%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : ALG042+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n018.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 18:29:04 EDT 2022 % Result : Theorem 41.92s 42.13s % Output : Proof 41.92s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : ALG042+1 : TPTP v8.1.0. Released v2.7.0. % 0.12/0.13 % Command : run_zenon %s %d % 0.15/0.35 % Computer : n018.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 600 % 0.15/0.35 % DateTime : Wed Jun 8 14:42:22 EDT 2022 % 0.15/0.35 % CPUTime : % 41.92/42.13 (* PROOF-FOUND *) % 41.92/42.13 % SZS status Theorem % 41.92/42.13 (* BEGIN-PROOF *) % 41.92/42.13 % SZS output start Proof % 41.92/42.13 Theorem co1 : (((((h (e10)) = (e20))\/(((h (e10)) = (e21))\/(((h (e10)) = (e22))\/((h (e10)) = (e23)))))/\((((h (e11)) = (e20))\/(((h (e11)) = (e21))\/(((h (e11)) = (e22))\/((h (e11)) = (e23)))))/\((((h (e12)) = (e20))\/(((h (e12)) = (e21))\/(((h (e12)) = (e22))\/((h (e12)) = (e23)))))/\((((h (e13)) = (e20))\/(((h (e13)) = (e21))\/(((h (e13)) = (e22))\/((h (e13)) = (e23)))))/\((((j (e20)) = (e10))\/(((j (e20)) = (e11))\/(((j (e20)) = (e12))\/((j (e20)) = (e13)))))/\((((j (e21)) = (e10))\/(((j (e21)) = (e11))\/(((j (e21)) = (e12))\/((j (e21)) = (e13)))))/\((((j (e22)) = (e10))\/(((j (e22)) = (e11))\/(((j (e22)) = (e12))\/((j (e22)) = (e13)))))/\(((j (e23)) = (e10))\/(((j (e23)) = (e11))\/(((j (e23)) = (e12))\/((j (e23)) = (e13))))))))))))->(~(((h (op1 (e10) (e10))) = (op2 (h (e10)) (h (e10))))/\(((h (op1 (e10) (e11))) = (op2 (h (e10)) (h (e11))))/\(((h (op1 (e10) (e12))) = (op2 (h (e10)) (h (e12))))/\(((h (op1 (e10) (e13))) = (op2 (h (e10)) (h (e13))))/\(((h (op1 (e11) (e10))) = (op2 (h (e11)) (h (e10))))/\(((h (op1 (e11) (e11))) = (op2 (h (e11)) (h (e11))))/\(((h (op1 (e11) (e12))) = (op2 (h (e11)) (h (e12))))/\(((h (op1 (e11) (e13))) = (op2 (h (e11)) (h (e13))))/\(((h (op1 (e12) (e10))) = (op2 (h (e12)) (h (e10))))/\(((h (op1 (e12) (e11))) = (op2 (h (e12)) (h (e11))))/\(((h (op1 (e12) (e12))) = (op2 (h (e12)) (h (e12))))/\(((h (op1 (e12) (e13))) = (op2 (h (e12)) (h (e13))))/\(((h (op1 (e13) (e10))) = (op2 (h (e13)) (h (e10))))/\(((h (op1 (e13) (e11))) = (op2 (h (e13)) (h (e11))))/\(((h (op1 (e13) (e12))) = (op2 (h (e13)) (h (e12))))/\(((h (op1 (e13) (e13))) = (op2 (h (e13)) (h (e13))))/\(((j (op2 (e20) (e20))) = (op1 (j (e20)) (j (e20))))/\(((j (op2 (e20) (e21))) = (op1 (j (e20)) (j (e21))))/\(((j (op2 (e20) (e22))) = (op1 (j (e20)) (j (e22))))/\(((j (op2 (e20) (e23))) = (op1 (j (e20)) (j (e23))))/\(((j (op2 (e21) (e20))) = (op1 (j (e21)) (j (e20))))/\(((j (op2 (e21) (e21))) = (op1 (j (e21)) (j (e21))))/\(((j (op2 (e21) (e22))) = (op1 (j (e21)) (j (e22))))/\(((j (op2 (e21) (e23))) = (op1 (j (e21)) (j (e23))))/\(((j (op2 (e22) (e20))) = (op1 (j (e22)) (j (e20))))/\(((j (op2 (e22) (e21))) = (op1 (j (e22)) (j (e21))))/\(((j (op2 (e22) (e22))) = (op1 (j (e22)) (j (e22))))/\(((j (op2 (e22) (e23))) = (op1 (j (e22)) (j (e23))))/\(((j (op2 (e23) (e20))) = (op1 (j (e23)) (j (e20))))/\(((j (op2 (e23) (e21))) = (op1 (j (e23)) (j (e21))))/\(((j (op2 (e23) (e22))) = (op1 (j (e23)) (j (e22))))/\(((j (op2 (e23) (e23))) = (op1 (j (e23)) (j (e23))))/\(((h (j (e20))) = (e20))/\(((h (j (e21))) = (e21))/\(((h (j (e22))) = (e22))/\(((h (j (e23))) = (e23))/\(((j (h (e10))) = (e10))/\(((j (h (e11))) = (e11))/\(((j (h (e12))) = (e12))/\((j (h (e13))) = (e13))))))))))))))))))))))))))))))))))))))))))). % 41.92/42.13 Proof. % 41.92/42.13 assert (zenon_L1_ : (~((e10) = (e10))) -> False). % 41.92/42.13 do 0 intro. intros zenon_H6. % 41.92/42.13 apply zenon_H6. apply refl_equal. % 41.92/42.13 (* end of lemma zenon_L1_ *) % 41.92/42.13 assert (zenon_L2_ : (~((e11) = (e11))) -> False). % 41.92/42.13 do 0 intro. intros zenon_H7. % 41.92/42.13 apply zenon_H7. apply refl_equal. % 41.92/42.13 (* end of lemma zenon_L2_ *) % 41.92/42.14 assert (zenon_L3_ : (~((j (e20)) = (j (op2 (e20) (e20))))) -> ((op2 (e20) (e20)) = (e20)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H8 zenon_H9. % 41.92/42.14 cut (((e20) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Ha]. % 41.92/42.14 congruence. % 41.92/42.14 apply zenon_Ha. apply sym_equal. exact zenon_H9. % 41.92/42.14 (* end of lemma zenon_L3_ *) % 41.92/42.14 assert (zenon_L4_ : (~((op1 (j (e20)) (j (e20))) = (op1 (e11) (e11)))) -> ((j (e20)) = (e11)) -> False). % 41.92/42.14 do 0 intro. intros zenon_Hb zenon_Hc. % 41.92/42.14 cut (((j (e20)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Hd]. % 41.92/42.14 cut (((j (e20)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Hd]. % 41.92/42.14 congruence. % 41.92/42.14 exact (zenon_Hd zenon_Hc). % 41.92/42.14 exact (zenon_Hd zenon_Hc). % 41.92/42.14 (* end of lemma zenon_L4_ *) % 41.92/42.14 assert (zenon_L5_ : (~((op1 (j (e20)) (j (e20))) = (op1 (e13) (e13)))) -> ((op1 (e11) (e11)) = (e10)) -> ((j (e20)) = (e11)) -> ((op1 (e13) (e13)) = (e10)) -> False). % 41.92/42.14 do 0 intro. intros zenon_He zenon_Hf zenon_Hc zenon_H10. % 41.92/42.14 cut (((op1 (e11) (e11)) = (e10)) = ((op1 (j (e20)) (j (e20))) = (op1 (e13) (e13)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_He. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_Hf. % 41.92/42.14 cut (((e10) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H11]. % 41.92/42.14 cut (((op1 (e11) (e11)) = (op1 (j (e20)) (j (e20))))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((op1 (j (e20)) (j (e20))) = (op1 (j (e20)) (j (e20))))); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 41.92/42.14 cut (((op1 (j (e20)) (j (e20))) = (op1 (j (e20)) (j (e20)))) = ((op1 (e11) (e11)) = (op1 (j (e20)) (j (e20))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H12. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H13. % 41.92/42.14 cut (((op1 (j (e20)) (j (e20))) = (op1 (j (e20)) (j (e20))))); [idtac | apply NNPP; zenon_intro zenon_H14]. % 41.92/42.14 cut (((op1 (j (e20)) (j (e20))) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hb]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L4_); trivial. % 41.92/42.14 apply zenon_H14. apply refl_equal. % 41.92/42.14 apply zenon_H14. apply refl_equal. % 41.92/42.14 apply zenon_H11. apply sym_equal. exact zenon_H10. % 41.92/42.14 (* end of lemma zenon_L5_ *) % 41.92/42.14 assert (zenon_L6_ : ((j (op2 (e20) (e20))) = (op1 (j (e20)) (j (e20)))) -> ((j (e20)) = (e11)) -> ((op1 (e13) (e13)) = (e10)) -> ((op1 (e11) (e11)) = (e10)) -> ((op2 (e20) (e20)) = (e20)) -> (~((e10) = (e11))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H15 zenon_Hc zenon_H10 zenon_Hf zenon_H9 zenon_H16. % 41.92/42.14 elim (classic ((e11) = (e11))); [ zenon_intro zenon_H17 | zenon_intro zenon_H7 ]. % 41.92/42.14 cut (((e11) = (e11)) = ((e10) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H16. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H17. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((e11) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H18]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((op1 (e13) (e13)) = (e10)) = ((e11) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H18. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H10. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H19]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e11) = (e11))); [ zenon_intro zenon_H17 | zenon_intro zenon_H7 ]. % 41.92/42.14 cut (((e11) = (e11)) = ((op1 (e13) (e13)) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H19. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H17. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((e11) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1a]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H1b | zenon_intro zenon_H1c ]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((e11) = (op1 (e13) (e13)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H1a. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H1b. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H19]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e20)) = (e11)) = ((op1 (e13) (e13)) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H19. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_Hc. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((j (e20)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H1b | zenon_intro zenon_H1c ]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((j (e20)) = (op1 (e13) (e13)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H1d. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H1b. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (j (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (e20)) = (j (e20)))); [ zenon_intro zenon_H1f | zenon_intro zenon_H20 ]. % 41.92/42.14 cut (((j (e20)) = (j (e20))) = ((op1 (e13) (e13)) = (j (e20)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H1e. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H1f. % 41.92/42.14 cut (((j (e20)) = (j (e20)))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 41.92/42.14 cut (((j (e20)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (op2 (e20) (e20))) = (op1 (j (e20)) (j (e20)))) = ((j (e20)) = (op1 (e13) (e13)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H1d. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H15. % 41.92/42.14 cut (((op1 (j (e20)) (j (e20))) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_He]. % 41.92/42.14 cut (((j (op2 (e20) (e20))) = (j (e20)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (e20)) = (j (e20)))); [ zenon_intro zenon_H1f | zenon_intro zenon_H20 ]. % 41.92/42.14 cut (((j (e20)) = (j (e20))) = ((j (op2 (e20) (e20))) = (j (e20)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H21. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H1f. % 41.92/42.14 cut (((j (e20)) = (j (e20)))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 41.92/42.14 cut (((j (e20)) = (j (op2 (e20) (e20))))); [idtac | apply NNPP; zenon_intro zenon_H8]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L3_); trivial. % 41.92/42.14 apply zenon_H20. apply refl_equal. % 41.92/42.14 apply zenon_H20. apply refl_equal. % 41.92/42.14 apply (zenon_L5_); trivial. % 41.92/42.14 apply zenon_H20. apply refl_equal. % 41.92/42.14 apply zenon_H20. apply refl_equal. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L6_ *) % 41.92/42.14 assert (zenon_L7_ : (~((op1 (j (e20)) (j (e20))) = (op1 (e12) (e12)))) -> ((j (e20)) = (e12)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H22 zenon_H23. % 41.92/42.14 cut (((j (e20)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 41.92/42.14 cut (((j (e20)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 41.92/42.14 congruence. % 41.92/42.14 exact (zenon_H24 zenon_H23). % 41.92/42.14 exact (zenon_H24 zenon_H23). % 41.92/42.14 (* end of lemma zenon_L7_ *) % 41.92/42.14 assert (zenon_L8_ : (~((op1 (j (e20)) (j (e20))) = (op1 (e13) (e13)))) -> ((op1 (e12) (e12)) = (e10)) -> ((j (e20)) = (e12)) -> ((op1 (e13) (e13)) = (e10)) -> False). % 41.92/42.14 do 0 intro. intros zenon_He zenon_H25 zenon_H23 zenon_H10. % 41.92/42.14 cut (((op1 (e12) (e12)) = (e10)) = ((op1 (j (e20)) (j (e20))) = (op1 (e13) (e13)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_He. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H25. % 41.92/42.14 cut (((e10) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H11]. % 41.92/42.14 cut (((op1 (e12) (e12)) = (op1 (j (e20)) (j (e20))))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((op1 (j (e20)) (j (e20))) = (op1 (j (e20)) (j (e20))))); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 41.92/42.14 cut (((op1 (j (e20)) (j (e20))) = (op1 (j (e20)) (j (e20)))) = ((op1 (e12) (e12)) = (op1 (j (e20)) (j (e20))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H26. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H13. % 41.92/42.14 cut (((op1 (j (e20)) (j (e20))) = (op1 (j (e20)) (j (e20))))); [idtac | apply NNPP; zenon_intro zenon_H14]. % 41.92/42.14 cut (((op1 (j (e20)) (j (e20))) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L7_); trivial. % 41.92/42.14 apply zenon_H14. apply refl_equal. % 41.92/42.14 apply zenon_H14. apply refl_equal. % 41.92/42.14 apply zenon_H11. apply sym_equal. exact zenon_H10. % 41.92/42.14 (* end of lemma zenon_L8_ *) % 41.92/42.14 assert (zenon_L9_ : (~((e12) = (e12))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H27. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L9_ *) % 41.92/42.14 assert (zenon_L10_ : ((j (op2 (e20) (e20))) = (op1 (j (e20)) (j (e20)))) -> ((j (e20)) = (e12)) -> ((op1 (e13) (e13)) = (e10)) -> ((op1 (e12) (e12)) = (e10)) -> ((op2 (e20) (e20)) = (e20)) -> (~((e10) = (e12))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H15 zenon_H23 zenon_H10 zenon_H25 zenon_H9 zenon_H28. % 41.92/42.14 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H29 | zenon_intro zenon_H27 ]. % 41.92/42.14 cut (((e12) = (e12)) = ((e10) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H28. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H29. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((e12) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((op1 (e13) (e13)) = (e10)) = ((e12) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H2a. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H10. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H29 | zenon_intro zenon_H27 ]. % 41.92/42.14 cut (((e12) = (e12)) = ((op1 (e13) (e13)) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H2b. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H29. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((e12) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H2c]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H1b | zenon_intro zenon_H1c ]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((e12) = (op1 (e13) (e13)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H2c. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H1b. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e20)) = (e12)) = ((op1 (e13) (e13)) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H2b. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H23. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((j (e20)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H1b | zenon_intro zenon_H1c ]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((j (e20)) = (op1 (e13) (e13)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H1d. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H1b. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (j (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (e20)) = (j (e20)))); [ zenon_intro zenon_H1f | zenon_intro zenon_H20 ]. % 41.92/42.14 cut (((j (e20)) = (j (e20))) = ((op1 (e13) (e13)) = (j (e20)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H1e. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H1f. % 41.92/42.14 cut (((j (e20)) = (j (e20)))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 41.92/42.14 cut (((j (e20)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (op2 (e20) (e20))) = (op1 (j (e20)) (j (e20)))) = ((j (e20)) = (op1 (e13) (e13)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H1d. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H15. % 41.92/42.14 cut (((op1 (j (e20)) (j (e20))) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_He]. % 41.92/42.14 cut (((j (op2 (e20) (e20))) = (j (e20)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (e20)) = (j (e20)))); [ zenon_intro zenon_H1f | zenon_intro zenon_H20 ]. % 41.92/42.14 cut (((j (e20)) = (j (e20))) = ((j (op2 (e20) (e20))) = (j (e20)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H21. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H1f. % 41.92/42.14 cut (((j (e20)) = (j (e20)))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 41.92/42.14 cut (((j (e20)) = (j (op2 (e20) (e20))))); [idtac | apply NNPP; zenon_intro zenon_H8]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L3_); trivial. % 41.92/42.14 apply zenon_H20. apply refl_equal. % 41.92/42.14 apply zenon_H20. apply refl_equal. % 41.92/42.14 apply (zenon_L8_); trivial. % 41.92/42.14 apply zenon_H20. apply refl_equal. % 41.92/42.14 apply zenon_H20. apply refl_equal. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L10_ *) % 41.92/42.14 assert (zenon_L11_ : (~((op1 (j (e20)) (j (e20))) = (op1 (e13) (e13)))) -> ((j (e20)) = (e13)) -> False). % 41.92/42.14 do 0 intro. intros zenon_He zenon_H2d. % 41.92/42.14 cut (((j (e20)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 41.92/42.14 cut (((j (e20)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 41.92/42.14 congruence. % 41.92/42.14 exact (zenon_H2e zenon_H2d). % 41.92/42.14 exact (zenon_H2e zenon_H2d). % 41.92/42.14 (* end of lemma zenon_L11_ *) % 41.92/42.14 assert (zenon_L12_ : (~((e13) = (e13))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H2f. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L12_ *) % 41.92/42.14 assert (zenon_L13_ : ((op1 (e13) (e13)) = (e10)) -> ((j (op2 (e20) (e20))) = (op1 (j (e20)) (j (e20)))) -> ((j (e20)) = (e13)) -> ((op2 (e20) (e20)) = (e20)) -> (~((e10) = (e13))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H10 zenon_H15 zenon_H2d zenon_H9 zenon_H30. % 41.92/42.14 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H31 | zenon_intro zenon_H2f ]. % 41.92/42.14 cut (((e13) = (e13)) = ((e10) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H30. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H31. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((e13) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((op1 (e13) (e13)) = (e10)) = ((e13) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H32. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H10. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H31 | zenon_intro zenon_H2f ]. % 41.92/42.14 cut (((e13) = (e13)) = ((op1 (e13) (e13)) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H33. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H31. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((e13) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H1b | zenon_intro zenon_H1c ]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((e13) = (op1 (e13) (e13)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H34. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H1b. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e20)) = (e13)) = ((op1 (e13) (e13)) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H33. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H2d. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((j (e20)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H1b | zenon_intro zenon_H1c ]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((j (e20)) = (op1 (e13) (e13)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H1d. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H1b. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (j (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (e20)) = (j (e20)))); [ zenon_intro zenon_H1f | zenon_intro zenon_H20 ]. % 41.92/42.14 cut (((j (e20)) = (j (e20))) = ((op1 (e13) (e13)) = (j (e20)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H1e. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H1f. % 41.92/42.14 cut (((j (e20)) = (j (e20)))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 41.92/42.14 cut (((j (e20)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (op2 (e20) (e20))) = (op1 (j (e20)) (j (e20)))) = ((j (e20)) = (op1 (e13) (e13)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H1d. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H15. % 41.92/42.14 cut (((op1 (j (e20)) (j (e20))) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_He]. % 41.92/42.14 cut (((j (op2 (e20) (e20))) = (j (e20)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (e20)) = (j (e20)))); [ zenon_intro zenon_H1f | zenon_intro zenon_H20 ]. % 41.92/42.14 cut (((j (e20)) = (j (e20))) = ((j (op2 (e20) (e20))) = (j (e20)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H21. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H1f. % 41.92/42.14 cut (((j (e20)) = (j (e20)))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 41.92/42.14 cut (((j (e20)) = (j (op2 (e20) (e20))))); [idtac | apply NNPP; zenon_intro zenon_H8]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L3_); trivial. % 41.92/42.14 apply zenon_H20. apply refl_equal. % 41.92/42.14 apply zenon_H20. apply refl_equal. % 41.92/42.14 apply (zenon_L11_); trivial. % 41.92/42.14 apply zenon_H20. apply refl_equal. % 41.92/42.14 apply zenon_H20. apply refl_equal. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L13_ *) % 41.92/42.14 assert (zenon_L14_ : (((j (e20)) = (e10))\/(((j (e20)) = (e11))\/(((j (e20)) = (e12))\/((j (e20)) = (e13))))) -> ((h (e11)) = (e20)) -> ((j (h (e11))) = (e11)) -> (~((e10) = (e11))) -> ((op1 (e11) (e11)) = (e10)) -> (~((e10) = (e12))) -> ((op1 (e12) (e12)) = (e10)) -> ((op1 (e13) (e13)) = (e10)) -> ((j (op2 (e20) (e20))) = (op1 (j (e20)) (j (e20)))) -> ((op2 (e20) (e20)) = (e20)) -> (~((e10) = (e13))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H35 zenon_H36 zenon_H37 zenon_H16 zenon_Hf zenon_H28 zenon_H25 zenon_H10 zenon_H15 zenon_H9 zenon_H30. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ]. % 41.92/42.14 cut (((j (h (e11))) = (e11)) = ((e10) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H16. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H37. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((j (h (e11))) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e10) = (e10))); [ zenon_intro zenon_H3b | zenon_intro zenon_H6 ]. % 41.92/42.14 cut (((e10) = (e10)) = ((j (h (e11))) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H3a. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3b. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((e10) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3c]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e11))) = (j (h (e11))))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11)))) = ((e10) = (j (h (e11))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H3c. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3d. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 41.92/42.14 cut (((j (h (e11))) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e20)) = (e10)) = ((j (h (e11))) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H3a. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H39. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((j (e20)) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e11))) = (j (h (e11))))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11)))) = ((j (e20)) = (j (h (e11))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H3f. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3d. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 41.92/42.14 cut (((j (h (e11))) = (j (e20)))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((h (e11)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 41.92/42.14 congruence. % 41.92/42.14 exact (zenon_H41 zenon_H36). % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_Hc | zenon_intro zenon_H42 ]. % 41.92/42.14 apply (zenon_L6_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H23 | zenon_intro zenon_H2d ]. % 41.92/42.14 apply (zenon_L10_); trivial. % 41.92/42.14 apply (zenon_L13_); trivial. % 41.92/42.14 (* end of lemma zenon_L14_ *) % 41.92/42.14 assert (zenon_L15_ : (~((j (h (e12))) = (j (e20)))) -> ((h (e12)) = (e20)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H43 zenon_H44. % 41.92/42.14 cut (((h (e12)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 41.92/42.14 congruence. % 41.92/42.14 exact (zenon_H45 zenon_H44). % 41.92/42.14 (* end of lemma zenon_L15_ *) % 41.92/42.14 assert (zenon_L16_ : (((j (e20)) = (e10))\/(((j (e20)) = (e11))\/(((j (e20)) = (e12))\/((j (e20)) = (e13))))) -> ((h (e12)) = (e20)) -> ((j (h (e12))) = (e12)) -> (~((e11) = (e12))) -> (~((e10) = (e12))) -> ((op1 (e12) (e12)) = (e10)) -> ((op1 (e13) (e13)) = (e10)) -> ((j (op2 (e20) (e20))) = (op1 (j (e20)) (j (e20)))) -> ((op2 (e20) (e20)) = (e20)) -> (~((e10) = (e13))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H35 zenon_H44 zenon_H46 zenon_H47 zenon_H28 zenon_H25 zenon_H10 zenon_H15 zenon_H9 zenon_H30. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ]. % 41.92/42.14 cut (((j (h (e12))) = (e12)) = ((e10) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H28. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H46. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((j (h (e12))) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H48]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e10) = (e10))); [ zenon_intro zenon_H3b | zenon_intro zenon_H6 ]. % 41.92/42.14 cut (((e10) = (e10)) = ((j (h (e12))) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H48. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3b. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((e10) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e12))) = (j (h (e12))))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12)))) = ((e10) = (j (h (e12))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H49. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H4a. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 41.92/42.14 cut (((j (h (e12))) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H48]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e20)) = (e10)) = ((j (h (e12))) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H48. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H39. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((j (e20)) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e12))) = (j (h (e12))))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12)))) = ((j (e20)) = (j (h (e12))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H4c. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H4a. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 41.92/42.14 cut (((j (h (e12))) = (j (e20)))); [idtac | apply NNPP; zenon_intro zenon_H43]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L15_); trivial. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_Hc | zenon_intro zenon_H42 ]. % 41.92/42.14 cut (((j (h (e12))) = (e12)) = ((e11) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H47. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H46. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((j (h (e12))) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e11) = (e11))); [ zenon_intro zenon_H17 | zenon_intro zenon_H7 ]. % 41.92/42.14 cut (((e11) = (e11)) = ((j (h (e12))) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H4d. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H17. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((e11) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e12))) = (j (h (e12))))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12)))) = ((e11) = (j (h (e12))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H4e. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H4a. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 41.92/42.14 cut (((j (h (e12))) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e20)) = (e11)) = ((j (h (e12))) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H4d. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_Hc. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((j (e20)) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e12))) = (j (h (e12))))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12)))) = ((j (e20)) = (j (h (e12))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H4c. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H4a. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 41.92/42.14 cut (((j (h (e12))) = (j (e20)))); [idtac | apply NNPP; zenon_intro zenon_H43]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L15_); trivial. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H23 | zenon_intro zenon_H2d ]. % 41.92/42.14 apply (zenon_L10_); trivial. % 41.92/42.14 apply (zenon_L13_); trivial. % 41.92/42.14 (* end of lemma zenon_L16_ *) % 41.92/42.14 assert (zenon_L17_ : (~((j (h (e12))) = (j (e21)))) -> ((h (e12)) = (e21)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H4f zenon_H50. % 41.92/42.14 cut (((h (e12)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H51]. % 41.92/42.14 congruence. % 41.92/42.14 exact (zenon_H51 zenon_H50). % 41.92/42.14 (* end of lemma zenon_L17_ *) % 41.92/42.14 assert (zenon_L18_ : (~((e10) = (e12))) -> ((j (h (e12))) = (e12)) -> ((h (e12)) = (e21)) -> ((j (e21)) = (e10)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H28 zenon_H46 zenon_H50 zenon_H52. % 41.92/42.14 cut (((j (h (e12))) = (e12)) = ((e10) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H28. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H46. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((j (h (e12))) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H48]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e10) = (e10))); [ zenon_intro zenon_H3b | zenon_intro zenon_H6 ]. % 41.92/42.14 cut (((e10) = (e10)) = ((j (h (e12))) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H48. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3b. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((e10) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e12))) = (j (h (e12))))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12)))) = ((e10) = (j (h (e12))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H49. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H4a. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 41.92/42.14 cut (((j (h (e12))) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H48]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e21)) = (e10)) = ((j (h (e12))) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H48. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H52. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((j (e21)) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e12))) = (j (h (e12))))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12)))) = ((j (e21)) = (j (h (e12))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H53. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H4a. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 41.92/42.14 cut (((j (h (e12))) = (j (e21)))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L17_); trivial. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L18_ *) % 41.92/42.14 assert (zenon_L19_ : (~((e11) = (e12))) -> ((j (h (e12))) = (e12)) -> ((h (e12)) = (e21)) -> ((j (e21)) = (e11)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H47 zenon_H46 zenon_H50 zenon_H54. % 41.92/42.14 cut (((j (h (e12))) = (e12)) = ((e11) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H47. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H46. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((j (h (e12))) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e11) = (e11))); [ zenon_intro zenon_H17 | zenon_intro zenon_H7 ]. % 41.92/42.14 cut (((e11) = (e11)) = ((j (h (e12))) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H4d. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H17. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((e11) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e12))) = (j (h (e12))))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12)))) = ((e11) = (j (h (e12))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H4e. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H4a. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 41.92/42.14 cut (((j (h (e12))) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e21)) = (e11)) = ((j (h (e12))) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H4d. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H54. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((j (e21)) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e12))) = (j (h (e12))))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12)))) = ((j (e21)) = (j (h (e12))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H53. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H4a. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 41.92/42.14 cut (((j (h (e12))) = (j (e21)))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L17_); trivial. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L19_ *) % 41.92/42.14 assert (zenon_L20_ : (~((j (h (e11))) = (j (e21)))) -> ((h (e11)) = (e21)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H55 zenon_H56. % 41.92/42.14 cut (((h (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 41.92/42.14 congruence. % 41.92/42.14 exact (zenon_H57 zenon_H56). % 41.92/42.14 (* end of lemma zenon_L20_ *) % 41.92/42.14 assert (zenon_L21_ : ((j (h (e11))) = (e11)) -> ((h (e11)) = (e21)) -> ((j (e21)) = (e12)) -> (~((e11) = (e12))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H37 zenon_H56 zenon_H58 zenon_H47. % 41.92/42.14 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H29 | zenon_intro zenon_H27 ]. % 41.92/42.14 cut (((e12) = (e12)) = ((e11) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H47. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H29. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((e12) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (h (e11))) = (e11)) = ((e12) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H59. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H37. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((j (h (e11))) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H29 | zenon_intro zenon_H27 ]. % 41.92/42.14 cut (((e12) = (e12)) = ((j (h (e11))) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H5a. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H29. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((e12) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e11))) = (j (h (e11))))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11)))) = ((e12) = (j (h (e11))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H5b. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3d. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 41.92/42.14 cut (((j (h (e11))) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e21)) = (e12)) = ((j (h (e11))) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H5a. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H58. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((j (e21)) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e11))) = (j (h (e11))))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11)))) = ((j (e21)) = (j (h (e11))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H5c. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3d. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 41.92/42.14 cut (((j (h (e11))) = (j (e21)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L20_); trivial. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L21_ *) % 41.92/42.14 assert (zenon_L22_ : ((j (h (e11))) = (e11)) -> ((h (e11)) = (e21)) -> ((j (e21)) = (e13)) -> (~((e11) = (e13))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H37 zenon_H56 zenon_H5d zenon_H5e. % 41.92/42.14 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H31 | zenon_intro zenon_H2f ]. % 41.92/42.14 cut (((e13) = (e13)) = ((e11) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H5e. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H31. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((e13) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (h (e11))) = (e11)) = ((e13) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H5f. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H37. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((j (h (e11))) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H31 | zenon_intro zenon_H2f ]. % 41.92/42.14 cut (((e13) = (e13)) = ((j (h (e11))) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H60. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H31. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((e13) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e11))) = (j (h (e11))))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11)))) = ((e13) = (j (h (e11))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H61. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3d. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 41.92/42.14 cut (((j (h (e11))) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e21)) = (e13)) = ((j (h (e11))) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H60. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H5d. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((j (e21)) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e11))) = (j (h (e11))))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11)))) = ((j (e21)) = (j (h (e11))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H5c. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3d. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 41.92/42.14 cut (((j (h (e11))) = (j (e21)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L20_); trivial. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L22_ *) % 41.92/42.14 assert (zenon_L23_ : (((j (e21)) = (e10))\/(((j (e21)) = (e11))\/(((j (e21)) = (e12))\/((j (e21)) = (e13))))) -> (~((e10) = (e12))) -> ((h (e12)) = (e21)) -> ((j (h (e12))) = (e12)) -> (~((e11) = (e12))) -> ((j (h (e11))) = (e11)) -> ((h (e11)) = (e21)) -> (~((e11) = (e13))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H62 zenon_H28 zenon_H50 zenon_H46 zenon_H47 zenon_H37 zenon_H56 zenon_H5e. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H52 | zenon_intro zenon_H63 ]. % 41.92/42.14 apply (zenon_L18_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H54 | zenon_intro zenon_H64 ]. % 41.92/42.14 apply (zenon_L19_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H58 | zenon_intro zenon_H5d ]. % 41.92/42.14 apply (zenon_L21_); trivial. % 41.92/42.14 apply (zenon_L22_); trivial. % 41.92/42.14 (* end of lemma zenon_L23_ *) % 41.92/42.14 assert (zenon_L24_ : (~((j (h (e13))) = (j (e20)))) -> ((h (e13)) = (e20)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H65 zenon_H66. % 41.92/42.14 cut (((h (e13)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 41.92/42.14 congruence. % 41.92/42.14 exact (zenon_H67 zenon_H66). % 41.92/42.14 (* end of lemma zenon_L24_ *) % 41.92/42.14 assert (zenon_L25_ : (((j (e20)) = (e10))\/(((j (e20)) = (e11))\/(((j (e20)) = (e12))\/((j (e20)) = (e13))))) -> (~((e11) = (e13))) -> ((h (e13)) = (e20)) -> ((j (h (e13))) = (e13)) -> (~((e12) = (e13))) -> ((op1 (e13) (e13)) = (e10)) -> ((j (op2 (e20) (e20))) = (op1 (j (e20)) (j (e20)))) -> ((op2 (e20) (e20)) = (e20)) -> (~((e10) = (e13))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H35 zenon_H5e zenon_H66 zenon_H68 zenon_H69 zenon_H10 zenon_H15 zenon_H9 zenon_H30. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ]. % 41.92/42.14 cut (((j (h (e13))) = (e13)) = ((e10) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H30. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H68. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((j (h (e13))) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e10) = (e10))); [ zenon_intro zenon_H3b | zenon_intro zenon_H6 ]. % 41.92/42.14 cut (((e10) = (e10)) = ((j (h (e13))) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H6a. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3b. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((e10) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e13))) = (j (h (e13))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13)))) = ((e10) = (j (h (e13))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H6b. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H6c. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 41.92/42.14 cut (((j (h (e13))) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e20)) = (e10)) = ((j (h (e13))) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H6a. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H39. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((j (e20)) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e13))) = (j (h (e13))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13)))) = ((j (e20)) = (j (h (e13))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H6e. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H6c. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 41.92/42.14 cut (((j (h (e13))) = (j (e20)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L24_); trivial. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_Hc | zenon_intro zenon_H42 ]. % 41.92/42.14 cut (((j (h (e13))) = (e13)) = ((e11) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H5e. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H68. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((j (h (e13))) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e11) = (e11))); [ zenon_intro zenon_H17 | zenon_intro zenon_H7 ]. % 41.92/42.14 cut (((e11) = (e11)) = ((j (h (e13))) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H6f. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H17. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((e11) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e13))) = (j (h (e13))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13)))) = ((e11) = (j (h (e13))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H70. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H6c. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 41.92/42.14 cut (((j (h (e13))) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e20)) = (e11)) = ((j (h (e13))) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H6f. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_Hc. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((j (e20)) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e13))) = (j (h (e13))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13)))) = ((j (e20)) = (j (h (e13))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H6e. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H6c. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 41.92/42.14 cut (((j (h (e13))) = (j (e20)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L24_); trivial. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H23 | zenon_intro zenon_H2d ]. % 41.92/42.14 cut (((j (h (e13))) = (e13)) = ((e12) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H69. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H68. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((j (h (e13))) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H29 | zenon_intro zenon_H27 ]. % 41.92/42.14 cut (((e12) = (e12)) = ((j (h (e13))) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H71. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H29. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((e12) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e13))) = (j (h (e13))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13)))) = ((e12) = (j (h (e13))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H72. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H6c. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 41.92/42.14 cut (((j (h (e13))) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e20)) = (e12)) = ((j (h (e13))) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H71. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H23. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((j (e20)) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e13))) = (j (h (e13))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13)))) = ((j (e20)) = (j (h (e13))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H6e. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H6c. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 41.92/42.14 cut (((j (h (e13))) = (j (e20)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L24_); trivial. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply (zenon_L13_); trivial. % 41.92/42.14 (* end of lemma zenon_L25_ *) % 41.92/42.14 assert (zenon_L26_ : (~((j (h (e13))) = (j (e21)))) -> ((h (e13)) = (e21)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H73 zenon_H74. % 41.92/42.14 cut (((h (e13)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H75]. % 41.92/42.14 congruence. % 41.92/42.14 exact (zenon_H75 zenon_H74). % 41.92/42.14 (* end of lemma zenon_L26_ *) % 41.92/42.14 assert (zenon_L27_ : (~((e10) = (e13))) -> ((j (h (e13))) = (e13)) -> ((h (e13)) = (e21)) -> ((j (e21)) = (e10)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H30 zenon_H68 zenon_H74 zenon_H52. % 41.92/42.14 cut (((j (h (e13))) = (e13)) = ((e10) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H30. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H68. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((j (h (e13))) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e10) = (e10))); [ zenon_intro zenon_H3b | zenon_intro zenon_H6 ]. % 41.92/42.14 cut (((e10) = (e10)) = ((j (h (e13))) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H6a. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3b. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((e10) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e13))) = (j (h (e13))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13)))) = ((e10) = (j (h (e13))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H6b. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H6c. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 41.92/42.14 cut (((j (h (e13))) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e21)) = (e10)) = ((j (h (e13))) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H6a. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H52. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((j (e21)) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e13))) = (j (h (e13))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13)))) = ((j (e21)) = (j (h (e13))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H76. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H6c. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 41.92/42.14 cut (((j (h (e13))) = (j (e21)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L26_); trivial. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L27_ *) % 41.92/42.14 assert (zenon_L28_ : (~((e11) = (e13))) -> ((j (h (e13))) = (e13)) -> ((h (e13)) = (e21)) -> ((j (e21)) = (e11)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H5e zenon_H68 zenon_H74 zenon_H54. % 41.92/42.14 cut (((j (h (e13))) = (e13)) = ((e11) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H5e. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H68. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((j (h (e13))) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e11) = (e11))); [ zenon_intro zenon_H17 | zenon_intro zenon_H7 ]. % 41.92/42.14 cut (((e11) = (e11)) = ((j (h (e13))) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H6f. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H17. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((e11) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e13))) = (j (h (e13))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13)))) = ((e11) = (j (h (e13))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H70. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H6c. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 41.92/42.14 cut (((j (h (e13))) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e21)) = (e11)) = ((j (h (e13))) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H6f. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H54. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((j (e21)) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e13))) = (j (h (e13))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13)))) = ((j (e21)) = (j (h (e13))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H76. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H6c. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 41.92/42.14 cut (((j (h (e13))) = (j (e21)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L26_); trivial. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L28_ *) % 41.92/42.14 assert (zenon_L29_ : (~((e12) = (e13))) -> ((j (h (e13))) = (e13)) -> ((h (e13)) = (e21)) -> ((j (e21)) = (e12)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H69 zenon_H68 zenon_H74 zenon_H58. % 41.92/42.14 cut (((j (h (e13))) = (e13)) = ((e12) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H69. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H68. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((j (h (e13))) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H29 | zenon_intro zenon_H27 ]. % 41.92/42.14 cut (((e12) = (e12)) = ((j (h (e13))) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H71. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H29. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((e12) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e13))) = (j (h (e13))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13)))) = ((e12) = (j (h (e13))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H72. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H6c. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 41.92/42.14 cut (((j (h (e13))) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e21)) = (e12)) = ((j (h (e13))) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H71. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H58. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((j (e21)) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e13))) = (j (h (e13))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13)))) = ((j (e21)) = (j (h (e13))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H76. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H6c. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 41.92/42.14 cut (((j (h (e13))) = (j (e21)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L26_); trivial. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L29_ *) % 41.92/42.14 assert (zenon_L30_ : (((j (e21)) = (e10))\/(((j (e21)) = (e11))\/(((j (e21)) = (e12))\/((j (e21)) = (e13))))) -> (~((e10) = (e13))) -> ((h (e13)) = (e21)) -> ((j (h (e13))) = (e13)) -> (~((e12) = (e13))) -> ((j (h (e11))) = (e11)) -> ((h (e11)) = (e21)) -> (~((e11) = (e13))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H62 zenon_H30 zenon_H74 zenon_H68 zenon_H69 zenon_H37 zenon_H56 zenon_H5e. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H52 | zenon_intro zenon_H63 ]. % 41.92/42.14 apply (zenon_L27_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H54 | zenon_intro zenon_H64 ]. % 41.92/42.14 apply (zenon_L28_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H58 | zenon_intro zenon_H5d ]. % 41.92/42.14 apply (zenon_L29_); trivial. % 41.92/42.14 apply (zenon_L22_); trivial. % 41.92/42.14 (* end of lemma zenon_L30_ *) % 41.92/42.14 assert (zenon_L31_ : (~((j (h (e13))) = (j (e22)))) -> ((h (e13)) = (e22)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H77 zenon_H78. % 41.92/42.14 cut (((h (e13)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 41.92/42.14 congruence. % 41.92/42.14 exact (zenon_H79 zenon_H78). % 41.92/42.14 (* end of lemma zenon_L31_ *) % 41.92/42.14 assert (zenon_L32_ : (~((e10) = (e13))) -> ((j (h (e13))) = (e13)) -> ((h (e13)) = (e22)) -> ((j (e22)) = (e10)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H30 zenon_H68 zenon_H78 zenon_H7a. % 41.92/42.14 cut (((j (h (e13))) = (e13)) = ((e10) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H30. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H68. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((j (h (e13))) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e10) = (e10))); [ zenon_intro zenon_H3b | zenon_intro zenon_H6 ]. % 41.92/42.14 cut (((e10) = (e10)) = ((j (h (e13))) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H6a. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3b. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((e10) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e13))) = (j (h (e13))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13)))) = ((e10) = (j (h (e13))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H6b. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H6c. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 41.92/42.14 cut (((j (h (e13))) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e22)) = (e10)) = ((j (h (e13))) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H6a. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H7a. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((j (e22)) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e13))) = (j (h (e13))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13)))) = ((j (e22)) = (j (h (e13))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H7b. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H6c. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 41.92/42.14 cut (((j (h (e13))) = (j (e22)))); [idtac | apply NNPP; zenon_intro zenon_H77]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L31_); trivial. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L32_ *) % 41.92/42.14 assert (zenon_L33_ : (~((e11) = (e13))) -> ((j (h (e13))) = (e13)) -> ((h (e13)) = (e22)) -> ((j (e22)) = (e11)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H5e zenon_H68 zenon_H78 zenon_H7c. % 41.92/42.14 cut (((j (h (e13))) = (e13)) = ((e11) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H5e. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H68. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((j (h (e13))) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e11) = (e11))); [ zenon_intro zenon_H17 | zenon_intro zenon_H7 ]. % 41.92/42.14 cut (((e11) = (e11)) = ((j (h (e13))) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H6f. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H17. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((e11) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e13))) = (j (h (e13))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13)))) = ((e11) = (j (h (e13))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H70. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H6c. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 41.92/42.14 cut (((j (h (e13))) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e22)) = (e11)) = ((j (h (e13))) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H6f. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H7c. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((j (e22)) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e13))) = (j (h (e13))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13)))) = ((j (e22)) = (j (h (e13))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H7b. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H6c. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 41.92/42.14 cut (((j (h (e13))) = (j (e22)))); [idtac | apply NNPP; zenon_intro zenon_H77]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L31_); trivial. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L33_ *) % 41.92/42.14 assert (zenon_L34_ : (~((e12) = (e13))) -> ((j (h (e13))) = (e13)) -> ((h (e13)) = (e22)) -> ((j (e22)) = (e12)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H69 zenon_H68 zenon_H78 zenon_H7d. % 41.92/42.14 cut (((j (h (e13))) = (e13)) = ((e12) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H69. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H68. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((j (h (e13))) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H29 | zenon_intro zenon_H27 ]. % 41.92/42.14 cut (((e12) = (e12)) = ((j (h (e13))) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H71. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H29. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((e12) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e13))) = (j (h (e13))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13)))) = ((e12) = (j (h (e13))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H72. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H6c. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 41.92/42.14 cut (((j (h (e13))) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e22)) = (e12)) = ((j (h (e13))) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H71. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H7d. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((j (e22)) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e13))) = (j (h (e13))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13)))) = ((j (e22)) = (j (h (e13))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H7b. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H6c. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 41.92/42.14 cut (((j (h (e13))) = (j (e22)))); [idtac | apply NNPP; zenon_intro zenon_H77]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L31_); trivial. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L34_ *) % 41.92/42.14 assert (zenon_L35_ : (~((j (h (e12))) = (j (e22)))) -> ((h (e12)) = (e22)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H7e zenon_H7f. % 41.92/42.14 cut (((h (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 41.92/42.14 congruence. % 41.92/42.14 exact (zenon_H80 zenon_H7f). % 41.92/42.14 (* end of lemma zenon_L35_ *) % 41.92/42.14 assert (zenon_L36_ : ((j (h (e12))) = (e12)) -> ((h (e12)) = (e22)) -> ((j (e22)) = (e13)) -> (~((e12) = (e13))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H46 zenon_H7f zenon_H81 zenon_H69. % 41.92/42.14 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H31 | zenon_intro zenon_H2f ]. % 41.92/42.14 cut (((e13) = (e13)) = ((e12) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H69. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H31. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((e13) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (h (e12))) = (e12)) = ((e13) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H82. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H46. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((j (h (e12))) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H31 | zenon_intro zenon_H2f ]. % 41.92/42.14 cut (((e13) = (e13)) = ((j (h (e12))) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H83. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H31. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((e13) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e12))) = (j (h (e12))))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12)))) = ((e13) = (j (h (e12))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H84. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H4a. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 41.92/42.14 cut (((j (h (e12))) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e22)) = (e13)) = ((j (h (e12))) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H83. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H81. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((j (e22)) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e12))) = (j (h (e12))))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12)))) = ((j (e22)) = (j (h (e12))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H85. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H4a. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 41.92/42.14 cut (((j (h (e12))) = (j (e22)))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L35_); trivial. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L36_ *) % 41.92/42.14 assert (zenon_L37_ : (((j (e22)) = (e10))\/(((j (e22)) = (e11))\/(((j (e22)) = (e12))\/((j (e22)) = (e13))))) -> (~((e10) = (e13))) -> (~((e11) = (e13))) -> ((h (e13)) = (e22)) -> ((j (h (e13))) = (e13)) -> ((j (h (e12))) = (e12)) -> ((h (e12)) = (e22)) -> (~((e12) = (e13))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H86 zenon_H30 zenon_H5e zenon_H78 zenon_H68 zenon_H46 zenon_H7f zenon_H69. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7a | zenon_intro zenon_H87 ]. % 41.92/42.14 apply (zenon_L32_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H7c | zenon_intro zenon_H88 ]. % 41.92/42.14 apply (zenon_L33_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H88); [ zenon_intro zenon_H7d | zenon_intro zenon_H81 ]. % 41.92/42.14 apply (zenon_L34_); trivial. % 41.92/42.14 apply (zenon_L36_); trivial. % 41.92/42.14 (* end of lemma zenon_L37_ *) % 41.92/42.14 assert (zenon_L38_ : (~((e10) = (e11))) -> ((j (h (e11))) = (e11)) -> ((h (e11)) = (e21)) -> ((j (e21)) = (e10)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H16 zenon_H37 zenon_H56 zenon_H52. % 41.92/42.14 cut (((j (h (e11))) = (e11)) = ((e10) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H16. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H37. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((j (h (e11))) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e10) = (e10))); [ zenon_intro zenon_H3b | zenon_intro zenon_H6 ]. % 41.92/42.14 cut (((e10) = (e10)) = ((j (h (e11))) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H3a. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3b. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((e10) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3c]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e11))) = (j (h (e11))))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11)))) = ((e10) = (j (h (e11))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H3c. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3d. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 41.92/42.14 cut (((j (h (e11))) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e21)) = (e10)) = ((j (h (e11))) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H3a. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H52. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((j (e21)) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e11))) = (j (h (e11))))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11)))) = ((j (e21)) = (j (h (e11))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H5c. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3d. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 41.92/42.14 cut (((j (h (e11))) = (j (e21)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L20_); trivial. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L38_ *) % 41.92/42.14 assert (zenon_L39_ : (~((j (h (e13))) = (j (e23)))) -> ((h (e13)) = (e23)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H89 zenon_H8a. % 41.92/42.14 cut (((h (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 41.92/42.14 congruence. % 41.92/42.14 exact (zenon_H8b zenon_H8a). % 41.92/42.14 (* end of lemma zenon_L39_ *) % 41.92/42.14 assert (zenon_L40_ : (~((e10) = (e13))) -> ((j (h (e13))) = (e13)) -> ((h (e13)) = (e23)) -> ((j (e23)) = (e10)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H30 zenon_H68 zenon_H8a zenon_H8c. % 41.92/42.14 cut (((j (h (e13))) = (e13)) = ((e10) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H30. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H68. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((j (h (e13))) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e10) = (e10))); [ zenon_intro zenon_H3b | zenon_intro zenon_H6 ]. % 41.92/42.14 cut (((e10) = (e10)) = ((j (h (e13))) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H6a. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3b. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((e10) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e13))) = (j (h (e13))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13)))) = ((e10) = (j (h (e13))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H6b. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H6c. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 41.92/42.14 cut (((j (h (e13))) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e23)) = (e10)) = ((j (h (e13))) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H6a. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H8c. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((j (e23)) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H8d]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e13))) = (j (h (e13))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13)))) = ((j (e23)) = (j (h (e13))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H8d. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H6c. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 41.92/42.14 cut (((j (h (e13))) = (j (e23)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L39_); trivial. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L40_ *) % 41.92/42.14 assert (zenon_L41_ : (~((e11) = (e13))) -> ((j (h (e13))) = (e13)) -> ((h (e13)) = (e23)) -> ((j (e23)) = (e11)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H5e zenon_H68 zenon_H8a zenon_H8e. % 41.92/42.14 cut (((j (h (e13))) = (e13)) = ((e11) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H5e. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H68. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((j (h (e13))) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e11) = (e11))); [ zenon_intro zenon_H17 | zenon_intro zenon_H7 ]. % 41.92/42.14 cut (((e11) = (e11)) = ((j (h (e13))) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H6f. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H17. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((e11) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e13))) = (j (h (e13))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13)))) = ((e11) = (j (h (e13))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H70. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H6c. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 41.92/42.14 cut (((j (h (e13))) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e23)) = (e11)) = ((j (h (e13))) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H6f. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H8e. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((j (e23)) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H8d]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e13))) = (j (h (e13))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13)))) = ((j (e23)) = (j (h (e13))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H8d. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H6c. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 41.92/42.14 cut (((j (h (e13))) = (j (e23)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L39_); trivial. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L41_ *) % 41.92/42.14 assert (zenon_L42_ : (~((j (e23)) = (j (op2 (e21) (e21))))) -> ((op2 (e21) (e21)) = (e23)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H8f zenon_H90. % 41.92/42.14 cut (((e23) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H91]. % 41.92/42.14 congruence. % 41.92/42.14 apply zenon_H91. apply sym_equal. exact zenon_H90. % 41.92/42.14 (* end of lemma zenon_L42_ *) % 41.92/42.14 assert (zenon_L43_ : (~((op1 (j (e21)) (j (e21))) = (op1 (e11) (e11)))) -> ((j (e21)) = (e11)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H92 zenon_H54. % 41.92/42.14 cut (((j (e21)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H93]. % 41.92/42.14 cut (((j (e21)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H93]. % 41.92/42.14 congruence. % 41.92/42.14 exact (zenon_H93 zenon_H54). % 41.92/42.14 exact (zenon_H93 zenon_H54). % 41.92/42.14 (* end of lemma zenon_L43_ *) % 41.92/42.14 assert (zenon_L44_ : (~((op1 (j (e21)) (j (e21))) = (op1 (e13) (e13)))) -> ((op1 (e11) (e11)) = (e10)) -> ((j (e21)) = (e11)) -> ((op1 (e13) (e13)) = (e10)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H94 zenon_Hf zenon_H54 zenon_H10. % 41.92/42.14 cut (((op1 (e11) (e11)) = (e10)) = ((op1 (j (e21)) (j (e21))) = (op1 (e13) (e13)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H94. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_Hf. % 41.92/42.14 cut (((e10) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H11]. % 41.92/42.14 cut (((op1 (e11) (e11)) = (op1 (j (e21)) (j (e21))))); [idtac | apply NNPP; zenon_intro zenon_H95]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((op1 (j (e21)) (j (e21))) = (op1 (j (e21)) (j (e21))))); [ zenon_intro zenon_H96 | zenon_intro zenon_H97 ]. % 41.92/42.14 cut (((op1 (j (e21)) (j (e21))) = (op1 (j (e21)) (j (e21)))) = ((op1 (e11) (e11)) = (op1 (j (e21)) (j (e21))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H95. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H96. % 41.92/42.14 cut (((op1 (j (e21)) (j (e21))) = (op1 (j (e21)) (j (e21))))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 41.92/42.14 cut (((op1 (j (e21)) (j (e21))) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H92]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L43_); trivial. % 41.92/42.14 apply zenon_H97. apply refl_equal. % 41.92/42.14 apply zenon_H97. apply refl_equal. % 41.92/42.14 apply zenon_H11. apply sym_equal. exact zenon_H10. % 41.92/42.14 (* end of lemma zenon_L44_ *) % 41.92/42.14 assert (zenon_L45_ : ((j (op2 (e21) (e21))) = (op1 (j (e21)) (j (e21)))) -> ((op2 (e21) (e21)) = (e23)) -> ((op1 (e11) (e11)) = (e10)) -> ((op1 (e13) (e13)) = (e10)) -> ((j (e21)) = (e11)) -> (~((op1 (e13) (e13)) = (j (e23)))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H98 zenon_H90 zenon_Hf zenon_H10 zenon_H54 zenon_H99. % 41.92/42.14 elim (classic ((j (e23)) = (j (e23)))); [ zenon_intro zenon_H9a | zenon_intro zenon_H9b ]. % 41.92/42.14 cut (((j (e23)) = (j (e23))) = ((op1 (e13) (e13)) = (j (e23)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H99. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H9a. % 41.92/42.14 cut (((j (e23)) = (j (e23)))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 41.92/42.14 cut (((j (e23)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (op2 (e21) (e21))) = (op1 (j (e21)) (j (e21)))) = ((j (e23)) = (op1 (e13) (e13)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H9c. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H98. % 41.92/42.14 cut (((op1 (j (e21)) (j (e21))) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 41.92/42.14 cut (((j (op2 (e21) (e21))) = (j (e23)))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (e23)) = (j (e23)))); [ zenon_intro zenon_H9a | zenon_intro zenon_H9b ]. % 41.92/42.14 cut (((j (e23)) = (j (e23))) = ((j (op2 (e21) (e21))) = (j (e23)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H9d. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H9a. % 41.92/42.14 cut (((j (e23)) = (j (e23)))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 41.92/42.14 cut (((j (e23)) = (j (op2 (e21) (e21))))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L42_); trivial. % 41.92/42.14 apply zenon_H9b. apply refl_equal. % 41.92/42.14 apply zenon_H9b. apply refl_equal. % 41.92/42.14 apply (zenon_L44_); trivial. % 41.92/42.14 apply zenon_H9b. apply refl_equal. % 41.92/42.14 apply zenon_H9b. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L45_ *) % 41.92/42.14 assert (zenon_L46_ : ((j (op2 (e21) (e21))) = (op1 (j (e21)) (j (e21)))) -> ((j (e21)) = (e11)) -> ((op1 (e13) (e13)) = (e10)) -> ((op1 (e11) (e11)) = (e10)) -> ((op2 (e21) (e21)) = (e23)) -> ((j (e23)) = (e12)) -> (~((e10) = (e12))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H98 zenon_H54 zenon_H10 zenon_Hf zenon_H90 zenon_H9e zenon_H28. % 41.92/42.14 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H29 | zenon_intro zenon_H27 ]. % 41.92/42.14 cut (((e12) = (e12)) = ((e10) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H28. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H29. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((e12) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((op1 (e13) (e13)) = (e10)) = ((e12) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H2a. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H10. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H29 | zenon_intro zenon_H27 ]. % 41.92/42.14 cut (((e12) = (e12)) = ((op1 (e13) (e13)) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H2b. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H29. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((e12) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H2c]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H1b | zenon_intro zenon_H1c ]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((e12) = (op1 (e13) (e13)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H2c. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H1b. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e23)) = (e12)) = ((op1 (e13) (e13)) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H2b. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H9e. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((j (e23)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H1b | zenon_intro zenon_H1c ]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((j (e23)) = (op1 (e13) (e13)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H9c. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H1b. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (j (e23)))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L45_); trivial. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L46_ *) % 41.92/42.14 assert (zenon_L47_ : (~((e12) = (e13))) -> ((j (h (e13))) = (e13)) -> ((h (e13)) = (e23)) -> ((j (e23)) = (e12)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H69 zenon_H68 zenon_H8a zenon_H9e. % 41.92/42.14 cut (((j (h (e13))) = (e13)) = ((e12) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H69. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H68. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((j (h (e13))) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H29 | zenon_intro zenon_H27 ]. % 41.92/42.14 cut (((e12) = (e12)) = ((j (h (e13))) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H71. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H29. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((e12) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e13))) = (j (h (e13))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13)))) = ((e12) = (j (h (e13))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H72. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H6c. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 41.92/42.14 cut (((j (h (e13))) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e23)) = (e12)) = ((j (h (e13))) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H71. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H9e. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((j (e23)) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H8d]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e13))) = (j (h (e13))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13)))) = ((j (e23)) = (j (h (e13))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H8d. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H6c. % 41.92/42.14 cut (((j (h (e13))) = (j (h (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 41.92/42.14 cut (((j (h (e13))) = (j (e23)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L39_); trivial. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H6d. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L47_ *) % 41.92/42.14 assert (zenon_L48_ : (~((op1 (j (e21)) (j (e21))) = (op1 (e12) (e12)))) -> ((j (e21)) = (e12)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H9f zenon_H58. % 41.92/42.14 cut (((j (e21)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 41.92/42.14 cut (((j (e21)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 41.92/42.14 congruence. % 41.92/42.14 exact (zenon_Ha0 zenon_H58). % 41.92/42.14 exact (zenon_Ha0 zenon_H58). % 41.92/42.14 (* end of lemma zenon_L48_ *) % 41.92/42.14 assert (zenon_L49_ : (~((op1 (j (e21)) (j (e21))) = (op1 (e13) (e13)))) -> ((op1 (e12) (e12)) = (e10)) -> ((j (e21)) = (e12)) -> ((op1 (e13) (e13)) = (e10)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H94 zenon_H25 zenon_H58 zenon_H10. % 41.92/42.14 cut (((op1 (e12) (e12)) = (e10)) = ((op1 (j (e21)) (j (e21))) = (op1 (e13) (e13)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H94. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H25. % 41.92/42.14 cut (((e10) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H11]. % 41.92/42.14 cut (((op1 (e12) (e12)) = (op1 (j (e21)) (j (e21))))); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((op1 (j (e21)) (j (e21))) = (op1 (j (e21)) (j (e21))))); [ zenon_intro zenon_H96 | zenon_intro zenon_H97 ]. % 41.92/42.14 cut (((op1 (j (e21)) (j (e21))) = (op1 (j (e21)) (j (e21)))) = ((op1 (e12) (e12)) = (op1 (j (e21)) (j (e21))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_Ha1. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H96. % 41.92/42.14 cut (((op1 (j (e21)) (j (e21))) = (op1 (j (e21)) (j (e21))))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 41.92/42.14 cut (((op1 (j (e21)) (j (e21))) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H9f]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L48_); trivial. % 41.92/42.14 apply zenon_H97. apply refl_equal. % 41.92/42.14 apply zenon_H97. apply refl_equal. % 41.92/42.14 apply zenon_H11. apply sym_equal. exact zenon_H10. % 41.92/42.14 (* end of lemma zenon_L49_ *) % 41.92/42.14 assert (zenon_L50_ : ((j (op2 (e21) (e21))) = (op1 (j (e21)) (j (e21)))) -> ((op2 (e21) (e21)) = (e23)) -> ((op1 (e12) (e12)) = (e10)) -> ((op1 (e13) (e13)) = (e10)) -> ((j (e21)) = (e12)) -> (~((op1 (e13) (e13)) = (j (e23)))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H98 zenon_H90 zenon_H25 zenon_H10 zenon_H58 zenon_H99. % 41.92/42.14 elim (classic ((j (e23)) = (j (e23)))); [ zenon_intro zenon_H9a | zenon_intro zenon_H9b ]. % 41.92/42.14 cut (((j (e23)) = (j (e23))) = ((op1 (e13) (e13)) = (j (e23)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H99. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H9a. % 41.92/42.14 cut (((j (e23)) = (j (e23)))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 41.92/42.14 cut (((j (e23)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (op2 (e21) (e21))) = (op1 (j (e21)) (j (e21)))) = ((j (e23)) = (op1 (e13) (e13)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H9c. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H98. % 41.92/42.14 cut (((op1 (j (e21)) (j (e21))) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 41.92/42.14 cut (((j (op2 (e21) (e21))) = (j (e23)))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (e23)) = (j (e23)))); [ zenon_intro zenon_H9a | zenon_intro zenon_H9b ]. % 41.92/42.14 cut (((j (e23)) = (j (e23))) = ((j (op2 (e21) (e21))) = (j (e23)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H9d. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H9a. % 41.92/42.14 cut (((j (e23)) = (j (e23)))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 41.92/42.14 cut (((j (e23)) = (j (op2 (e21) (e21))))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L42_); trivial. % 41.92/42.14 apply zenon_H9b. apply refl_equal. % 41.92/42.14 apply zenon_H9b. apply refl_equal. % 41.92/42.14 apply (zenon_L49_); trivial. % 41.92/42.14 apply zenon_H9b. apply refl_equal. % 41.92/42.14 apply zenon_H9b. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L50_ *) % 41.92/42.14 assert (zenon_L51_ : (((j (e23)) = (e10))\/(((j (e23)) = (e11))\/(((j (e23)) = (e12))\/((j (e23)) = (e13))))) -> (~((e11) = (e13))) -> ((h (e13)) = (e23)) -> ((j (h (e13))) = (e13)) -> (~((e12) = (e13))) -> ((j (op2 (e21) (e21))) = (op1 (j (e21)) (j (e21)))) -> ((j (e21)) = (e12)) -> ((op1 (e13) (e13)) = (e10)) -> ((op1 (e12) (e12)) = (e10)) -> ((op2 (e21) (e21)) = (e23)) -> (~((e10) = (e13))) -> False). % 41.92/42.14 do 0 intro. intros zenon_Ha2 zenon_H5e zenon_H8a zenon_H68 zenon_H69 zenon_H98 zenon_H58 zenon_H10 zenon_H25 zenon_H90 zenon_H30. % 41.92/42.14 apply (zenon_or_s _ _ zenon_Ha2); [ zenon_intro zenon_H8c | zenon_intro zenon_Ha3 ]. % 41.92/42.14 apply (zenon_L40_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_Ha3); [ zenon_intro zenon_H8e | zenon_intro zenon_Ha4 ]. % 41.92/42.14 apply (zenon_L41_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_Ha4); [ zenon_intro zenon_H9e | zenon_intro zenon_Ha5 ]. % 41.92/42.14 apply (zenon_L47_); trivial. % 41.92/42.14 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H31 | zenon_intro zenon_H2f ]. % 41.92/42.14 cut (((e13) = (e13)) = ((e10) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H30. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H31. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((e13) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((op1 (e13) (e13)) = (e10)) = ((e13) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H32. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H10. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H31 | zenon_intro zenon_H2f ]. % 41.92/42.14 cut (((e13) = (e13)) = ((op1 (e13) (e13)) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H33. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H31. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((e13) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H1b | zenon_intro zenon_H1c ]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((e13) = (op1 (e13) (e13)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H34. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H1b. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e23)) = (e13)) = ((op1 (e13) (e13)) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H33. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_Ha5. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((j (e23)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H1b | zenon_intro zenon_H1c ]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((j (e23)) = (op1 (e13) (e13)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H9c. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H1b. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (j (e23)))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L50_); trivial. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L51_ *) % 41.92/42.14 assert (zenon_L52_ : (~((j (h (e12))) = (j (e23)))) -> ((h (e12)) = (e23)) -> False). % 41.92/42.14 do 0 intro. intros zenon_Ha6 zenon_Ha7. % 41.92/42.14 cut (((h (e12)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 41.92/42.14 congruence. % 41.92/42.14 exact (zenon_Ha8 zenon_Ha7). % 41.92/42.14 (* end of lemma zenon_L52_ *) % 41.92/42.14 assert (zenon_L53_ : (~((e10) = (e12))) -> ((j (h (e12))) = (e12)) -> ((h (e12)) = (e23)) -> ((j (e23)) = (e10)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H28 zenon_H46 zenon_Ha7 zenon_H8c. % 41.92/42.14 cut (((j (h (e12))) = (e12)) = ((e10) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H28. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H46. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((j (h (e12))) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H48]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e10) = (e10))); [ zenon_intro zenon_H3b | zenon_intro zenon_H6 ]. % 41.92/42.14 cut (((e10) = (e10)) = ((j (h (e12))) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H48. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3b. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((e10) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e12))) = (j (h (e12))))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12)))) = ((e10) = (j (h (e12))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H49. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H4a. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 41.92/42.14 cut (((j (h (e12))) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H48]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e23)) = (e10)) = ((j (h (e12))) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H48. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H8c. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((j (e23)) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e12))) = (j (h (e12))))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12)))) = ((j (e23)) = (j (h (e12))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_Ha9. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H4a. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 41.92/42.14 cut (((j (h (e12))) = (j (e23)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L52_); trivial. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L53_ *) % 41.92/42.14 assert (zenon_L54_ : (~((e11) = (e12))) -> ((j (h (e12))) = (e12)) -> ((h (e12)) = (e23)) -> ((j (e23)) = (e11)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H47 zenon_H46 zenon_Ha7 zenon_H8e. % 41.92/42.14 cut (((j (h (e12))) = (e12)) = ((e11) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H47. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H46. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((j (h (e12))) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e11) = (e11))); [ zenon_intro zenon_H17 | zenon_intro zenon_H7 ]. % 41.92/42.14 cut (((e11) = (e11)) = ((j (h (e12))) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H4d. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H17. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((e11) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e12))) = (j (h (e12))))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12)))) = ((e11) = (j (h (e12))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H4e. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H4a. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 41.92/42.14 cut (((j (h (e12))) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e23)) = (e11)) = ((j (h (e12))) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H4d. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H8e. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((j (e23)) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e12))) = (j (h (e12))))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12)))) = ((j (e23)) = (j (h (e12))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_Ha9. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H4a. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 41.92/42.14 cut (((j (h (e12))) = (j (e23)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L52_); trivial. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L54_ *) % 41.92/42.14 assert (zenon_L55_ : ((j (h (e12))) = (e12)) -> ((h (e12)) = (e23)) -> ((j (e23)) = (e13)) -> (~((e12) = (e13))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H46 zenon_Ha7 zenon_Ha5 zenon_H69. % 41.92/42.14 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H31 | zenon_intro zenon_H2f ]. % 41.92/42.14 cut (((e13) = (e13)) = ((e12) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H69. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H31. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((e13) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (h (e12))) = (e12)) = ((e13) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H82. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H46. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((j (h (e12))) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H31 | zenon_intro zenon_H2f ]. % 41.92/42.14 cut (((e13) = (e13)) = ((j (h (e12))) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H83. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H31. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((e13) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e12))) = (j (h (e12))))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12)))) = ((e13) = (j (h (e12))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H84. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H4a. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 41.92/42.14 cut (((j (h (e12))) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e23)) = (e13)) = ((j (h (e12))) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H83. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_Ha5. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((j (e23)) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e12))) = (j (h (e12))))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12)))) = ((j (e23)) = (j (h (e12))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_Ha9. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H4a. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 41.92/42.14 cut (((j (h (e12))) = (j (e23)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L52_); trivial. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L55_ *) % 41.92/42.14 assert (zenon_L56_ : (~((op1 (j (e21)) (j (e21))) = (op1 (e13) (e13)))) -> ((j (e21)) = (e13)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H94 zenon_H5d. % 41.92/42.14 cut (((j (e21)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 41.92/42.14 cut (((j (e21)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 41.92/42.14 congruence. % 41.92/42.14 exact (zenon_Haa zenon_H5d). % 41.92/42.14 exact (zenon_Haa zenon_H5d). % 41.92/42.14 (* end of lemma zenon_L56_ *) % 41.92/42.14 assert (zenon_L57_ : ((j (op2 (e21) (e21))) = (op1 (j (e21)) (j (e21)))) -> ((op2 (e21) (e21)) = (e23)) -> ((j (e21)) = (e13)) -> (~((op1 (e13) (e13)) = (j (e23)))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H98 zenon_H90 zenon_H5d zenon_H99. % 41.92/42.14 elim (classic ((j (e23)) = (j (e23)))); [ zenon_intro zenon_H9a | zenon_intro zenon_H9b ]. % 41.92/42.14 cut (((j (e23)) = (j (e23))) = ((op1 (e13) (e13)) = (j (e23)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H99. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H9a. % 41.92/42.14 cut (((j (e23)) = (j (e23)))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 41.92/42.14 cut (((j (e23)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (op2 (e21) (e21))) = (op1 (j (e21)) (j (e21)))) = ((j (e23)) = (op1 (e13) (e13)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H9c. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H98. % 41.92/42.14 cut (((op1 (j (e21)) (j (e21))) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 41.92/42.14 cut (((j (op2 (e21) (e21))) = (j (e23)))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (e23)) = (j (e23)))); [ zenon_intro zenon_H9a | zenon_intro zenon_H9b ]. % 41.92/42.14 cut (((j (e23)) = (j (e23))) = ((j (op2 (e21) (e21))) = (j (e23)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H9d. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H9a. % 41.92/42.14 cut (((j (e23)) = (j (e23)))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 41.92/42.14 cut (((j (e23)) = (j (op2 (e21) (e21))))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L42_); trivial. % 41.92/42.14 apply zenon_H9b. apply refl_equal. % 41.92/42.14 apply zenon_H9b. apply refl_equal. % 41.92/42.14 apply (zenon_L56_); trivial. % 41.92/42.14 apply zenon_H9b. apply refl_equal. % 41.92/42.14 apply zenon_H9b. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L57_ *) % 41.92/42.14 assert (zenon_L58_ : ((op1 (e13) (e13)) = (e10)) -> ((j (op2 (e21) (e21))) = (op1 (j (e21)) (j (e21)))) -> ((j (e21)) = (e13)) -> ((op2 (e21) (e21)) = (e23)) -> ((j (e23)) = (e11)) -> (~((e10) = (e11))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H10 zenon_H98 zenon_H5d zenon_H90 zenon_H8e zenon_H16. % 41.92/42.14 elim (classic ((e11) = (e11))); [ zenon_intro zenon_H17 | zenon_intro zenon_H7 ]. % 41.92/42.14 cut (((e11) = (e11)) = ((e10) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H16. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H17. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((e11) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H18]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((op1 (e13) (e13)) = (e10)) = ((e11) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H18. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H10. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H19]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e11) = (e11))); [ zenon_intro zenon_H17 | zenon_intro zenon_H7 ]. % 41.92/42.14 cut (((e11) = (e11)) = ((op1 (e13) (e13)) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H19. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H17. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((e11) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1a]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H1b | zenon_intro zenon_H1c ]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((e11) = (op1 (e13) (e13)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H1a. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H1b. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H19]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e23)) = (e11)) = ((op1 (e13) (e13)) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H19. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H8e. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((j (e23)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H1b | zenon_intro zenon_H1c ]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((j (e23)) = (op1 (e13) (e13)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H9c. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H1b. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (j (e23)))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L57_); trivial. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L58_ *) % 41.92/42.14 assert (zenon_L59_ : (((j (e23)) = (e10))\/(((j (e23)) = (e11))\/(((j (e23)) = (e12))\/((j (e23)) = (e13))))) -> (~((e10) = (e11))) -> (~((e10) = (e12))) -> ((op2 (e21) (e21)) = (e23)) -> ((j (e21)) = (e13)) -> ((j (op2 (e21) (e21))) = (op1 (j (e21)) (j (e21)))) -> ((op1 (e13) (e13)) = (e10)) -> ((j (h (e12))) = (e12)) -> ((h (e12)) = (e23)) -> (~((e12) = (e13))) -> False). % 41.92/42.14 do 0 intro. intros zenon_Ha2 zenon_H16 zenon_H28 zenon_H90 zenon_H5d zenon_H98 zenon_H10 zenon_H46 zenon_Ha7 zenon_H69. % 41.92/42.14 apply (zenon_or_s _ _ zenon_Ha2); [ zenon_intro zenon_H8c | zenon_intro zenon_Ha3 ]. % 41.92/42.14 apply (zenon_L53_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_Ha3); [ zenon_intro zenon_H8e | zenon_intro zenon_Ha4 ]. % 41.92/42.14 apply (zenon_L58_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_Ha4); [ zenon_intro zenon_H9e | zenon_intro zenon_Ha5 ]. % 41.92/42.14 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H29 | zenon_intro zenon_H27 ]. % 41.92/42.14 cut (((e12) = (e12)) = ((e10) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H28. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H29. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((e12) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((op1 (e13) (e13)) = (e10)) = ((e12) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H2a. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H10. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H29 | zenon_intro zenon_H27 ]. % 41.92/42.14 cut (((e12) = (e12)) = ((op1 (e13) (e13)) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H2b. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H29. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((e12) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H2c]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H1b | zenon_intro zenon_H1c ]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((e12) = (op1 (e13) (e13)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H2c. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H1b. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e23)) = (e12)) = ((op1 (e13) (e13)) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H2b. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H9e. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((j (e23)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H1b | zenon_intro zenon_H1c ]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((j (e23)) = (op1 (e13) (e13)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H9c. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H1b. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (j (e23)))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L57_); trivial. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H1c. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply (zenon_L55_); trivial. % 41.92/42.14 (* end of lemma zenon_L59_ *) % 41.92/42.14 assert (zenon_L60_ : ((j (h (e12))) = (e12)) -> ((h (e12)) = (e21)) -> ((j (e21)) = (e13)) -> (~((e12) = (e13))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H46 zenon_H50 zenon_H5d zenon_H69. % 41.92/42.14 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H31 | zenon_intro zenon_H2f ]. % 41.92/42.14 cut (((e13) = (e13)) = ((e12) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H69. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H31. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((e13) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (h (e12))) = (e12)) = ((e13) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H82. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H46. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((j (h (e12))) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H31 | zenon_intro zenon_H2f ]. % 41.92/42.14 cut (((e13) = (e13)) = ((j (h (e12))) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H83. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H31. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((e13) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e12))) = (j (h (e12))))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12)))) = ((e13) = (j (h (e12))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H84. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H4a. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 41.92/42.14 cut (((j (h (e12))) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e21)) = (e13)) = ((j (h (e12))) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H83. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H5d. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((j (e21)) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e12))) = (j (h (e12))))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12)))) = ((j (e21)) = (j (h (e12))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H53. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H4a. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 41.92/42.14 cut (((j (h (e12))) = (j (e21)))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L17_); trivial. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L60_ *) % 41.92/42.14 assert (zenon_L61_ : (((j (e21)) = (e10))\/(((j (e21)) = (e11))\/(((j (e21)) = (e12))\/((j (e21)) = (e13))))) -> (~((e10) = (e13))) -> (~((e11) = (e13))) -> ((h (e13)) = (e21)) -> ((j (h (e13))) = (e13)) -> ((j (h (e12))) = (e12)) -> ((h (e12)) = (e21)) -> (~((e12) = (e13))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H62 zenon_H30 zenon_H5e zenon_H74 zenon_H68 zenon_H46 zenon_H50 zenon_H69. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H52 | zenon_intro zenon_H63 ]. % 41.92/42.14 apply (zenon_L27_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H54 | zenon_intro zenon_H64 ]. % 41.92/42.14 apply (zenon_L28_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H58 | zenon_intro zenon_H5d ]. % 41.92/42.14 apply (zenon_L29_); trivial. % 41.92/42.14 apply (zenon_L60_); trivial. % 41.92/42.14 (* end of lemma zenon_L61_ *) % 41.92/42.14 assert (zenon_L62_ : (~((j (h (e11))) = (j (e22)))) -> ((h (e11)) = (e22)) -> False). % 41.92/42.14 do 0 intro. intros zenon_Hab zenon_Hac. % 41.92/42.14 cut (((h (e11)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 41.92/42.14 congruence. % 41.92/42.14 exact (zenon_Had zenon_Hac). % 41.92/42.14 (* end of lemma zenon_L62_ *) % 41.92/42.14 assert (zenon_L63_ : ((j (h (e11))) = (e11)) -> ((h (e11)) = (e22)) -> ((j (e22)) = (e13)) -> (~((e11) = (e13))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H37 zenon_Hac zenon_H81 zenon_H5e. % 41.92/42.14 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H31 | zenon_intro zenon_H2f ]. % 41.92/42.14 cut (((e13) = (e13)) = ((e11) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H5e. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H31. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((e13) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (h (e11))) = (e11)) = ((e13) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H5f. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H37. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((j (h (e11))) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H31 | zenon_intro zenon_H2f ]. % 41.92/42.14 cut (((e13) = (e13)) = ((j (h (e11))) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H60. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H31. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((e13) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e11))) = (j (h (e11))))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11)))) = ((e13) = (j (h (e11))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H61. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3d. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 41.92/42.14 cut (((j (h (e11))) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e22)) = (e13)) = ((j (h (e11))) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H60. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H81. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((j (e22)) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_Hae]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e11))) = (j (h (e11))))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11)))) = ((j (e22)) = (j (h (e11))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_Hae. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3d. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 41.92/42.14 cut (((j (h (e11))) = (j (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L62_); trivial. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L63_ *) % 41.92/42.14 assert (zenon_L64_ : (((j (e22)) = (e10))\/(((j (e22)) = (e11))\/(((j (e22)) = (e12))\/((j (e22)) = (e13))))) -> (~((e10) = (e13))) -> ((h (e13)) = (e22)) -> ((j (h (e13))) = (e13)) -> (~((e12) = (e13))) -> ((j (h (e11))) = (e11)) -> ((h (e11)) = (e22)) -> (~((e11) = (e13))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H86 zenon_H30 zenon_H78 zenon_H68 zenon_H69 zenon_H37 zenon_Hac zenon_H5e. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7a | zenon_intro zenon_H87 ]. % 41.92/42.14 apply (zenon_L32_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H7c | zenon_intro zenon_H88 ]. % 41.92/42.14 apply (zenon_L33_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H88); [ zenon_intro zenon_H7d | zenon_intro zenon_H81 ]. % 41.92/42.14 apply (zenon_L34_); trivial. % 41.92/42.14 apply (zenon_L63_); trivial. % 41.92/42.14 (* end of lemma zenon_L64_ *) % 41.92/42.14 assert (zenon_L65_ : (~((e10) = (e12))) -> ((j (h (e12))) = (e12)) -> ((h (e12)) = (e22)) -> ((j (e22)) = (e10)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H28 zenon_H46 zenon_H7f zenon_H7a. % 41.92/42.14 cut (((j (h (e12))) = (e12)) = ((e10) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H28. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H46. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((j (h (e12))) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H48]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e10) = (e10))); [ zenon_intro zenon_H3b | zenon_intro zenon_H6 ]. % 41.92/42.14 cut (((e10) = (e10)) = ((j (h (e12))) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H48. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3b. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((e10) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e12))) = (j (h (e12))))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12)))) = ((e10) = (j (h (e12))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H49. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H4a. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 41.92/42.14 cut (((j (h (e12))) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H48]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e22)) = (e10)) = ((j (h (e12))) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H48. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H7a. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((j (e22)) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e12))) = (j (h (e12))))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12)))) = ((j (e22)) = (j (h (e12))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H85. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H4a. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 41.92/42.14 cut (((j (h (e12))) = (j (e22)))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L35_); trivial. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L65_ *) % 41.92/42.14 assert (zenon_L66_ : (~((e11) = (e12))) -> ((j (h (e12))) = (e12)) -> ((h (e12)) = (e22)) -> ((j (e22)) = (e11)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H47 zenon_H46 zenon_H7f zenon_H7c. % 41.92/42.14 cut (((j (h (e12))) = (e12)) = ((e11) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H47. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H46. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((j (h (e12))) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e11) = (e11))); [ zenon_intro zenon_H17 | zenon_intro zenon_H7 ]. % 41.92/42.14 cut (((e11) = (e11)) = ((j (h (e12))) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H4d. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H17. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((e11) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e12))) = (j (h (e12))))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12)))) = ((e11) = (j (h (e12))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H4e. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H4a. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 41.92/42.14 cut (((j (h (e12))) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e22)) = (e11)) = ((j (h (e12))) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H4d. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H7c. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((j (e22)) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e12))) = (j (h (e12))))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12)))) = ((j (e22)) = (j (h (e12))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H85. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H4a. % 41.92/42.14 cut (((j (h (e12))) = (j (h (e12))))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 41.92/42.14 cut (((j (h (e12))) = (j (e22)))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L35_); trivial. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H4b. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L66_ *) % 41.92/42.14 assert (zenon_L67_ : ((j (h (e11))) = (e11)) -> ((h (e11)) = (e22)) -> ((j (e22)) = (e12)) -> (~((e11) = (e12))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H37 zenon_Hac zenon_H7d zenon_H47. % 41.92/42.14 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H29 | zenon_intro zenon_H27 ]. % 41.92/42.14 cut (((e12) = (e12)) = ((e11) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H47. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H29. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((e12) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (h (e11))) = (e11)) = ((e12) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H59. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H37. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((j (h (e11))) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H29 | zenon_intro zenon_H27 ]. % 41.92/42.14 cut (((e12) = (e12)) = ((j (h (e11))) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H5a. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H29. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((e12) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e11))) = (j (h (e11))))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11)))) = ((e12) = (j (h (e11))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H5b. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3d. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 41.92/42.14 cut (((j (h (e11))) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e22)) = (e12)) = ((j (h (e11))) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H5a. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H7d. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((j (e22)) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_Hae]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e11))) = (j (h (e11))))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11)))) = ((j (e22)) = (j (h (e11))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_Hae. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3d. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 41.92/42.14 cut (((j (h (e11))) = (j (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L62_); trivial. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L67_ *) % 41.92/42.14 assert (zenon_L68_ : (((j (e22)) = (e10))\/(((j (e22)) = (e11))\/(((j (e22)) = (e12))\/((j (e22)) = (e13))))) -> (~((e10) = (e12))) -> (~((e11) = (e12))) -> ((h (e11)) = (e22)) -> ((j (h (e11))) = (e11)) -> ((j (h (e12))) = (e12)) -> ((h (e12)) = (e22)) -> (~((e12) = (e13))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H86 zenon_H28 zenon_H47 zenon_Hac zenon_H37 zenon_H46 zenon_H7f zenon_H69. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H86); [ zenon_intro zenon_H7a | zenon_intro zenon_H87 ]. % 41.92/42.14 apply (zenon_L65_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H7c | zenon_intro zenon_H88 ]. % 41.92/42.14 apply (zenon_L66_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H88); [ zenon_intro zenon_H7d | zenon_intro zenon_H81 ]. % 41.92/42.14 apply (zenon_L67_); trivial. % 41.92/42.14 apply (zenon_L36_); trivial. % 41.92/42.14 (* end of lemma zenon_L68_ *) % 41.92/42.14 assert (zenon_L69_ : (((j (e23)) = (e10))\/(((j (e23)) = (e11))\/(((j (e23)) = (e12))\/((j (e23)) = (e13))))) -> (~((e10) = (e13))) -> (~((e11) = (e13))) -> ((h (e13)) = (e23)) -> ((j (h (e13))) = (e13)) -> ((j (h (e12))) = (e12)) -> ((h (e12)) = (e23)) -> (~((e12) = (e13))) -> False). % 41.92/42.14 do 0 intro. intros zenon_Ha2 zenon_H30 zenon_H5e zenon_H8a zenon_H68 zenon_H46 zenon_Ha7 zenon_H69. % 41.92/42.14 apply (zenon_or_s _ _ zenon_Ha2); [ zenon_intro zenon_H8c | zenon_intro zenon_Ha3 ]. % 41.92/42.14 apply (zenon_L40_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_Ha3); [ zenon_intro zenon_H8e | zenon_intro zenon_Ha4 ]. % 41.92/42.14 apply (zenon_L41_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_Ha4); [ zenon_intro zenon_H9e | zenon_intro zenon_Ha5 ]. % 41.92/42.14 apply (zenon_L47_); trivial. % 41.92/42.14 apply (zenon_L55_); trivial. % 41.92/42.14 (* end of lemma zenon_L69_ *) % 41.92/42.14 assert (zenon_L70_ : (~((j (h (e11))) = (j (e23)))) -> ((h (e11)) = (e23)) -> False). % 41.92/42.14 do 0 intro. intros zenon_Haf zenon_Hb0. % 41.92/42.14 cut (((h (e11)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 41.92/42.14 congruence. % 41.92/42.14 exact (zenon_Hb1 zenon_Hb0). % 41.92/42.14 (* end of lemma zenon_L70_ *) % 41.92/42.14 assert (zenon_L71_ : (~((e10) = (e11))) -> ((j (h (e11))) = (e11)) -> ((h (e11)) = (e23)) -> ((j (e23)) = (e10)) -> False). % 41.92/42.14 do 0 intro. intros zenon_H16 zenon_H37 zenon_Hb0 zenon_H8c. % 41.92/42.14 cut (((j (h (e11))) = (e11)) = ((e10) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H16. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H37. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((j (h (e11))) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e10) = (e10))); [ zenon_intro zenon_H3b | zenon_intro zenon_H6 ]. % 41.92/42.14 cut (((e10) = (e10)) = ((j (h (e11))) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H3a. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3b. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((e10) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3c]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e11))) = (j (h (e11))))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11)))) = ((e10) = (j (h (e11))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H3c. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3d. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 41.92/42.14 cut (((j (h (e11))) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e23)) = (e10)) = ((j (h (e11))) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H3a. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H8c. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((j (e23)) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e11))) = (j (h (e11))))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11)))) = ((j (e23)) = (j (h (e11))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_Hb2. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3d. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 41.92/42.14 cut (((j (h (e11))) = (j (e23)))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L70_); trivial. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H6. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L71_ *) % 41.92/42.14 assert (zenon_L72_ : ((j (h (e11))) = (e11)) -> ((h (e11)) = (e23)) -> ((j (e23)) = (e12)) -> (~((e11) = (e12))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H37 zenon_Hb0 zenon_H9e zenon_H47. % 41.92/42.14 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H29 | zenon_intro zenon_H27 ]. % 41.92/42.14 cut (((e12) = (e12)) = ((e11) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H47. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H29. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((e12) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (h (e11))) = (e11)) = ((e12) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H59. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H37. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((j (h (e11))) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H29 | zenon_intro zenon_H27 ]. % 41.92/42.14 cut (((e12) = (e12)) = ((j (h (e11))) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H5a. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H29. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((e12) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e11))) = (j (h (e11))))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11)))) = ((e12) = (j (h (e11))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H5b. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3d. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 41.92/42.14 cut (((j (h (e11))) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e23)) = (e12)) = ((j (h (e11))) = (e12))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H5a. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H9e. % 41.92/42.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 41.92/42.14 cut (((j (e23)) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e11))) = (j (h (e11))))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11)))) = ((j (e23)) = (j (h (e11))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_Hb2. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3d. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 41.92/42.14 cut (((j (h (e11))) = (j (e23)))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L70_); trivial. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 apply zenon_H27. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L72_ *) % 41.92/42.14 assert (zenon_L73_ : ((j (h (e11))) = (e11)) -> ((h (e11)) = (e23)) -> ((j (e23)) = (e13)) -> (~((e11) = (e13))) -> False). % 41.92/42.14 do 0 intro. intros zenon_H37 zenon_Hb0 zenon_Ha5 zenon_H5e. % 41.92/42.14 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H31 | zenon_intro zenon_H2f ]. % 41.92/42.14 cut (((e13) = (e13)) = ((e11) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H5e. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H31. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((e13) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (h (e11))) = (e11)) = ((e13) = (e11))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H5f. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H37. % 41.92/42.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.14 cut (((j (h (e11))) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H31 | zenon_intro zenon_H2f ]. % 41.92/42.14 cut (((e13) = (e13)) = ((j (h (e11))) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H60. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H31. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((e13) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e11))) = (j (h (e11))))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11)))) = ((e13) = (j (h (e11))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H61. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3d. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 41.92/42.14 cut (((j (h (e11))) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((j (e23)) = (e13)) = ((j (h (e11))) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H60. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_Ha5. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((j (e23)) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((j (h (e11))) = (j (h (e11))))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11)))) = ((j (e23)) = (j (h (e11))))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_Hb2. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H3d. % 41.92/42.14 cut (((j (h (e11))) = (j (h (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 41.92/42.14 cut (((j (h (e11))) = (j (e23)))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 41.92/42.14 congruence. % 41.92/42.14 apply (zenon_L70_); trivial. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H3e. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H7. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 apply zenon_H2f. apply refl_equal. % 41.92/42.14 (* end of lemma zenon_L73_ *) % 41.92/42.14 assert (zenon_L74_ : (((j (e23)) = (e10))\/(((j (e23)) = (e11))\/(((j (e23)) = (e12))\/((j (e23)) = (e13))))) -> (~((e10) = (e11))) -> ((op2 (e21) (e21)) = (e23)) -> ((j (e21)) = (e13)) -> ((j (op2 (e21) (e21))) = (op1 (j (e21)) (j (e21)))) -> ((op1 (e13) (e13)) = (e10)) -> (~((e11) = (e12))) -> ((j (h (e11))) = (e11)) -> ((h (e11)) = (e23)) -> (~((e11) = (e13))) -> False). % 41.92/42.14 do 0 intro. intros zenon_Ha2 zenon_H16 zenon_H90 zenon_H5d zenon_H98 zenon_H10 zenon_H47 zenon_H37 zenon_Hb0 zenon_H5e. % 41.92/42.14 apply (zenon_or_s _ _ zenon_Ha2); [ zenon_intro zenon_H8c | zenon_intro zenon_Ha3 ]. % 41.92/42.14 apply (zenon_L71_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_Ha3); [ zenon_intro zenon_H8e | zenon_intro zenon_Ha4 ]. % 41.92/42.14 apply (zenon_L58_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_Ha4); [ zenon_intro zenon_H9e | zenon_intro zenon_Ha5 ]. % 41.92/42.14 apply (zenon_L72_); trivial. % 41.92/42.14 apply (zenon_L73_); trivial. % 41.92/42.14 (* end of lemma zenon_L74_ *) % 41.92/42.14 assert (zenon_L75_ : (((j (e23)) = (e10))\/(((j (e23)) = (e11))\/(((j (e23)) = (e12))\/((j (e23)) = (e13))))) -> (~((e10) = (e13))) -> ((h (e13)) = (e23)) -> ((j (h (e13))) = (e13)) -> (~((e12) = (e13))) -> ((j (h (e11))) = (e11)) -> ((h (e11)) = (e23)) -> (~((e11) = (e13))) -> False). % 41.92/42.14 do 0 intro. intros zenon_Ha2 zenon_H30 zenon_H8a zenon_H68 zenon_H69 zenon_H37 zenon_Hb0 zenon_H5e. % 41.92/42.14 apply (zenon_or_s _ _ zenon_Ha2); [ zenon_intro zenon_H8c | zenon_intro zenon_Ha3 ]. % 41.92/42.14 apply (zenon_L40_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_Ha3); [ zenon_intro zenon_H8e | zenon_intro zenon_Ha4 ]. % 41.92/42.14 apply (zenon_L41_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_Ha4); [ zenon_intro zenon_H9e | zenon_intro zenon_Ha5 ]. % 41.92/42.14 apply (zenon_L47_); trivial. % 41.92/42.14 apply (zenon_L73_); trivial. % 41.92/42.14 (* end of lemma zenon_L75_ *) % 41.92/42.14 assert (zenon_L76_ : (((j (e23)) = (e10))\/(((j (e23)) = (e11))\/(((j (e23)) = (e12))\/((j (e23)) = (e13))))) -> (~((e10) = (e12))) -> (~((e11) = (e12))) -> ((h (e11)) = (e23)) -> ((j (h (e11))) = (e11)) -> ((j (h (e12))) = (e12)) -> ((h (e12)) = (e23)) -> (~((e12) = (e13))) -> False). % 41.92/42.14 do 0 intro. intros zenon_Ha2 zenon_H28 zenon_H47 zenon_Hb0 zenon_H37 zenon_H46 zenon_Ha7 zenon_H69. % 41.92/42.14 apply (zenon_or_s _ _ zenon_Ha2); [ zenon_intro zenon_H8c | zenon_intro zenon_Ha3 ]. % 41.92/42.14 apply (zenon_L53_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_Ha3); [ zenon_intro zenon_H8e | zenon_intro zenon_Ha4 ]. % 41.92/42.14 apply (zenon_L54_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_Ha4); [ zenon_intro zenon_H9e | zenon_intro zenon_Ha5 ]. % 41.92/42.14 apply (zenon_L72_); trivial. % 41.92/42.14 apply (zenon_L55_); trivial. % 41.92/42.14 (* end of lemma zenon_L76_ *) % 41.92/42.14 apply NNPP. intro zenon_G. % 41.92/42.14 apply (zenon_and_s _ _ ax1). zenon_intro zenon_H16. zenon_intro zenon_Hb3. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_H28. zenon_intro zenon_Hb4. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hb4). zenon_intro zenon_H30. zenon_intro zenon_Hb5. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hb5). zenon_intro zenon_H47. zenon_intro zenon_Hb6. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hb6). zenon_intro zenon_H5e. zenon_intro zenon_H69. % 41.92/42.14 apply (zenon_and_s _ _ ax4). zenon_intro zenon_Hb8. zenon_intro zenon_Hb7. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hb7). zenon_intro zenon_Hba. zenon_intro zenon_Hb9. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hb9). zenon_intro zenon_Hbc. zenon_intro zenon_Hbb. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hbb). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hc0. zenon_intro zenon_Hbf. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hbf). zenon_intro zenon_Hf. zenon_intro zenon_Hc1. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_Hc3. zenon_intro zenon_Hc2. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_Hc5. zenon_intro zenon_Hc4. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hc4). zenon_intro zenon_Hc7. zenon_intro zenon_Hc6. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc9. zenon_intro zenon_Hc8. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_H25. zenon_intro zenon_Hca. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hca). zenon_intro zenon_Hcc. zenon_intro zenon_Hcb. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_Hce. zenon_intro zenon_Hcd. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hcd). zenon_intro zenon_Hd0. zenon_intro zenon_Hcf. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hcf). zenon_intro zenon_Hd1. zenon_intro zenon_H10. % 41.92/42.14 apply (zenon_and_s _ _ ax5). zenon_intro zenon_H9. zenon_intro zenon_Hd2. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hd2). zenon_intro zenon_Hd4. zenon_intro zenon_Hd3. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hd3). zenon_intro zenon_Hd6. zenon_intro zenon_Hd5. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hd5). zenon_intro zenon_Hd8. zenon_intro zenon_Hd7. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hd7). zenon_intro zenon_Hda. zenon_intro zenon_Hd9. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hd9). zenon_intro zenon_H90. zenon_intro zenon_Hdb. % 41.92/42.14 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_Hdd. zenon_intro zenon_Hdc. % 41.92/42.14 apply zenon_Hdc. zenon_intro zenon_Hde. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hde). zenon_intro zenon_He0. zenon_intro zenon_Hdf. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hdf). zenon_intro zenon_He2. zenon_intro zenon_He1. % 41.92/42.14 apply (zenon_and_s _ _ zenon_He1). zenon_intro zenon_He4. zenon_intro zenon_He3. % 41.92/42.14 apply (zenon_and_s _ _ zenon_He3). zenon_intro zenon_He6. zenon_intro zenon_He5. % 41.92/42.14 apply (zenon_and_s _ _ zenon_He5). zenon_intro zenon_He8. zenon_intro zenon_He7. % 41.92/42.14 apply (zenon_and_s _ _ zenon_He7). zenon_intro zenon_Hea. zenon_intro zenon_He9. % 41.92/42.14 apply (zenon_and_s _ _ zenon_He9). zenon_intro zenon_Hec. zenon_intro zenon_Heb. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Heb). zenon_intro zenon_Hee. zenon_intro zenon_Hed. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hed). zenon_intro zenon_Hf0. zenon_intro zenon_Hef. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hef). zenon_intro zenon_Hf2. zenon_intro zenon_Hf1. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hf1). zenon_intro zenon_Hf4. zenon_intro zenon_Hf3. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hf3). zenon_intro zenon_Hf6. zenon_intro zenon_Hf5. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hf5). zenon_intro zenon_Hf8. zenon_intro zenon_Hf7. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hf7). zenon_intro zenon_Hfa. zenon_intro zenon_Hf9. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hf9). zenon_intro zenon_Hfc. zenon_intro zenon_Hfb. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hfb). zenon_intro zenon_Hfe. zenon_intro zenon_Hfd. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hfd). zenon_intro zenon_H15. zenon_intro zenon_Hff. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hff). zenon_intro zenon_H101. zenon_intro zenon_H100. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H100). zenon_intro zenon_H103. zenon_intro zenon_H102. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H102). zenon_intro zenon_H105. zenon_intro zenon_H104. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H104). zenon_intro zenon_H107. zenon_intro zenon_H106. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H106). zenon_intro zenon_H98. zenon_intro zenon_H108. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H108). zenon_intro zenon_H10a. zenon_intro zenon_H109. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H109). zenon_intro zenon_H10c. zenon_intro zenon_H10b. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H10b). zenon_intro zenon_H10e. zenon_intro zenon_H10d. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H10d). zenon_intro zenon_H110. zenon_intro zenon_H10f. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H10f). zenon_intro zenon_H112. zenon_intro zenon_H111. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H111). zenon_intro zenon_H114. zenon_intro zenon_H113. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H113). zenon_intro zenon_H116. zenon_intro zenon_H115. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H115). zenon_intro zenon_H118. zenon_intro zenon_H117. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H117). zenon_intro zenon_H11a. zenon_intro zenon_H119. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H119). zenon_intro zenon_H11c. zenon_intro zenon_H11b. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H11b). zenon_intro zenon_H11e. zenon_intro zenon_H11d. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H11d). zenon_intro zenon_H120. zenon_intro zenon_H11f. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H11f). zenon_intro zenon_H122. zenon_intro zenon_H121. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H121). zenon_intro zenon_H124. zenon_intro zenon_H123. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H123). zenon_intro zenon_H126. zenon_intro zenon_H125. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H125). zenon_intro zenon_H37. zenon_intro zenon_H127. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H127). zenon_intro zenon_H46. zenon_intro zenon_H68. % 41.92/42.14 apply (zenon_and_s _ _ zenon_Hdd). zenon_intro zenon_H129. zenon_intro zenon_H128. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H128). zenon_intro zenon_H12b. zenon_intro zenon_H12a. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H12a). zenon_intro zenon_H12d. zenon_intro zenon_H12c. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H12c). zenon_intro zenon_H12f. zenon_intro zenon_H12e. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H12e). zenon_intro zenon_H35. zenon_intro zenon_H130. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H130). zenon_intro zenon_H62. zenon_intro zenon_H131. % 41.92/42.14 apply (zenon_and_s _ _ zenon_H131). zenon_intro zenon_H86. zenon_intro zenon_Ha2. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_H36 | zenon_intro zenon_H132 ]. % 41.92/42.14 apply (zenon_L14_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H56 | zenon_intro zenon_H133 ]. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H44 | zenon_intro zenon_H134 ]. % 41.92/42.14 apply (zenon_L16_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H50 | zenon_intro zenon_H135 ]. % 41.92/42.14 apply (zenon_L23_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_H7f | zenon_intro zenon_Ha7 ]. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H66 | zenon_intro zenon_H136 ]. % 41.92/42.14 apply (zenon_L25_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H74 | zenon_intro zenon_H137 ]. % 41.92/42.14 apply (zenon_L30_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H78 | zenon_intro zenon_H8a ]. % 41.92/42.14 apply (zenon_L37_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H52 | zenon_intro zenon_H63 ]. % 41.92/42.14 apply (zenon_L38_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H54 | zenon_intro zenon_H64 ]. % 41.92/42.14 apply (zenon_or_s _ _ zenon_Ha2); [ zenon_intro zenon_H8c | zenon_intro zenon_Ha3 ]. % 41.92/42.14 apply (zenon_L40_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_Ha3); [ zenon_intro zenon_H8e | zenon_intro zenon_Ha4 ]. % 41.92/42.14 apply (zenon_L41_); trivial. % 41.92/42.14 apply (zenon_or_s _ _ zenon_Ha4); [ zenon_intro zenon_H9e | zenon_intro zenon_Ha5 ]. % 41.92/42.14 apply (zenon_L46_); trivial. % 41.92/42.14 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H31 | zenon_intro zenon_H2f ]. % 41.92/42.14 cut (((e13) = (e13)) = ((e10) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H30. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H31. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((e13) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 41.92/42.14 congruence. % 41.92/42.14 cut (((op1 (e13) (e13)) = (e10)) = ((e13) = (e10))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H32. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H10. % 41.92/42.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H31 | zenon_intro zenon_H2f ]. % 41.92/42.14 cut (((e13) = (e13)) = ((op1 (e13) (e13)) = (e13))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H33. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H31. % 41.92/42.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.14 cut (((e13) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 41.92/42.14 congruence. % 41.92/42.14 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H1b | zenon_intro zenon_H1c ]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((e13) = (op1 (e13) (e13)))). % 41.92/42.14 intro zenon_D_pnotp. % 41.92/42.14 apply zenon_H34. % 41.92/42.14 rewrite <- zenon_D_pnotp. % 41.92/42.14 exact zenon_H1b. % 41.92/42.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 41.92/42.14 cut (((op1 (e13) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 41.92/42.15 congruence. % 41.92/42.15 cut (((j (e23)) = (e13)) = ((op1 (e13) (e13)) = (e13))). % 41.92/42.15 intro zenon_D_pnotp. % 41.92/42.15 apply zenon_H33. % 41.92/42.15 rewrite <- zenon_D_pnotp. % 41.92/42.15 exact zenon_Ha5. % 41.92/42.15 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 41.92/42.15 cut (((j (e23)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 41.92/42.15 congruence. % 41.92/42.15 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H1b | zenon_intro zenon_H1c ]. % 41.92/42.15 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((j (e23)) = (op1 (e13) (e13)))). % 41.92/42.15 intro zenon_D_pnotp. % 41.92/42.15 apply zenon_H9c. % 41.92/42.15 rewrite <- zenon_D_pnotp. % 41.92/42.15 exact zenon_H1b. % 41.92/42.15 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 41.92/42.15 cut (((op1 (e13) (e13)) = (j (e23)))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 41.92/42.15 congruence. % 41.92/42.15 apply (zenon_L45_); trivial. % 41.92/42.15 apply zenon_H1c. apply refl_equal. % 41.92/42.15 apply zenon_H1c. apply refl_equal. % 41.92/42.15 apply zenon_H2f. apply refl_equal. % 41.92/42.15 apply zenon_H1c. apply refl_equal. % 41.92/42.15 apply zenon_H1c. apply refl_equal. % 41.92/42.15 apply zenon_H2f. apply refl_equal. % 41.92/42.15 apply zenon_H2f. apply refl_equal. % 41.92/42.15 apply zenon_H6. apply refl_equal. % 41.92/42.15 apply zenon_H2f. apply refl_equal. % 41.92/42.15 apply zenon_H2f. apply refl_equal. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H58 | zenon_intro zenon_H5d ]. % 41.92/42.15 apply (zenon_L51_); trivial. % 41.92/42.15 apply (zenon_L22_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H52 | zenon_intro zenon_H63 ]. % 41.92/42.15 apply (zenon_L38_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H54 | zenon_intro zenon_H64 ]. % 41.92/42.15 apply (zenon_or_s _ _ zenon_Ha2); [ zenon_intro zenon_H8c | zenon_intro zenon_Ha3 ]. % 41.92/42.15 apply (zenon_L53_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_Ha3); [ zenon_intro zenon_H8e | zenon_intro zenon_Ha4 ]. % 41.92/42.15 apply (zenon_L54_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_Ha4); [ zenon_intro zenon_H9e | zenon_intro zenon_Ha5 ]. % 41.92/42.15 apply (zenon_L46_); trivial. % 41.92/42.15 apply (zenon_L55_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H58 | zenon_intro zenon_H5d ]. % 41.92/42.15 apply (zenon_L21_); trivial. % 41.92/42.15 apply (zenon_L59_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_Hac | zenon_intro zenon_Hb0 ]. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H44 | zenon_intro zenon_H134 ]. % 41.92/42.15 apply (zenon_L16_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H50 | zenon_intro zenon_H135 ]. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H66 | zenon_intro zenon_H136 ]. % 41.92/42.15 apply (zenon_L25_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H74 | zenon_intro zenon_H137 ]. % 41.92/42.15 apply (zenon_L61_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H78 | zenon_intro zenon_H8a ]. % 41.92/42.15 apply (zenon_L64_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H52 | zenon_intro zenon_H63 ]. % 41.92/42.15 apply (zenon_L18_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H54 | zenon_intro zenon_H64 ]. % 41.92/42.15 apply (zenon_L19_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H58 | zenon_intro zenon_H5d ]. % 41.92/42.15 apply (zenon_L51_); trivial. % 41.92/42.15 apply (zenon_L60_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_H7f | zenon_intro zenon_Ha7 ]. % 41.92/42.15 apply (zenon_L68_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H66 | zenon_intro zenon_H136 ]. % 41.92/42.15 apply (zenon_L25_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H74 | zenon_intro zenon_H137 ]. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H52 | zenon_intro zenon_H63 ]. % 41.92/42.15 apply (zenon_L27_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H54 | zenon_intro zenon_H64 ]. % 41.92/42.15 apply (zenon_L28_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H58 | zenon_intro zenon_H5d ]. % 41.92/42.15 apply (zenon_L29_); trivial. % 41.92/42.15 apply (zenon_L59_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H78 | zenon_intro zenon_H8a ]. % 41.92/42.15 apply (zenon_L64_); trivial. % 41.92/42.15 apply (zenon_L69_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H44 | zenon_intro zenon_H134 ]. % 41.92/42.15 apply (zenon_L16_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H134); [ zenon_intro zenon_H50 | zenon_intro zenon_H135 ]. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H52 | zenon_intro zenon_H63 ]. % 41.92/42.15 apply (zenon_L18_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H54 | zenon_intro zenon_H64 ]. % 41.92/42.15 apply (zenon_L19_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H58 | zenon_intro zenon_H5d ]. % 41.92/42.15 apply (zenon_or_s _ _ zenon_Ha2); [ zenon_intro zenon_H8c | zenon_intro zenon_Ha3 ]. % 41.92/42.15 apply (zenon_L71_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_Ha3); [ zenon_intro zenon_H8e | zenon_intro zenon_Ha4 ]. % 41.92/42.15 elim (classic ((e11) = (e11))); [ zenon_intro zenon_H17 | zenon_intro zenon_H7 ]. % 41.92/42.15 cut (((e11) = (e11)) = ((e10) = (e11))). % 41.92/42.15 intro zenon_D_pnotp. % 41.92/42.15 apply zenon_H16. % 41.92/42.15 rewrite <- zenon_D_pnotp. % 41.92/42.15 exact zenon_H17. % 41.92/42.15 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.15 cut (((e11) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H18]. % 41.92/42.15 congruence. % 41.92/42.15 cut (((op1 (e13) (e13)) = (e10)) = ((e11) = (e10))). % 41.92/42.15 intro zenon_D_pnotp. % 41.92/42.15 apply zenon_H18. % 41.92/42.15 rewrite <- zenon_D_pnotp. % 41.92/42.15 exact zenon_H10. % 41.92/42.15 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 41.92/42.15 cut (((op1 (e13) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H19]. % 41.92/42.15 congruence. % 41.92/42.15 elim (classic ((e11) = (e11))); [ zenon_intro zenon_H17 | zenon_intro zenon_H7 ]. % 41.92/42.15 cut (((e11) = (e11)) = ((op1 (e13) (e13)) = (e11))). % 41.92/42.15 intro zenon_D_pnotp. % 41.92/42.15 apply zenon_H19. % 41.92/42.15 rewrite <- zenon_D_pnotp. % 41.92/42.15 exact zenon_H17. % 41.92/42.15 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.15 cut (((e11) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1a]. % 41.92/42.15 congruence. % 41.92/42.15 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H1b | zenon_intro zenon_H1c ]. % 41.92/42.15 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((e11) = (op1 (e13) (e13)))). % 41.92/42.15 intro zenon_D_pnotp. % 41.92/42.15 apply zenon_H1a. % 41.92/42.15 rewrite <- zenon_D_pnotp. % 41.92/42.15 exact zenon_H1b. % 41.92/42.15 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 41.92/42.15 cut (((op1 (e13) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H19]. % 41.92/42.15 congruence. % 41.92/42.15 cut (((j (e23)) = (e11)) = ((op1 (e13) (e13)) = (e11))). % 41.92/42.15 intro zenon_D_pnotp. % 41.92/42.15 apply zenon_H19. % 41.92/42.15 rewrite <- zenon_D_pnotp. % 41.92/42.15 exact zenon_H8e. % 41.92/42.15 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H7]. % 41.92/42.15 cut (((j (e23)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 41.92/42.15 congruence. % 41.92/42.15 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H1b | zenon_intro zenon_H1c ]. % 41.92/42.15 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((j (e23)) = (op1 (e13) (e13)))). % 41.92/42.15 intro zenon_D_pnotp. % 41.92/42.15 apply zenon_H9c. % 41.92/42.15 rewrite <- zenon_D_pnotp. % 41.92/42.15 exact zenon_H1b. % 41.92/42.15 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 41.92/42.15 cut (((op1 (e13) (e13)) = (j (e23)))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 41.92/42.15 congruence. % 41.92/42.15 apply (zenon_L50_); trivial. % 41.92/42.15 apply zenon_H1c. apply refl_equal. % 41.92/42.15 apply zenon_H1c. apply refl_equal. % 41.92/42.15 apply zenon_H7. apply refl_equal. % 41.92/42.15 apply zenon_H1c. apply refl_equal. % 41.92/42.15 apply zenon_H1c. apply refl_equal. % 41.92/42.15 apply zenon_H7. apply refl_equal. % 41.92/42.15 apply zenon_H7. apply refl_equal. % 41.92/42.15 apply zenon_H6. apply refl_equal. % 41.92/42.15 apply zenon_H7. apply refl_equal. % 41.92/42.15 apply zenon_H7. apply refl_equal. % 41.92/42.15 apply (zenon_or_s _ _ zenon_Ha4); [ zenon_intro zenon_H9e | zenon_intro zenon_Ha5 ]. % 41.92/42.15 apply (zenon_L72_); trivial. % 41.92/42.15 apply (zenon_L73_); trivial. % 41.92/42.15 apply (zenon_L74_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_H7f | zenon_intro zenon_Ha7 ]. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H66 | zenon_intro zenon_H136 ]. % 41.92/42.15 apply (zenon_L25_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H74 | zenon_intro zenon_H137 ]. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H52 | zenon_intro zenon_H63 ]. % 41.92/42.15 apply (zenon_L27_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H54 | zenon_intro zenon_H64 ]. % 41.92/42.15 apply (zenon_L28_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H58 | zenon_intro zenon_H5d ]. % 41.92/42.15 apply (zenon_L29_); trivial. % 41.92/42.15 apply (zenon_L74_); trivial. % 41.92/42.15 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H78 | zenon_intro zenon_H8a ]. % 41.92/42.15 apply (zenon_L37_); trivial. % 41.92/42.15 apply (zenon_L75_); trivial. % 41.92/42.15 apply (zenon_L76_); trivial. % 41.92/42.15 Qed. % 41.92/42.15 % SZS output end Proof % 41.92/42.15 (* END-PROOF *) % 41.92/42.15 nodes searched: 649473 % 41.92/42.15 max branch formulas: 2748 % 41.92/42.15 proof nodes created: 1286 % 41.92/42.15 formulas created: 1273596 % 41.92/42.15 %------------------------------------------------------------------------------