply zenon_Hdd. apply refl_equal. % 19.63/19.85 apply zenon_Hc4. apply refl_equal. % 19.63/19.85 apply zenon_Hc4. apply refl_equal. % 19.63/19.85 (* end of lemma zenon_L119_ *) % 19.63/19.85 assert (zenon_L120_ : ((e11) = (op1 (e13) (e13))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e13) (e13)) = (op1 (e10) (e10)))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H6e zenon_Had zenon_H1a6. % 19.63/19.85 elim (classic ((op1 (e10) (e10)) = (op1 (e10) (e10)))); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H1a8 ]. % 19.63/19.85 cut (((op1 (e10) (e10)) = (op1 (e10) (e10))) = ((op1 (e13) (e13)) = (op1 (e10) (e10)))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H1a6. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H1a7. % 19.63/19.85 cut (((op1 (e10) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H1a8]. % 19.63/19.85 cut (((op1 (e10) (e10)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 19.63/19.85 congruence. % 19.63/19.85 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e10) (e10)) = (op1 (e13) (e13)))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H1a9. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H6e. % 19.63/19.85 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 19.63/19.85 cut (((e11) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H1aa]. % 19.63/19.85 congruence. % 19.63/19.85 elim (classic ((op1 (e10) (e10)) = (op1 (e10) (e10)))); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H1a8 ]. % 19.63/19.85 cut (((op1 (e10) (e10)) = (op1 (e10) (e10))) = ((e11) = (op1 (e10) (e10)))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H1aa. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H1a7. % 19.63/19.85 cut (((op1 (e10) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H1a8]. % 19.63/19.85 cut (((op1 (e10) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 19.63/19.85 congruence. % 19.63/19.85 exact (zenon_Haa zenon_Had). % 19.63/19.85 apply zenon_H1a8. apply refl_equal. % 19.63/19.85 apply zenon_H1a8. apply refl_equal. % 19.63/19.85 apply zenon_Ha7. apply refl_equal. % 19.63/19.85 apply zenon_H1a8. apply refl_equal. % 19.63/19.85 apply zenon_H1a8. apply refl_equal. % 19.63/19.85 (* end of lemma zenon_L120_ *) % 19.63/19.85 assert (zenon_L121_ : ((op1 (e11) (e10)) = (e11)) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H1ab zenon_H6e zenon_Had zenon_H1ac. % 19.63/19.85 elim (classic ((op1 (e11) (e10)) = (op1 (e11) (e10)))); [ zenon_intro zenon_H1ad | zenon_intro zenon_H1ae ]. % 19.63/19.85 cut (((op1 (e11) (e10)) = (op1 (e11) (e10))) = ((op1 (e10) (e10)) = (op1 (e11) (e10)))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H1ac. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H1ad. % 19.63/19.85 cut (((op1 (e11) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H1ae]. % 19.63/19.85 cut (((op1 (e11) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H1af]. % 19.63/19.85 congruence. % 19.63/19.85 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e11) (e10)) = (op1 (e10) (e10)))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H1af. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H6e. % 19.63/19.85 cut (((op1 (e13) (e13)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H1a6]. % 19.63/19.85 cut (((e11) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H1b0]. % 19.63/19.85 congruence. % 19.63/19.85 elim (classic ((op1 (e11) (e10)) = (op1 (e11) (e10)))); [ zenon_intro zenon_H1ad | zenon_intro zenon_H1ae ]. % 19.63/19.85 cut (((op1 (e11) (e10)) = (op1 (e11) (e10))) = ((e11) = (op1 (e11) (e10)))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H1b0. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H1ad. % 19.63/19.85 cut (((op1 (e11) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H1ae]. % 19.63/19.85 cut (((op1 (e11) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H1b1]. % 19.63/19.85 congruence. % 19.63/19.85 exact (zenon_H1b1 zenon_H1ab). % 19.63/19.85 apply zenon_H1ae. apply refl_equal. % 19.63/19.85 apply zenon_H1ae. apply refl_equal. % 19.63/19.85 apply (zenon_L120_); trivial. % 19.63/19.85 apply zenon_H1ae. apply refl_equal. % 19.63/19.85 apply zenon_H1ae. apply refl_equal. % 19.63/19.85 (* end of lemma zenon_L121_ *) % 19.63/19.85 assert (zenon_L122_ : ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e22))) -> (~((op2 (e22) (e21)) = (e22))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e23)) = (e22))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((e20) = (e21))) -> (~((op2 (e21) (e21)) = (e21))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op2 (e21) (e23)) = (e21))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op1 (e11) (e13)) = (e11)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> False). % 19.63/19.85 do 0 intro. intros zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H56 zenon_H55 zenon_Hfa zenon_H17c zenon_H2e zenon_H175 zenon_H168 zenon_H16a zenon_H16b zenon_H16c zenon_H167 zenon_Hdf zenon_H30 zenon_H1b2 zenon_Hfc zenon_H2b zenon_H10f zenon_H4c zenon_H1b3 zenon_H1ac zenon_H1b4 zenon_H1b5 zenon_H13 zenon_H1b6 zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8. % 19.63/19.85 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H57 | zenon_intro zenon_Haa ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H58 | zenon_intro zenon_H9b ]. % 19.63/19.85 apply (zenon_L45_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H58 | zenon_intro zenon_H74 ]. % 19.63/19.85 apply (zenon_L48_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H59 | zenon_intro zenon_H75 ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H73 | zenon_intro zenon_Haa ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H75 ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H17c); [ zenon_intro zenon_H18 | zenon_intro zenon_H181 ]. % 19.63/19.85 exact (zenon_H13 zenon_H18). % 19.63/19.85 apply (zenon_or_s _ _ zenon_H181); [ zenon_intro zenon_H183 | zenon_intro zenon_H182 ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1b8 ]. % 19.63/19.85 apply (zenon_L119_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H3a | zenon_intro zenon_H1b9 ]. % 19.63/19.85 exact (zenon_H30 zenon_H3a). % 19.63/19.85 apply (zenon_or_s _ _ zenon_H1b9); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1ba ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H55); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 19.63/19.85 exact (zenon_H56 zenon_H5b). % 19.63/19.85 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H5d | zenon_intro zenon_H5c ]. % 19.63/19.85 exact (zenon_H57 zenon_H5d). % 19.63/19.85 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_Had | zenon_intro zenon_Hac ]. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1bc ]. % 19.63/19.85 apply (zenon_L121_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H7d | zenon_intro zenon_H1bd ]. % 19.63/19.85 exact (zenon_H73 zenon_H7d). % 19.63/19.85 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H1bf | zenon_intro zenon_H1be ]. % 19.63/19.85 cut (((h4 (e11)) = (op2 (e23) (e23))) = ((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H1b3. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_Hfc. % 19.63/19.85 cut (((op2 (e23) (e23)) = (op2 (h4 (e11)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H1c0]. % 19.63/19.85 cut (((h4 (e11)) = (h4 (op1 (e11) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H1c1]. % 19.63/19.85 congruence. % 19.63/19.85 elim (classic ((h4 (op1 (e11) (e12))) = (h4 (op1 (e11) (e12))))); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H1c3 ]. % 19.63/19.85 cut (((h4 (op1 (e11) (e12))) = (h4 (op1 (e11) (e12)))) = ((h4 (e11)) = (h4 (op1 (e11) (e12))))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H1c1. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H1c2. % 19.63/19.85 cut (((h4 (op1 (e11) (e12))) = (h4 (op1 (e11) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H1c3]. % 19.63/19.85 cut (((h4 (op1 (e11) (e12))) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H1c4]. % 19.63/19.85 congruence. % 19.63/19.85 cut (((op1 (e11) (e12)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H1c5]. % 19.63/19.85 congruence. % 19.63/19.85 exact (zenon_H1c5 zenon_H1bf). % 19.63/19.85 apply zenon_H1c3. apply refl_equal. % 19.63/19.85 apply zenon_H1c3. apply refl_equal. % 19.63/19.85 elim (classic ((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12))))); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H1c7 ]. % 19.63/19.85 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12)))) = ((op2 (e23) (e23)) = (op2 (h4 (e11)) (h4 (e12))))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H1c0. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H1c6. % 19.63/19.85 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H1c7]. % 19.63/19.85 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1c8]. % 19.63/19.85 congruence. % 19.63/19.85 cut (((op2 (e21) (e22)) = (e21)) = ((op2 (h4 (e11)) (h4 (e12))) = (op2 (e23) (e23)))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H1c8. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H1bb. % 19.63/19.85 cut (((e21) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 19.63/19.85 cut (((op2 (e21) (e22)) = (op2 (h4 (e11)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H1c9]. % 19.63/19.85 congruence. % 19.63/19.85 elim (classic ((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12))))); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H1c7 ]. % 19.63/19.85 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12)))) = ((op2 (e21) (e22)) = (op2 (h4 (e11)) (h4 (e12))))). % 19.63/19.85 intro zenon_D_pnotp. % 19.63/19.85 apply zenon_H1c9. % 19.63/19.85 rewrite <- zenon_D_pnotp. % 19.63/19.85 exact zenon_H1c6. % 19.63/19.85 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H1c7]. % 19.63/19.85 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1ca]. % 19.63/19.85 congruence. % 19.63/19.85 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H118]. % 19.63/19.85 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H153]. % 19.63/19.85 congruence. % 19.63/19.85 apply (zenon_L97_); trivial. % 19.63/19.85 apply (zenon_L73_); trivial. % 19.63/19.85 apply zenon_H1c7. apply refl_equal. % 19.63/19.85 apply zenon_H1c7. apply refl_equal. % 19.63/19.85 exact (zenon_H107 zenon_H2b). % 19.63/19.85 apply zenon_H1c7. apply refl_equal. % 19.63/19.85 apply zenon_H1c7. apply refl_equal. % 19.63/19.85 exact (zenon_H1b7 zenon_H1be). % 19.63/19.85 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H82 | zenon_intro zenon_Hae ]. % 19.63/19.85 apply (zenon_L30_); trivial. % 19.63/19.85 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_Ha0 | zenon_intro zenon_Ha6 ]. % 19.63/19.85 apply (zenon_L32_); trivial. % 19.63/19.85 apply (zenon_L33_); trivial. % 19.63/19.85 exact (zenon_H59 zenon_H5e). % 19.63/19.85 exact (zenon_H1b4 zenon_H1ba). % 19.63/19.85 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H169 | zenon_intro zenon_H176 ]. % 19.63/19.85 apply (zenon_L100_); trivial. % 19.63/19.85 apply (zenon_L101_); trivial. % 19.63/19.85 apply (zenon_L23_); trivial. % 19.63/19.85 apply (zenon_L34_); trivial. % 19.63/19.85 apply (zenon_L66_); trivial. % 19.63/19.85 apply (zenon_L65_); trivial. % 19.63/19.85 (* end of lemma zenon_L122_ *) % 19.63/19.85 assert (zenon_L123_ : ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e11) (e13)) = (e11)))\/(~((op1 (e11) (e11)) = (e13)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> (~((op2 (e21) (e23)) = (e21))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((e20) = (e21))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e22) (e23)) = (e22))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e21)) = (e22))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H10b zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H1b6 zenon_H13 zenon_H1b5 zenon_H1b4 zenon_H1ac zenon_H1b3 zenon_H4c zenon_H10f zenon_H2b zenon_Hfc zenon_H1b2 zenon_H30 zenon_Hdf zenon_H167 zenon_H16c zenon_H16b zenon_H16a zenon_H168 zenon_H175 zenon_H2e zenon_H17c zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H56 | zenon_intro zenon_H56 ]. % 19.63/19.85 apply (zenon_L122_); trivial. % 19.63/19.85 apply (zenon_L122_); trivial. % 19.63/19.85 (* end of lemma zenon_L123_ *) % 19.63/19.85 assert (zenon_L124_ : ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e23))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> (~((op2 (e20) (e20)) = (e22))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e22))) -> (~((op2 (e22) (e21)) = (e22))) -> (~((op2 (e22) (e22)) = (e22))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((e20) = (e21))) -> (~((op2 (e21) (e21)) = (e21))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op2 (e21) (e23)) = (e21))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op1 (e11) (e13)) = (e11)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> False). % 19.63/19.85 do 0 intro. intros zenon_H192 zenon_H50 zenon_H4b zenon_H4f zenon_H3d zenon_H2f zenon_H2d zenon_H1d zenon_H28 zenon_H47 zenon_H3e zenon_H41 zenon_H48 zenon_H51 zenon_H40 zenon_H54 zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_H17c zenon_H2e zenon_H175 zenon_H168 zenon_H16a zenon_H16b zenon_H167 zenon_Hdf zenon_H30 zenon_H1b2 zenon_Hfc zenon_H2b zenon_H10f zenon_H4c zenon_H1b3 zenon_H1ac zenon_H1b4 zenon_H1b5 zenon_H13 zenon_H1b6 zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_H10b. % 19.63/19.85 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H16c | zenon_intro zenon_H32 ]. % 19.63/19.85 apply (zenon_L123_); trivial. % 19.63/19.85 apply (zenon_L69_); trivial. % 19.63/19.85 (* end of lemma zenon_L124_ *) % 19.63/19.85 assert (zenon_L125_ : ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e11) (e13)) = (e11)))\/(~((op1 (e11) (e11)) = (e13)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> (~((op2 (e21) (e23)) = (e21))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((e20) = (e21))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e22))) -> (~((op2 (e20) (e20)) = (e21))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> False). % 19.63/19.86 do 0 intro. intros zenon_H193 zenon_H10b zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H1b6 zenon_H13 zenon_H1b5 zenon_H1b4 zenon_H1ac zenon_H1b3 zenon_H4c zenon_H10f zenon_H2b zenon_Hfc zenon_H1b2 zenon_H30 zenon_Hdf zenon_H167 zenon_H16b zenon_H168 zenon_H175 zenon_H2e zenon_H17c zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9 zenon_H3e zenon_H40 zenon_H3f zenon_H194. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H16a | zenon_intro zenon_H2c ]. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H16c | zenon_intro zenon_H41 ]. % 19.63/19.86 apply (zenon_L123_); trivial. % 19.63/19.86 apply (zenon_L8_); trivial. % 19.63/19.86 apply zenon_H2c. apply sym_equal. exact zenon_H2b. % 19.63/19.86 (* end of lemma zenon_L125_ *) % 19.63/19.86 assert (zenon_L126_ : ((~((op2 (e21) (e23)) = (e21)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e23))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> (~((op2 (e20) (e20)) = (e22))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e22))) -> (~((op2 (e22) (e22)) = (e22))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((e20) = (e21))) -> (~((op2 (e21) (e21)) = (e21))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op1 (e11) (e13)) = (e11)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e20) (e20)) = (e21)))) -> False). % 19.63/19.86 do 0 intro. intros zenon_H1cb zenon_H192 zenon_H50 zenon_H4b zenon_H4f zenon_H3d zenon_H2f zenon_H2d zenon_H1d zenon_H28 zenon_H47 zenon_H3e zenon_H41 zenon_H48 zenon_H51 zenon_H40 zenon_H54 zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_H17c zenon_H2e zenon_H175 zenon_H168 zenon_H16b zenon_H167 zenon_Hdf zenon_H30 zenon_H1b2 zenon_Hfc zenon_H2b zenon_H10f zenon_H4c zenon_H1b3 zenon_H1ac zenon_H1b5 zenon_H13 zenon_H1b6 zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_H10b zenon_H193 zenon_H194 zenon_H196. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H32 ]. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H196); [ zenon_intro zenon_H16a | zenon_intro zenon_H3f ]. % 19.63/19.86 apply (zenon_L124_); trivial. % 19.63/19.86 apply (zenon_L125_); trivial. % 19.63/19.86 apply (zenon_L13_); trivial. % 19.63/19.86 (* end of lemma zenon_L126_ *) % 19.63/19.86 assert (zenon_L127_ : ((~((op2 (e21) (e23)) = (e21)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> (~((op2 (e20) (e20)) = (e21))) -> (~((op2 (e20) (e20)) = (e22))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e22))) -> (~((op2 (e22) (e22)) = (e22))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((e20) = (e21))) -> (~((op2 (e21) (e21)) = (e21))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op1 (e11) (e13)) = (e11)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> False). % 19.63/19.86 do 0 intro. intros zenon_H1cc zenon_H194 zenon_H3f zenon_H40 zenon_H3e zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_H17c zenon_H2e zenon_H175 zenon_H168 zenon_H16b zenon_H167 zenon_Hdf zenon_H30 zenon_H1b2 zenon_Hfc zenon_H2b zenon_H10f zenon_H4c zenon_H1b3 zenon_H1ac zenon_H1b5 zenon_H13 zenon_H1b6 zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_H10b zenon_H193. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H41 ]. % 19.63/19.86 apply (zenon_L125_); trivial. % 19.63/19.86 apply (zenon_L8_); trivial. % 19.63/19.86 (* end of lemma zenon_L127_ *) % 19.63/19.86 assert (zenon_L128_ : ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e11) (e13)) = (e11)))\/(~((op1 (e11) (e11)) = (e13)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((e20) = (e21))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e22))) -> (~((op2 (e20) (e20)) = (e21))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e21) (e23)) = (e21)))\/(~((op2 (e20) (e20)) = (e23)))) -> False). % 19.63/19.86 do 0 intro. intros zenon_H4f zenon_H193 zenon_H10b zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H1b6 zenon_H13 zenon_H1b5 zenon_H1ac zenon_H1b3 zenon_H4c zenon_H10f zenon_H2b zenon_Hfc zenon_H1b2 zenon_Hdf zenon_H167 zenon_H16b zenon_H168 zenon_H175 zenon_H2e zenon_H17c zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9 zenon_H3e zenon_H40 zenon_H3f zenon_H194 zenon_H1cc. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H30 | zenon_intro zenon_H30 ]. % 19.63/19.86 apply (zenon_L127_); trivial. % 19.63/19.86 apply (zenon_L127_); trivial. % 19.63/19.86 (* end of lemma zenon_L128_ *) % 19.63/19.86 assert (zenon_L129_ : ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e11) (e13)) = (e11)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((e20) = (e21))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e21) (e23)) = (e21)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e21) (e23)) = (e21)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e22) (e22)) = (e22)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e20) (e20)) = (e22)))) -> False). % 19.63/19.86 do 0 intro. intros zenon_H10c zenon_H10d zenon_H127 zenon_H54 zenon_H53 zenon_H52 zenon_H51 zenon_H48 zenon_H3e zenon_H47 zenon_H28 zenon_H1d zenon_H2d zenon_H2b zenon_H2e zenon_H2f zenon_H3d zenon_H4f zenon_H4b zenon_H4c zenon_H50 zenon_H13 zenon_H12 zenon_H152 zenon_H196 zenon_H193 zenon_H10b zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H1b6 zenon_H1b5 zenon_H1ac zenon_H1b3 zenon_H10f zenon_Hfc zenon_H1b2 zenon_Hdf zenon_H167 zenon_H168 zenon_H175 zenon_H17c zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9 zenon_H192 zenon_H194 zenon_H1cb zenon_H1cc zenon_H195 zenon_H10e. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3f ]. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.63/19.86 apply (zenon_L17_); trivial. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H15 | zenon_intro zenon_H31 ]. % 19.63/19.86 apply (zenon_L78_); trivial. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H15 | zenon_intro zenon_H16b ]. % 19.63/19.86 apply (zenon_L95_); trivial. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H30 | zenon_intro zenon_H3f ]. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H41 ]. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H196); [ zenon_intro zenon_H16a | zenon_intro zenon_H3f ]. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H16c | zenon_intro zenon_H41 ]. % 19.63/19.86 apply (zenon_L123_); trivial. % 19.63/19.86 apply (zenon_L124_); trivial. % 19.63/19.86 apply (zenon_L125_); trivial. % 19.63/19.86 apply (zenon_L126_); trivial. % 19.63/19.86 apply (zenon_L128_); trivial. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H14 | zenon_intro zenon_H30 ]. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.63/19.86 apply (zenon_L16_); trivial. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H15 | zenon_intro zenon_H31 ]. % 19.63/19.86 apply (zenon_L78_); trivial. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H15 | zenon_intro zenon_H16b ]. % 19.63/19.86 apply (zenon_L95_); trivial. % 19.63/19.86 apply (zenon_L128_); trivial. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H14 | zenon_intro zenon_H2c ]. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.63/19.86 apply (zenon_L17_); trivial. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H15 | zenon_intro zenon_H31 ]. % 19.63/19.86 apply (zenon_L78_); trivial. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H15 | zenon_intro zenon_H16b ]. % 19.63/19.86 apply (zenon_L95_); trivial. % 19.63/19.86 apply (zenon_L127_); trivial. % 19.63/19.86 apply zenon_H2c. apply sym_equal. exact zenon_H2b. % 19.63/19.86 (* end of lemma zenon_L129_ *) % 19.63/19.86 assert (zenon_L130_ : (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((op1 (e11) (e13)) = (e12)) -> ((op2 (e21) (e23)) = (e22)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> False). % 19.63/19.86 do 0 intro. intros zenon_H1cd zenon_H10f zenon_H1ce zenon_H1cf zenon_H4c zenon_Hfc zenon_H2b zenon_H12b. % 19.63/19.86 cut (((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) = ((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))). % 19.63/19.86 intro zenon_D_pnotp. % 19.63/19.86 apply zenon_H1cd. % 19.63/19.86 rewrite <- zenon_D_pnotp. % 19.63/19.86 exact zenon_H10f. % 19.63/19.86 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23))) = (op2 (h4 (e11)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H1d0]. % 19.63/19.86 cut (((h4 (e12)) = (h4 (op1 (e11) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H1d1]. % 19.63/19.86 congruence. % 19.63/19.86 elim (classic ((h4 (op1 (e11) (e13))) = (h4 (op1 (e11) (e13))))); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H1d3 ]. % 19.63/19.86 cut (((h4 (op1 (e11) (e13))) = (h4 (op1 (e11) (e13)))) = ((h4 (e12)) = (h4 (op1 (e11) (e13))))). % 19.63/19.86 intro zenon_D_pnotp. % 19.63/19.86 apply zenon_H1d1. % 19.63/19.86 rewrite <- zenon_D_pnotp. % 19.63/19.86 exact zenon_H1d2. % 19.63/19.86 cut (((h4 (op1 (e11) (e13))) = (h4 (op1 (e11) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H1d3]. % 19.63/19.86 cut (((h4 (op1 (e11) (e13))) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H1d4]. % 19.63/19.86 congruence. % 19.63/19.86 cut (((op1 (e11) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H1d5]. % 19.63/19.86 congruence. % 19.63/19.86 exact (zenon_H1d5 zenon_H1ce). % 19.63/19.86 apply zenon_H1d3. apply refl_equal. % 19.63/19.86 apply zenon_H1d3. apply refl_equal. % 19.63/19.86 elim (classic ((op2 (h4 (e11)) (h4 (e13))) = (op2 (h4 (e11)) (h4 (e13))))); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H1d7 ]. % 19.63/19.86 cut (((op2 (h4 (e11)) (h4 (e13))) = (op2 (h4 (e11)) (h4 (e13)))) = ((op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23))) = (op2 (h4 (e11)) (h4 (e13))))). % 19.63/19.86 intro zenon_D_pnotp. % 19.63/19.86 apply zenon_H1d0. % 19.63/19.86 rewrite <- zenon_D_pnotp. % 19.63/19.86 exact zenon_H1d6. % 19.63/19.86 cut (((op2 (h4 (e11)) (h4 (e13))) = (op2 (h4 (e11)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H1d7]. % 19.63/19.86 cut (((op2 (h4 (e11)) (h4 (e13))) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H1d8]. % 19.63/19.86 congruence. % 19.63/19.86 cut (((op2 (e21) (e23)) = (e22)) = ((op2 (h4 (e11)) (h4 (e13))) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23))))). % 19.63/19.86 intro zenon_D_pnotp. % 19.63/19.86 apply zenon_H1d8. % 19.63/19.86 rewrite <- zenon_D_pnotp. % 19.63/19.86 exact zenon_H1cf. % 19.63/19.86 cut (((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H1d9]. % 19.63/19.86 cut (((op2 (e21) (e23)) = (op2 (h4 (e11)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 19.63/19.86 congruence. % 19.63/19.86 elim (classic ((op2 (h4 (e11)) (h4 (e13))) = (op2 (h4 (e11)) (h4 (e13))))); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H1d7 ]. % 19.63/19.86 cut (((op2 (h4 (e11)) (h4 (e13))) = (op2 (h4 (e11)) (h4 (e13)))) = ((op2 (e21) (e23)) = (op2 (h4 (e11)) (h4 (e13))))). % 19.63/19.86 intro zenon_D_pnotp. % 19.63/19.86 apply zenon_H1da. % 19.63/19.86 rewrite <- zenon_D_pnotp. % 19.63/19.86 exact zenon_H1d6. % 19.63/19.86 cut (((op2 (h4 (e11)) (h4 (e13))) = (op2 (h4 (e11)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H1d7]. % 19.63/19.86 cut (((op2 (h4 (e11)) (h4 (e13))) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 19.63/19.86 congruence. % 19.63/19.86 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 19.63/19.86 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H153]. % 19.63/19.86 congruence. % 19.63/19.86 apply (zenon_L97_); trivial. % 19.63/19.86 exact (zenon_H137 zenon_H12b). % 19.63/19.86 apply zenon_H1d7. apply refl_equal. % 19.63/19.86 apply zenon_H1d7. apply refl_equal. % 19.63/19.86 exact (zenon_H1d9 zenon_H4c). % 19.63/19.86 apply zenon_H1d7. apply refl_equal. % 19.63/19.86 apply zenon_H1d7. apply refl_equal. % 19.63/19.86 (* end of lemma zenon_L130_ *) % 19.63/19.86 assert (zenon_L131_ : (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> ((h4 (e13)) = (e23)) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e22)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> (~((op1 (e12) (e13)) = (e12))) -> (~((op1 (e13) (e13)) = (e12))) -> False). % 19.63/19.86 do 0 intro. intros zenon_H1dc zenon_H94 zenon_H71 zenon_H6e zenon_H8b zenon_H12b zenon_H2b zenon_Hfc zenon_H4c zenon_H1cf zenon_H10f zenon_H1cd zenon_H159 zenon_H1dd. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H1dc); [ zenon_intro zenon_H93 | zenon_intro zenon_H1de ]. % 19.63/19.86 apply (zenon_L29_); trivial. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H1ce | zenon_intro zenon_H1df ]. % 19.63/19.86 apply (zenon_L130_); trivial. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_H160 | zenon_intro zenon_H1e0 ]. % 19.63/19.86 exact (zenon_H159 zenon_H160). % 19.63/19.86 exact (zenon_H1dd zenon_H1e0). % 19.63/19.86 (* end of lemma zenon_L131_ *) % 19.63/19.86 assert (zenon_L132_ : ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> (~((op2 (e22) (e23)) = (e22))) -> (~((op2 (e23) (e23)) = (e22))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e13) (e13)) = (e12)))) -> False). % 19.63/19.86 do 0 intro. intros zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H56 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H17f zenon_Hd4 zenon_H4c zenon_H2e zenon_H2b zenon_H1dc zenon_Hfc zenon_H12b zenon_H10f zenon_H1cd zenon_H16c zenon_H1e1 zenon_H1e2 zenon_H1e3. % 19.63/19.86 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H57 | zenon_intro zenon_Haa ]. % 19.63/19.86 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H58 | zenon_intro zenon_H9b ]. % 19.63/19.86 apply (zenon_L45_); trivial. % 19.63/19.86 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H58 | zenon_intro zenon_H74 ]. % 19.63/19.86 apply (zenon_L48_); trivial. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H58 | zenon_intro zenon_H1dd ]. % 19.63/19.86 apply (zenon_L96_); trivial. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H159 | zenon_intro zenon_H75 ]. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H1e4 ]. % 19.63/19.86 apply (zenon_L53_); trivial. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H1cf | zenon_intro zenon_H1e5 ]. % 19.63/19.86 apply (zenon_L131_); trivial. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H1e5); [ zenon_intro zenon_H173 | zenon_intro zenon_H1e6 ]. % 19.63/19.86 exact (zenon_H16c zenon_H173). % 19.63/19.86 exact (zenon_H1e1 zenon_H1e6). % 19.63/19.86 apply (zenon_L66_); trivial. % 19.63/19.86 apply (zenon_L65_); trivial. % 19.63/19.86 (* end of lemma zenon_L132_ *) % 19.63/19.86 assert (zenon_L133_ : ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e13) (e13)) = (e12)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e23) (e23)) = (e22))) -> (~((op2 (e22) (e23)) = (e22))) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> False). % 19.63/19.86 do 0 intro. intros zenon_H10b zenon_H1e3 zenon_H1e2 zenon_H1e1 zenon_H16c zenon_H1cd zenon_H10f zenon_H12b zenon_Hfc zenon_H1dc zenon_H2b zenon_H2e zenon_H4c zenon_Hd4 zenon_H17f zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H56 | zenon_intro zenon_H56 ]. % 19.63/19.86 apply (zenon_L132_); trivial. % 19.63/19.86 apply (zenon_L132_); trivial. % 19.63/19.86 (* end of lemma zenon_L133_ *) % 19.63/19.86 assert (zenon_L134_ : ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e23))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> (~((op2 (e20) (e20)) = (e22))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> (~((op2 (e23) (e23)) = (e22))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e13) (e13)) = (e12)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> False). % 19.63/19.86 do 0 intro. intros zenon_H192 zenon_H50 zenon_H4b zenon_H4f zenon_H3d zenon_H2f zenon_H2d zenon_H1d zenon_H28 zenon_H47 zenon_H3e zenon_H41 zenon_H13 zenon_H48 zenon_H51 zenon_H40 zenon_H54 zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H17f zenon_Hd4 zenon_H4c zenon_H2e zenon_H2b zenon_H1dc zenon_Hfc zenon_H12b zenon_H10f zenon_H1cd zenon_H1e1 zenon_H1e2 zenon_H1e3 zenon_H10b. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H16c | zenon_intro zenon_H32 ]. % 19.63/19.86 apply (zenon_L133_); trivial. % 19.63/19.86 apply (zenon_L69_); trivial. % 19.63/19.86 (* end of lemma zenon_L134_ *) % 19.63/19.86 assert (zenon_L135_ : ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e23) (e23)) = (e22)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e13) (e13)) = (e12)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> (~((op2 (e20) (e20)) = (e22))) -> (~((op2 (e20) (e20)) = (e21))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> (~((op2 (e20) (e21)) = (e20))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (e22))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> False). % 19.63/19.86 do 0 intro. intros zenon_H1e7 zenon_H10b zenon_H1e3 zenon_H1e2 zenon_H1cd zenon_H10f zenon_H12b zenon_Hfc zenon_H1dc zenon_Hd4 zenon_H17f zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9 zenon_H40 zenon_H3f zenon_H194 zenon_H12 zenon_H14 zenon_H13 zenon_H54 zenon_H53 zenon_H50 zenon_H4b zenon_H4c zenon_H48 zenon_H3e zenon_H1d zenon_H28 zenon_H47 zenon_H52 zenon_H4f zenon_H2f zenon_H2e zenon_H2b zenon_H31 zenon_H2d. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H15 | zenon_intro zenon_H1e1 ]. % 19.63/19.86 apply (zenon_L95_); trivial. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H16c | zenon_intro zenon_H41 ]. % 19.63/19.86 apply (zenon_L133_); trivial. % 19.63/19.86 apply (zenon_L8_); trivial. % 19.63/19.86 (* end of lemma zenon_L135_ *) % 19.63/19.86 assert (zenon_L136_ : ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> (~((op2 (e20) (e20)) = (e21))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e13) (e13)) = (e12)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e23) (e23)) = (e22)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e20) (e20)) = (e22)))) -> False). % 19.63/19.86 do 0 intro. intros zenon_H10d zenon_H54 zenon_H53 zenon_H52 zenon_H51 zenon_H48 zenon_H3e zenon_H47 zenon_H28 zenon_H1d zenon_H2d zenon_H2b zenon_H2e zenon_H2f zenon_H3d zenon_H4f zenon_H4b zenon_H4c zenon_H50 zenon_H13 zenon_H12 zenon_H152 zenon_H194 zenon_H3f zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H17f zenon_Hd4 zenon_H1dc zenon_Hfc zenon_H12b zenon_H10f zenon_H1cd zenon_H1e2 zenon_H1e3 zenon_H10b zenon_H1e7 zenon_H10e. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H14 | zenon_intro zenon_H2c ]. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.63/19.86 apply (zenon_L17_); trivial. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H15 | zenon_intro zenon_H31 ]. % 19.63/19.86 apply (zenon_L78_); trivial. % 19.63/19.86 apply (zenon_L135_); trivial. % 19.63/19.86 apply zenon_H2c. apply sym_equal. exact zenon_H2b. % 19.63/19.86 (* end of lemma zenon_L136_ *) % 19.63/19.86 assert (zenon_L137_ : ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e13) (e13)) = (e12)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e23) (e23)) = (e22)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e20) (e20)) = (e22)))) -> False). % 19.63/19.86 do 0 intro. intros zenon_H10c zenon_H10d zenon_H54 zenon_H53 zenon_H52 zenon_H51 zenon_H48 zenon_H3e zenon_H47 zenon_H28 zenon_H1d zenon_H2d zenon_H2b zenon_H2e zenon_H2f zenon_H3d zenon_H4f zenon_H4b zenon_H4c zenon_H50 zenon_H13 zenon_H12 zenon_H152 zenon_H194 zenon_H192 zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H17f zenon_Hd4 zenon_H1dc zenon_Hfc zenon_H12b zenon_H10f zenon_H1cd zenon_H1e2 zenon_H1e3 zenon_H10b zenon_H1e7 zenon_H10e. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3f ]. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.63/19.86 apply (zenon_L17_); trivial. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H15 | zenon_intro zenon_H31 ]. % 19.63/19.86 apply (zenon_L78_); trivial. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H15 | zenon_intro zenon_H1e1 ]. % 19.63/19.86 apply (zenon_L95_); trivial. % 19.63/19.86 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H16c | zenon_intro zenon_H41 ]. % 19.63/19.86 apply (zenon_L133_); trivial. % 19.63/19.86 apply (zenon_L134_); trivial. % 19.63/19.86 apply (zenon_L136_); trivial. % 19.63/19.86 (* end of lemma zenon_L137_ *) % 19.63/19.86 assert (zenon_L138_ : (~((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))) -> ((op1 (e12) (e10)) = (e12)) -> ((op2 (e22) (e20)) = (e22)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> False). % 19.63/19.86 do 0 intro. intros zenon_H1e8 zenon_H15b zenon_H16e zenon_H10f zenon_H4c zenon_Hc2 zenon_H2e. % 19.63/19.86 cut (((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) = ((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))). % 19.63/19.86 intro zenon_D_pnotp. % 19.63/19.86 apply zenon_H1e8. % 19.63/19.86 rewrite <- zenon_D_pnotp. % 19.63/19.86 exact zenon_H10f. % 19.63/19.86 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23))) = (op2 (h4 (e12)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H1e9]. % 19.63/19.86 cut (((h4 (e12)) = (h4 (op1 (e12) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H1ea]. % 19.63/19.86 congruence. % 19.63/19.86 elim (classic ((h4 (op1 (e12) (e10))) = (h4 (op1 (e12) (e10))))); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1ec ]. % 19.63/19.86 cut (((h4 (op1 (e12) (e10))) = (h4 (op1 (e12) (e10)))) = ((h4 (e12)) = (h4 (op1 (e12) (e10))))). % 19.63/19.86 intro zenon_D_pnotp. % 19.63/19.86 apply zenon_H1ea. % 19.63/19.86 rewrite <- zenon_D_pnotp. % 19.63/19.86 exact zenon_H1eb. % 19.63/19.86 cut (((h4 (op1 (e12) (e10))) = (h4 (op1 (e12) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H1ec]. % 19.63/19.86 cut (((h4 (op1 (e12) (e10))) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H1ed]. % 19.63/19.86 congruence. % 19.63/19.86 cut (((op1 (e12) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H15d]. % 19.63/19.86 congruence. % 19.63/19.86 exact (zenon_H15d zenon_H15b). % 19.63/19.86 apply zenon_H1ec. apply refl_equal. % 19.63/19.86 apply zenon_H1ec. apply refl_equal. % 19.63/19.86 elim (classic ((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10))))); [ zenon_intro zenon_H1ee | zenon_intro zenon_H1ef ]. % 19.63/19.86 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10)))) = ((op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23))) = (op2 (h4 (e12)) (h4 (e10))))). % 19.63/19.86 intro zenon_D_pnotp. % 19.63/19.86 apply zenon_H1e9. % 19.63/19.86 rewrite <- zenon_D_pnotp. % 19.63/19.86 exact zenon_H1ee. % 19.63/19.86 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 19.63/19.87 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H1f0]. % 19.63/19.87 congruence. % 19.63/19.87 cut (((op2 (e22) (e20)) = (e22)) = ((op2 (h4 (e12)) (h4 (e10))) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23))))). % 19.63/19.87 intro zenon_D_pnotp. % 19.63/19.87 apply zenon_H1f0. % 19.63/19.87 rewrite <- zenon_D_pnotp. % 19.63/19.87 exact zenon_H16e. % 19.63/19.87 cut (((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H1d9]. % 19.63/19.87 cut (((op2 (e22) (e20)) = (op2 (h4 (e12)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H1f1]. % 19.63/19.87 congruence. % 19.63/19.87 elim (classic ((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10))))); [ zenon_intro zenon_H1ee | zenon_intro zenon_H1ef ]. % 19.63/19.87 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10)))) = ((op2 (e22) (e20)) = (op2 (h4 (e12)) (h4 (e10))))). % 19.63/19.87 intro zenon_D_pnotp. % 19.63/19.87 apply zenon_H1f1. % 19.63/19.87 rewrite <- zenon_D_pnotp. % 19.63/19.87 exact zenon_H1ee. % 19.63/19.87 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 19.63/19.87 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1f2]. % 19.63/19.87 congruence. % 19.63/19.87 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_Hc1]. % 19.63/19.87 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H118]. % 19.63/19.87 congruence. % 19.63/19.87 apply (zenon_L73_); trivial. % 19.63/19.87 apply (zenon_L49_); trivial. % 19.63/19.87 apply zenon_H1ef. apply refl_equal. % 19.63/19.87 apply zenon_H1ef. apply refl_equal. % 19.63/19.87 exact (zenon_H1d9 zenon_H4c). % 19.63/19.87 apply zenon_H1ef. apply refl_equal. % 19.63/19.87 apply zenon_H1ef. apply refl_equal. % 19.63/19.87 (* end of lemma zenon_L138_ *) % 19.63/19.87 assert (zenon_L139_ : (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((op2 (e22) (e20)) = (e22)) -> (~((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))) -> (~((op1 (e12) (e11)) = (e12))) -> (~((op1 (e12) (e12)) = (e12))) -> (~((op1 (e12) (e13)) = (e12))) -> False). % 19.63/19.87 do 0 intro. intros zenon_H155 zenon_H2e zenon_Hc2 zenon_H4c zenon_H10f zenon_H16e zenon_H1e8 zenon_H158 zenon_Heb zenon_H159. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H15b | zenon_intro zenon_H15a ]. % 19.63/19.87 apply (zenon_L138_); trivial. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 19.63/19.87 exact (zenon_H158 zenon_H15f). % 19.63/19.87 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H160 ]. % 19.63/19.87 exact (zenon_Heb zenon_Hf2). % 19.63/19.87 exact (zenon_H159 zenon_H160). % 19.63/19.87 (* end of lemma zenon_L139_ *) % 19.63/19.87 assert (zenon_L140_ : ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e22) (e23)) = (e22))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e21)) = (e22))) -> (~((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> False). % 19.63/19.87 do 0 intro. intros zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H56 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H17b zenon_H167 zenon_H16c zenon_H16b zenon_H16a zenon_H1e8 zenon_H2e zenon_Hc2 zenon_H4c zenon_H10f zenon_H155 zenon_H17f zenon_H180. % 19.63/19.87 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H57 | zenon_intro zenon_Haa ]. % 19.63/19.87 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H58 | zenon_intro zenon_H9b ]. % 19.63/19.87 apply (zenon_L45_); trivial. % 19.63/19.87 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H58 | zenon_intro zenon_H74 ]. % 19.63/19.87 apply (zenon_L48_); trivial. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H58 | zenon_intro zenon_Heb ]. % 19.63/19.87 apply (zenon_L96_); trivial. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H17b); [ zenon_intro zenon_H158 | zenon_intro zenon_Haa ]. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H159 | zenon_intro zenon_H75 ]. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_H16e | zenon_intro zenon_H16d ]. % 19.63/19.87 apply (zenon_L139_); trivial. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H172 | zenon_intro zenon_H171 ]. % 19.63/19.87 exact (zenon_H16a zenon_H172). % 19.63/19.87 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H174 | zenon_intro zenon_H173 ]. % 19.63/19.87 exact (zenon_H16b zenon_H174). % 19.63/19.87 exact (zenon_H16c zenon_H173). % 19.63/19.87 apply (zenon_L66_); trivial. % 19.63/19.87 apply (zenon_L43_); trivial. % 19.63/19.87 apply (zenon_L65_); trivial. % 19.63/19.87 (* end of lemma zenon_L140_ *) % 19.63/19.87 assert (zenon_L141_ : ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))) -> (~((op2 (e22) (e21)) = (e22))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e23)) = (e22))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> False). % 19.63/19.87 do 0 intro. intros zenon_H10b zenon_H180 zenon_H17f zenon_H155 zenon_H10f zenon_H4c zenon_Hc2 zenon_H2e zenon_H1e8 zenon_H16a zenon_H16b zenon_H16c zenon_H167 zenon_H17b zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H56 | zenon_intro zenon_H56 ]. % 19.63/19.87 apply (zenon_L140_); trivial. % 19.63/19.87 apply (zenon_L140_); trivial. % 19.63/19.87 (* end of lemma zenon_L141_ *) % 19.63/19.87 assert (zenon_L142_ : ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e23))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> (~((op2 (e20) (e20)) = (e22))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e21)) = (e22))) -> (~((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> False). % 19.63/19.87 do 0 intro. intros zenon_H192 zenon_H50 zenon_H4b zenon_H4f zenon_H3d zenon_H2f zenon_H2b zenon_H2d zenon_H1d zenon_H28 zenon_H47 zenon_H3e zenon_H41 zenon_H13 zenon_H48 zenon_H51 zenon_H40 zenon_H54 zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H17b zenon_H167 zenon_H16b zenon_H16a zenon_H1e8 zenon_H2e zenon_Hc2 zenon_H4c zenon_H10f zenon_H155 zenon_H17f zenon_H180 zenon_H10b. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H16c | zenon_intro zenon_H32 ]. % 19.63/19.87 apply (zenon_L141_); trivial. % 19.63/19.87 apply (zenon_L69_); trivial. % 19.63/19.87 (* end of lemma zenon_L142_ *) % 19.63/19.87 assert (zenon_L143_ : ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> (~((op2 (e20) (e20)) = (e21))) -> (~((op2 (e20) (e20)) = (e22))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e20))) -> (~((op2 (e20) (e21)) = (e20))) -> (~((op2 (e20) (e22)) = (e20))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> False). % 19.63/19.87 do 0 intro. intros zenon_H53 zenon_H3f zenon_H40 zenon_H3e zenon_H13 zenon_H14 zenon_H15 zenon_H12. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H16 | zenon_intro zenon_H41 ]. % 19.63/19.87 apply (zenon_L1_); trivial. % 19.63/19.87 apply (zenon_L8_); trivial. % 19.63/19.87 (* end of lemma zenon_L143_ *) % 19.63/19.87 assert (zenon_L144_ : ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))) -> (~((op2 (e22) (e22)) = (e22))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e22))) -> (~((op2 (e20) (e20)) = (e21))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> False). % 19.63/19.87 do 0 intro. intros zenon_H193 zenon_H2b zenon_H10b zenon_H180 zenon_H17f zenon_H155 zenon_H10f zenon_H4c zenon_Hc2 zenon_H2e zenon_H1e8 zenon_H16b zenon_H167 zenon_H17b zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9 zenon_H3e zenon_H40 zenon_H3f zenon_H13 zenon_H194. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H16a | zenon_intro zenon_H2c ]. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H16c | zenon_intro zenon_H41 ]. % 19.63/19.87 apply (zenon_L141_); trivial. % 19.63/19.87 apply (zenon_L8_); trivial. % 19.63/19.87 apply zenon_H2c. apply sym_equal. exact zenon_H2b. % 19.63/19.87 (* end of lemma zenon_L144_ *) % 19.63/19.87 assert (zenon_L145_ : ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e22) (e22)) = (e22)))) -> (~((op2 (e20) (e20)) = (e21))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e20) (e20)) = (e22)))) -> False). % 19.63/19.87 do 0 intro. intros zenon_H10d zenon_H54 zenon_H53 zenon_H52 zenon_H51 zenon_H48 zenon_H3e zenon_H47 zenon_H28 zenon_H1d zenon_H2d zenon_H2b zenon_H2e zenon_H2f zenon_H3d zenon_H4f zenon_H4b zenon_H4c zenon_H50 zenon_H13 zenon_H12 zenon_H152 zenon_H193 zenon_H10b zenon_H180 zenon_H17f zenon_H155 zenon_H10f zenon_Hc2 zenon_H1e8 zenon_H167 zenon_H17b zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9 zenon_H194 zenon_H195 zenon_H3f zenon_H10e. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H14 | zenon_intro zenon_H2c ]. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.63/19.87 apply (zenon_L17_); trivial. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H15 | zenon_intro zenon_H31 ]. % 19.63/19.87 apply (zenon_L143_); trivial. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H15 | zenon_intro zenon_H16b ]. % 19.63/19.87 apply (zenon_L95_); trivial. % 19.63/19.87 apply (zenon_L144_); trivial. % 19.63/19.87 apply zenon_H2c. apply sym_equal. exact zenon_H2b. % 19.63/19.87 (* end of lemma zenon_L145_ *) % 19.63/19.87 assert (zenon_L146_ : ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e20) (e20)) = (e22)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e22) (e22)) = (e22)))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> False). % 19.63/19.87 do 0 intro. intros zenon_H10c zenon_H54 zenon_H53 zenon_H52 zenon_H51 zenon_H48 zenon_H3e zenon_H47 zenon_H28 zenon_H1d zenon_H2d zenon_H2b zenon_H2e zenon_H2f zenon_H3d zenon_H4f zenon_H4b zenon_H4c zenon_H50 zenon_H13 zenon_H12 zenon_H196 zenon_H10e zenon_H195 zenon_H193 zenon_H152 zenon_H10d zenon_H10b zenon_H180 zenon_H17f zenon_H155 zenon_H10f zenon_Hc2 zenon_H1e8 zenon_H167 zenon_H17b zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9 zenon_H192 zenon_H194. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3f ]. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.63/19.87 apply (zenon_L17_); trivial. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H15 | zenon_intro zenon_H31 ]. % 19.63/19.87 apply (zenon_L78_); trivial. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H15 | zenon_intro zenon_H16b ]. % 19.63/19.87 apply (zenon_L95_); trivial. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H196); [ zenon_intro zenon_H16a | zenon_intro zenon_H3f ]. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H16c | zenon_intro zenon_H41 ]. % 19.63/19.87 apply (zenon_L141_); trivial. % 19.63/19.87 apply (zenon_L142_); trivial. % 19.63/19.87 apply (zenon_L145_); trivial. % 19.63/19.87 apply (zenon_L145_); trivial. % 19.63/19.87 (* end of lemma zenon_L146_ *) % 19.63/19.87 assert (zenon_L147_ : ((h4 (e11)) = (op2 (e23) (e23))) -> ((op1 (e12) (e11)) = (e11)) -> ((e21) = (op2 (e23) (e23))) -> (~((e21) = (h4 (op1 (e12) (e11))))) -> False). % 19.63/19.87 do 0 intro. intros zenon_Hfc zenon_H1f3 zenon_H2b zenon_H1f4. % 19.63/19.87 elim (classic ((h4 (op1 (e12) (e11))) = (h4 (op1 (e12) (e11))))); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H1f6 ]. % 19.63/19.87 cut (((h4 (op1 (e12) (e11))) = (h4 (op1 (e12) (e11)))) = ((e21) = (h4 (op1 (e12) (e11))))). % 19.63/19.87 intro zenon_D_pnotp. % 19.63/19.87 apply zenon_H1f4. % 19.63/19.87 rewrite <- zenon_D_pnotp. % 19.63/19.87 exact zenon_H1f5. % 19.63/19.87 cut (((h4 (op1 (e12) (e11))) = (h4 (op1 (e12) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 19.63/19.87 cut (((h4 (op1 (e12) (e11))) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1f7]. % 19.63/19.87 congruence. % 19.63/19.87 cut (((h4 (e11)) = (op2 (e23) (e23))) = ((h4 (op1 (e12) (e11))) = (e21))). % 19.63/19.87 intro zenon_D_pnotp. % 19.63/19.87 apply zenon_H1f7. % 19.63/19.87 rewrite <- zenon_D_pnotp. % 19.63/19.87 exact zenon_Hfc. % 19.63/19.87 cut (((op2 (e23) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H2c]. % 19.63/19.87 cut (((h4 (e11)) = (h4 (op1 (e12) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H1f8]. % 19.63/19.87 congruence. % 19.63/19.87 elim (classic ((h4 (op1 (e12) (e11))) = (h4 (op1 (e12) (e11))))); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H1f6 ]. % 19.63/19.87 cut (((h4 (op1 (e12) (e11))) = (h4 (op1 (e12) (e11)))) = ((h4 (e11)) = (h4 (op1 (e12) (e11))))). % 19.63/19.87 intro zenon_D_pnotp. % 19.63/19.87 apply zenon_H1f8. % 19.63/19.87 rewrite <- zenon_D_pnotp. % 19.63/19.87 exact zenon_H1f5. % 19.63/19.87 cut (((h4 (op1 (e12) (e11))) = (h4 (op1 (e12) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 19.63/19.87 cut (((h4 (op1 (e12) (e11))) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H1f9]. % 19.63/19.87 congruence. % 19.63/19.87 cut (((op1 (e12) (e11)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H1fa]. % 19.63/19.87 congruence. % 19.63/19.87 exact (zenon_H1fa zenon_H1f3). % 19.63/19.87 apply zenon_H1f6. apply refl_equal. % 19.63/19.87 apply zenon_H1f6. apply refl_equal. % 19.63/19.87 apply zenon_H2c. apply sym_equal. exact zenon_H2b. % 19.63/19.87 apply zenon_H1f6. apply refl_equal. % 19.63/19.87 apply zenon_H1f6. apply refl_equal. % 19.63/19.87 (* end of lemma zenon_L147_ *) % 19.63/19.87 assert (zenon_L148_ : (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e13) (e11)) = (e11)) -> False). % 19.63/19.87 do 0 intro. intros zenon_H1fb zenon_H6e zenon_H1fc. % 19.63/19.87 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e13) (e11)) = (op1 (e13) (e13)))). % 19.63/19.87 intro zenon_D_pnotp. % 19.63/19.87 apply zenon_H1fb. % 19.63/19.87 rewrite <- zenon_D_pnotp. % 19.63/19.87 exact zenon_H6e. % 19.63/19.87 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 19.63/19.87 cut (((e11) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H1fd]. % 19.63/19.87 congruence. % 19.63/19.87 elim (classic ((op1 (e13) (e11)) = (op1 (e13) (e11)))); [ zenon_intro zenon_H1fe | zenon_intro zenon_H1ff ]. % 19.63/19.87 cut (((op1 (e13) (e11)) = (op1 (e13) (e11))) = ((e11) = (op1 (e13) (e11)))). % 19.63/19.87 intro zenon_D_pnotp. % 19.63/19.87 apply zenon_H1fd. % 19.63/19.87 rewrite <- zenon_D_pnotp. % 19.63/19.87 exact zenon_H1fe. % 19.63/19.87 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H1ff]. % 19.63/19.87 cut (((op1 (e13) (e11)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H200]. % 19.63/19.87 congruence. % 19.63/19.87 exact (zenon_H200 zenon_H1fc). % 19.63/19.87 apply zenon_H1ff. apply refl_equal. % 19.63/19.87 apply zenon_H1ff. apply refl_equal. % 19.63/19.87 apply zenon_Ha7. apply refl_equal. % 19.63/19.87 (* end of lemma zenon_L148_ *) % 19.63/19.87 assert (zenon_L149_ : (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e23) (e21)) = (e21)) -> False). % 19.63/19.87 do 0 intro. intros zenon_H201 zenon_H2b zenon_H202. % 19.63/19.87 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e23) (e21)) = (op2 (e23) (e23)))). % 19.63/19.87 intro zenon_D_pnotp. % 19.63/19.87 apply zenon_H201. % 19.63/19.87 rewrite <- zenon_D_pnotp. % 19.63/19.87 exact zenon_H2b. % 19.63/19.87 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_He5]. % 19.63/19.87 cut (((e21) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H203]. % 19.63/19.87 congruence. % 19.63/19.87 elim (classic ((op2 (e23) (e21)) = (op2 (e23) (e21)))); [ zenon_intro zenon_H204 | zenon_intro zenon_H205 ]. % 19.63/19.87 cut (((op2 (e23) (e21)) = (op2 (e23) (e21))) = ((e21) = (op2 (e23) (e21)))). % 19.63/19.87 intro zenon_D_pnotp. % 19.63/19.87 apply zenon_H203. % 19.63/19.87 rewrite <- zenon_D_pnotp. % 19.63/19.87 exact zenon_H204. % 19.63/19.87 cut (((op2 (e23) (e21)) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H205]. % 19.63/19.87 cut (((op2 (e23) (e21)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H206]. % 19.63/19.87 congruence. % 19.63/19.87 exact (zenon_H206 zenon_H202). % 19.63/19.87 apply zenon_H205. apply refl_equal. % 19.63/19.87 apply zenon_H205. apply refl_equal. % 19.63/19.87 apply zenon_He5. apply refl_equal. % 19.63/19.87 (* end of lemma zenon_L149_ *) % 19.63/19.87 assert (zenon_L150_ : ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op2 (e20) (e20)) = (e22))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((e21) = (e22))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> False). % 19.63/19.87 do 0 intro. intros zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H56 zenon_H55 zenon_Hfa zenon_H40 zenon_H207 zenon_H201 zenon_H208 zenon_H1fb zenon_H2b zenon_Hfc zenon_H4c zenon_H10f zenon_H209 zenon_H30 zenon_Hc7 zenon_Hcd zenon_H2e zenon_Hd4 zenon_Hda zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8. % 19.63/19.87 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H57 | zenon_intro zenon_Haa ]. % 19.63/19.87 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H58 | zenon_intro zenon_H9b ]. % 19.63/19.87 apply (zenon_L45_); trivial. % 19.63/19.87 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H58 | zenon_intro zenon_H74 ]. % 19.63/19.87 apply (zenon_L48_); trivial. % 19.63/19.87 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H59 | zenon_intro zenon_H75 ]. % 19.63/19.87 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H73 | zenon_intro zenon_Haa ]. % 19.63/19.87 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H46 | zenon_intro zenon_Hdb ]. % 19.63/19.87 exact (zenon_H40 zenon_H46). % 19.63/19.87 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hdc ]. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_Hc5 | zenon_intro zenon_H20a ]. % 19.63/19.87 apply (zenon_L51_); trivial. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H3a | zenon_intro zenon_H20b ]. % 19.63/19.87 exact (zenon_H30 zenon_H3a). % 19.63/19.87 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H20c | zenon_intro zenon_H202 ]. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H9a); [ zenon_intro zenon_H9d | zenon_intro zenon_H9c ]. % 19.63/19.87 exact (zenon_H9b zenon_H9d). % 19.63/19.87 apply (zenon_or_s _ _ zenon_H9c); [ zenon_intro zenon_H83 | zenon_intro zenon_H9e ]. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H82 | zenon_intro zenon_H20d ]. % 19.63/19.87 apply (zenon_L26_); trivial. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H7d | zenon_intro zenon_H20e ]. % 19.63/19.87 exact (zenon_H73 zenon_H7d). % 19.63/19.87 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H1fc ]. % 19.63/19.87 elim (classic ((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11))))); [ zenon_intro zenon_H20f | zenon_intro zenon_H210 ]. % 19.63/19.87 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11)))) = ((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))). % 19.63/19.87 intro zenon_D_pnotp. % 19.63/19.87 apply zenon_H209. % 19.63/19.87 rewrite <- zenon_D_pnotp. % 19.63/19.87 exact zenon_H20f. % 19.63/19.87 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H210]. % 19.63/19.87 cut (((op2 (h4 (e12)) (h4 (e11))) = (h4 (op1 (e12) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H211]. % 19.63/19.87 congruence. % 19.63/19.87 cut (((op2 (e22) (e21)) = (e21)) = ((op2 (h4 (e12)) (h4 (e11))) = (h4 (op1 (e12) (e11))))). % 19.63/19.87 intro zenon_D_pnotp. % 19.63/19.87 apply zenon_H211. % 19.63/19.87 rewrite <- zenon_D_pnotp. % 19.63/19.87 exact zenon_H20c. % 19.63/19.87 cut (((e21) = (h4 (op1 (e12) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H1f4]. % 19.63/19.87 cut (((op2 (e22) (e21)) = (op2 (h4 (e12)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 19.63/19.87 congruence. % 19.63/19.87 elim (classic ((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11))))); [ zenon_intro zenon_H20f | zenon_intro zenon_H210 ]. % 19.63/19.87 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11)))) = ((op2 (e22) (e21)) = (op2 (h4 (e12)) (h4 (e11))))). % 19.63/19.87 intro zenon_D_pnotp. % 19.63/19.87 apply zenon_H212. % 19.63/19.87 rewrite <- zenon_D_pnotp. % 19.63/19.87 exact zenon_H20f. % 19.63/19.87 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H210]. % 19.63/19.87 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H213]. % 19.63/19.87 congruence. % 19.63/19.87 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H153]. % 19.63/19.87 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H118]. % 19.63/19.87 congruence. % 19.63/19.87 apply (zenon_L73_); trivial. % 19.63/19.87 apply (zenon_L97_); trivial. % 19.63/19.87 apply zenon_H210. apply refl_equal. % 19.63/19.87 apply zenon_H210. apply refl_equal. % 19.63/19.87 apply (zenon_L147_); trivial. % 19.63/19.87 apply zenon_H210. apply refl_equal. % 19.63/19.87 apply zenon_H210. apply refl_equal. % 19.63/19.87 apply (zenon_L148_); trivial. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H9e); [ zenon_intro zenon_H8c | zenon_intro zenon_H93 ]. % 19.63/19.87 apply (zenon_L28_); trivial. % 19.63/19.87 apply (zenon_L29_); trivial. % 19.63/19.87 apply (zenon_L149_); trivial. % 19.63/19.87 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hd3 ]. % 19.63/19.87 apply (zenon_L52_); trivial. % 19.63/19.87 apply (zenon_L53_); trivial. % 19.63/19.87 apply (zenon_L34_); trivial. % 19.63/19.87 apply (zenon_L66_); trivial. % 19.63/19.87 apply (zenon_L65_); trivial. % 19.63/19.87 (* end of lemma zenon_L150_ *) % 19.63/19.87 assert (zenon_L151_ : ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e22)))) -> (~((e21) = (e22))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e20) (e20)) = (e22))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> False). % 19.63/19.87 do 0 intro. intros zenon_H10b zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_Hda zenon_Hd4 zenon_H2e zenon_Hcd zenon_Hc7 zenon_H30 zenon_H209 zenon_H10f zenon_H4c zenon_Hfc zenon_H2b zenon_H1fb zenon_H208 zenon_H201 zenon_H207 zenon_H40 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H56 | zenon_intro zenon_H56 ]. % 19.63/19.87 apply (zenon_L150_); trivial. % 19.63/19.87 apply (zenon_L150_); trivial. % 19.63/19.87 (* end of lemma zenon_L151_ *) % 19.63/19.87 assert (zenon_L152_ : ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op2 (e20) (e20)) = (e22))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> (~((e21) = (e22))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> False). % 19.63/19.87 do 0 intro. intros zenon_H4f zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_H40 zenon_H207 zenon_H201 zenon_H208 zenon_H1fb zenon_H2b zenon_Hfc zenon_H4c zenon_H10f zenon_H209 zenon_Hc7 zenon_Hcd zenon_H2e zenon_Hd4 zenon_Hda zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_H10b. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H30 | zenon_intro zenon_H30 ]. % 19.63/19.87 apply (zenon_L151_); trivial. % 19.63/19.87 apply (zenon_L151_); trivial. % 19.63/19.87 (* end of lemma zenon_L152_ *) % 19.63/19.87 assert (zenon_L153_ : ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> (~((e21) = (e22))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e22)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e20) (e20)) = (e22)))) -> False). % 19.63/19.87 do 0 intro. intros zenon_H10c zenon_H10d zenon_H127 zenon_H54 zenon_H53 zenon_H52 zenon_H51 zenon_H48 zenon_H3e zenon_H47 zenon_H28 zenon_H1d zenon_H2d zenon_H2b zenon_H2e zenon_H2f zenon_H3d zenon_H4f zenon_H4b zenon_H4c zenon_H50 zenon_H13 zenon_H12 zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_H207 zenon_H201 zenon_H208 zenon_H1fb zenon_Hfc zenon_H10f zenon_H209 zenon_Hc7 zenon_Hcd zenon_Hd4 zenon_Hda zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_H10b zenon_H10e. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3f ]. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.63/19.87 apply (zenon_L17_); trivial. % 19.63/19.87 apply (zenon_L152_); trivial. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H14 | zenon_intro zenon_H30 ]. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.63/19.87 apply (zenon_L16_); trivial. % 19.63/19.87 apply (zenon_L152_); trivial. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H14 | zenon_intro zenon_H2c ]. % 19.63/19.87 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.63/19.87 apply (zenon_L17_); trivial. % 19.63/19.87 apply (zenon_L151_); trivial. % 19.63/19.87 apply zenon_H2c. apply sym_equal. exact zenon_H2b. % 19.63/19.87 (* end of lemma zenon_L153_ *) % 19.63/19.87 assert (zenon_L154_ : (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e21) (e22)) = (e21)) -> ((op2 (e22) (e22)) = (e21)) -> False). % 19.63/19.87 do 0 intro. intros zenon_H214 zenon_H1bb zenon_H215. % 19.63/19.87 cut (((op2 (e21) (e22)) = (e21)) = ((op2 (e21) (e22)) = (op2 (e22) (e22)))). % 19.63/19.87 intro zenon_D_pnotp. % 19.63/19.87 apply zenon_H214. % 19.63/19.87 rewrite <- zenon_D_pnotp. % 19.63/19.87 exact zenon_H1bb. % 19.63/19.87 cut (((e21) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H216]. % 19.63/19.87 cut (((op2 (e21) (e22)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H217]. % 19.63/19.87 congruence. % 19.63/19.87 apply zenon_H217. apply refl_equal. % 19.63/19.87 apply zenon_H216. apply sym_equal. exact zenon_H215. % 19.63/19.87 (* end of lemma zenon_L154_ *) % 19.63/19.87 assert (zenon_L155_ : (~((op1 (e13) (e13)) = (op1 (e12) (e11)))) -> ((op1 (e10) (e10)) = (e11)) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e12) (e11)) = (e11)) -> False). % 19.63/19.87 do 0 intro. intros zenon_H218 zenon_Had zenon_H6e zenon_H1f3. % 19.63/19.87 cut (((op1 (e10) (e10)) = (e11)) = ((op1 (e13) (e13)) = (op1 (e12) (e11)))). % 19.63/19.87 intro zenon_D_pnotp. % 19.63/19.87 apply zenon_H218. % 19.63/19.87 rewrite <- zenon_D_pnotp. % 19.63/19.87 exact zenon_Had. % 19.63/19.87 cut (((e11) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H219]. % 19.63/19.87 cut (((op1 (e10) (e10)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 19.63/19.87 congruence. % 19.63/19.87 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H21a | zenon_intro zenon_Ha7 ]. % 19.63/19.87 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (e10) (e10)) = (op1 (e13) (e13)))). % 19.63/19.87 intro zenon_D_pnotp. % 19.63/19.87 apply zenon_H1a9. % 19.63/19.87 rewrite <- zenon_D_pnotp. % 19.63/19.87 exact zenon_H21a. % 19.63/19.87 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 19.63/19.87 cut (((op1 (e13) (e13)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H1a6]. % 19.63/19.87 congruence. % 19.63/19.87 apply (zenon_L120_); trivial. % 19.63/19.87 apply zenon_Ha7. apply refl_equal. % 19.63/19.87 apply zenon_Ha7. apply refl_equal. % 19.63/19.87 apply zenon_H219. apply sym_equal. exact zenon_H1f3. % 19.63/19.87 (* end of lemma zenon_L155_ *) % 19.63/19.87 assert (zenon_L156_ : (~((op1 (e13) (e13)) = (op1 (e11) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e10) (e10)) = (e11)) -> ((op1 (e12) (e11)) = (e11)) -> ((op1 (e11) (e12)) = (e11)) -> False). % 19.63/19.87 do 0 intro. intros zenon_H21b zenon_H6e zenon_Had zenon_H1f3 zenon_H1bf. % 19.63/19.87 cut (((op1 (e12) (e11)) = (e11)) = ((op1 (e13) (e13)) = (op1 (e11) (e12)))). % 19.63/19.87 intro zenon_D_pnotp. % 19.63/19.87 apply zenon_H21b. % 19.63/19.87 rewrite <- zenon_D_pnotp. % 19.63/19.87 exact zenon_H1f3. % 19.63/19.87 cut (((e11) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H21c]. % 19.63/19.87 cut (((op1 (e12) (e11)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H21d]. % 19.63/19.87 congruence. % 19.63/19.87 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H21a | zenon_intro zenon_Ha7 ]. % 19.63/19.87 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (e12) (e11)) = (op1 (e13) (e13)))). % 19.63/19.87 intro zenon_D_pnotp. % 19.63/19.87 apply zenon_H21d. % 19.63/19.87 rewrite <- zenon_D_pnotp. % 19.63/19.87 exact zenon_H21a. % 19.63/19.87 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 19.63/19.87 cut (((op1 (e13) (e13)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 19.63/19.87 congruence. % 19.63/19.87 apply (zenon_L155_); trivial. % 19.63/19.87 apply zenon_Ha7. apply refl_equal. % 19.63/19.87 apply zenon_Ha7. apply refl_equal. % 19.63/19.87 apply zenon_H21c. apply sym_equal. exact zenon_H1bf. % 19.63/19.87 (* end of lemma zenon_L156_ *) % 19.63/19.87 assert (zenon_L157_ : (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op1 (e12) (e12)) = (e13)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> False). % 19.63/19.87 do 0 intro. intros zenon_H21e zenon_H12b zenon_Hf1 zenon_H21f zenon_H10f zenon_H4c. % 19.63/19.87 cut (((h4 (e13)) = (e23)) = ((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))). % 19.63/19.87 intro zenon_D_pnotp. % 19.63/19.87 apply zenon_H21e. % 19.63/19.87 rewrite <- zenon_D_pnotp. % 19.63/19.87 exact zenon_H12b. % 19.63/19.87 cut (((e23) = (op2 (h4 (e12)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H220]. % 19.63/19.87 cut (((h4 (e13)) = (h4 (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H221]. % 19.63/19.87 congruence. % 19.63/19.87 elim (classic ((h4 (op1 (e12) (e12))) = (h4 (op1 (e12) (e12))))); [ zenon_intro zenon_H222 | zenon_intro zenon_H223 ]. % 19.63/19.87 cut (((h4 (op1 (e12) (e12))) = (h4 (op1 (e12) (e12)))) = ((h4 (e13)) = (h4 (op1 (e12) (e12))))). % 19.63/19.87 intro zenon_D_pnotp. % 19.63/19.87 apply zenon_H221. % 19.63/19.87 rewrite <- zenon_D_pnotp. % 19.63/19.87 exact zenon_H222. % 19.63/19.87 cut (((h4 (op1 (e12) (e12))) = (h4 (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H223]. % 19.63/19.87 cut (((h4 (op1 (e12) (e12))) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H224]. % 19.63/19.87 congruence. % 19.63/19.87 cut (((op1 (e12) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_Hec]. % 19.63/19.87 congruence. % 19.63/19.87 exact (zenon_Hec zenon_Hf1). % 19.63/19.88 apply zenon_H223. apply refl_equal. % 19.63/19.88 apply zenon_H223. apply refl_equal. % 19.63/19.88 elim (classic ((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12))))); [ zenon_intro zenon_H225 | zenon_intro zenon_H226 ]. % 19.63/19.88 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12)))) = ((e23) = (op2 (h4 (e12)) (h4 (e12))))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H220. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H225. % 19.63/19.88 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H226]. % 19.63/19.88 cut (((op2 (h4 (e12)) (h4 (e12))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H227]. % 19.63/19.88 congruence. % 19.63/19.88 cut (((op2 (e22) (e22)) = (e23)) = ((op2 (h4 (e12)) (h4 (e12))) = (e23))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H227. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H21f. % 19.63/19.88 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 19.63/19.88 cut (((op2 (e22) (e22)) = (op2 (h4 (e12)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H228]. % 19.63/19.88 congruence. % 19.63/19.88 elim (classic ((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12))))); [ zenon_intro zenon_H225 | zenon_intro zenon_H226 ]. % 19.63/19.88 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12)))) = ((op2 (e22) (e22)) = (op2 (h4 (e12)) (h4 (e12))))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H228. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H225. % 19.63/19.88 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H226]. % 19.63/19.88 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H229]. % 19.63/19.88 congruence. % 19.63/19.88 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H118]. % 19.63/19.88 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H118]. % 19.63/19.88 congruence. % 19.63/19.88 apply (zenon_L73_); trivial. % 19.63/19.88 apply (zenon_L73_); trivial. % 19.63/19.88 apply zenon_H226. apply refl_equal. % 19.63/19.88 apply zenon_H226. apply refl_equal. % 19.63/19.88 apply zenon_H29. apply refl_equal. % 19.63/19.88 apply zenon_H226. apply refl_equal. % 19.63/19.88 apply zenon_H226. apply refl_equal. % 19.63/19.88 (* end of lemma zenon_L157_ *) % 19.63/19.88 assert (zenon_L158_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (e10))) -> (~((op1 (e10) (e11)) = (e10))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (e12))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e13)) = (e11))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e11)) = (e11))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (~((op1 (e12) (e12)) = (e12))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (e10))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (e10))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H55 zenon_H56 zenon_H57 zenon_H6e zenon_Ha5 zenon_Ha1 zenon_H9a zenon_H9b zenon_H84 zenon_H8d zenon_H8b zenon_H71 zenon_H94 zenon_H1b7 zenon_H208 zenon_H73 zenon_H4c zenon_H10f zenon_H21f zenon_H12b zenon_H21e zenon_Heb zenon_H22a zenon_He9 zenon_He8 zenon_H1fb zenon_H1ac zenon_H1b2 zenon_Hab zenon_H59. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H55); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 19.63/19.88 exact (zenon_H56 zenon_H5b). % 19.63/19.88 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H5d | zenon_intro zenon_H5c ]. % 19.63/19.88 exact (zenon_H57 zenon_H5d). % 19.63/19.88 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ]. % 19.63/19.88 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_Had | zenon_intro zenon_Hac ]. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H9a); [ zenon_intro zenon_H9d | zenon_intro zenon_H9c ]. % 19.63/19.88 exact (zenon_H9b zenon_H9d). % 19.63/19.88 apply (zenon_or_s _ _ zenon_H9c); [ zenon_intro zenon_H83 | zenon_intro zenon_H9e ]. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1bc ]. % 19.63/19.88 apply (zenon_L121_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H7d | zenon_intro zenon_H1bd ]. % 19.63/19.88 exact (zenon_H73 zenon_H7d). % 19.63/19.88 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H1bf | zenon_intro zenon_H1be ]. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H82 | zenon_intro zenon_H20d ]. % 19.63/19.88 apply (zenon_L26_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H7d | zenon_intro zenon_H20e ]. % 19.63/19.88 exact (zenon_H73 zenon_H7d). % 19.63/19.88 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H1fc ]. % 19.63/19.88 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hee | zenon_intro zenon_Hed ]. % 19.63/19.88 exact (zenon_He9 zenon_Hee). % 19.63/19.88 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hef ]. % 19.63/19.88 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H22b | zenon_intro zenon_H22c ]. % 19.63/19.88 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (e11) (e12)) = (op1 (e12) (e12)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H22a. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H22b. % 19.63/19.88 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H22c]. % 19.63/19.88 cut (((op1 (e12) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H22d]. % 19.63/19.88 congruence. % 19.63/19.88 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e12) (e12)) = (op1 (e11) (e12)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H22d. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H6e. % 19.63/19.88 cut (((op1 (e13) (e13)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H21b]. % 19.63/19.88 cut (((e11) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H22e]. % 19.63/19.88 congruence. % 19.63/19.88 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H22b | zenon_intro zenon_H22c ]. % 19.63/19.88 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((e11) = (op1 (e12) (e12)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H22e. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H22b. % 19.63/19.88 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H22c]. % 19.63/19.88 cut (((op1 (e12) (e12)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Hea]. % 19.63/19.88 congruence. % 19.63/19.88 exact (zenon_Hea zenon_Hf0). % 19.63/19.88 apply zenon_H22c. apply refl_equal. % 19.63/19.88 apply zenon_H22c. apply refl_equal. % 19.63/19.88 apply (zenon_L156_); trivial. % 19.63/19.88 apply zenon_H22c. apply refl_equal. % 19.63/19.88 apply zenon_H22c. apply refl_equal. % 19.63/19.88 apply (zenon_or_s _ _ zenon_Hef); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf1 ]. % 19.63/19.88 exact (zenon_Heb zenon_Hf2). % 19.63/19.88 apply (zenon_L157_); trivial. % 19.63/19.88 apply (zenon_L148_); trivial. % 19.63/19.88 exact (zenon_H1b7 zenon_H1be). % 19.63/19.88 apply (zenon_or_s _ _ zenon_H9e); [ zenon_intro zenon_H8c | zenon_intro zenon_H93 ]. % 19.63/19.88 apply (zenon_L28_); trivial. % 19.63/19.88 apply (zenon_L29_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H82 | zenon_intro zenon_Hae ]. % 19.63/19.88 apply (zenon_L30_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_Ha0 | zenon_intro zenon_Ha6 ]. % 19.63/19.88 apply (zenon_L32_); trivial. % 19.63/19.88 apply (zenon_L33_); trivial. % 19.63/19.88 exact (zenon_H59 zenon_H5e). % 19.63/19.88 (* end of lemma zenon_L158_ *) % 19.63/19.88 assert (zenon_L159_ : (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> (~((op2 (e20) (e20)) = (e20))) -> (~((op2 (e21) (e23)) = (e21))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((op2 (e22) (e22)) = (e20))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (e10))) -> (~((op1 (e10) (e11)) = (e10))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (e12))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e13)) = (e11))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e11)) = (e11))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (~((op1 (e12) (e12)) = (e12))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (e10))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (e10))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((e20) = (e21))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> (~((op2 (e22) (e23)) = (e22))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e21)) = (e22))) -> (~((e20) = (e22))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H17c zenon_H13 zenon_H1b4 zenon_H22f zenon_H230 zenon_H214 zenon_H55 zenon_H56 zenon_H57 zenon_H6e zenon_Ha5 zenon_Ha1 zenon_H9a zenon_H9b zenon_H84 zenon_H8d zenon_H8b zenon_H71 zenon_H94 zenon_H1b7 zenon_H208 zenon_H73 zenon_H4c zenon_H10f zenon_H12b zenon_H21e zenon_Heb zenon_H22a zenon_He9 zenon_He8 zenon_H1fb zenon_H1ac zenon_H1b2 zenon_Hab zenon_H59 zenon_H30 zenon_Hdf zenon_H1b5 zenon_H16c zenon_H16b zenon_H16a zenon_H168 zenon_H167 zenon_H175 zenon_H2e zenon_H2b. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H17c); [ zenon_intro zenon_H18 | zenon_intro zenon_H181 ]. % 19.63/19.88 exact (zenon_H13 zenon_H18). % 19.63/19.88 apply (zenon_or_s _ _ zenon_H181); [ zenon_intro zenon_H183 | zenon_intro zenon_H182 ]. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1b8 ]. % 19.63/19.88 apply (zenon_L119_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H3a | zenon_intro zenon_H1b9 ]. % 19.63/19.88 exact (zenon_H30 zenon_H3a). % 19.63/19.88 apply (zenon_or_s _ _ zenon_H1b9); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1ba ]. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H232 | zenon_intro zenon_H231 ]. % 19.63/19.88 exact (zenon_H230 zenon_H232). % 19.63/19.88 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H215 | zenon_intro zenon_H233 ]. % 19.63/19.88 apply (zenon_L154_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H174 | zenon_intro zenon_H21f ]. % 19.63/19.88 exact (zenon_H16b zenon_H174). % 19.63/19.88 apply (zenon_L158_); trivial. % 19.63/19.88 exact (zenon_H1b4 zenon_H1ba). % 19.63/19.88 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H169 | zenon_intro zenon_H176 ]. % 19.63/19.88 apply (zenon_L100_); trivial. % 19.63/19.88 apply (zenon_L101_); trivial. % 19.63/19.88 (* end of lemma zenon_L159_ *) % 19.63/19.88 assert (zenon_L160_ : ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e11) (e13)) = (e11)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e22))) -> (~((op2 (e22) (e21)) = (e22))) -> (~((op2 (e22) (e23)) = (e22))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((e20) = (e21))) -> (~((op2 (e21) (e21)) = (e21))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (e20))) -> (~((op2 (e21) (e23)) = (e21))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op1 (e12) (e10)) = (e12)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H56 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H1b6 zenon_H17b zenon_H155 zenon_H17f zenon_H17c zenon_H2b zenon_H2e zenon_H175 zenon_H168 zenon_H16a zenon_H16c zenon_H167 zenon_Hdf zenon_H30 zenon_H22f zenon_H1b2 zenon_H10f zenon_H4c zenon_H12b zenon_H21e zenon_H22a zenon_H1fb zenon_H208 zenon_H1ac zenon_H16b zenon_H214 zenon_H230 zenon_H1b4 zenon_H1b5 zenon_H13 zenon_H234 zenon_H180. % 19.63/19.88 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H57 | zenon_intro zenon_Haa ]. % 19.63/19.88 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H58 | zenon_intro zenon_H9b ]. % 19.63/19.88 apply (zenon_L45_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H58 | zenon_intro zenon_H74 ]. % 19.63/19.88 apply (zenon_L48_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H58 | zenon_intro zenon_Heb ]. % 19.63/19.88 apply (zenon_L96_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H59 | zenon_intro zenon_H75 ]. % 19.63/19.88 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H73 | zenon_intro zenon_Haa ]. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H75 ]. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H15d | zenon_intro zenon_He9 ]. % 19.63/19.88 apply (zenon_L110_); trivial. % 19.63/19.88 apply (zenon_L159_); trivial. % 19.63/19.88 apply (zenon_L66_); trivial. % 19.63/19.88 apply (zenon_L65_); trivial. % 19.63/19.88 apply (zenon_L66_); trivial. % 19.63/19.88 apply (zenon_L65_); trivial. % 19.63/19.88 (* end of lemma zenon_L160_ *) % 19.63/19.88 assert (zenon_L161_ : ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e12) (e10)) = (e12)))\/(~((op1 (e12) (e12)) = (e10)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> (~((op2 (e21) (e23)) = (e21))) -> (~((op2 (e22) (e22)) = (e20))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((e20) = (e21))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e22) (e23)) = (e22))) -> (~((op2 (e22) (e21)) = (e22))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e11) (e13)) = (e11)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H10b zenon_H180 zenon_H234 zenon_H13 zenon_H1b5 zenon_H1b4 zenon_H230 zenon_H214 zenon_H16b zenon_H1ac zenon_H208 zenon_H1fb zenon_H22a zenon_H21e zenon_H12b zenon_H4c zenon_H10f zenon_H1b2 zenon_H22f zenon_H30 zenon_Hdf zenon_H167 zenon_H16c zenon_H16a zenon_H168 zenon_H175 zenon_H2e zenon_H2b zenon_H17c zenon_H17f zenon_H155 zenon_H17b zenon_H1b6 zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H56 | zenon_intro zenon_H56 ]. % 19.63/19.88 apply (zenon_L160_); trivial. % 19.63/19.88 apply (zenon_L160_); trivial. % 19.63/19.88 (* end of lemma zenon_L161_ *) % 19.63/19.88 assert (zenon_L162_ : ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e23))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> (~((op2 (e20) (e20)) = (e22))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e11) (e13)) = (e11)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e22))) -> (~((op2 (e22) (e21)) = (e22))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((e20) = (e21))) -> (~((op2 (e21) (e21)) = (e21))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (e20))) -> (~((op2 (e21) (e23)) = (e21))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op1 (e12) (e10)) = (e12)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H192 zenon_H50 zenon_H4b zenon_H4f zenon_H3d zenon_H2f zenon_H2d zenon_H1d zenon_H28 zenon_H47 zenon_H3e zenon_H41 zenon_H48 zenon_H51 zenon_H40 zenon_H54 zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H1b6 zenon_H17b zenon_H155 zenon_H17f zenon_H17c zenon_H2b zenon_H2e zenon_H175 zenon_H168 zenon_H16a zenon_H167 zenon_Hdf zenon_H30 zenon_H22f zenon_H1b2 zenon_H10f zenon_H4c zenon_H12b zenon_H21e zenon_H22a zenon_H1fb zenon_H208 zenon_H1ac zenon_H16b zenon_H214 zenon_H230 zenon_H1b4 zenon_H1b5 zenon_H13 zenon_H234 zenon_H180 zenon_H10b. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H16c | zenon_intro zenon_H32 ]. % 19.63/19.88 apply (zenon_L161_); trivial. % 19.63/19.88 apply (zenon_L69_); trivial. % 19.63/19.88 (* end of lemma zenon_L162_ *) % 19.63/19.88 assert (zenon_L163_ : ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e12) (e10)) = (e12)))\/(~((op1 (e12) (e12)) = (e10)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> (~((op2 (e21) (e23)) = (e21))) -> (~((op2 (e22) (e22)) = (e20))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((e20) = (e21))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e11) (e13)) = (e11)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e22))) -> (~((op2 (e20) (e20)) = (e21))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H193 zenon_H10b zenon_H180 zenon_H234 zenon_H13 zenon_H1b5 zenon_H1b4 zenon_H230 zenon_H214 zenon_H16b zenon_H1ac zenon_H208 zenon_H1fb zenon_H22a zenon_H21e zenon_H12b zenon_H4c zenon_H10f zenon_H1b2 zenon_H22f zenon_H30 zenon_Hdf zenon_H167 zenon_H168 zenon_H175 zenon_H2e zenon_H2b zenon_H17c zenon_H17f zenon_H155 zenon_H17b zenon_H1b6 zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9 zenon_H3e zenon_H40 zenon_H3f zenon_H194. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H16a | zenon_intro zenon_H2c ]. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H16c | zenon_intro zenon_H41 ]. % 19.63/19.88 apply (zenon_L161_); trivial. % 19.63/19.88 apply (zenon_L8_); trivial. % 19.63/19.88 apply zenon_H2c. apply sym_equal. exact zenon_H2b. % 19.63/19.88 (* end of lemma zenon_L163_ *) % 19.63/19.88 assert (zenon_L164_ : ((~((op2 (e22) (e20)) = (e22)))\/(~((op2 (e22) (e22)) = (e20)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> (~((op2 (e20) (e20)) = (e21))) -> (~((op2 (e20) (e20)) = (e22))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e11) (e13)) = (e11)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e22))) -> (~((e20) = (e21))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e21) (e23)) = (e21))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op1 (e12) (e10)) = (e12)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((op2 (e21) (e21)) = (e22))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (~((op2 (e22) (e22)) = (e22))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H235 zenon_H194 zenon_H3f zenon_H40 zenon_H3e zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H1b6 zenon_H17b zenon_H155 zenon_H17f zenon_H17c zenon_H175 zenon_H168 zenon_Hdf zenon_H22f zenon_H1b2 zenon_H10f zenon_H4c zenon_H12b zenon_H21e zenon_H22a zenon_H1fb zenon_H208 zenon_H1ac zenon_H214 zenon_H1b4 zenon_H1b5 zenon_H13 zenon_H234 zenon_H180 zenon_H10b zenon_H192 zenon_H2f zenon_H2e zenon_H2b zenon_H30 zenon_H31 zenon_H2d zenon_H16b zenon_H167 zenon_H193. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H170 | zenon_intro zenon_H230 ]. % 19.63/19.88 apply (zenon_L109_); trivial. % 19.63/19.88 apply (zenon_L163_); trivial. % 19.63/19.88 (* end of lemma zenon_L164_ *) % 19.63/19.88 assert (zenon_L165_ : ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> (~((op2 (e21) (e21)) = (e22))) -> ((~((op2 (e22) (e20)) = (e22)))\/(~((op2 (e22) (e22)) = (e20)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e12) (e10)) = (e12)))\/(~((op1 (e12) (e12)) = (e10)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> (~((op2 (e21) (e23)) = (e21))) -> (~((op2 (e22) (e22)) = (e20))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((e20) = (e21))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e11) (e13)) = (e11)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> (~((op2 (e20) (e20)) = (e22))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H196 zenon_H193 zenon_H31 zenon_H235 zenon_H10b zenon_H180 zenon_H234 zenon_H13 zenon_H1b5 zenon_H1b4 zenon_H230 zenon_H214 zenon_H16b zenon_H1ac zenon_H208 zenon_H1fb zenon_H22a zenon_H21e zenon_H12b zenon_H4c zenon_H10f zenon_H1b2 zenon_H22f zenon_H30 zenon_Hdf zenon_H167 zenon_H168 zenon_H175 zenon_H2e zenon_H2b zenon_H17c zenon_H17f zenon_H155 zenon_H17b zenon_H1b6 zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9 zenon_H192 zenon_H50 zenon_H4b zenon_H4f zenon_H3d zenon_H2f zenon_H2d zenon_H1d zenon_H28 zenon_H47 zenon_H3e zenon_H48 zenon_H51 zenon_H40 zenon_H54 zenon_H194. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H196); [ zenon_intro zenon_H16a | zenon_intro zenon_H3f ]. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H16c | zenon_intro zenon_H41 ]. % 19.63/19.88 apply (zenon_L161_); trivial. % 19.63/19.88 apply (zenon_L162_); trivial. % 19.63/19.88 apply (zenon_L164_); trivial. % 19.63/19.88 (* end of lemma zenon_L165_ *) % 19.63/19.88 assert (zenon_L166_ : ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> (~((op2 (e21) (e21)) = (e22))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e22) (e20)) = (e22)))\/(~((op2 (e22) (e22)) = (e20)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e12) (e10)) = (e12)))\/(~((op1 (e12) (e12)) = (e10)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> (~((op2 (e21) (e23)) = (e21))) -> (~((op2 (e22) (e22)) = (e20))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((e20) = (e21))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e11) (e13)) = (e11)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> (~((op2 (e20) (e20)) = (e22))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (~((op2 (e20) (e20)) = (e23))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H196 zenon_H193 zenon_H31 zenon_H194 zenon_H235 zenon_H10b zenon_H180 zenon_H234 zenon_H13 zenon_H1b5 zenon_H1b4 zenon_H230 zenon_H214 zenon_H16b zenon_H1ac zenon_H208 zenon_H1fb zenon_H22a zenon_H21e zenon_H12b zenon_H4c zenon_H10f zenon_H1b2 zenon_H22f zenon_H30 zenon_Hdf zenon_H167 zenon_H168 zenon_H175 zenon_H2e zenon_H2b zenon_H17c zenon_H17f zenon_H155 zenon_H17b zenon_H1b6 zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9 zenon_H54 zenon_H40 zenon_H51 zenon_H48 zenon_H41 zenon_H3e zenon_H47 zenon_H28 zenon_H1d zenon_H2d zenon_H2f zenon_H3d zenon_H4f zenon_H4b zenon_H50 zenon_H192. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H196); [ zenon_intro zenon_H16a | zenon_intro zenon_H3f ]. % 19.63/19.88 apply (zenon_L162_); trivial. % 19.63/19.88 apply (zenon_L164_); trivial. % 19.63/19.88 (* end of lemma zenon_L166_ *) % 19.63/19.88 assert (zenon_L167_ : ((~((op2 (e21) (e23)) = (e21)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e22) (e22)) = (e22))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (~((op2 (e21) (e21)) = (e22))) -> (~((op2 (e21) (e21)) = (e21))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e22) (e20)) = (e22)))\/(~((op2 (e22) (e22)) = (e20)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e12) (e10)) = (e12)))\/(~((op1 (e12) (e12)) = (e10)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((e20) = (e21))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e11) (e13)) = (e11)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> (~((op2 (e20) (e20)) = (e22))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (~((op2 (e20) (e20)) = (e23))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H1cb zenon_H193 zenon_H167 zenon_H16b zenon_H2d zenon_H31 zenon_H30 zenon_H2b zenon_H2e zenon_H2f zenon_H192 zenon_H196 zenon_H194 zenon_H235 zenon_H10b zenon_H180 zenon_H234 zenon_H13 zenon_H1b5 zenon_H214 zenon_H1ac zenon_H208 zenon_H1fb zenon_H22a zenon_H21e zenon_H12b zenon_H4c zenon_H10f zenon_H1b2 zenon_H22f zenon_Hdf zenon_H168 zenon_H175 zenon_H17c zenon_H17f zenon_H155 zenon_H17b zenon_H1b6 zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9 zenon_H54 zenon_H40 zenon_H51 zenon_H48 zenon_H41 zenon_H3e zenon_H47 zenon_H28 zenon_H1d zenon_H3d zenon_H4f zenon_H4b zenon_H50. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H32 ]. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H170 | zenon_intro zenon_H230 ]. % 19.63/19.88 apply (zenon_L109_); trivial. % 19.63/19.88 apply (zenon_L166_); trivial. % 19.63/19.88 apply (zenon_L6_); trivial. % 19.63/19.88 (* end of lemma zenon_L167_ *) % 19.63/19.88 assert (zenon_L168_ : ((~((op2 (e21) (e23)) = (e21)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e22) (e22)) = (e22))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (~((op2 (e21) (e21)) = (e22))) -> (~((op2 (e21) (e21)) = (e21))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e12) (e10)) = (e12)))\/(~((op1 (e12) (e12)) = (e10)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((e20) = (e21))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e11) (e13)) = (e11)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e22))) -> (~((op2 (e20) (e20)) = (e21))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e22) (e20)) = (e22)))\/(~((op2 (e22) (e22)) = (e20)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H1cc zenon_H193 zenon_H167 zenon_H16b zenon_H2d zenon_H31 zenon_H30 zenon_H2b zenon_H2e zenon_H2f zenon_H192 zenon_H10b zenon_H180 zenon_H234 zenon_H13 zenon_H1b5 zenon_H214 zenon_H1ac zenon_H208 zenon_H1fb zenon_H22a zenon_H21e zenon_H12b zenon_H4c zenon_H10f zenon_H1b2 zenon_H22f zenon_Hdf zenon_H168 zenon_H175 zenon_H17c zenon_H17f zenon_H155 zenon_H17b zenon_H1b6 zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9 zenon_H3e zenon_H40 zenon_H3f zenon_H194 zenon_H235. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H41 ]. % 19.63/19.88 apply (zenon_L164_); trivial. % 19.63/19.88 apply (zenon_L8_); trivial. % 19.63/19.88 (* end of lemma zenon_L168_ *) % 19.63/19.88 assert (zenon_L169_ : ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e21))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e22) (e20)) = (e22)))\/(~((op2 (e22) (e22)) = (e20)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e11) (e13)) = (e11)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e22))) -> (~((e20) = (e21))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> ((~((op1 (e12) (e10)) = (e12)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e21) (e23)) = (e21)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e22) (e22)) = (e22)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e20) (e20)) = (e22)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H127 zenon_H10d zenon_H4f zenon_H12 zenon_H13 zenon_H52 zenon_H47 zenon_H2b zenon_H28 zenon_H1d zenon_H3e zenon_H3f zenon_H48 zenon_H2d zenon_H2e zenon_H4c zenon_H4b zenon_H50 zenon_H53 zenon_H152 zenon_H235 zenon_H194 zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H1b6 zenon_H17b zenon_H155 zenon_H17f zenon_H17c zenon_H175 zenon_H168 zenon_Hdf zenon_H22f zenon_H1b2 zenon_H10f zenon_H12b zenon_H21e zenon_H22a zenon_H1fb zenon_H208 zenon_H1ac zenon_H214 zenon_H1b5 zenon_H234 zenon_H180 zenon_H10b zenon_H192 zenon_H167 zenon_H193 zenon_H1cc zenon_H195 zenon_H3d zenon_H2f zenon_H51 zenon_H54 zenon_H10e. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H14 | zenon_intro zenon_H30 ]. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.63/19.88 apply (zenon_L16_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H15 | zenon_intro zenon_H31 ]. % 19.63/19.88 apply (zenon_L78_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H15 | zenon_intro zenon_H16b ]. % 19.63/19.88 apply (zenon_L95_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H30 | zenon_intro zenon_H30 ]. % 19.63/19.88 apply (zenon_L168_); trivial. % 19.63/19.88 apply (zenon_L168_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H14 | zenon_intro zenon_H2c ]. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.63/19.88 apply (zenon_L17_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H15 | zenon_intro zenon_H31 ]. % 19.63/19.88 apply (zenon_L78_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H15 | zenon_intro zenon_H16b ]. % 19.63/19.88 apply (zenon_L95_); trivial. % 19.63/19.88 apply (zenon_L168_); trivial. % 19.63/19.88 apply zenon_H2c. apply sym_equal. exact zenon_H2b. % 19.63/19.88 (* end of lemma zenon_L169_ *) % 19.63/19.88 assert (zenon_L170_ : ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e20) (e20)) = (e22)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e22) (e22)) = (e22)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e11) (e13)) = (e11)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e22))) -> (~((e20) = (e21))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/((op2 (e21) (e23)) = (e21))))) -> ((~((op1 (e12) (e10)) = (e12)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op2 (e22) (e20)) = (e22)))\/(~((op2 (e22) (e22)) = (e20)))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e21) (e23)) = (e21)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e21) (e23)) = (e21)))\/(~((op2 (e20) (e20)) = (e23)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H10c zenon_H54 zenon_H53 zenon_H52 zenon_H51 zenon_H48 zenon_H3e zenon_H47 zenon_H28 zenon_H1d zenon_H2d zenon_H2b zenon_H2e zenon_H2f zenon_H3d zenon_H4f zenon_H4b zenon_H4c zenon_H50 zenon_H13 zenon_H12 zenon_H10e zenon_H195 zenon_H152 zenon_H10d zenon_H127 zenon_H194 zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H1b6 zenon_H17b zenon_H155 zenon_H17f zenon_H17c zenon_H175 zenon_H168 zenon_Hdf zenon_H22f zenon_H1b2 zenon_H10f zenon_H12b zenon_H21e zenon_H22a zenon_H1fb zenon_H208 zenon_H1ac zenon_H214 zenon_H1b5 zenon_H234 zenon_H180 zenon_H10b zenon_H235 zenon_H196 zenon_H192 zenon_H167 zenon_H193 zenon_H1cb zenon_H1cc. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3f ]. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.63/19.88 apply (zenon_L17_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H15 | zenon_intro zenon_H31 ]. % 19.63/19.88 apply (zenon_L78_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H15 | zenon_intro zenon_H16b ]. % 19.63/19.88 apply (zenon_L95_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H30 | zenon_intro zenon_H3f ]. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H41 ]. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H170 | zenon_intro zenon_H230 ]. % 19.63/19.88 apply (zenon_L109_); trivial. % 19.63/19.88 apply (zenon_L165_); trivial. % 19.63/19.88 apply (zenon_L167_); trivial. % 19.63/19.88 apply (zenon_L169_); trivial. % 19.63/19.88 apply (zenon_L169_); trivial. % 19.63/19.88 (* end of lemma zenon_L170_ *) % 19.63/19.88 assert (zenon_L171_ : (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op2 (e22) (e23)) = (e20)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> False). % 19.63/19.88 do 0 intro. intros zenon_H236 zenon_Hc2 zenon_H237 zenon_H238 zenon_H2e zenon_H10f zenon_H4c zenon_H12b. % 19.63/19.88 cut (((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) = ((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H236. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_Hc2. % 19.63/19.88 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (h4 (e12)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H239]. % 19.63/19.88 cut (((h4 (e10)) = (h4 (op1 (e12) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H23a]. % 19.63/19.88 congruence. % 19.63/19.88 elim (classic ((h4 (op1 (e12) (e13))) = (h4 (op1 (e12) (e13))))); [ zenon_intro zenon_H23b | zenon_intro zenon_H23c ]. % 19.63/19.88 cut (((h4 (op1 (e12) (e13))) = (h4 (op1 (e12) (e13)))) = ((h4 (e10)) = (h4 (op1 (e12) (e13))))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H23a. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H23b. % 19.63/19.88 cut (((h4 (op1 (e12) (e13))) = (h4 (op1 (e12) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H23c]. % 19.63/19.88 cut (((h4 (op1 (e12) (e13))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H23d]. % 19.63/19.88 congruence. % 19.63/19.88 cut (((op1 (e12) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H23e]. % 19.63/19.88 congruence. % 19.63/19.88 exact (zenon_H23e zenon_H237). % 19.63/19.88 apply zenon_H23c. apply refl_equal. % 19.63/19.88 apply zenon_H23c. apply refl_equal. % 19.63/19.88 elim (classic ((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13))))); [ zenon_intro zenon_H23f | zenon_intro zenon_H240 ]. % 19.63/19.88 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13)))) = ((op2 (e23) (op2 (e23) (e23))) = (op2 (h4 (e12)) (h4 (e13))))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H239. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H23f. % 19.63/19.88 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H240]. % 19.63/19.88 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H241]. % 19.63/19.88 congruence. % 19.63/19.88 cut (((op2 (e22) (e23)) = (e20)) = ((op2 (h4 (e12)) (h4 (e13))) = (op2 (e23) (op2 (e23) (e23))))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H241. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H238. % 19.63/19.88 cut (((e20) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H124]. % 19.63/19.88 cut (((op2 (e22) (e23)) = (op2 (h4 (e12)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H242]. % 19.63/19.88 congruence. % 19.63/19.88 elim (classic ((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13))))); [ zenon_intro zenon_H23f | zenon_intro zenon_H240 ]. % 19.63/19.88 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13)))) = ((op2 (e22) (e23)) = (op2 (h4 (e12)) (h4 (e13))))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H242. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H23f. % 19.63/19.88 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H240]. % 19.63/19.88 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H243]. % 19.63/19.88 congruence. % 19.63/19.88 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 19.63/19.88 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H118]. % 19.63/19.88 congruence. % 19.63/19.88 apply (zenon_L73_); trivial. % 19.63/19.88 exact (zenon_H137 zenon_H12b). % 19.63/19.88 apply zenon_H240. apply refl_equal. % 19.63/19.88 apply zenon_H240. apply refl_equal. % 19.63/19.88 exact (zenon_H124 zenon_H2e). % 19.63/19.88 apply zenon_H240. apply refl_equal. % 19.63/19.88 apply zenon_H240. apply refl_equal. % 19.63/19.88 (* end of lemma zenon_L171_ *) % 19.63/19.88 assert (zenon_L172_ : (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e12) (e13)) = (e11)) -> False). % 19.63/19.88 do 0 intro. intros zenon_H244 zenon_H6e zenon_H245. % 19.63/19.88 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e12) (e13)) = (op1 (e13) (e13)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H244. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H6e. % 19.63/19.88 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 19.63/19.88 cut (((e11) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H246]. % 19.63/19.88 congruence. % 19.63/19.88 elim (classic ((op1 (e12) (e13)) = (op1 (e12) (e13)))); [ zenon_intro zenon_H247 | zenon_intro zenon_H248 ]. % 19.63/19.88 cut (((op1 (e12) (e13)) = (op1 (e12) (e13))) = ((e11) = (op1 (e12) (e13)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H246. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H247. % 19.63/19.88 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H248]. % 19.63/19.88 cut (((op1 (e12) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H249]. % 19.63/19.88 congruence. % 19.63/19.88 exact (zenon_H249 zenon_H245). % 19.63/19.88 apply zenon_H248. apply refl_equal. % 19.63/19.88 apply zenon_H248. apply refl_equal. % 19.63/19.88 apply zenon_Ha7. apply refl_equal. % 19.63/19.88 (* end of lemma zenon_L172_ *) % 19.63/19.88 assert (zenon_L173_ : (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e13)) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e13)) -> False). % 19.63/19.88 do 0 intro. intros zenon_H24a zenon_H12b zenon_H4c zenon_H10f zenon_H2e zenon_H238 zenon_Hc2 zenon_H236 zenon_H6e zenon_H244 zenon_H159 zenon_H13e zenon_H129. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H237 | zenon_intro zenon_H24b ]. % 19.63/19.88 apply (zenon_L171_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H245 | zenon_intro zenon_H24c ]. % 19.63/19.88 apply (zenon_L172_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H160 | zenon_intro zenon_H13f ]. % 19.63/19.88 exact (zenon_H159 zenon_H160). % 19.63/19.88 apply (zenon_L82_); trivial. % 19.63/19.88 (* end of lemma zenon_L173_ *) % 19.63/19.88 assert (zenon_L174_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e13)) = (e12))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (e10))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e13)) = (e13))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H141 zenon_H159 zenon_H244 zenon_H236 zenon_Hc2 zenon_H238 zenon_H2e zenon_H10f zenon_H4c zenon_H12b zenon_H24a zenon_H138 zenon_H13e zenon_H8b zenon_H6e zenon_H71 zenon_H94 zenon_Ha5 zenon_H59 zenon_H13b zenon_H64. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H129 | zenon_intro zenon_H142 ]. % 19.63/19.88 apply (zenon_L173_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H139 | zenon_intro zenon_H143 ]. % 19.63/19.88 apply (zenon_L81_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H13f | zenon_intro zenon_H69 ]. % 19.63/19.88 apply (zenon_L83_); trivial. % 19.63/19.88 exact (zenon_H64 zenon_H69). % 19.63/19.88 (* end of lemma zenon_L174_ *) % 19.63/19.88 assert (zenon_L175_ : (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e22) (e23)) = (e21)) -> False). % 19.63/19.88 do 0 intro. intros zenon_H24d zenon_H2b zenon_H24e. % 19.63/19.88 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e22) (e23)) = (op2 (e23) (e23)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H24d. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H2b. % 19.63/19.88 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_He5]. % 19.63/19.88 cut (((e21) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H24f]. % 19.63/19.88 congruence. % 19.63/19.88 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_H250 | zenon_intro zenon_H251 ]. % 19.63/19.88 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((e21) = (op2 (e22) (e23)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H24f. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H250. % 19.63/19.88 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H251]. % 19.63/19.88 cut (((op2 (e22) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H252]. % 19.63/19.88 congruence. % 19.63/19.88 exact (zenon_H252 zenon_H24e). % 19.63/19.88 apply zenon_H251. apply refl_equal. % 19.63/19.88 apply zenon_H251. apply refl_equal. % 19.63/19.88 apply zenon_He5. apply refl_equal. % 19.63/19.88 (* end of lemma zenon_L175_ *) % 19.63/19.88 assert (zenon_L176_ : (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (~((op1 (e13) (e13)) = (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (e10))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e13)) = (e12))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e23)) = (e22))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e23)) -> False). % 19.63/19.88 do 0 intro. intros zenon_H253 zenon_H64 zenon_H13b zenon_H59 zenon_Ha5 zenon_H94 zenon_H71 zenon_H6e zenon_H8b zenon_H13e zenon_H138 zenon_H24a zenon_H12b zenon_H4c zenon_H10f zenon_H2e zenon_Hc2 zenon_H236 zenon_H244 zenon_H159 zenon_H141 zenon_H2b zenon_H24d zenon_H16c zenon_H14a zenon_H12a. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H238 | zenon_intro zenon_H254 ]. % 19.63/19.88 apply (zenon_L174_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H24e | zenon_intro zenon_H255 ]. % 19.63/19.88 apply (zenon_L175_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H255); [ zenon_intro zenon_H173 | zenon_intro zenon_H14b ]. % 19.63/19.88 exact (zenon_H16c zenon_H173). % 19.63/19.88 apply (zenon_L87_); trivial. % 19.63/19.88 (* end of lemma zenon_L176_ *) % 19.63/19.88 assert (zenon_L177_ : ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (~((op1 (e11) (e11)) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> (~((op1 (e10) (e10)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e23) (e23)) = (e23))) -> (~((op2 (e20) (e23)) = (e20))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (e10))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e22) (e23)) = (e22))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (e11))) -> (~((op1 (e11) (e11)) = (e10))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e11) (e11)) = (e13)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H17f zenon_H74 zenon_H72 zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_H6b zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_Hbf zenon_Hbc zenon_Hb5 zenon_H60 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha1 zenon_H84 zenon_H8d zenon_H9a zenon_Hb6 zenon_Hbb zenon_Hbd zenon_H56 zenon_H55 zenon_Hbe zenon_Hc0 zenon_H14d zenon_H21 zenon_H16 zenon_He3 zenon_Hd4 zenon_H144 zenon_H147 zenon_H141 zenon_H59 zenon_Ha5 zenon_H94 zenon_H8b zenon_H71 zenon_H138 zenon_H13b zenon_H236 zenon_Hc2 zenon_H12b zenon_H4c zenon_H10f zenon_H2e zenon_H244 zenon_H6e zenon_H13e zenon_H24a zenon_H24d zenon_H2b zenon_H16c zenon_H14a zenon_H253 zenon_H70 zenon_Hb8 zenon_H73 zenon_H7b zenon_H14e. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H159 | zenon_intro zenon_H75 ]. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H64 | zenon_intro zenon_H75 ]. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_H12a | zenon_intro zenon_H14f ]. % 19.63/19.88 apply (zenon_L176_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H145 | zenon_intro zenon_H150 ]. % 19.63/19.88 apply (zenon_L86_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H14b | zenon_intro zenon_H26 ]. % 19.63/19.88 apply (zenon_L88_); trivial. % 19.63/19.88 exact (zenon_H21 zenon_H26). % 19.63/19.88 apply (zenon_L39_); trivial. % 19.63/19.88 apply (zenon_L66_); trivial. % 19.63/19.88 (* end of lemma zenon_L177_ *) % 19.63/19.88 assert (zenon_L178_ : ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e12) (e10)) = (e12)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e23)) = (e22))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (e20))) -> (~((op2 (e23) (e23)) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H56 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H1a2 zenon_H14e zenon_H253 zenon_H14a zenon_H16c zenon_H2b zenon_H24d zenon_H24a zenon_H13e zenon_H244 zenon_H2e zenon_H10f zenon_H4c zenon_H12b zenon_Hc2 zenon_H236 zenon_H13b zenon_H138 zenon_H141 zenon_H147 zenon_H144 zenon_Hd4 zenon_He3 zenon_H16 zenon_H21 zenon_H14d zenon_H17f zenon_H155 zenon_H17b zenon_H180. % 19.63/19.88 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H57 | zenon_intro zenon_Haa ]. % 19.63/19.88 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H58 | zenon_intro zenon_H9b ]. % 19.63/19.88 apply (zenon_L45_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H58 | zenon_intro zenon_H74 ]. % 19.63/19.88 apply (zenon_L48_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H58 | zenon_intro zenon_Heb ]. % 19.63/19.88 apply (zenon_L96_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H59 | zenon_intro zenon_H75 ]. % 19.63/19.88 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H73 | zenon_intro zenon_Haa ]. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H15d | zenon_intro zenon_H7b ]. % 19.63/19.88 apply (zenon_L110_); trivial. % 19.63/19.88 apply (zenon_L177_); trivial. % 19.63/19.88 apply (zenon_L43_); trivial. % 19.63/19.88 apply (zenon_L66_); trivial. % 19.63/19.88 apply (zenon_L65_); trivial. % 19.63/19.88 (* end of lemma zenon_L178_ *) % 19.63/19.88 assert (zenon_L179_ : ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e21) (e21)) = (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((op2 (e21) (e21)) = (e22))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e12) (e10)) = (e12)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e23)) = (e22))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (e20))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H151 zenon_H2f zenon_H30 zenon_H31 zenon_H2d zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H1a2 zenon_H14e zenon_H253 zenon_H14a zenon_H16c zenon_H2b zenon_H24d zenon_H24a zenon_H13e zenon_H244 zenon_H2e zenon_H10f zenon_H4c zenon_H12b zenon_Hc2 zenon_H236 zenon_H13b zenon_H138 zenon_H141 zenon_H147 zenon_H144 zenon_Hd4 zenon_He3 zenon_H16 zenon_H14d zenon_H17f zenon_H155 zenon_H17b zenon_H180 zenon_H10b. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H21 | zenon_intro zenon_H32 ]. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H56 | zenon_intro zenon_H56 ]. % 19.63/19.88 apply (zenon_L178_); trivial. % 19.63/19.88 apply (zenon_L178_); trivial. % 19.63/19.88 apply (zenon_L6_); trivial. % 19.63/19.88 (* end of lemma zenon_L179_ *) % 19.63/19.88 assert (zenon_L180_ : ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e23))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> (~((op2 (e20) (e20)) = (e22))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (e20))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e12) (e10)) = (e12)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (~((op2 (e21) (e21)) = (e22))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e21) (e21)) = (e23)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H192 zenon_H50 zenon_H4b zenon_H4f zenon_H3d zenon_H1d zenon_H28 zenon_H47 zenon_H3e zenon_H41 zenon_H13 zenon_H48 zenon_H51 zenon_H40 zenon_H54 zenon_H10b zenon_H180 zenon_H17b zenon_H155 zenon_H17f zenon_H14d zenon_H16 zenon_He3 zenon_Hd4 zenon_H144 zenon_H147 zenon_H141 zenon_H138 zenon_H13b zenon_H236 zenon_Hc2 zenon_H12b zenon_H4c zenon_H10f zenon_H2e zenon_H244 zenon_H13e zenon_H24a zenon_H24d zenon_H2b zenon_H14a zenon_H253 zenon_H14e zenon_H1a2 zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9 zenon_H2d zenon_H31 zenon_H30 zenon_H2f zenon_H151. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H16c | zenon_intro zenon_H32 ]. % 19.63/19.88 apply (zenon_L179_); trivial. % 19.63/19.88 apply (zenon_L69_); trivial. % 19.63/19.88 (* end of lemma zenon_L180_ *) % 19.63/19.88 assert (zenon_L181_ : ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> (~((op2 (e20) (e20)) = (e20))) -> (~((op2 (e20) (e20)) = (e21))) -> (~((op2 (e20) (e20)) = (e22))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (e20))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e12) (e10)) = (e12)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (~((op2 (e21) (e21)) = (e22))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e21) (e21)) = (e23)))) -> False). % 19.73/19.89 do 0 intro. intros zenon_H194 zenon_H13 zenon_H3f zenon_H40 zenon_H3e zenon_H10b zenon_H180 zenon_H17b zenon_H155 zenon_H17f zenon_H14d zenon_H16 zenon_He3 zenon_Hd4 zenon_H144 zenon_H147 zenon_H141 zenon_H138 zenon_H13b zenon_H236 zenon_Hc2 zenon_H12b zenon_H4c zenon_H10f zenon_H2e zenon_H244 zenon_H13e zenon_H24a zenon_H24d zenon_H2b zenon_H14a zenon_H253 zenon_H14e zenon_H1a2 zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9 zenon_H2d zenon_H31 zenon_H30 zenon_H2f zenon_H151. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H16c | zenon_intro zenon_H41 ]. % 19.73/19.89 apply (zenon_L179_); trivial. % 19.73/19.89 apply (zenon_L8_); trivial. % 19.73/19.89 (* end of lemma zenon_L181_ *) % 19.73/19.89 assert (zenon_L182_ : ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e21) (e21)) = (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (e22))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e12) (e10)) = (e12)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (e20))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e22))) -> (~((op2 (e20) (e20)) = (e21))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> False). % 19.73/19.89 do 0 intro. intros zenon_H4f zenon_H151 zenon_H2f zenon_H31 zenon_H2d zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H1a2 zenon_H14e zenon_H253 zenon_H14a zenon_H2b zenon_H24d zenon_H24a zenon_H13e zenon_H244 zenon_H2e zenon_H10f zenon_H4c zenon_H12b zenon_Hc2 zenon_H236 zenon_H13b zenon_H138 zenon_H141 zenon_H147 zenon_H144 zenon_Hd4 zenon_He3 zenon_H16 zenon_H14d zenon_H17f zenon_H155 zenon_H17b zenon_H180 zenon_H10b zenon_H3e zenon_H40 zenon_H3f zenon_H13 zenon_H194. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H30 | zenon_intro zenon_H30 ]. % 19.73/19.89 apply (zenon_L181_); trivial. % 19.73/19.89 apply (zenon_L181_); trivial. % 19.73/19.89 (* end of lemma zenon_L182_ *) % 19.73/19.89 assert (zenon_L183_ : ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e23))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> (~((op2 (e20) (e20)) = (e22))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e12) (e10)) = (e12)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (~((op2 (e21) (e21)) = (e22))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> False). % 19.73/19.89 do 0 intro. intros zenon_H52 zenon_H192 zenon_H50 zenon_H4b zenon_H4f zenon_H3d zenon_H1d zenon_H28 zenon_H47 zenon_H3e zenon_H41 zenon_H13 zenon_H48 zenon_H51 zenon_H40 zenon_H54 zenon_H10b zenon_H180 zenon_H17b zenon_H155 zenon_H17f zenon_H14d zenon_He3 zenon_Hd4 zenon_H144 zenon_H147 zenon_H141 zenon_H138 zenon_H13b zenon_H236 zenon_Hc2 zenon_H12b zenon_H4c zenon_H10f zenon_H2e zenon_H244 zenon_H13e zenon_H24a zenon_H24d zenon_H2b zenon_H14a zenon_H253 zenon_H14e zenon_H1a2 zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9 zenon_H2d zenon_H31 zenon_H2f zenon_H151 zenon_H194. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H16 | zenon_intro zenon_H32 ]. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H30 | zenon_intro zenon_H3f ]. % 19.73/19.89 apply (zenon_L180_); trivial. % 19.73/19.89 apply (zenon_L182_); trivial. % 19.73/19.89 apply (zenon_L69_); trivial. % 19.73/19.89 (* end of lemma zenon_L183_ *) % 19.73/19.89 assert (zenon_L184_ : ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e21))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e12) (e10)) = (e12)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e20) (e20)) = (e22)))) -> False). % 19.73/19.89 do 0 intro. intros zenon_H127 zenon_H10d zenon_H4f zenon_H12 zenon_H13 zenon_H52 zenon_H47 zenon_H2b zenon_H28 zenon_H1d zenon_H3e zenon_H3f zenon_H48 zenon_H2d zenon_H2e zenon_H4c zenon_H4b zenon_H50 zenon_H53 zenon_H152 zenon_H151 zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H1a2 zenon_H14e zenon_H253 zenon_H14a zenon_H24d zenon_H24a zenon_H13e zenon_H244 zenon_H10f zenon_H12b zenon_Hc2 zenon_H236 zenon_H13b zenon_H138 zenon_H141 zenon_H147 zenon_H144 zenon_Hd4 zenon_He3 zenon_H14d zenon_H17f zenon_H155 zenon_H17b zenon_H180 zenon_H10b zenon_H194 zenon_H3d zenon_H2f zenon_H51 zenon_H54 zenon_H10e. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H14 | zenon_intro zenon_H30 ]. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.73/19.89 apply (zenon_L16_); trivial. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H15 | zenon_intro zenon_H31 ]. % 19.73/19.89 apply (zenon_L78_); trivial. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H16 | zenon_intro zenon_H41 ]. % 19.73/19.89 apply (zenon_L182_); trivial. % 19.73/19.89 apply (zenon_L8_); trivial. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H14 | zenon_intro zenon_H2c ]. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.73/19.89 apply (zenon_L17_); trivial. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H15 | zenon_intro zenon_H31 ]. % 19.73/19.89 apply (zenon_L78_); trivial. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H16 | zenon_intro zenon_H41 ]. % 19.73/19.89 apply (zenon_L181_); trivial. % 19.73/19.89 apply (zenon_L8_); trivial. % 19.73/19.89 apply zenon_H2c. apply sym_equal. exact zenon_H2b. % 19.73/19.89 (* end of lemma zenon_L184_ *) % 19.73/19.89 assert (zenon_L185_ : ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e12) (e10)) = (e12)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op1 (e12) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e12) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e20) (e20)) = (e22)))) -> False). % 19.73/19.89 do 0 intro. intros zenon_H10c zenon_H10d zenon_H127 zenon_H54 zenon_H53 zenon_H52 zenon_H51 zenon_H48 zenon_H3e zenon_H47 zenon_H28 zenon_H1d zenon_H2d zenon_H2b zenon_H2e zenon_H2f zenon_H3d zenon_H4f zenon_H4b zenon_H4c zenon_H50 zenon_H13 zenon_H12 zenon_H152 zenon_H151 zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H1a2 zenon_H14e zenon_H253 zenon_H14a zenon_H24d zenon_H24a zenon_H13e zenon_H244 zenon_H10f zenon_H12b zenon_Hc2 zenon_H236 zenon_H13b zenon_H138 zenon_H141 zenon_H147 zenon_H144 zenon_Hd4 zenon_He3 zenon_H14d zenon_H17f zenon_H155 zenon_H17b zenon_H180 zenon_H10b zenon_H192 zenon_H194 zenon_H10e. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3f ]. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.73/19.89 apply (zenon_L17_); trivial. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H15 | zenon_intro zenon_H31 ]. % 19.73/19.89 apply (zenon_L78_); trivial. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H16 | zenon_intro zenon_H41 ]. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H30 | zenon_intro zenon_H3f ]. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H16c | zenon_intro zenon_H41 ]. % 19.73/19.89 apply (zenon_L179_); trivial. % 19.73/19.89 apply (zenon_L183_); trivial. % 19.73/19.89 apply (zenon_L182_); trivial. % 19.73/19.89 apply (zenon_L183_); trivial. % 19.73/19.89 apply (zenon_L184_); trivial. % 19.73/19.89 (* end of lemma zenon_L185_ *) % 19.73/19.89 assert (zenon_L186_ : ((op2 (e23) (e20)) = (e22)) -> ((op2 (e22) (e20)) = (e22)) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> False). % 19.73/19.89 do 0 intro. intros zenon_H256 zenon_H16e zenon_H257. % 19.73/19.89 elim (classic ((op2 (e23) (e20)) = (op2 (e23) (e20)))); [ zenon_intro zenon_H178 | zenon_intro zenon_H179 ]. % 19.73/19.89 cut (((op2 (e23) (e20)) = (op2 (e23) (e20))) = ((op2 (e22) (e20)) = (op2 (e23) (e20)))). % 19.73/19.89 intro zenon_D_pnotp. % 19.73/19.89 apply zenon_H257. % 19.73/19.89 rewrite <- zenon_D_pnotp. % 19.73/19.89 exact zenon_H178. % 19.73/19.89 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H179]. % 19.73/19.89 cut (((op2 (e23) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H258]. % 19.73/19.89 congruence. % 19.73/19.89 cut (((op2 (e23) (e20)) = (e22)) = ((op2 (e23) (e20)) = (op2 (e22) (e20)))). % 19.73/19.89 intro zenon_D_pnotp. % 19.73/19.89 apply zenon_H258. % 19.73/19.89 rewrite <- zenon_D_pnotp. % 19.73/19.89 exact zenon_H256. % 19.73/19.89 cut (((e22) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H259]. % 19.73/19.89 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H179]. % 19.73/19.89 congruence. % 19.73/19.89 apply zenon_H179. apply refl_equal. % 19.73/19.89 apply zenon_H259. apply sym_equal. exact zenon_H16e. % 19.73/19.89 apply zenon_H179. apply refl_equal. % 19.73/19.89 apply zenon_H179. apply refl_equal. % 19.73/19.89 (* end of lemma zenon_L186_ *) % 19.73/19.89 assert (zenon_L187_ : ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((op2 (e23) (e21)) = (e22)) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> False). % 19.73/19.89 do 0 intro. intros zenon_H4c zenon_H25a zenon_H2b zenon_H2e zenon_H25b. % 19.73/19.89 elim (classic ((op2 (e23) (e21)) = (op2 (e23) (e21)))); [ zenon_intro zenon_H204 | zenon_intro zenon_H205 ]. % 19.73/19.89 cut (((op2 (e23) (e21)) = (op2 (e23) (e21))) = ((op2 (e20) (e21)) = (op2 (e23) (e21)))). % 19.73/19.89 intro zenon_D_pnotp. % 19.73/19.89 apply zenon_H25b. % 19.73/19.89 rewrite <- zenon_D_pnotp. % 19.73/19.89 exact zenon_H204. % 19.73/19.89 cut (((op2 (e23) (e21)) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H205]. % 19.73/19.89 cut (((op2 (e23) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H25c]. % 19.73/19.89 congruence. % 19.73/19.89 cut (((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) = ((op2 (e23) (e21)) = (op2 (e20) (e21)))). % 19.73/19.89 intro zenon_D_pnotp. % 19.73/19.89 apply zenon_H25c. % 19.73/19.89 rewrite <- zenon_D_pnotp. % 19.73/19.89 exact zenon_H4c. % 19.73/19.89 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23))) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 19.73/19.89 cut (((e22) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H25d]. % 19.73/19.89 congruence. % 19.73/19.89 elim (classic ((op2 (e23) (e21)) = (op2 (e23) (e21)))); [ zenon_intro zenon_H204 | zenon_intro zenon_H205 ]. % 19.73/19.89 cut (((op2 (e23) (e21)) = (op2 (e23) (e21))) = ((e22) = (op2 (e23) (e21)))). % 19.73/19.89 intro zenon_D_pnotp. % 19.73/19.89 apply zenon_H25d. % 19.73/19.89 rewrite <- zenon_D_pnotp. % 19.73/19.89 exact zenon_H204. % 19.73/19.89 cut (((op2 (e23) (e21)) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H205]. % 19.73/19.89 cut (((op2 (e23) (e21)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 19.73/19.89 congruence. % 19.73/19.89 exact (zenon_H25e zenon_H25a). % 19.73/19.89 apply zenon_H205. apply refl_equal. % 19.73/19.89 apply zenon_H205. apply refl_equal. % 19.73/19.89 apply (zenon_L10_); trivial. % 19.73/19.89 apply zenon_H205. apply refl_equal. % 19.73/19.89 apply zenon_H205. apply refl_equal. % 19.73/19.89 (* end of lemma zenon_L187_ *) % 19.73/19.89 assert (zenon_L188_ : (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e23) (e20)) = (e21)) -> False). % 19.73/19.89 do 0 intro. intros zenon_H25f zenon_H2b zenon_H260. % 19.73/19.89 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e23) (e20)) = (op2 (e23) (e23)))). % 19.73/19.89 intro zenon_D_pnotp. % 19.73/19.89 apply zenon_H25f. % 19.73/19.89 rewrite <- zenon_D_pnotp. % 19.73/19.89 exact zenon_H2b. % 19.73/19.89 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_He5]. % 19.73/19.89 cut (((e21) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H261]. % 19.73/19.89 congruence. % 19.73/19.89 elim (classic ((op2 (e23) (e20)) = (op2 (e23) (e20)))); [ zenon_intro zenon_H178 | zenon_intro zenon_H179 ]. % 19.73/19.89 cut (((op2 (e23) (e20)) = (op2 (e23) (e20))) = ((e21) = (op2 (e23) (e20)))). % 19.73/19.89 intro zenon_D_pnotp. % 19.73/19.89 apply zenon_H261. % 19.73/19.89 rewrite <- zenon_D_pnotp. % 19.73/19.89 exact zenon_H178. % 19.73/19.89 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H179]. % 19.73/19.89 cut (((op2 (e23) (e20)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H262]. % 19.73/19.89 congruence. % 19.73/19.89 exact (zenon_H262 zenon_H260). % 19.73/19.89 apply zenon_H179. apply refl_equal. % 19.73/19.89 apply zenon_H179. apply refl_equal. % 19.73/19.89 apply zenon_He5. apply refl_equal. % 19.73/19.89 (* end of lemma zenon_L188_ *) % 19.73/19.89 assert (zenon_L189_ : (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e20)) = (e22)) -> ((op2 (e23) (e22)) = (e22)) -> False). % 19.73/19.89 do 0 intro. intros zenon_H263 zenon_H256 zenon_H264. % 19.73/19.89 cut (((op2 (e23) (e20)) = (e22)) = ((op2 (e23) (e20)) = (op2 (e23) (e22)))). % 19.73/19.89 intro zenon_D_pnotp. % 19.73/19.89 apply zenon_H263. % 19.73/19.89 rewrite <- zenon_D_pnotp. % 19.73/19.89 exact zenon_H256. % 19.73/19.89 cut (((e22) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H265]. % 19.73/19.89 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H179]. % 19.73/19.89 congruence. % 19.73/19.89 apply zenon_H179. apply refl_equal. % 19.73/19.89 apply zenon_H265. apply sym_equal. exact zenon_H264. % 19.73/19.89 (* end of lemma zenon_L189_ *) % 19.73/19.89 assert (zenon_L190_ : ((op1 (e13) (e10)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> False). % 19.73/19.89 do 0 intro. intros zenon_H266 zenon_H15b zenon_H267. % 19.73/19.89 elim (classic ((op1 (e13) (e10)) = (op1 (e13) (e10)))); [ zenon_intro zenon_H164 | zenon_intro zenon_H165 ]. % 19.73/19.89 cut (((op1 (e13) (e10)) = (op1 (e13) (e10))) = ((op1 (e12) (e10)) = (op1 (e13) (e10)))). % 19.73/19.89 intro zenon_D_pnotp. % 19.73/19.89 apply zenon_H267. % 19.73/19.89 rewrite <- zenon_D_pnotp. % 19.73/19.89 exact zenon_H164. % 19.73/19.89 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H165]. % 19.73/19.89 cut (((op1 (e13) (e10)) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H268]. % 19.73/19.89 congruence. % 19.73/19.89 cut (((op1 (e13) (e10)) = (e12)) = ((op1 (e13) (e10)) = (op1 (e12) (e10)))). % 19.73/19.89 intro zenon_D_pnotp. % 19.73/19.89 apply zenon_H268. % 19.73/19.89 rewrite <- zenon_D_pnotp. % 19.73/19.89 exact zenon_H266. % 19.73/19.89 cut (((e12) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H269]. % 19.73/19.89 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H165]. % 19.73/19.89 congruence. % 19.73/19.89 apply zenon_H165. apply refl_equal. % 19.73/19.89 apply zenon_H269. apply sym_equal. exact zenon_H15b. % 19.73/19.89 apply zenon_H165. apply refl_equal. % 19.73/19.89 apply zenon_H165. apply refl_equal. % 19.73/19.89 (* end of lemma zenon_L190_ *) % 19.73/19.89 assert (zenon_L191_ : ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> ((op1 (e13) (e11)) = (e12)) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> False). % 19.73/19.89 do 0 intro. intros zenon_H8b zenon_H26a zenon_H6e zenon_H71 zenon_H26b. % 19.73/19.89 elim (classic ((op1 (e13) (e11)) = (op1 (e13) (e11)))); [ zenon_intro zenon_H1fe | zenon_intro zenon_H1ff ]. % 19.73/19.89 cut (((op1 (e13) (e11)) = (op1 (e13) (e11))) = ((op1 (e10) (e11)) = (op1 (e13) (e11)))). % 19.73/19.89 intro zenon_D_pnotp. % 19.73/19.89 apply zenon_H26b. % 19.73/19.89 rewrite <- zenon_D_pnotp. % 19.73/19.89 exact zenon_H1fe. % 19.73/19.89 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H1ff]. % 19.73/19.89 cut (((op1 (e13) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H26c]. % 19.73/19.89 congruence. % 19.73/19.89 cut (((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) = ((op1 (e13) (e11)) = (op1 (e10) (e11)))). % 19.73/19.89 intro zenon_D_pnotp. % 19.73/19.89 apply zenon_H26c. % 19.73/19.89 rewrite <- zenon_D_pnotp. % 19.73/19.89 exact zenon_H8b. % 19.73/19.89 cut (((op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13))) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 19.73/19.89 cut (((e12) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H26d]. % 19.73/19.89 congruence. % 19.73/19.89 elim (classic ((op1 (e13) (e11)) = (op1 (e13) (e11)))); [ zenon_intro zenon_H1fe | zenon_intro zenon_H1ff ]. % 19.73/19.89 cut (((op1 (e13) (e11)) = (op1 (e13) (e11))) = ((e12) = (op1 (e13) (e11)))). % 19.73/19.89 intro zenon_D_pnotp. % 19.73/19.89 apply zenon_H26d. % 19.73/19.89 rewrite <- zenon_D_pnotp. % 19.73/19.89 exact zenon_H1fe. % 19.73/19.89 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H1ff]. % 19.73/19.89 cut (((op1 (e13) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H26e]. % 19.73/19.89 congruence. % 19.73/19.89 exact (zenon_H26e zenon_H26a). % 19.73/19.89 apply zenon_H1ff. apply refl_equal. % 19.73/19.89 apply zenon_H1ff. apply refl_equal. % 19.73/19.89 apply (zenon_L27_); trivial. % 19.73/19.89 apply zenon_H1ff. apply refl_equal. % 19.73/19.89 apply zenon_H1ff. apply refl_equal. % 19.73/19.89 (* end of lemma zenon_L191_ *) % 19.73/19.89 assert (zenon_L192_ : (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e13) (e10)) = (e11)) -> False). % 19.73/19.89 do 0 intro. intros zenon_H26f zenon_H6e zenon_H270. % 19.73/19.89 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e13) (e10)) = (op1 (e13) (e13)))). % 19.73/19.89 intro zenon_D_pnotp. % 19.73/19.89 apply zenon_H26f. % 19.73/19.89 rewrite <- zenon_D_pnotp. % 19.73/19.89 exact zenon_H6e. % 19.73/19.89 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 19.73/19.89 cut (((e11) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H271]. % 19.73/19.89 congruence. % 19.73/19.89 elim (classic ((op1 (e13) (e10)) = (op1 (e13) (e10)))); [ zenon_intro zenon_H164 | zenon_intro zenon_H165 ]. % 19.73/19.89 cut (((op1 (e13) (e10)) = (op1 (e13) (e10))) = ((e11) = (op1 (e13) (e10)))). % 19.73/19.89 intro zenon_D_pnotp. % 19.73/19.89 apply zenon_H271. % 19.73/19.89 rewrite <- zenon_D_pnotp. % 19.73/19.89 exact zenon_H164. % 19.73/19.89 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H165]. % 19.73/19.89 cut (((op1 (e13) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H272]. % 19.73/19.89 congruence. % 19.73/19.89 exact (zenon_H272 zenon_H270). % 19.73/19.89 apply zenon_H165. apply refl_equal. % 19.73/19.89 apply zenon_H165. apply refl_equal. % 19.73/19.89 apply zenon_Ha7. apply refl_equal. % 19.73/19.89 (* end of lemma zenon_L192_ *) % 19.73/19.89 assert (zenon_L193_ : (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> ((op1 (e13) (e12)) = (e12)) -> False). % 19.73/19.89 do 0 intro. intros zenon_H273 zenon_H266 zenon_H274. % 19.73/19.89 cut (((op1 (e13) (e10)) = (e12)) = ((op1 (e13) (e10)) = (op1 (e13) (e12)))). % 19.73/19.89 intro zenon_D_pnotp. % 19.73/19.89 apply zenon_H273. % 19.73/19.89 rewrite <- zenon_D_pnotp. % 19.73/19.89 exact zenon_H266. % 19.73/19.89 cut (((e12) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H275]. % 19.73/19.89 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H165]. % 19.73/19.89 congruence. % 19.73/19.89 apply zenon_H165. apply refl_equal. % 19.73/19.89 apply zenon_H275. apply sym_equal. exact zenon_H274. % 19.73/19.89 (* end of lemma zenon_L193_ *) % 19.73/19.89 assert (zenon_L194_ : ((h4 (e13)) = (e23)) -> ((op1 (e13) (e10)) = (e13)) -> (~((e23) = (h4 (op1 (e13) (e10))))) -> False). % 19.73/19.89 do 0 intro. intros zenon_H12b zenon_H66 zenon_H276. % 19.73/19.89 elim (classic ((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10))))); [ zenon_intro zenon_H277 | zenon_intro zenon_H278 ]. % 19.73/19.89 cut (((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10)))) = ((e23) = (h4 (op1 (e13) (e10))))). % 19.73/19.89 intro zenon_D_pnotp. % 19.73/19.89 apply zenon_H276. % 19.73/19.89 rewrite <- zenon_D_pnotp. % 19.73/19.89 exact zenon_H277. % 19.73/19.89 cut (((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H278]. % 19.73/19.89 cut (((h4 (op1 (e13) (e10))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H279]. % 19.73/19.89 congruence. % 19.73/19.89 cut (((h4 (e13)) = (e23)) = ((h4 (op1 (e13) (e10))) = (e23))). % 19.73/19.89 intro zenon_D_pnotp. % 19.73/19.89 apply zenon_H279. % 19.73/19.89 rewrite <- zenon_D_pnotp. % 19.73/19.89 exact zenon_H12b. % 19.73/19.89 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 19.73/19.89 cut (((h4 (e13)) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H27a]. % 19.73/19.89 congruence. % 19.73/19.89 elim (classic ((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10))))); [ zenon_intro zenon_H277 | zenon_intro zenon_H278 ]. % 19.73/19.89 cut (((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10)))) = ((h4 (e13)) = (h4 (op1 (e13) (e10))))). % 19.73/19.89 intro zenon_D_pnotp. % 19.73/19.89 apply zenon_H27a. % 19.73/19.89 rewrite <- zenon_D_pnotp. % 19.73/19.89 exact zenon_H277. % 19.73/19.89 cut (((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H278]. % 19.73/19.89 cut (((h4 (op1 (e13) (e10))) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H27b]. % 19.73/19.89 congruence. % 19.73/19.89 cut (((op1 (e13) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 19.73/19.89 congruence. % 19.73/19.89 exact (zenon_H61 zenon_H66). % 19.73/19.89 apply zenon_H278. apply refl_equal. % 19.73/19.89 apply zenon_H278. apply refl_equal. % 19.73/19.89 apply zenon_H29. apply refl_equal. % 19.73/19.89 apply zenon_H278. apply refl_equal. % 19.73/19.89 apply zenon_H278. apply refl_equal. % 19.73/19.89 (* end of lemma zenon_L194_ *) % 19.73/19.89 assert (zenon_L195_ : ((op2 (e23) (e20)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> ((op1 (e13) (e10)) = (e13)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> False). % 19.73/19.89 do 0 intro. intros zenon_H23 zenon_Hc2 zenon_H2e zenon_H12b zenon_H66 zenon_H27c. % 19.73/19.89 elim (classic ((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10))))); [ zenon_intro zenon_H27d | zenon_intro zenon_H27e ]. % 19.73/19.89 cut (((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10)))) = ((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))). % 19.73/19.89 intro zenon_D_pnotp. % 19.73/19.89 apply zenon_H27c. % 19.73/19.89 rewrite <- zenon_D_pnotp. % 19.73/19.89 exact zenon_H27d. % 19.73/19.89 cut (((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H27e]. % 19.73/19.89 cut (((op2 (h4 (e13)) (h4 (e10))) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H27f]. % 19.73/19.89 congruence. % 19.73/19.89 cut (((op2 (e23) (e20)) = (e23)) = ((op2 (h4 (e13)) (h4 (e10))) = (h4 (op1 (e13) (e10))))). % 19.73/19.89 intro zenon_D_pnotp. % 19.73/19.89 apply zenon_H27f. % 19.73/19.89 rewrite <- zenon_D_pnotp. % 19.73/19.89 exact zenon_H23. % 19.73/19.89 cut (((e23) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H276]. % 19.73/19.89 cut (((op2 (e23) (e20)) = (op2 (h4 (e13)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H280]. % 19.73/19.89 congruence. % 19.73/19.89 elim (classic ((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10))))); [ zenon_intro zenon_H27d | zenon_intro zenon_H27e ]. % 19.73/19.89 cut (((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10)))) = ((op2 (e23) (e20)) = (op2 (h4 (e13)) (h4 (e10))))). % 19.73/19.89 intro zenon_D_pnotp. % 19.73/19.89 apply zenon_H280. % 19.73/19.89 rewrite <- zenon_D_pnotp. % 19.73/19.89 exact zenon_H27d. % 19.73/19.89 cut (((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H27e]. % 19.73/19.89 cut (((op2 (h4 (e13)) (h4 (e10))) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H281]. % 19.73/19.89 congruence. % 19.73/19.89 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_Hc1]. % 19.73/19.89 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 19.73/19.89 congruence. % 19.73/19.89 exact (zenon_H137 zenon_H12b). % 19.73/19.89 apply (zenon_L49_); trivial. % 19.73/19.89 apply zenon_H27e. apply refl_equal. % 19.73/19.89 apply zenon_H27e. apply refl_equal. % 19.73/19.89 apply (zenon_L194_); trivial. % 19.73/19.89 apply zenon_H27e. apply refl_equal. % 19.73/19.89 apply zenon_H27e. apply refl_equal. % 19.73/19.89 (* end of lemma zenon_L195_ *) % 19.73/19.89 assert (zenon_L196_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e12)) = (e12)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op2 (e23) (e20)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> False). % 19.73/19.89 do 0 intro. intros zenon_H282 zenon_H71 zenon_H161 zenon_H6e zenon_H26f zenon_H274 zenon_H273 zenon_H23 zenon_Hc2 zenon_H2e zenon_H12b zenon_H27c. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H162 | zenon_intro zenon_H283 ]. % 19.73/19.89 apply (zenon_L99_); trivial. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_H270 | zenon_intro zenon_H284 ]. % 19.73/19.89 apply (zenon_L192_); trivial. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_H266 | zenon_intro zenon_H66 ]. % 19.73/19.89 apply (zenon_L193_); trivial. % 19.73/19.89 apply (zenon_L195_); trivial. % 19.73/19.89 (* end of lemma zenon_L196_ *) % 19.73/19.89 assert (zenon_L197_ : (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e23)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e13)) = (e12))) -> False). % 19.73/19.89 do 0 intro. intros zenon_H285 zenon_H267 zenon_H15b zenon_H26b zenon_H8b zenon_H27c zenon_H12b zenon_H2e zenon_Hc2 zenon_H23 zenon_H273 zenon_H26f zenon_H6e zenon_H161 zenon_H71 zenon_H282 zenon_H1dd. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H266 | zenon_intro zenon_H286 ]. % 19.73/19.89 apply (zenon_L190_); trivial. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H26a | zenon_intro zenon_H287 ]. % 19.73/19.89 apply (zenon_L191_); trivial. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H274 | zenon_intro zenon_H1e0 ]. % 19.73/19.89 apply (zenon_L196_); trivial. % 19.73/19.89 exact (zenon_H1dd zenon_H1e0). % 19.73/19.89 (* end of lemma zenon_L197_ *) % 19.73/19.89 assert (zenon_L198_ : (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e13) (e13)) = (e12))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op2 (e23) (e20)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e11)) = (e12))) -> (~((op1 (e12) (e12)) = (e12))) -> (~((op1 (e12) (e13)) = (e12))) -> False). % 19.73/19.89 do 0 intro. intros zenon_H155 zenon_H1dd zenon_H282 zenon_H71 zenon_H161 zenon_H6e zenon_H26f zenon_H273 zenon_H23 zenon_Hc2 zenon_H2e zenon_H12b zenon_H27c zenon_H8b zenon_H26b zenon_H267 zenon_H285 zenon_H158 zenon_Heb zenon_H159. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H15b | zenon_intro zenon_H15a ]. % 19.73/19.89 apply (zenon_L197_); trivial. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 19.73/19.89 exact (zenon_H158 zenon_H15f). % 19.73/19.89 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H160 ]. % 19.73/19.89 exact (zenon_Heb zenon_Hf2). % 19.73/19.89 exact (zenon_H159 zenon_H160). % 19.73/19.89 (* end of lemma zenon_L198_ *) % 19.73/19.89 assert (zenon_L199_ : (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e22)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e13) (e13)) = (e12))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e11)) = (e12))) -> (~((op1 (e12) (e12)) = (e12))) -> (~((op1 (e12) (e13)) = (e12))) -> False). % 19.73/19.89 do 0 intro. intros zenon_H288 zenon_H175 zenon_H2b zenon_H25f zenon_H264 zenon_H263 zenon_H155 zenon_H1dd zenon_H282 zenon_H71 zenon_H161 zenon_H6e zenon_H26f zenon_H273 zenon_Hc2 zenon_H2e zenon_H12b zenon_H27c zenon_H8b zenon_H26b zenon_H267 zenon_H285 zenon_H158 zenon_Heb zenon_H159. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H288); [ zenon_intro zenon_H176 | zenon_intro zenon_H289 ]. % 19.73/19.89 apply (zenon_L101_); trivial. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H260 | zenon_intro zenon_H28a ]. % 19.73/19.89 apply (zenon_L188_); trivial. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H256 | zenon_intro zenon_H23 ]. % 19.73/19.89 apply (zenon_L189_); trivial. % 19.73/19.89 apply (zenon_L198_); trivial. % 19.73/19.89 (* end of lemma zenon_L199_ *) % 19.73/19.89 assert (zenon_L200_ : (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e22) (e20)) = (e22)) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((op1 (e12) (e13)) = (e12))) -> (~((op1 (e12) (e12)) = (e12))) -> (~((op1 (e12) (e11)) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e13)) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e23) (e23)) = (e22))) -> False). % 19.73/19.89 do 0 intro. intros zenon_H28b zenon_H257 zenon_H16e zenon_H25b zenon_H4c zenon_H159 zenon_Heb zenon_H158 zenon_H285 zenon_H267 zenon_H26b zenon_H8b zenon_H27c zenon_H12b zenon_H2e zenon_Hc2 zenon_H273 zenon_H26f zenon_H6e zenon_H161 zenon_H71 zenon_H282 zenon_H1dd zenon_H155 zenon_H263 zenon_H25f zenon_H2b zenon_H175 zenon_H288 zenon_H1e1. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H256 | zenon_intro zenon_H28c ]. % 19.73/19.89 apply (zenon_L186_); trivial. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H28c); [ zenon_intro zenon_H25a | zenon_intro zenon_H28d ]. % 19.73/19.89 apply (zenon_L187_); trivial. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H264 | zenon_intro zenon_H1e6 ]. % 19.73/19.89 apply (zenon_L199_); trivial. % 19.73/19.89 exact (zenon_H1e1 zenon_H1e6). % 19.73/19.89 (* end of lemma zenon_L200_ *) % 19.73/19.89 assert (zenon_L201_ : ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e13) (e13)) = (e12)))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e23) (e23)) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e21)) = (e22))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e23)) = (e22))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> False). % 19.73/19.89 do 0 intro. intros zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H56 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H1e3 zenon_H17f zenon_H28b zenon_H1e1 zenon_H175 zenon_H25f zenon_H263 zenon_H155 zenon_H267 zenon_H26b zenon_H282 zenon_Hc2 zenon_H12b zenon_H27c zenon_H273 zenon_H26f zenon_H161 zenon_H285 zenon_H288 zenon_H2b zenon_H2e zenon_H4c zenon_H25b zenon_H257 zenon_H16a zenon_H16b zenon_H16c zenon_H167 zenon_H17b zenon_H180. % 19.73/19.89 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H57 | zenon_intro zenon_Haa ]. % 19.73/19.89 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H58 | zenon_intro zenon_H9b ]. % 19.73/19.89 apply (zenon_L45_); trivial. % 19.73/19.89 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H58 | zenon_intro zenon_H74 ]. % 19.73/19.89 apply (zenon_L48_); trivial. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H58 | zenon_intro zenon_Heb ]. % 19.73/19.89 apply (zenon_L96_); trivial. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H58 | zenon_intro zenon_H1dd ]. % 19.73/19.89 apply (zenon_L96_); trivial. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H17b); [ zenon_intro zenon_H158 | zenon_intro zenon_Haa ]. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H159 | zenon_intro zenon_H75 ]. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_H16e | zenon_intro zenon_H16d ]. % 19.73/19.89 apply (zenon_L200_); trivial. % 19.73/19.89 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H172 | zenon_intro zenon_H171 ]. % 19.73/19.89 exact (zenon_H16a zenon_H172). % 19.73/19.89 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H174 | zenon_intro zenon_H173 ]. % 19.73/19.89 exact (zenon_H16b zenon_H174). % 19.73/19.89 exact (zenon_H16c zenon_H173). % 19.73/19.89 apply (zenon_L66_); trivial. % 19.73/19.89 apply (zenon_L43_); trivial. % 19.73/19.89 apply (zenon_L65_); trivial. % 19.73/19.89 (* end of lemma zenon_L201_ *) % 19.73/19.89 assert (zenon_L202_ : ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e22) (e23)) = (e22))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e21)) = (e22))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e23)) = (e22))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e13) (e13)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> False). % 19.74/19.90 do 0 intro. intros zenon_H10b zenon_H180 zenon_H17b zenon_H167 zenon_H16c zenon_H16b zenon_H16a zenon_H257 zenon_H25b zenon_H4c zenon_H2e zenon_H2b zenon_H288 zenon_H285 zenon_H161 zenon_H26f zenon_H273 zenon_H27c zenon_H12b zenon_Hc2 zenon_H282 zenon_H26b zenon_H267 zenon_H155 zenon_H263 zenon_H25f zenon_H175 zenon_H1e1 zenon_H28b zenon_H17f zenon_H1e3 zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H56 | zenon_intro zenon_H56 ]. % 19.74/19.90 apply (zenon_L201_); trivial. % 19.74/19.90 apply (zenon_L201_); trivial. % 19.74/19.90 (* end of lemma zenon_L202_ *) % 19.74/19.90 assert (zenon_L203_ : ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e23))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> (~((op2 (e20) (e20)) = (e22))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e13) (e13)) = (e12)))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e23) (e23)) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e21)) = (e22))) -> (~((op2 (e22) (e22)) = (e22))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> False). % 19.74/19.90 do 0 intro. intros zenon_H192 zenon_H50 zenon_H4b zenon_H4f zenon_H3d zenon_H2f zenon_H2d zenon_H1d zenon_H28 zenon_H47 zenon_H3e zenon_H41 zenon_H13 zenon_H48 zenon_H51 zenon_H40 zenon_H54 zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H1e3 zenon_H17f zenon_H28b zenon_H1e1 zenon_H175 zenon_H25f zenon_H263 zenon_H155 zenon_H267 zenon_H26b zenon_H282 zenon_Hc2 zenon_H12b zenon_H27c zenon_H273 zenon_H26f zenon_H161 zenon_H285 zenon_H288 zenon_H2b zenon_H2e zenon_H4c zenon_H25b zenon_H257 zenon_H16a zenon_H16b zenon_H167 zenon_H17b zenon_H180 zenon_H10b. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H16c | zenon_intro zenon_H32 ]. % 19.74/19.90 apply (zenon_L202_); trivial. % 19.74/19.90 apply (zenon_L69_); trivial. % 19.74/19.90 (* end of lemma zenon_L203_ *) % 19.74/19.90 assert (zenon_L204_ : ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e23)) = (e22))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e13) (e13)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e22))) -> (~((op2 (e20) (e20)) = (e21))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> False). % 19.74/19.90 do 0 intro. intros zenon_H193 zenon_H10b zenon_H180 zenon_H17b zenon_H167 zenon_H16b zenon_H257 zenon_H25b zenon_H4c zenon_H2e zenon_H2b zenon_H288 zenon_H285 zenon_H161 zenon_H26f zenon_H273 zenon_H27c zenon_H12b zenon_Hc2 zenon_H282 zenon_H26b zenon_H267 zenon_H155 zenon_H263 zenon_H25f zenon_H175 zenon_H1e1 zenon_H28b zenon_H17f zenon_H1e3 zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9 zenon_H3e zenon_H40 zenon_H3f zenon_H13 zenon_H194. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H16a | zenon_intro zenon_H2c ]. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H16c | zenon_intro zenon_H41 ]. % 19.74/19.90 apply (zenon_L202_); trivial. % 19.74/19.90 apply (zenon_L8_); trivial. % 19.74/19.90 apply zenon_H2c. apply sym_equal. exact zenon_H2b. % 19.74/19.90 (* end of lemma zenon_L204_ *) % 19.74/19.90 assert (zenon_L205_ : ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e21))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e23) (e23)) = (e22)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e13) (e13)) = (e12)))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e22) (e22)) = (e22)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e20) (e20)) = (e22)))) -> False). % 19.74/19.90 do 0 intro. intros zenon_H10d zenon_H4f zenon_H12 zenon_H13 zenon_H52 zenon_H47 zenon_H2b zenon_H28 zenon_H1d zenon_H3e zenon_H3f zenon_H48 zenon_H2d zenon_H2e zenon_H4c zenon_H4b zenon_H50 zenon_H53 zenon_H152 zenon_H1e7 zenon_H194 zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H1e3 zenon_H17f zenon_H28b zenon_H175 zenon_H25f zenon_H263 zenon_H155 zenon_H267 zenon_H26b zenon_H282 zenon_Hc2 zenon_H12b zenon_H27c zenon_H273 zenon_H26f zenon_H161 zenon_H285 zenon_H288 zenon_H25b zenon_H257 zenon_H167 zenon_H17b zenon_H180 zenon_H10b zenon_H193 zenon_H195 zenon_H3d zenon_H2f zenon_H51 zenon_H54 zenon_H10e. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H14 | zenon_intro zenon_H2c ]. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.74/19.90 apply (zenon_L16_); trivial. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H15 | zenon_intro zenon_H31 ]. % 19.74/19.90 apply (zenon_L78_); trivial. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H15 | zenon_intro zenon_H16b ]. % 19.74/19.90 apply (zenon_L95_); trivial. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H15 | zenon_intro zenon_H1e1 ]. % 19.74/19.90 apply (zenon_L95_); trivial. % 19.74/19.90 apply (zenon_L204_); trivial. % 19.74/19.90 apply zenon_H2c. apply sym_equal. exact zenon_H2b. % 19.74/19.90 (* end of lemma zenon_L205_ *) % 19.74/19.90 assert (zenon_L206_ : ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e13) (e13)) = (e12)))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e23) (e23)) = (e22)))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e22) (e22)) = (e22)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e20) (e20)) = (e22)))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e20) (e20)) = (e21)))) -> False). % 19.74/19.90 do 0 intro. intros zenon_H10c zenon_H54 zenon_H53 zenon_H52 zenon_H51 zenon_H48 zenon_H3e zenon_H47 zenon_H28 zenon_H1d zenon_H2d zenon_H2b zenon_H2e zenon_H2f zenon_H3d zenon_H4f zenon_H4b zenon_H4c zenon_H50 zenon_H13 zenon_H12 zenon_H194 zenon_H192 zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H1e3 zenon_H17f zenon_H28b zenon_H175 zenon_H25f zenon_H263 zenon_H155 zenon_H267 zenon_H26b zenon_H282 zenon_Hc2 zenon_H12b zenon_H27c zenon_H273 zenon_H26f zenon_H161 zenon_H285 zenon_H288 zenon_H25b zenon_H257 zenon_H167 zenon_H17b zenon_H180 zenon_H10b zenon_H10d zenon_H152 zenon_H1e7 zenon_H193 zenon_H195 zenon_H10e zenon_H196. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H14 | zenon_intro zenon_H3f ]. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.74/19.90 apply (zenon_L17_); trivial. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H15 | zenon_intro zenon_H31 ]. % 19.74/19.90 apply (zenon_L78_); trivial. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H15 | zenon_intro zenon_H16b ]. % 19.74/19.90 apply (zenon_L95_); trivial. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H15 | zenon_intro zenon_H1e1 ]. % 19.74/19.90 apply (zenon_L95_); trivial. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H196); [ zenon_intro zenon_H16a | zenon_intro zenon_H3f ]. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H16c | zenon_intro zenon_H41 ]. % 19.74/19.90 apply (zenon_L202_); trivial. % 19.74/19.90 apply (zenon_L203_); trivial. % 19.74/19.90 apply (zenon_L205_); trivial. % 19.74/19.90 apply (zenon_L205_); trivial. % 19.74/19.90 (* end of lemma zenon_L206_ *) % 19.74/19.90 assert (zenon_L207_ : (~((h4 (op1 (e13) (e11))) = (op2 (h4 (e13)) (h4 (e11))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op1 (e13) (e11)) = (e10)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> False). % 19.74/19.90 do 0 intro. intros zenon_H28e zenon_Hc2 zenon_H28f zenon_Hfc zenon_H12b. % 19.74/19.90 cut (((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) = ((h4 (op1 (e13) (e11))) = (op2 (h4 (e13)) (h4 (e11))))). % 19.74/19.90 intro zenon_D_pnotp. % 19.74/19.90 apply zenon_H28e. % 19.74/19.90 rewrite <- zenon_D_pnotp. % 19.74/19.90 exact zenon_Hc2. % 19.74/19.90 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (h4 (e13)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H290]. % 19.74/19.90 cut (((h4 (e10)) = (h4 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H291]. % 19.74/19.90 congruence. % 19.74/19.90 elim (classic ((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11))))); [ zenon_intro zenon_H292 | zenon_intro zenon_H293 ]. % 19.74/19.90 cut (((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11)))) = ((h4 (e10)) = (h4 (op1 (e13) (e11))))). % 19.74/19.90 intro zenon_D_pnotp. % 19.74/19.90 apply zenon_H291. % 19.74/19.90 rewrite <- zenon_D_pnotp. % 19.74/19.90 exact zenon_H292. % 19.74/19.90 cut (((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H293]. % 19.74/19.90 cut (((h4 (op1 (e13) (e11))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H294]. % 19.74/19.90 congruence. % 19.74/19.90 cut (((op1 (e13) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H295]. % 19.74/19.90 congruence. % 19.74/19.90 exact (zenon_H295 zenon_H28f). % 19.74/19.90 apply zenon_H293. apply refl_equal. % 19.74/19.90 apply zenon_H293. apply refl_equal. % 19.74/19.90 cut (((op2 (e23) (e23)) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 19.74/19.90 cut (((e23) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H296]. % 19.74/19.90 congruence. % 19.74/19.90 apply zenon_H296. apply sym_equal. exact zenon_H12b. % 19.74/19.90 apply zenon_H116. apply sym_equal. exact zenon_Hfc. % 19.74/19.90 (* end of lemma zenon_L207_ *) % 19.74/19.90 assert (zenon_L208_ : ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e13) (e12)) = (e10)) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> False). % 19.74/19.90 do 0 intro. intros zenon_H71 zenon_H297 zenon_H6e zenon_H298. % 19.74/19.90 elim (classic ((op1 (e13) (e12)) = (op1 (e13) (e12)))); [ zenon_intro zenon_H299 | zenon_intro zenon_H29a ]. % 19.74/19.90 cut (((op1 (e13) (e12)) = (op1 (e13) (e12))) = ((op1 (e13) (e11)) = (op1 (e13) (e12)))). % 19.74/19.90 intro zenon_D_pnotp. % 19.74/19.90 apply zenon_H298. % 19.74/19.90 rewrite <- zenon_D_pnotp. % 19.74/19.90 exact zenon_H299. % 19.74/19.90 cut (((op1 (e13) (e12)) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H29a]. % 19.74/19.90 cut (((op1 (e13) (e12)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H29b]. % 19.74/19.90 congruence. % 19.74/19.90 cut (((e10) = (op1 (e13) (op1 (e13) (e13)))) = ((op1 (e13) (e12)) = (op1 (e13) (e11)))). % 19.74/19.90 intro zenon_D_pnotp. % 19.74/19.90 apply zenon_H29b. % 19.74/19.90 rewrite <- zenon_D_pnotp. % 19.74/19.90 exact zenon_H71. % 19.74/19.90 cut (((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 19.74/19.90 cut (((e10) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H29c]. % 19.74/19.90 congruence. % 19.74/19.90 elim (classic ((op1 (e13) (e12)) = (op1 (e13) (e12)))); [ zenon_intro zenon_H299 | zenon_intro zenon_H29a ]. % 19.74/19.90 cut (((op1 (e13) (e12)) = (op1 (e13) (e12))) = ((e10) = (op1 (e13) (e12)))). % 19.74/19.90 intro zenon_D_pnotp. % 19.74/19.90 apply zenon_H29c. % 19.74/19.90 rewrite <- zenon_D_pnotp. % 19.74/19.90 exact zenon_H299. % 19.74/19.90 cut (((op1 (e13) (e12)) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H29a]. % 19.74/19.90 cut (((op1 (e13) (e12)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H29d]. % 19.74/19.90 congruence. % 19.74/19.90 exact (zenon_H29d zenon_H297). % 19.74/19.90 apply zenon_H29a. apply refl_equal. % 19.74/19.90 apply zenon_H29a. apply refl_equal. % 19.74/19.90 apply (zenon_L22_); trivial. % 19.74/19.90 apply zenon_H29a. apply refl_equal. % 19.74/19.90 apply zenon_H29a. apply refl_equal. % 19.74/19.90 (* end of lemma zenon_L208_ *) % 19.74/19.90 assert (zenon_L209_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((h4 (e13)) = (e23)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e13) (e11))) = (op2 (h4 (e13)) (h4 (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e13)) = (e10))) -> False). % 19.74/19.90 do 0 intro. intros zenon_H29e zenon_H161 zenon_H12b zenon_Hfc zenon_Hc2 zenon_H28e zenon_H298 zenon_H6e zenon_H71 zenon_H29f. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H29e); [ zenon_intro zenon_H162 | zenon_intro zenon_H2a0 ]. % 19.74/19.90 apply (zenon_L99_); trivial. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H2a0); [ zenon_intro zenon_H28f | zenon_intro zenon_H2a1 ]. % 19.74/19.90 apply (zenon_L207_); trivial. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H297 | zenon_intro zenon_H2a2 ]. % 19.74/19.90 apply (zenon_L208_); trivial. % 19.74/19.90 exact (zenon_H29f zenon_H2a2). % 19.74/19.90 (* end of lemma zenon_L209_ *) % 19.74/19.90 assert (zenon_L210_ : ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e13) (e11))) = (op2 (h4 (e13)) (h4 (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((~((op1 (e12) (e10)) = (e12)))\/(~((op1 (e13) (e13)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> False). % 19.74/19.90 do 0 intro. intros zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H56 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H17b zenon_H155 zenon_H17f zenon_H29e zenon_H298 zenon_Hfc zenon_H12b zenon_Hc2 zenon_H28e zenon_H161 zenon_H2a3 zenon_H180. % 19.74/19.90 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H57 | zenon_intro zenon_Haa ]. % 19.74/19.90 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H58 | zenon_intro zenon_H9b ]. % 19.74/19.90 apply (zenon_L45_); trivial. % 19.74/19.90 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H58 | zenon_intro zenon_H74 ]. % 19.74/19.90 apply (zenon_L48_); trivial. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H58 | zenon_intro zenon_Heb ]. % 19.74/19.90 apply (zenon_L96_); trivial. % 19.74/19.90 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H73 | zenon_intro zenon_Haa ]. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H2a3); [ zenon_intro zenon_H15d | zenon_intro zenon_H29f ]. % 19.74/19.90 apply (zenon_L110_); trivial. % 19.74/19.90 apply (zenon_L209_); trivial. % 19.74/19.90 apply (zenon_L65_); trivial. % 19.74/19.90 apply (zenon_L65_); trivial. % 19.74/19.90 (* end of lemma zenon_L210_ *) % 19.74/19.90 assert (zenon_L211_ : ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e12) (e10)) = (e12)))\/(~((op1 (e13) (e13)) = (e10)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((h4 (op1 (e13) (e11))) = (op2 (h4 (e13)) (h4 (e11))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> False). % 19.74/19.90 do 0 intro. intros zenon_H10b zenon_H180 zenon_H2a3 zenon_H161 zenon_H28e zenon_Hc2 zenon_H12b zenon_Hfc zenon_H298 zenon_H29e zenon_H17f zenon_H155 zenon_H17b zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H56 | zenon_intro zenon_H56 ]. % 19.74/19.90 apply (zenon_L210_); trivial. % 19.74/19.90 apply (zenon_L210_); trivial. % 19.74/19.90 (* end of lemma zenon_L211_ *) % 19.74/19.90 assert (zenon_L212_ : (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e23) (e20)) = (e22)) -> (~((op2 (e22) (e21)) = (e22))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e23)) = (e22))) -> False). % 19.74/19.90 do 0 intro. intros zenon_H167 zenon_H257 zenon_H256 zenon_H16a zenon_H16b zenon_H16c. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_H16e | zenon_intro zenon_H16d ]. % 19.74/19.90 apply (zenon_L186_); trivial. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H172 | zenon_intro zenon_H171 ]. % 19.74/19.90 exact (zenon_H16a zenon_H172). % 19.74/19.90 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H174 | zenon_intro zenon_H173 ]. % 19.74/19.90 exact (zenon_H16b zenon_H174). % 19.74/19.90 exact (zenon_H16c zenon_H173). % 19.74/19.90 (* end of lemma zenon_L212_ *) % 19.74/19.90 assert (zenon_L213_ : (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e11)) = (e12))) -> (~((op1 (e12) (e12)) = (e12))) -> (~((op1 (e12) (e13)) = (e12))) -> False). % 19.74/19.90 do 0 intro. intros zenon_H155 zenon_H267 zenon_H266 zenon_H158 zenon_Heb zenon_H159. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H15b | zenon_intro zenon_H15a ]. % 19.74/19.90 apply (zenon_L190_); trivial. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H15f | zenon_intro zenon_H15e ]. % 19.74/19.90 exact (zenon_H158 zenon_H15f). % 19.74/19.90 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H160 ]. % 19.74/19.90 exact (zenon_Heb zenon_Hf2). % 19.74/19.90 exact (zenon_H159 zenon_H160). % 19.74/19.90 (* end of lemma zenon_L213_ *) % 19.74/19.90 assert (zenon_L214_ : ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((op1 (e13) (e12)) = (e12)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((e22) = (h4 (op1 (e13) (e12))))) -> False). % 19.74/19.90 do 0 intro. intros zenon_H10f zenon_H274 zenon_H4c zenon_H2a4. % 19.74/19.90 elim (classic ((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12))))); [ zenon_intro zenon_H2a5 | zenon_intro zenon_H2a6 ]. % 19.74/19.90 cut (((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12)))) = ((e22) = (h4 (op1 (e13) (e12))))). % 19.74/19.90 intro zenon_D_pnotp. % 19.74/19.90 apply zenon_H2a4. % 19.74/19.90 rewrite <- zenon_D_pnotp. % 19.74/19.90 exact zenon_H2a5. % 19.74/19.90 cut (((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H2a6]. % 19.74/19.90 cut (((h4 (op1 (e13) (e12))) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H2a7]. % 19.74/19.90 congruence. % 19.74/19.90 cut (((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) = ((h4 (op1 (e13) (e12))) = (e22))). % 19.74/19.90 intro zenon_D_pnotp. % 19.74/19.90 apply zenon_H2a7. % 19.74/19.90 rewrite <- zenon_D_pnotp. % 19.74/19.90 exact zenon_H10f. % 19.74/19.90 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23))) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 19.74/19.90 cut (((h4 (e12)) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H2a8]. % 19.74/19.90 congruence. % 19.74/19.90 elim (classic ((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12))))); [ zenon_intro zenon_H2a5 | zenon_intro zenon_H2a6 ]. % 19.74/19.90 cut (((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12)))) = ((h4 (e12)) = (h4 (op1 (e13) (e12))))). % 19.74/19.90 intro zenon_D_pnotp. % 19.74/19.90 apply zenon_H2a8. % 19.74/19.90 rewrite <- zenon_D_pnotp. % 19.74/19.90 exact zenon_H2a5. % 19.74/19.90 cut (((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H2a6]. % 19.74/19.90 cut (((h4 (op1 (e13) (e12))) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H2a9]. % 19.74/19.90 congruence. % 19.74/19.90 cut (((op1 (e13) (e12)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H2aa]. % 19.74/19.90 congruence. % 19.74/19.90 exact (zenon_H2aa zenon_H274). % 19.74/19.90 apply zenon_H2a6. apply refl_equal. % 19.74/19.90 apply zenon_H2a6. apply refl_equal. % 19.74/19.90 apply zenon_H119. apply sym_equal. exact zenon_H4c. % 19.74/19.90 apply zenon_H2a6. apply refl_equal. % 19.74/19.90 apply zenon_H2a6. apply refl_equal. % 19.74/19.90 (* end of lemma zenon_L214_ *) % 19.74/19.90 assert (zenon_L215_ : ((op2 (e23) (e22)) = (e22)) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((op1 (e13) (e12)) = (e12)) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> False). % 19.74/19.90 do 0 intro. intros zenon_H264 zenon_H12b zenon_H10f zenon_H4c zenon_H274 zenon_H2ab. % 19.74/19.90 elim (classic ((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12))))); [ zenon_intro zenon_H2ac | zenon_intro zenon_H2ad ]. % 19.74/19.90 cut (((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12)))) = ((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))). % 19.74/19.90 intro zenon_D_pnotp. % 19.74/19.90 apply zenon_H2ab. % 19.74/19.90 rewrite <- zenon_D_pnotp. % 19.74/19.90 exact zenon_H2ac. % 19.74/19.90 cut (((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H2ad]. % 19.74/19.90 cut (((op2 (h4 (e13)) (h4 (e12))) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H2ae]. % 19.74/19.90 congruence. % 19.74/19.90 cut (((op2 (e23) (e22)) = (e22)) = ((op2 (h4 (e13)) (h4 (e12))) = (h4 (op1 (e13) (e12))))). % 19.74/19.90 intro zenon_D_pnotp. % 19.74/19.90 apply zenon_H2ae. % 19.74/19.90 rewrite <- zenon_D_pnotp. % 19.74/19.90 exact zenon_H264. % 19.74/19.90 cut (((e22) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H2a4]. % 19.74/19.90 cut (((op2 (e23) (e22)) = (op2 (h4 (e13)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H2af]. % 19.74/19.90 congruence. % 19.74/19.90 elim (classic ((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12))))); [ zenon_intro zenon_H2ac | zenon_intro zenon_H2ad ]. % 19.74/19.90 cut (((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12)))) = ((op2 (e23) (e22)) = (op2 (h4 (e13)) (h4 (e12))))). % 19.74/19.90 intro zenon_D_pnotp. % 19.74/19.90 apply zenon_H2af. % 19.74/19.90 rewrite <- zenon_D_pnotp. % 19.74/19.90 exact zenon_H2ac. % 19.74/19.90 cut (((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H2ad]. % 19.74/19.90 cut (((op2 (h4 (e13)) (h4 (e12))) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H2b0]. % 19.74/19.90 congruence. % 19.74/19.90 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H118]. % 19.74/19.90 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 19.74/19.90 congruence. % 19.74/19.90 exact (zenon_H137 zenon_H12b). % 19.74/19.90 apply (zenon_L73_); trivial. % 19.74/19.90 apply zenon_H2ad. apply refl_equal. % 19.74/19.90 apply zenon_H2ad. apply refl_equal. % 19.74/19.90 apply (zenon_L214_); trivial. % 19.74/19.90 apply zenon_H2ad. apply refl_equal. % 19.74/19.90 apply zenon_H2ad. apply refl_equal. % 19.74/19.90 (* end of lemma zenon_L215_ *) % 19.74/19.90 assert (zenon_L216_ : (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e13)) = (e12))) -> (~((op1 (e12) (e12)) = (e12))) -> (~((op1 (e12) (e11)) = (e12))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> ((op2 (e23) (e22)) = (e22)) -> (~((op1 (e13) (e13)) = (e12))) -> False). % 19.74/19.90 do 0 intro. intros zenon_H285 zenon_H159 zenon_Heb zenon_H158 zenon_H267 zenon_H155 zenon_H26b zenon_H71 zenon_H6e zenon_H8b zenon_H2ab zenon_H4c zenon_H10f zenon_H12b zenon_H264 zenon_H1dd. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H266 | zenon_intro zenon_H286 ]. % 19.74/19.90 apply (zenon_L213_); trivial. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H26a | zenon_intro zenon_H287 ]. % 19.74/19.90 apply (zenon_L191_); trivial. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H274 | zenon_intro zenon_H1e0 ]. % 19.74/19.90 apply (zenon_L215_); trivial. % 19.74/19.90 exact (zenon_H1dd zenon_H1e0). % 19.74/19.90 (* end of lemma zenon_L216_ *) % 19.74/19.90 assert (zenon_L217_ : ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e23) (e23)) = (e22))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e21)) = (e22))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e23)) = (e22))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (~((op1 (e10) (e10)) = (e12))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e13) (e13)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (e10))) -> (~((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (e12))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> False). % 19.74/19.90 do 0 intro. intros zenon_H180 zenon_H17b zenon_H28b zenon_H1e1 zenon_H155 zenon_H267 zenon_H26b zenon_H2ab zenon_H12b zenon_H10f zenon_H285 zenon_H2b zenon_H2e zenon_H4c zenon_H25b zenon_H257 zenon_H16a zenon_H16b zenon_H16c zenon_H167 zenon_H17f zenon_H9b zenon_H1e3 zenon_H55 zenon_H57 zenon_H56 zenon_Hc0 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hb8 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_H60 zenon_Hb5 zenon_Hbc zenon_Hbf zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_H6b zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_H72 zenon_H71 zenon_H6e zenon_H74 zenon_H70. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H58 | zenon_intro zenon_Heb ]. % 19.74/19.90 apply (zenon_L96_); trivial. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H58 | zenon_intro zenon_H1dd ]. % 19.74/19.90 apply (zenon_L96_); trivial. % 19.74/19.90 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H59 | zenon_intro zenon_H75 ]. % 19.74/19.90 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H73 | zenon_intro zenon_Haa ]. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H17b); [ zenon_intro zenon_H158 | zenon_intro zenon_Haa ]. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H159 | zenon_intro zenon_H75 ]. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H256 | zenon_intro zenon_H28c ]. % 19.74/19.90 apply (zenon_L212_); trivial. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H28c); [ zenon_intro zenon_H25a | zenon_intro zenon_H28d ]. % 19.74/19.90 apply (zenon_L187_); trivial. % 19.74/19.90 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H264 | zenon_intro zenon_H1e6 ]. % 19.74/19.90 apply (zenon_L216_); trivial. % 19.74/19.90 exact (zenon_H1e1 zenon_H1e6). % 19.74/19.90 apply (zenon_L66_); trivial. % 19.74/19.90 apply (zenon_L58_); trivial. % 19.74/19.90 apply (zenon_L34_); trivial. % 19.74/19.90 apply (zenon_L66_); trivial. % 19.74/19.90 (* end of lemma zenon_L217_ *) % 19.74/19.90 assert (zenon_L218_ : ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e13) (e13)) = (e12)))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e22) (e23)) = (e22))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e21)) = (e22))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op2 (e23) (e23)) = (e22))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (e10))) -> (~((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (e12))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> False). % 19.74/19.90 do 0 intro. intros zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_Hbe zenon_H1e3 zenon_H17f zenon_H167 zenon_H16c zenon_H16b zenon_H16a zenon_H257 zenon_H25b zenon_H4c zenon_H2e zenon_H2b zenon_H285 zenon_H10f zenon_H12b zenon_H2ab zenon_H26b zenon_H267 zenon_H155 zenon_H1e1 zenon_H28b zenon_H17b zenon_H180 zenon_H55 zenon_H57 zenon_H56 zenon_Hbb zenon_Hb8 zenon_H9b zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hbd zenon_Hbc zenon_Hbf. % 19.74/19.90 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_H58 | zenon_intro zenon_H74 ]. % 19.74/19.90 apply (zenon_L48_); trivial. % 19.74/19.90 apply (zenon_L217_); trivial. % 19.74/19.90 (* end of lemma zenon_L218_ *) % 19.74/19.90 assert (zenon_L219_ : ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e13) (e13)) = (e12)))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e22) (e23)) = (e22))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e21)) = (e22))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op2 (e23) (e23)) = (e22))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> False). % 19.75/19.90 do 0 intro. intros zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H56 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H1e3 zenon_H17f zenon_H167 zenon_H16c zenon_H16b zenon_H16a zenon_H257 zenon_H25b zenon_H4c zenon_H2e zenon_H2b zenon_H285 zenon_H10f zenon_H12b zenon_H2ab zenon_H26b zenon_H267 zenon_H155 zenon_H1e1 zenon_H28b zenon_H17b zenon_H180. % 19.75/19.90 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H57 | zenon_intro zenon_Haa ]. % 19.75/19.90 apply (zenon_or_s _ _ zenon_Hbe); [ zenon_intro zenon_H58 | zenon_intro zenon_H9b ]. % 19.75/19.90 apply (zenon_L45_); trivial. % 19.75/19.90 apply (zenon_L218_); trivial. % 19.75/19.90 apply (zenon_L65_); trivial. % 19.75/19.90 (* end of lemma zenon_L219_ *) % 19.75/19.90 assert (zenon_L220_ : ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e23) (e23)) = (e22))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e21)) = (e22))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e23)) = (e22))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e13) (e13)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> False). % 19.75/19.90 do 0 intro. intros zenon_H10b zenon_H180 zenon_H17b zenon_H28b zenon_H1e1 zenon_H155 zenon_H267 zenon_H26b zenon_H2ab zenon_H12b zenon_H10f zenon_H285 zenon_H2b zenon_H2e zenon_H4c zenon_H25b zenon_H257 zenon_H16a zenon_H16b zenon_H16c zenon_H167 zenon_H17f zenon_H1e3 zenon_Hf5 zenon_Hf6 zenon_Hf4 zenon_He8 zenon_Hf3 zenon_Hf7 zenon_Hf8 zenon_Hfa zenon_H55 zenon_Hb8 zenon_Hbe zenon_Hbd zenon_Hbb zenon_Hbc zenon_Hbf zenon_Hc0 zenon_H80 zenon_H72 zenon_H71 zenon_H6e zenon_H70 zenon_H60 zenon_H6b zenon_Hb5 zenon_Hb4 zenon_Haf zenon_Hab zenon_Ha5 zenon_Ha1 zenon_H84 zenon_H8d zenon_H8b zenon_H94 zenon_H9a zenon_Hb6 zenon_Hb7 zenon_Hf9. % 19.75/19.90 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H56 | zenon_intro zenon_H56 ]. % 19.75/19.90 apply (zenon_L219_); trivial. % 19.75/19.90 apply (zenon_L219_); trivial. % 19.75/19.90 (* end of lemma zenon_L220_ *) % 19.75/19.90 assert (zenon_L221_ : ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (e23))) -> (~((op2 (e20) (e20)) = (e20))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> (~((op2 (e20) (e20)) = (e22))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e13) (e13)) = (e12)))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e21)) = (e22))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op2 (e23) (e23)) = (e22))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> False). % 19.75/19.90 do 0 intro. intros zenon_H192 zenon_H50 zenon_H4b zenon_H4f zenon_H3d zenon_H2f zenon_H2d zenon_H1d zenon_H28 zenon_H47 zenon_H3e zenon_H41 zenon_H13 zenon_H48 zenon_H51 zenon_H40 zenon_H54 zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H1e3 zenon_H17f zenon_H167 zenon_H16b zenon_H16a zenon_H257 zenon_H25b zenon_H4c zenon_H2e zenon_H2b zenon_H285 zenon_H10f zenon_H12b zenon_H2ab zenon_H26b zenon_H267 zenon_H155 zenon_H1e1 zenon_H28b zenon_H17b zenon_H180 zenon_H10b. % 19.75/19.90 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H16c | zenon_intro zenon_H32 ]. % 19.75/19.90 apply (zenon_L220_); trivial. % 19.75/19.90 apply (zenon_L69_); trivial. % 19.75/19.90 (* end of lemma zenon_L221_ *) % 19.75/19.90 assert (zenon_L222_ : ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> (~((op2 (e20) (e20)) = (e22))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e13) (e13)) = (e12)))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e21)) = (e22))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op2 (e23) (e23)) = (e22))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> False). % 19.75/19.90 do 0 intro. intros zenon_H194 zenon_H54 zenon_H40 zenon_H51 zenon_H48 zenon_H13 zenon_H3e zenon_H47 zenon_H28 zenon_H1d zenon_H2d zenon_H2f zenon_H3d zenon_H4f zenon_H4b zenon_H50 zenon_H192 zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H1e3 zenon_H17f zenon_H167 zenon_H16b zenon_H16a zenon_H257 zenon_H25b zenon_H4c zenon_H2e zenon_H2b zenon_H285 zenon_H10f zenon_H12b zenon_H2ab zenon_H26b zenon_H267 zenon_H155 zenon_H1e1 zenon_H28b zenon_H17b zenon_H180 zenon_H10b. % 19.75/19.90 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H16c | zenon_intro zenon_H41 ]. % 19.75/19.90 apply (zenon_L220_); trivial. % 19.75/19.90 apply (zenon_L221_); trivial. % 19.75/19.90 (* end of lemma zenon_L222_ *) % 19.75/19.90 assert (zenon_L223_ : ((~((op2 (e20) (e21)) = (e20)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e20) (e23)) = (e20)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e20) (e20)) = (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e20) (e20)) = (e22)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e20)) = (e22))\/((op2 (e20) (e20)) = (e23))))) -> ((~((op2 (e23) (e21)) = (e23)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e23) (e23)) = (e23)))\/(~((op2 (e23) (e23)) = (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e22)) = (e23)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e21) (e21)) = (e21)))\/(~((op2 (e21) (e21)) = (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((~((op2 (e23) (e20)) = (e23)))\/(~((op2 (e21) (e21)) = (e20)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e21) (e21)) = (e22)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e23) (e23)) = (e22)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e20) (e20)) = (e23)))) -> ((~((op2 (e22) (e23)) = (e22)))\/(~((op2 (e21) (e21)) = (e23)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e10) (e10)) = (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((e11) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e10)) = (e12))\/((op1 (e10) (e10)) = (e13))))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e10) (e10)) = (e13)))) -> ((~((op1 (e13) (e11)) = (e13)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e13)) = (e13)))\/(~((op1 (e13) (e13)) = (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e12)) = (e13)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e11) (e11)) = (e13)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e13) (e13)) = (e13)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e11) (e11)) = (e10)))) -> ((~((op1 (e11) (e11)) = (e11)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e10) (e10)) = (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e11) (e11)) = (e12)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e11) (e11)) = (e11)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e13) (e13)) = (e11)))) -> ((~((op1 (e13) (e10)) = (e13)))\/(~((op1 (e12) (e12)) = (e10)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e12)))\/(~((op1 (e10) (e10)) = (e12)))) -> ((~((op1 (e10) (e13)) = (e10)))\/(~((op1 (e12) (e12)) = (e13)))) -> ((~((op1 (e10) (e11)) = (e10)))\/(~((op1 (e12) (e12)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e13) (e13)) = (e12)))) -> ((~((op1 (e12) (e13)) = (e12)))\/(~((op1 (e11) (e11)) = (e13)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((~((op1 (e12) (e11)) = (e12)))\/(~((op1 (e10) (e10)) = (e11)))) -> ((~((op1 (e10) (e12)) = (e10)))\/(~((op1 (e12) (e12)) = (e12)))) -> ((~((op1 (e10) (e10)) = (e10)))\/(~((op1 (e10) (e10)) = (e10)))) -> ((~((op2 (e22) (e21)) = (e22)))\/(~((op2 (e23) (e23)) = (e21)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e22) (e22)) = (e22)))) -> ((~((op2 (e20) (e22)) = (e20)))\/(~((op2 (e20) (e20)) = (e22)))) -> False). % 19.75/19.90 do 0 intro. intros zenon_H10d zenon_H54 zenon_H53 zenon_H52 zenon_H51 zenon_H48 zenon_H3e zenon_H47 zenon_H28 zenon_H1d zenon_H2d zenon_H2b zenon_H2e zenon_H2f zenon_H3d zenon_H4f zenon_H4b zenon_H4c zenon_H50 zenon_H13 zenon_H12 zenon_H152 zenon_H1e7 zenon_H194 zenon_H192 zenon_Hf9 zenon_Hb7 zenon_Hb6 zenon_H9a zenon_H94 zenon_H8b zenon_H8d zenon_H84 zenon_Ha1 zenon_Ha5 zenon_Hab zenon_Haf zenon_Hb4 zenon_Hb5 zenon_H6b zenon_H60 zenon_H70 zenon_H6e zenon_H71 zenon_H72 zenon_H80 zenon_Hc0 zenon_Hbf zenon_Hbc zenon_Hbb zenon_Hbd zenon_Hbe zenon_Hb8 zenon_H55 zenon_Hfa zenon_Hf8 zenon_Hf7 zenon_Hf3 zenon_He8 zenon_Hf4 zenon_Hf6 zenon_Hf5 zenon_H1e3 zenon_H17f zenon_H167 zenon_H257 zenon_H25b zenon_H285 zenon_H10f zenon_H12b zenon_H2ab zenon_H26b zenon_H267 zenon_H155 zenon_H28b zenon_H17b zenon_H180 zenon_H10b zenon_H193 zenon_H195 zenon_H10e. % 19.75/19.90 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H14 | zenon_intro zenon_H2c ]. % 19.75/19.90 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_H15 | zenon_intro zenon_H40 ]. % 19.75/19.90 apply (zenon_L17_); trivial. % 19.75/19.90 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H15 | zenon_intro zenon_H31 ]. % 19.75/19.90 apply (zenon_L78_); trivial. % 19.75/19.90 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H15 | zenon_intro zenon_H16b ]. % 19.75/19.90 apply (zenon_L95_); trivial. % 19.75/19.90 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H15 | zenon_intro zenon_H1e1 ]. % 19.75/19.90 apply (zenon_L95_); trivial. % 19.75/19.90 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H16a | zenon_intro zenon_H2c ]. % 19.75/19.90 apply (zenon_L222_); trivial. % 19.75/19.90 apply zenon_H2c. apply sym_equal. exact zenon_H2b. % 19.75/19.90 apply zenon_H2c. apply sym_equal. exact zenon_H2b. % 19.75/19.90 (* end of lemma zenon_L223_ *) % 19.75/19.90 assert (zenon_L224_ : (~((h4 (op1 (e13) (e13))) = (op2 (h4 (e13)) (h4 (e13))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e11) = (op1 (e13) (e13))) -> ((h4 (e13)) = (e23)) -> False). % 19.75/19.90 do 0 intro. intros zenon_H2b1 zenon_Hfc zenon_H6e zenon_H12b. % 19.75/19.90 cut (((h4 (e11)) = (op2 (e23) (e23))) = ((h4 (op1 (e13) (e13))) = (op2 (h4 (e13)) (h4 (e13))))). % 19.75/19.90 intro zenon_D_pnotp. % 19.75/19.90 apply zenon_H2b1. % 19.75/19.90 rewrite <- zenon_D_pnotp. % 19.75/19.90 exact zenon_Hfc. % 19.75/19.90 cut (((op2 (e23) (e23)) = (op2 (h4 (e13)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H2b2]. % 19.75/19.90 cut (((h4 (e11)) = (h4 (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H2b3]. % 19.75/19.90 congruence. % 19.75/19.90 elim (classic ((h4 (op1 (e13) (e13))) = (h4 (op1 (e13) (e13))))); [ zenon_intro zenon_H2b4 | zenon_intro zenon_H2b5 ]. % 19.75/19.90 cut (((h4 (op1 (e13) (e13))) = (h4 (op1 (e13) (e13)))) = ((h4 (e11)) = (h4 (op1 (e13) (e13))))). % 19.75/19.90 intro zenon_D_pnotp. % 19.75/19.90 apply zenon_H2b3. % 19.75/19.90 rewrite <- zenon_D_pnotp. % 19.75/19.90 exact zenon_H2b4. % 19.75/19.90 cut (((h4 (op1 (e13) (e13))) = (h4 (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H2b5]. % 19.75/19.90 cut (((h4 (op1 (e13) (e13))) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H2b6]. % 19.75/19.90 congruence. % 19.75/19.90 cut (((op1 (e13) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 19.75/19.90 congruence. % 19.75/19.90 apply zenon_H6f. apply sym_equal. exact zenon_H6e. % 19.75/19.90 apply zenon_H2b5. apply refl_equal. % 19.75/19.90 apply zenon_H2b5. apply refl_equal. % 19.75/19.90 cut (((e23) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H296]. % 19.75/19.90 cut (((e23) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H296]. % 19.75/19.90 congruence. % 19.75/19.90 apply zenon_H296. apply sym_equal. exact zenon_H12b. % 19.75/19.90 apply zenon_H296. apply sym_equal. exact zenon_H12b. % 19.75/19.90 (* end of lemma zenon_L224_ *) % 19.75/19.90 assert (zenon_L225_ : (~(((h4 (e10)) = (e20))\/(((h4 (e11)) = (e20))\/(((h4 (e12)) = (e20))\/((h4 (e13)) = (e20)))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> False). % 19.75/19.90 do 0 intro. intros zenon_H2b7 zenon_Hc2 zenon_H2e. % 19.75/19.90 apply (zenon_notor_s _ _ zenon_H2b7). zenon_intro zenon_Hc1. zenon_intro zenon_H2b8. % 19.75/19.90 apply (zenon_L49_); trivial. % 19.75/19.90 (* end of lemma zenon_L225_ *) % 19.75/19.90 assert (zenon_L226_ : (~(((h4 (e10)) = (e21))\/(((h4 (e11)) = (e21))\/(((h4 (e12)) = (e21))\/((h4 (e13)) = (e21)))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 19.75/19.90 do 0 intro. intros zenon_H2b9 zenon_Hfc zenon_H2b. % 19.75/19.90 apply (zenon_notor_s _ _ zenon_H2b9). zenon_intro zenon_H2bb. zenon_intro zenon_H2ba. % 19.75/19.90 apply (zenon_notor_s _ _ zenon_H2ba). zenon_intro zenon_H153. zenon_intro zenon_H2bc. % 19.75/19.90 apply (zenon_L97_); trivial. % 19.75/19.90 (* end of lemma zenon_L226_ *) % 19.75/19.90 assert (zenon_L227_ : (~(((h4 (e10)) = (e22))\/(((h4 (e11)) = (e22))\/(((h4 (e12)) = (e22))\/((h4 (e13)) = (e22)))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (op2 (e23) (e23)))) -> False). % 19.75/19.90 do 0 intro. intros zenon_H2bd zenon_H10f zenon_H4c. % 19.75/19.90 apply (zenon_notor_s _ _ zenon_H2bd). zenon_intro zenon_H2bf. zenon_intro zenon_H2be. % 19.75/19.90 apply (zenon_notor_s _ _ zenon_H2be). zenon_intro zenon_H2c1. zenon_intro zenon_H2c0. % 19.75/19.90 apply (zenon_notor_s _ _ zenon_H2c0). zenon_intro zenon_H118. zenon_intro zenon_H2c2. % 19.75/19.90 apply (zenon_L73_); trivial. % 19.75/19.90 (* end of lemma zenon_L227_ *) % 19.75/19.90 assert (zenon_L228_ : (~(((h4 (e10)) = (e23))\/(((h4 (e11)) = (e23))\/(((h4 (e12)) = (e23))\/((h4 (e13)) = (e23)))))) -> ((h4 (e13)) = (e23)) -> False). % 19.75/19.90 do 0 intro. intros zenon_H2c3 zenon_H12b. % 19.75/19.90 apply (zenon_notor_s _ _ zenon_H2c3). zenon_intro zenon_H2c5. zenon_intro zenon_H2c4. % 19.75/19.90 apply (zenon_notor_s _ _ zenon_H2c4). zenon_intro zenon_H2c7. zenon_intro zenon_H2c6. % 19.75/19.90 apply (zenon_notor_s _ _ zenon_H2c6). zenon_intro zenon_H2c8. zenon_intro zenon_H137. % 19.75/19.90 exact (zenon_H137 zenon_H12b). % 19.75/19.90 (* end of lemma zenon_L228_ *) % 19.75/19.90 apply NNPP. intro zenon_G. % 19.75/19.90 apply (zenon_and_s _ _ ax1). zenon_intro zenon_Haf. zenon_intro zenon_H2c9. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2c9). zenon_intro zenon_H2cb. zenon_intro zenon_H2ca. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2ca). zenon_intro zenon_H2cd. zenon_intro zenon_H2cc. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2cc). zenon_intro zenon_H13b. zenon_intro zenon_H2ce. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2ce). zenon_intro zenon_H2d0. zenon_intro zenon_H2cf. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2cf). zenon_intro zenon_H70. zenon_intro zenon_H2d1. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2d1). zenon_intro zenon_H2d3. zenon_intro zenon_H2d2. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2d2). zenon_intro zenon_H2d5. zenon_intro zenon_H2d4. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2d4). zenon_intro zenon_H2d7. zenon_intro zenon_H2d6. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2d6). zenon_intro zenon_H2d9. zenon_intro zenon_H2d8. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2d8). zenon_intro zenon_He8. zenon_intro zenon_H2da. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2da). zenon_intro zenon_H24a. zenon_intro zenon_H2db. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2db). zenon_intro zenon_H282. zenon_intro zenon_H2dc. % 19.75/19.90 apply (zenon_and_s _ _ ax2). zenon_intro zenon_H55. zenon_intro zenon_H2dd. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2dd). zenon_intro zenon_H17e. zenon_intro zenon_H2de. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2de). zenon_intro zenon_Hab. zenon_intro zenon_H2df. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2df). zenon_intro zenon_H2e1. zenon_intro zenon_H2e0. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2e0). zenon_intro zenon_H9a. zenon_intro zenon_H2e2. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2e2). zenon_intro zenon_H2e4. zenon_intro zenon_H2e3. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2e3). zenon_intro zenon_H2e6. zenon_intro zenon_H2e5. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2e5). zenon_intro zenon_H2e8. zenon_intro zenon_H2e7. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2e7). zenon_intro zenon_H2ea. zenon_intro zenon_H2e9. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2e9). zenon_intro zenon_H2ec. zenon_intro zenon_H2eb. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2eb). zenon_intro zenon_H1b2. zenon_intro zenon_H2ed. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2ed). zenon_intro zenon_H208. zenon_intro zenon_H2ee. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H2f0. zenon_intro zenon_H2ef. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_H2f2. zenon_intro zenon_H2f1. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2f1). zenon_intro zenon_H2f4. zenon_intro zenon_H2f3. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2f3). zenon_intro zenon_H2f6. zenon_intro zenon_H2f5. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2f5). zenon_intro zenon_H2f8. zenon_intro zenon_H2f7. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2f7). zenon_intro zenon_H2fa. zenon_intro zenon_H2f9. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2f9). zenon_intro zenon_H2fc. zenon_intro zenon_H2fb. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2fb). zenon_intro zenon_H2fe. zenon_intro zenon_H2fd. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2fd). zenon_intro zenon_H155. zenon_intro zenon_H2ff. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H2ff). zenon_intro zenon_H301. zenon_intro zenon_H300. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H300). zenon_intro zenon_H303. zenon_intro zenon_H302. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H302). zenon_intro zenon_H305. zenon_intro zenon_H304. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H304). zenon_intro zenon_H29e. zenon_intro zenon_H306. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H306). zenon_intro zenon_H308. zenon_intro zenon_H307. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H307). zenon_intro zenon_H30a. zenon_intro zenon_H309. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H309). zenon_intro zenon_H30c. zenon_intro zenon_H30b. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H30b). zenon_intro zenon_H285. zenon_intro zenon_H30d. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H30d). zenon_intro zenon_H1dc. zenon_intro zenon_H30e. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H30e). zenon_intro zenon_H60. zenon_intro zenon_H141. % 19.75/19.90 apply (zenon_and_s _ _ ax3). zenon_intro zenon_H3e. zenon_intro zenon_H30f. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H30f). zenon_intro zenon_H311. zenon_intro zenon_H310. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H310). zenon_intro zenon_H313. zenon_intro zenon_H312. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H312). zenon_intro zenon_H147. zenon_intro zenon_H314. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H314). zenon_intro zenon_H316. zenon_intro zenon_H315. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H315). zenon_intro zenon_H2d. zenon_intro zenon_H317. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H317). zenon_intro zenon_H319. zenon_intro zenon_H318. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H318). zenon_intro zenon_H31b. zenon_intro zenon_H31a. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H31a). zenon_intro zenon_H31d. zenon_intro zenon_H31c. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H31c). zenon_intro zenon_H31f. zenon_intro zenon_H31e. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H31e). zenon_intro zenon_H22f. zenon_intro zenon_H320. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H320). zenon_intro zenon_H253. zenon_intro zenon_H321. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H321). zenon_intro zenon_H288. zenon_intro zenon_H322. % 19.75/19.90 apply (zenon_and_s _ _ ax4). zenon_intro zenon_H12. zenon_intro zenon_H323. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H323). zenon_intro zenon_H17c. zenon_intro zenon_H324. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H324). zenon_intro zenon_Hfd. zenon_intro zenon_H325. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H325). zenon_intro zenon_H327. zenon_intro zenon_H326. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H326). zenon_intro zenon_Hda. zenon_intro zenon_H328. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H328). zenon_intro zenon_H32a. zenon_intro zenon_H329. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H329). zenon_intro zenon_H32c. zenon_intro zenon_H32b. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H32b). zenon_intro zenon_H32e. zenon_intro zenon_H32d. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H32d). zenon_intro zenon_H330. zenon_intro zenon_H32f. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H32f). zenon_intro zenon_H332. zenon_intro zenon_H331. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H331). zenon_intro zenon_H1b5. zenon_intro zenon_H333. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H333). zenon_intro zenon_H207. zenon_intro zenon_H334. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H334). zenon_intro zenon_H336. zenon_intro zenon_H335. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H335). zenon_intro zenon_H338. zenon_intro zenon_H337. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H337). zenon_intro zenon_H33a. zenon_intro zenon_H339. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H339). zenon_intro zenon_H33c. zenon_intro zenon_H33b. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H33b). zenon_intro zenon_H33e. zenon_intro zenon_H33d. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H33d). zenon_intro zenon_H340. zenon_intro zenon_H33f. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H33f). zenon_intro zenon_H342. zenon_intro zenon_H341. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H341). zenon_intro zenon_H344. zenon_intro zenon_H343. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H343). zenon_intro zenon_H167. zenon_intro zenon_H345. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H345). zenon_intro zenon_H347. zenon_intro zenon_H346. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H346). zenon_intro zenon_H349. zenon_intro zenon_H348. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H348). zenon_intro zenon_H34b. zenon_intro zenon_H34a. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H34a). zenon_intro zenon_H34d. zenon_intro zenon_H34c. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H34c). zenon_intro zenon_H34f. zenon_intro zenon_H34e. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H34e). zenon_intro zenon_H351. zenon_intro zenon_H350. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H350). zenon_intro zenon_H353. zenon_intro zenon_H352. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H352). zenon_intro zenon_H28b. zenon_intro zenon_H354. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H354). zenon_intro zenon_H1e2. zenon_intro zenon_H355. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H355). zenon_intro zenon_H1d. zenon_intro zenon_H14d. % 19.75/19.90 apply (zenon_and_s _ _ ax5). zenon_intro zenon_H1ac. zenon_intro zenon_H356. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H356). zenon_intro zenon_H358. zenon_intro zenon_H357. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H357). zenon_intro zenon_H35a. zenon_intro zenon_H359. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H359). zenon_intro zenon_H35c. zenon_intro zenon_H35b. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H35b). zenon_intro zenon_H35e. zenon_intro zenon_H35d. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H35d). zenon_intro zenon_H267. zenon_intro zenon_H35f. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H35f). zenon_intro zenon_Hb8. zenon_intro zenon_H360. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H360). zenon_intro zenon_H362. zenon_intro zenon_H361. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H361). zenon_intro zenon_H26b. zenon_intro zenon_H363. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H363). zenon_intro zenon_H365. zenon_intro zenon_H364. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H364). zenon_intro zenon_H72. zenon_intro zenon_H366. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H366). zenon_intro zenon_H368. zenon_intro zenon_H367. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H367). zenon_intro zenon_H36a. zenon_intro zenon_H369. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H369). zenon_intro zenon_H36c. zenon_intro zenon_H36b. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H36b). zenon_intro zenon_H36e. zenon_intro zenon_H36d. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H36d). zenon_intro zenon_H22a. zenon_intro zenon_H36f. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H36f). zenon_intro zenon_H371. zenon_intro zenon_H370. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H370). zenon_intro zenon_H373. zenon_intro zenon_H372. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H372). zenon_intro zenon_H138. zenon_intro zenon_H374. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H374). zenon_intro zenon_H13e. zenon_intro zenon_H375. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H375). zenon_intro zenon_Ha5. zenon_intro zenon_H376. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H376). zenon_intro zenon_H378. zenon_intro zenon_H377. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H377). zenon_intro zenon_H37a. zenon_intro zenon_H379. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H379). zenon_intro zenon_H244. zenon_intro zenon_H37b. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H37b). zenon_intro zenon_H37d. zenon_intro zenon_H37c. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H37c). zenon_intro zenon_H37f. zenon_intro zenon_H37e. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H37e). zenon_intro zenon_H381. zenon_intro zenon_H380. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H380). zenon_intro zenon_H8d. zenon_intro zenon_H382. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H382). zenon_intro zenon_H94. zenon_intro zenon_H383. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H383). zenon_intro zenon_H385. zenon_intro zenon_H384. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H384). zenon_intro zenon_H387. zenon_intro zenon_H386. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H386). zenon_intro zenon_H389. zenon_intro zenon_H388. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H388). zenon_intro zenon_H38b. zenon_intro zenon_H38a. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H38a). zenon_intro zenon_H38d. zenon_intro zenon_H38c. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H38c). zenon_intro zenon_H38f. zenon_intro zenon_H38e. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H38e). zenon_intro zenon_H391. zenon_intro zenon_H390. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H390). zenon_intro zenon_H393. zenon_intro zenon_H392. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H392). zenon_intro zenon_H395. zenon_intro zenon_H394. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H394). zenon_intro zenon_H397. zenon_intro zenon_H396. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H396). zenon_intro zenon_H399. zenon_intro zenon_H398. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H398). zenon_intro zenon_H39b. zenon_intro zenon_H39a. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H39a). zenon_intro zenon_H39d. zenon_intro zenon_H39c. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H39c). zenon_intro zenon_H161. zenon_intro zenon_H39e. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H39e). zenon_intro zenon_H273. zenon_intro zenon_H39f. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H39f). zenon_intro zenon_H26f. zenon_intro zenon_H3a0. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3a0). zenon_intro zenon_H298. zenon_intro zenon_H3a1. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3a1). zenon_intro zenon_H1fb. zenon_intro zenon_H3a2. % 19.75/19.90 apply (zenon_and_s _ _ ax6). zenon_intro zenon_H3a4. zenon_intro zenon_H3a3. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3a3). zenon_intro zenon_H3a6. zenon_intro zenon_H3a5. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3a5). zenon_intro zenon_H3a8. zenon_intro zenon_H3a7. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3a7). zenon_intro zenon_H3aa. zenon_intro zenon_H3a9. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3a9). zenon_intro zenon_H3ac. zenon_intro zenon_H3ab. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3ab). zenon_intro zenon_H257. zenon_intro zenon_H3ad. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3ad). zenon_intro zenon_H4b. zenon_intro zenon_H3ae. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3ae). zenon_intro zenon_H3b0. zenon_intro zenon_H3af. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3af). zenon_intro zenon_H25b. zenon_intro zenon_H3b1. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3b1). zenon_intro zenon_H3b3. zenon_intro zenon_H3b2. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3b2). zenon_intro zenon_H2f. zenon_intro zenon_H3b4. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3b4). zenon_intro zenon_H3b6. zenon_intro zenon_H3b5. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3b5). zenon_intro zenon_H3b8. zenon_intro zenon_H3b7. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3b7). zenon_intro zenon_H3ba. zenon_intro zenon_H3b9. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3b9). zenon_intro zenon_H3bc. zenon_intro zenon_H3bb. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3bb). zenon_intro zenon_H214. zenon_intro zenon_H3bd. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3bd). zenon_intro zenon_H3bf. zenon_intro zenon_H3be. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3be). zenon_intro zenon_H3c1. zenon_intro zenon_H3c0. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3c0). zenon_intro zenon_H144. zenon_intro zenon_H3c2. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3c2). zenon_intro zenon_H14a. zenon_intro zenon_H3c3. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3c3). zenon_intro zenon_He3. zenon_intro zenon_H3c4. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3c4). zenon_intro zenon_H3c6. zenon_intro zenon_H3c5. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3c5). zenon_intro zenon_H3c8. zenon_intro zenon_H3c7. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3c7). zenon_intro zenon_H24d. zenon_intro zenon_H3c9. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3c9). zenon_intro zenon_H3cb. zenon_intro zenon_H3ca. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3ca). zenon_intro zenon_H3cd. zenon_intro zenon_H3cc. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3cc). zenon_intro zenon_H3cf. zenon_intro zenon_H3ce. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3ce). zenon_intro zenon_Hcd. zenon_intro zenon_H3d0. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3d0). zenon_intro zenon_Hd4. zenon_intro zenon_H3d1. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3d1). zenon_intro zenon_H3d3. zenon_intro zenon_H3d2. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3d2). zenon_intro zenon_H3d5. zenon_intro zenon_H3d4. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3d4). zenon_intro zenon_H3d7. zenon_intro zenon_H3d6. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3d6). zenon_intro zenon_H3d9. zenon_intro zenon_H3d8. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3d8). zenon_intro zenon_H3db. zenon_intro zenon_H3da. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3da). zenon_intro zenon_H3dd. zenon_intro zenon_H3dc. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3dc). zenon_intro zenon_H3df. zenon_intro zenon_H3de. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3de). zenon_intro zenon_H3e1. zenon_intro zenon_H3e0. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3e0). zenon_intro zenon_H3e3. zenon_intro zenon_H3e2. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3e2). zenon_intro zenon_H3e5. zenon_intro zenon_H3e4. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3e4). zenon_intro zenon_H3e7. zenon_intro zenon_H3e6. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3e6). zenon_intro zenon_H3e9. zenon_intro zenon_H3e8. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3e8). zenon_intro zenon_H3eb. zenon_intro zenon_H3ea. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3ea). zenon_intro zenon_H175. zenon_intro zenon_H3ec. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3ec). zenon_intro zenon_H263. zenon_intro zenon_H3ed. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3ed). zenon_intro zenon_H25f. zenon_intro zenon_H3ee. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3ee). zenon_intro zenon_H3f0. zenon_intro zenon_H3ef. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3ef). zenon_intro zenon_H201. zenon_intro zenon_H3f1. % 19.75/19.90 apply (zenon_and_s _ _ ax7). zenon_intro zenon_Ha1. zenon_intro zenon_H3f2. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3f2). zenon_intro zenon_H156. zenon_intro zenon_H3f3. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3f3). zenon_intro zenon_H3f5. zenon_intro zenon_H3f4. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3f4). zenon_intro zenon_H84. zenon_intro zenon_H3f6. % 19.75/19.90 apply (zenon_and_s _ _ ax8). zenon_intro zenon_Hdf. zenon_intro zenon_H3f7. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3f7). zenon_intro zenon_H168. zenon_intro zenon_H3f8. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3f8). zenon_intro zenon_H3fa. zenon_intro zenon_H3f9. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3f9). zenon_intro zenon_Hc7. zenon_intro zenon_H3fb. % 19.75/19.90 apply (zenon_and_s _ _ ax10). zenon_intro zenon_H10b. zenon_intro zenon_H3fc. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3fc). zenon_intro zenon_H3fe. zenon_intro zenon_H3fd. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3fd). zenon_intro zenon_H400. zenon_intro zenon_H3ff. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H3ff). zenon_intro zenon_H402. zenon_intro zenon_H401. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H401). zenon_intro zenon_Hf9. zenon_intro zenon_H403. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H403). zenon_intro zenon_Hf8. zenon_intro zenon_H404. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H404). zenon_intro zenon_Hf5. zenon_intro zenon_H405. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H405). zenon_intro zenon_Hf7. zenon_intro zenon_H406. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H406). zenon_intro zenon_Hbe. zenon_intro zenon_H407. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H407). zenon_intro zenon_Hfa. zenon_intro zenon_H408. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H408). zenon_intro zenon_H180. zenon_intro zenon_H409. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H409). zenon_intro zenon_H1e3. zenon_intro zenon_H40a. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H40a). zenon_intro zenon_Hb4. zenon_intro zenon_H40b. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H40b). zenon_intro zenon_Hbf. zenon_intro zenon_H40c. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H40c). zenon_intro zenon_Hf6. zenon_intro zenon_H40d. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H40d). zenon_intro zenon_Hbc. zenon_intro zenon_H40e. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H40e). zenon_intro zenon_H410. zenon_intro zenon_H40f. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H40f). zenon_intro zenon_H412. zenon_intro zenon_H411. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H411). zenon_intro zenon_H414. zenon_intro zenon_H413. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H413). zenon_intro zenon_H416. zenon_intro zenon_H415. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H415). zenon_intro zenon_Hc0. zenon_intro zenon_H417. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H417). zenon_intro zenon_Hbd. zenon_intro zenon_H418. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H418). zenon_intro zenon_H41a. zenon_intro zenon_H419. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H419). zenon_intro zenon_H41c. zenon_intro zenon_H41b. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H41b). zenon_intro zenon_H41e. zenon_intro zenon_H41d. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H41d). zenon_intro zenon_H420. zenon_intro zenon_H41f. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H41f). zenon_intro zenon_H422. zenon_intro zenon_H421. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H421). zenon_intro zenon_H424. zenon_intro zenon_H423. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H423). zenon_intro zenon_H426. zenon_intro zenon_H425. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H425). zenon_intro zenon_H1b6. zenon_intro zenon_H427. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H427). zenon_intro zenon_H429. zenon_intro zenon_H428. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H428). zenon_intro zenon_H42b. zenon_intro zenon_H42a. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H42a). zenon_intro zenon_H42d. zenon_intro zenon_H42c. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H42c). zenon_intro zenon_H1a2. zenon_intro zenon_H42e. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H42e). zenon_intro zenon_H234. zenon_intro zenon_H42f. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H42f). zenon_intro zenon_H2a3. zenon_intro zenon_H430. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H430). zenon_intro zenon_H17b. zenon_intro zenon_H431. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H431). zenon_intro zenon_H433. zenon_intro zenon_H432. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H432). zenon_intro zenon_H435. zenon_intro zenon_H434. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H434). zenon_intro zenon_H437. zenon_intro zenon_H436. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H436). zenon_intro zenon_Hf4. zenon_intro zenon_H438. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H438). zenon_intro zenon_H43a. zenon_intro zenon_H439. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H439). zenon_intro zenon_H43c. zenon_intro zenon_H43b. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H43b). zenon_intro zenon_H43e. zenon_intro zenon_H43d. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H43d). zenon_intro zenon_H440. zenon_intro zenon_H43f. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H43f). zenon_intro zenon_H17f. zenon_intro zenon_H441. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H441). zenon_intro zenon_H443. zenon_intro zenon_H442. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H442). zenon_intro zenon_H445. zenon_intro zenon_H444. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H444). zenon_intro zenon_H447. zenon_intro zenon_H446. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H446). zenon_intro zenon_Hbb. zenon_intro zenon_H448. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H448). zenon_intro zenon_Hf3. zenon_intro zenon_H449. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H449). zenon_intro zenon_H44b. zenon_intro zenon_H44a. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H44a). zenon_intro zenon_Hb7. zenon_intro zenon_H44c. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H44c). zenon_intro zenon_H44e. zenon_intro zenon_H44d. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H44d). zenon_intro zenon_H450. zenon_intro zenon_H44f. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H44f). zenon_intro zenon_Hb5. zenon_intro zenon_H451. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H451). zenon_intro zenon_Hb6. zenon_intro zenon_H452. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H452). zenon_intro zenon_H80. zenon_intro zenon_H453. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H453). zenon_intro zenon_H455. zenon_intro zenon_H454. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H454). zenon_intro zenon_H457. zenon_intro zenon_H456. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H456). zenon_intro zenon_H459. zenon_intro zenon_H458. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H458). zenon_intro zenon_H14e. zenon_intro zenon_H45a. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H45a). zenon_intro zenon_H45b. zenon_intro zenon_H6b. % 19.75/19.90 apply (zenon_and_s _ _ ax11). zenon_intro zenon_H45d. zenon_intro zenon_H45c. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H45c). zenon_intro zenon_H45f. zenon_intro zenon_H45e. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H45e). zenon_intro zenon_H461. zenon_intro zenon_H460. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H460). zenon_intro zenon_H463. zenon_intro zenon_H462. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H462). zenon_intro zenon_H10c. zenon_intro zenon_H464. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H464). zenon_intro zenon_H127. zenon_intro zenon_H465. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H465). zenon_intro zenon_H467. zenon_intro zenon_H466. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H466). zenon_intro zenon_H10d. zenon_intro zenon_H468. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H468). zenon_intro zenon_H10e. zenon_intro zenon_H469. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H469). zenon_intro zenon_H152. zenon_intro zenon_H46a. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H46a). zenon_intro zenon_H195. zenon_intro zenon_H46b. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H46b). zenon_intro zenon_H1e7. zenon_intro zenon_H46c. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H46c). zenon_intro zenon_H53. zenon_intro zenon_H46d. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H46d). zenon_intro zenon_H52. zenon_intro zenon_H46e. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H46e). zenon_intro zenon_H470. zenon_intro zenon_H46f. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H46f). zenon_intro zenon_H472. zenon_intro zenon_H471. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H471). zenon_intro zenon_H474. zenon_intro zenon_H473. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H473). zenon_intro zenon_H476. zenon_intro zenon_H475. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H475). zenon_intro zenon_H478. zenon_intro zenon_H477. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H477). zenon_intro zenon_H47a. zenon_intro zenon_H479. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H479). zenon_intro zenon_H54. zenon_intro zenon_H47b. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H47b). zenon_intro zenon_H4f. zenon_intro zenon_H47c. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H47c). zenon_intro zenon_H47e. zenon_intro zenon_H47d. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H47d). zenon_intro zenon_H480. zenon_intro zenon_H47f. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H47f). zenon_intro zenon_H482. zenon_intro zenon_H481. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H481). zenon_intro zenon_H484. zenon_intro zenon_H483. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H483). zenon_intro zenon_H486. zenon_intro zenon_H485. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H485). zenon_intro zenon_H488. zenon_intro zenon_H487. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H487). zenon_intro zenon_H1cc. zenon_intro zenon_H489. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H489). zenon_intro zenon_H1cb. zenon_intro zenon_H48a. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H48a). zenon_intro zenon_H48c. zenon_intro zenon_H48b. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H48b). zenon_intro zenon_H48e. zenon_intro zenon_H48d. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H48d). zenon_intro zenon_H490. zenon_intro zenon_H48f. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H48f). zenon_intro zenon_H1a3. zenon_intro zenon_H491. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H491). zenon_intro zenon_H235. zenon_intro zenon_H492. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H492). zenon_intro zenon_H494. zenon_intro zenon_H493. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H493). zenon_intro zenon_H196. zenon_intro zenon_H495. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H495). zenon_intro zenon_H497. zenon_intro zenon_H496. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H496). zenon_intro zenon_H499. zenon_intro zenon_H498. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H498). zenon_intro zenon_H193. zenon_intro zenon_H49a. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H49a). zenon_intro zenon_H49c. zenon_intro zenon_H49b. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H49b). zenon_intro zenon_H49e. zenon_intro zenon_H49d. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H49d). zenon_intro zenon_H4a0. zenon_intro zenon_H49f. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H49f). zenon_intro zenon_H4a2. zenon_intro zenon_H4a1. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H4a1). zenon_intro zenon_H194. zenon_intro zenon_H4a3. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H4a3). zenon_intro zenon_H192. zenon_intro zenon_H4a4. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H4a4). zenon_intro zenon_H4a6. zenon_intro zenon_H4a5. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H4a5). zenon_intro zenon_H4a8. zenon_intro zenon_H4a7. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H4a7). zenon_intro zenon_H4aa. zenon_intro zenon_H4a9. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H4a9). zenon_intro zenon_H50. zenon_intro zenon_H4ab. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H4ab). zenon_intro zenon_H4ad. zenon_intro zenon_H4ac. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H4ac). zenon_intro zenon_H4af. zenon_intro zenon_H4ae. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H4ae). zenon_intro zenon_H51. zenon_intro zenon_H4b0. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H4b0). zenon_intro zenon_H4b2. zenon_intro zenon_H4b1. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H4b1). zenon_intro zenon_H4b4. zenon_intro zenon_H4b3. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H4b3). zenon_intro zenon_H47. zenon_intro zenon_H4b5. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H4b5). zenon_intro zenon_H48. zenon_intro zenon_H4b6. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H4b6). zenon_intro zenon_H3d. zenon_intro zenon_H4b7. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H4b7). zenon_intro zenon_H4b9. zenon_intro zenon_H4b8. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H4b8). zenon_intro zenon_H4bb. zenon_intro zenon_H4ba. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H4ba). zenon_intro zenon_H4bd. zenon_intro zenon_H4bc. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H4bc). zenon_intro zenon_H151. zenon_intro zenon_H4be. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H4be). zenon_intro zenon_H4bf. zenon_intro zenon_H28. % 19.75/19.90 apply (zenon_and_s _ _ ax12). zenon_intro zenon_H71. zenon_intro zenon_H4c0. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H4c0). zenon_intro zenon_H6e. zenon_intro zenon_H8b. % 19.75/19.90 apply (zenon_and_s _ _ ax13). zenon_intro zenon_H2e. zenon_intro zenon_H4c1. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H4c1). zenon_intro zenon_H2b. zenon_intro zenon_H4c. % 19.75/19.90 apply (zenon_and_s _ _ ax17). zenon_intro zenon_H12b. zenon_intro zenon_H4c2. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H4c2). zenon_intro zenon_Hc2. zenon_intro zenon_H4c3. % 19.75/19.90 apply (zenon_and_s _ _ zenon_H4c3). zenon_intro zenon_Hfc. zenon_intro zenon_H10f. % 19.75/19.90 apply (zenon_notor_s _ _ zenon_G). zenon_intro zenon_H4c5. zenon_intro zenon_H4c4. % 19.75/19.90 apply (zenon_notor_s _ _ zenon_H4c4). zenon_intro zenon_H4c7. zenon_intro zenon_H4c6. % 19.75/19.90 apply (zenon_notor_s _ _ zenon_H4c6). zenon_intro zenon_H4c9. zenon_intro zenon_H4c8. % 19.75/19.90 apply (zenon_notand_s _ _ zenon_H4c8); [ zenon_intro zenon_Hfb | zenon_intro zenon_H4ca ]. % 19.75/19.90 apply (zenon_or_s _ _ zenon_H45d); [ zenon_intro zenon_H13 | zenon_intro zenon_H13 ]. % 19.75/19.90 apply (zenon_L70_); trivial. % 19.75/19.90 apply (zenon_L70_); trivial. % 19.75/19.90 apply (zenon_notand_s _ _ zenon_H4ca); [ zenon_intro zenon_H110 | zenon_intro zenon_H4cb ]. % 19.75/19.90 apply (zenon_L72_); trivial. % 19.75/19.90 apply (zenon_notand_s _ _ zenon_H4cb); [ zenon_intro zenon_H11b | zenon_intro zenon_H4cc ]. % 19.75/19.90 apply (zenon_or_s _ _ zenon_H45d); [ zenon_intro zenon_H13 | zenon_intro zenon_H13 ]. % 19.75/19.90 apply (zenon_L77_); trivial. % 19.75/19.90 apply (zenon_L77_); trivial. % 19.75/19.90 apply (zenon_notand_s _ _ zenon_H4cc); [ zenon_intro zenon_H128 | zenon_intro zenon_H4cd ]. % 19.75/19.90 apply (zenon_or_s _ _ zenon_H45d); [ zenon_intro zenon_H13 | zenon_intro zenon_H13 ]. % 19.75/19.90 apply (zenon_L94_); trivial. % 19.75/19.90 apply (zenon_L94_); trivial. % 19.75/19.90 apply (zenon_notand_s _ _ zenon_H4cd); [ zenon_intro zenon_H17d | zenon_intro zenon_H4ce ]. % 19.75/19.90 apply (zenon_or_s _ _ zenon_H45d); [ zenon_intro zenon_H13 | zenon_intro zenon_H13 ]. % 19.75/19.90 apply (zenon_L107_); trivial. % 19.75/19.90 apply (zenon_L107_); trivial. % 19.75/19.90 apply (zenon_notand_s _ _ zenon_H4ce); [ zenon_intro zenon_H197 | zenon_intro zenon_H4cf ]. % 19.75/19.90 apply (zenon_or_s _ _ zenon_H45d); [ zenon_intro zenon_H13 | zenon_intro zenon_H13 ]. % 19.75/19.90 apply (zenon_L118_); trivial. % 19.75/19.90 apply (zenon_L118_); trivial. % 19.75/19.90 apply (zenon_notand_s _ _ zenon_H4cf); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H4d0 ]. % 19.75/19.90 apply (zenon_or_s _ _ zenon_H45d); [ zenon_intro zenon_H13 | zenon_intro zenon_H13 ]. % 19.75/19.90 apply (zenon_L129_); trivial. % 19.75/19.90 apply (zenon_L129_); trivial. % 19.75/19.90 apply (zenon_notand_s _ _ zenon_H4d0); [ zenon_intro zenon_H1cd | zenon_intro zenon_H4d1 ]. % 19.75/19.90 apply (zenon_or_s _ _ zenon_H45d); [ zenon_intro zenon_H13 | zenon_intro zenon_H13 ]. % 19.75/19.90 apply (zenon_L137_); trivial. % 19.75/19.90 apply (zenon_L137_); trivial. % 19.75/19.90 apply (zenon_notand_s _ _ zenon_H4d1); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H4d2 ]. % 19.75/19.90 apply (zenon_or_s _ _ zenon_H45d); [ zenon_intro zenon_H13 | zenon_intro zenon_H13 ]. % 19.75/19.90 apply (zenon_L146_); trivial. % 19.75/19.90 apply (zenon_L146_); trivial. % 19.75/19.90 apply (zenon_notand_s _ _ zenon_H4d2); [ zenon_intro zenon_H209 | zenon_intro zenon_H4d3 ]. % 19.75/19.90 apply (zenon_or_s _ _ zenon_H45d); [ zenon_intro zenon_H13 | zenon_intro zenon_H13 ]. % 19.75/19.90 apply (zenon_L153_); trivial. % 19.75/19.90 apply (zenon_L153_); trivial. % 19.75/19.90 apply (zenon_notand_s _ _ zenon_H4d3); [ zenon_intro zenon_H21e | zenon_intro zenon_H4d4 ]. % 19.75/19.90 apply (zenon_or_s _ _ zenon_H45d); [ zenon_intro zenon_H13 | zenon_intro zenon_H13 ]. % 19.75/19.90 apply (zenon_L170_); trivial. % 19.75/19.90 apply (zenon_L170_); trivial. % 19.75/19.90 apply (zenon_notand_s _ _ zenon_H4d4); [ zenon_intro zenon_H236 | zenon_intro zenon_H4d5 ]. % 19.75/19.90 apply (zenon_or_s _ _ zenon_H45d); [ zenon_intro zenon_H13 | zenon_intro zenon_H13 ]. % 19.75/19.90 apply (zenon_L185_); trivial. % 19.75/19.90 apply (zenon_L185_); trivial. % 19.75/19.90 apply (zenon_notand_s _ _ zenon_H4d5); [ zenon_intro zenon_H27c | zenon_intro zenon_H4d6 ]. % 19.75/19.90 apply (zenon_or_s _ _ zenon_H45d); [ zenon_intro zenon_H13 | zenon_intro zenon_H13 ]. % 19.75/19.90 apply (zenon_L206_); trivial. % 19.75/19.90 apply (zenon_L206_); trivial. % 19.75/19.90 apply (zenon_notand_s _ _ zenon_H4d6); [ zenon_intro zenon_H28e | zenon_intro zenon_H4d7 ]. % 19.75/19.90 apply (zenon_L211_); trivial. % 19.75/19.90 apply (zenon_notand_s _ _ zenon_H4d7); [ zenon_intro zenon_H2ab | zenon_intro zenon_H4d8 ]. % 19.75/19.90 apply (zenon_or_s _ _ zenon_H45d); [ zenon_intro zenon_H13 | zenon_intro zenon_H13 ]. % 19.75/19.90 apply (zenon_L223_); trivial. % 19.75/19.90 apply (zenon_L223_); trivial. % 19.75/19.90 apply (zenon_notand_s _ _ zenon_H4d8); [ zenon_intro zenon_H2b1 | zenon_intro zenon_H4d9 ]. % 19.75/19.90 apply (zenon_L224_); trivial. % 19.75/19.90 apply (zenon_notand_s _ _ zenon_H4d9); [ zenon_intro zenon_H2b7 | zenon_intro zenon_H4da ]. % 19.75/19.90 apply (zenon_L225_); trivial. % 19.75/19.90 apply (zenon_notand_s _ _ zenon_H4da); [ zenon_intro zenon_H2b9 | zenon_intro zenon_H4db ]. % 19.75/19.90 apply (zenon_L226_); trivial. % 19.75/19.90 apply (zenon_notand_s _ _ zenon_H4db); [ zenon_intro zenon_H2bd | zenon_intro zenon_H2c3 ]. % 19.75/19.90 apply (zenon_L227_); trivial. % 19.75/19.90 apply (zenon_L228_); trivial. % 19.75/19.90 Qed. % 19.75/19.90 % SZS output end Proof % 19.75/19.90 (* END-PROOF *) % 19.75/19.90 nodes searched: 1247279 % 19.75/19.90 max branch formulas: 2001 % 19.75/19.90 proof nodes created: 12720 % 19.75/19.90 formulas created: 557154 % 19.75/19.90 %------------------------------------------------------------------------------