%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : KRS140+1 : TPTP v8.1.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n021.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 : Sun Jul 17 03:39:34 EDT 2022 % Result : Theorem 0.40s 0.62s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : KRS140+1 : TPTP v8.1.0. Released v3.1.0. % 0.03/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n021.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Tue Jun 7 15:04:06 EDT 2022 % 0.12/0.33 % CPUTime : % 0.40/0.62 (* PROOF-FOUND *) % 0.40/0.62 % SZS status Theorem % 0.40/0.62 (* BEGIN-PROOF *) % 0.40/0.62 % SZS output start Proof % 0.40/0.62 Theorem the_axiom : ((forall X : zenon_U, ((cowlThing X)/\(~(cowlNothing X))))/\((forall X : zenon_U, ((xsd_string X)<->(~(xsd_integer X))))/\((forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((rsymProp X Y)/\(rsymProp Y Z))->(rsymProp X Z)))))/\(exists X : zenon_U, ((rsymProp (ia) X)/\(cowlThing X)))))). % 0.40/0.62 Proof. % 0.40/0.62 assert (zenon_L1_ : forall (zenon_TX_t : zenon_U) (zenon_TY_u : zenon_U), (forall Y : zenon_U, ((rsymProp zenon_TY_u Y)->((Y = (ia))\/(Y = (ib))))) -> (rsymProp zenon_TX_t zenon_TY_u) -> (~((ia) = zenon_TX_t)) -> (~((ib) = zenon_TX_t)) -> False). % 0.40/0.62 do 2 intro. intros zenon_Hf zenon_H10 zenon_H11 zenon_H12. % 0.40/0.62 generalize (zenon_Hf zenon_TX_t). zenon_intro zenon_H15. % 0.40/0.62 apply (zenon_imply_s _ _ zenon_H15); [ zenon_intro zenon_H17 | zenon_intro zenon_H16 ]. % 0.40/0.62 generalize (axiom_3 zenon_TX_t). zenon_intro zenon_H18. % 0.40/0.62 generalize (zenon_H18 zenon_TY_u). zenon_intro zenon_H19. % 0.40/0.62 apply (zenon_imply_s _ _ zenon_H19); [ zenon_intro zenon_H1b | zenon_intro zenon_H1a ]. % 0.40/0.62 exact (zenon_H1b zenon_H10). % 0.40/0.62 exact (zenon_H17 zenon_H1a). % 0.40/0.62 apply (zenon_or_s _ _ zenon_H16); [ zenon_intro zenon_H1d | zenon_intro zenon_H1c ]. % 0.40/0.62 apply zenon_H11. apply sym_equal. exact zenon_H1d. % 0.40/0.62 apply zenon_H12. apply sym_equal. exact zenon_H1c. % 0.40/0.62 (* end of lemma zenon_L1_ *) % 0.40/0.62 assert (zenon_L2_ : forall (zenon_TY_u : zenon_U) (zenon_TX_t : zenon_U), (~((ib) = zenon_TX_t)) -> (~((ia) = zenon_TX_t)) -> (rsymProp zenon_TX_t zenon_TY_u) -> False). % 0.40/0.62 do 2 intro. intros zenon_H12 zenon_H11 zenon_H10. % 0.40/0.62 generalize (axiom_2 zenon_TY_u). zenon_intro zenon_Hf. % 0.40/0.62 apply (zenon_L1_ zenon_TX_t zenon_TY_u); trivial. % 0.40/0.62 (* end of lemma zenon_L2_ *) % 0.40/0.62 assert (zenon_L3_ : forall (zenon_TZ_bh : zenon_U) (zenon_TY_u : zenon_U), (forall Y : zenon_U, ((rsymProp zenon_TY_u Y)->((Y = (ia))\/(Y = (ib))))) -> (rsymProp zenon_TY_u zenon_TZ_bh) -> (~((ia) = zenon_TZ_bh)) -> (~((ib) = zenon_TZ_bh)) -> False). % 0.40/0.62 do 2 intro. intros zenon_Hf zenon_H1e zenon_H1f zenon_H20. % 0.40/0.62 generalize (zenon_Hf zenon_TZ_bh). zenon_intro zenon_H22. % 0.40/0.62 apply (zenon_imply_s _ _ zenon_H22); [ zenon_intro zenon_H24 | zenon_intro zenon_H23 ]. % 0.40/0.62 exact (zenon_H24 zenon_H1e). % 0.40/0.62 apply (zenon_or_s _ _ zenon_H23); [ zenon_intro zenon_H26 | zenon_intro zenon_H25 ]. % 0.40/0.62 apply zenon_H1f. apply sym_equal. exact zenon_H26. % 0.40/0.62 apply zenon_H20. apply sym_equal. exact zenon_H25. % 0.40/0.62 (* end of lemma zenon_L3_ *) % 0.40/0.62 assert (zenon_L4_ : forall (zenon_TZ_bh : zenon_U) (zenon_TY_u : zenon_U), (~(zenon_TY_u = zenon_TZ_bh)) -> (zenon_TY_u = (ia)) -> (forall Y : zenon_U, ((rsymProp zenon_TY_u Y)->((Y = (ia))\/(Y = (ib))))) -> (rsymProp zenon_TY_u zenon_TZ_bh) -> (~((ib) = zenon_TZ_bh)) -> False). % 0.40/0.62 do 2 intro. intros zenon_H27 zenon_H28 zenon_Hf zenon_H1e zenon_H20. % 0.40/0.62 cut ((zenon_TY_u = (ia)) = (zenon_TY_u = zenon_TZ_bh)). % 0.40/0.62 intro zenon_D_pnotp. % 0.40/0.62 apply zenon_H27. % 0.40/0.62 rewrite <- zenon_D_pnotp. % 0.40/0.62 exact zenon_H28. % 0.40/0.62 cut (((ia) = zenon_TZ_bh)); [idtac | apply NNPP; zenon_intro zenon_H1f]. % 0.40/0.62 cut ((zenon_TY_u = zenon_TY_u)); [idtac | apply NNPP; zenon_intro zenon_H29]. % 0.40/0.62 congruence. % 0.40/0.62 apply zenon_H29. apply refl_equal. % 0.40/0.62 apply (zenon_L3_ zenon_TZ_bh zenon_TY_u); trivial. % 0.40/0.62 (* end of lemma zenon_L4_ *) % 0.40/0.62 assert (zenon_L5_ : forall (zenon_TY_u : zenon_U) (zenon_TZ_bh : zenon_U) (zenon_TX_t : zenon_U), (~(rsymProp zenon_TX_t zenon_TZ_bh)) -> (rsymProp zenon_TX_t zenon_TY_u) -> (forall Y : zenon_U, ((rsymProp zenon_TY_u Y)->((Y = (ia))\/(Y = (ib))))) -> (rsymProp zenon_TY_u zenon_TZ_bh) -> (~((ib) = zenon_TZ_bh)) -> (zenon_TY_u = (ia)) -> False). % 0.40/0.62 do 3 intro. intros zenon_H2a zenon_H10 zenon_Hf zenon_H1e zenon_H20 zenon_H28. % 0.40/0.62 cut ((rsymProp zenon_TX_t zenon_TY_u) = (rsymProp zenon_TX_t zenon_TZ_bh)). % 0.40/0.62 intro zenon_D_pnotp. % 0.40/0.62 apply zenon_H2a. % 0.40/0.62 rewrite <- zenon_D_pnotp. % 0.40/0.62 exact zenon_H10. % 0.40/0.62 cut ((zenon_TY_u = zenon_TZ_bh)); [idtac | apply NNPP; zenon_intro zenon_H27]. % 0.40/0.62 cut ((zenon_TX_t = zenon_TX_t)); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 0.40/0.62 congruence. % 0.40/0.62 apply zenon_H2b. apply refl_equal. % 0.40/0.62 apply (zenon_L4_ zenon_TZ_bh zenon_TY_u); trivial. % 0.40/0.62 (* end of lemma zenon_L5_ *) % 0.40/0.62 assert (zenon_L6_ : forall (zenon_TY_u : zenon_U) (zenon_TZ_bh : zenon_U) (zenon_TX_t : zenon_U), (~(rsymProp zenon_TX_t zenon_TZ_bh)) -> (rsymProp zenon_TY_u zenon_TZ_bh) -> (zenon_TX_t = (ib)) -> (zenon_TY_u = (ib)) -> False). % 0.40/0.62 do 3 intro. intros zenon_H2a zenon_H1e zenon_H1c zenon_H2c. % 0.40/0.62 cut ((rsymProp zenon_TY_u zenon_TZ_bh) = (rsymProp zenon_TX_t zenon_TZ_bh)). % 0.40/0.62 intro zenon_D_pnotp. % 0.40/0.62 apply zenon_H2a. % 0.40/0.62 rewrite <- zenon_D_pnotp. % 0.40/0.62 exact zenon_H1e. % 0.40/0.62 cut ((zenon_TZ_bh = zenon_TZ_bh)); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 0.40/0.62 cut ((zenon_TY_u = zenon_TX_t)); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 0.40/0.62 congruence. % 0.40/0.62 cut ((zenon_TY_u = (ib)) = (zenon_TY_u = zenon_TX_t)). % 0.40/0.62 intro zenon_D_pnotp. % 0.40/0.62 apply zenon_H2e. % 0.40/0.62 rewrite <- zenon_D_pnotp. % 0.40/0.62 exact zenon_H2c. % 0.40/0.62 cut (((ib) = zenon_TX_t)); [idtac | apply NNPP; zenon_intro zenon_H12]. % 0.40/0.62 cut ((zenon_TY_u = zenon_TY_u)); [idtac | apply NNPP; zenon_intro zenon_H29]. % 0.40/0.62 congruence. % 0.40/0.62 apply zenon_H29. apply refl_equal. % 0.40/0.62 apply zenon_H12. apply sym_equal. exact zenon_H1c. % 0.40/0.62 apply zenon_H2d. apply refl_equal. % 0.40/0.62 (* end of lemma zenon_L6_ *) % 0.40/0.62 assert (zenon_L7_ : forall (zenon_TZ_bh : zenon_U) (zenon_TX_t : zenon_U) (zenon_TY_u : zenon_U), ((rsymProp zenon_TY_u zenon_TX_t)->((zenon_TX_t = (ia))\/(zenon_TX_t = (ib)))) -> (rsymProp zenon_TX_t zenon_TY_u) -> (~((ia) = zenon_TX_t)) -> (~(rsymProp zenon_TX_t zenon_TZ_bh)) -> (rsymProp zenon_TY_u zenon_TZ_bh) -> (zenon_TY_u = (ib)) -> False). % 0.40/0.62 do 3 intro. intros zenon_H15 zenon_H10 zenon_H11 zenon_H2a zenon_H1e zenon_H2c. % 0.40/0.62 apply (zenon_imply_s _ _ zenon_H15); [ zenon_intro zenon_H17 | zenon_intro zenon_H16 ]. % 0.40/0.62 generalize (axiom_3 zenon_TX_t). zenon_intro zenon_H18. % 0.40/0.62 generalize (zenon_H18 zenon_TY_u). zenon_intro zenon_H19. % 0.40/0.62 apply (zenon_imply_s _ _ zenon_H19); [ zenon_intro zenon_H1b | zenon_intro zenon_H1a ]. % 0.40/0.62 exact (zenon_H1b zenon_H10). % 0.40/0.62 exact (zenon_H17 zenon_H1a). % 0.40/0.62 apply (zenon_or_s _ _ zenon_H16); [ zenon_intro zenon_H1d | zenon_intro zenon_H1c ]. % 0.40/0.62 apply zenon_H11. apply sym_equal. exact zenon_H1d. % 0.40/0.62 apply (zenon_L6_ zenon_TY_u zenon_TZ_bh zenon_TX_t); trivial. % 0.40/0.62 (* end of lemma zenon_L7_ *) % 0.40/0.62 assert (zenon_L8_ : forall (zenon_TZ_bh : zenon_U) (zenon_TX_t : zenon_U) (zenon_TY_u : zenon_U), (forall Y : zenon_U, ((rsymProp zenon_TY_u Y)->((Y = (ia))\/(Y = (ib))))) -> (rsymProp zenon_TX_t zenon_TY_u) -> (~((ia) = zenon_TX_t)) -> (~(rsymProp zenon_TX_t zenon_TZ_bh)) -> (rsymProp zenon_TY_u zenon_TZ_bh) -> (zenon_TY_u = (ib)) -> False). % 0.40/0.62 do 3 intro. intros zenon_Hf zenon_H10 zenon_H11 zenon_H2a zenon_H1e zenon_H2c. % 0.40/0.62 generalize (zenon_Hf zenon_TX_t). zenon_intro zenon_H15. % 0.40/0.62 apply (zenon_L7_ zenon_TZ_bh zenon_TX_t zenon_TY_u); trivial. % 0.40/0.62 (* end of lemma zenon_L8_ *) % 0.40/0.62 assert (zenon_L9_ : forall (zenon_TZ_bh : zenon_U) (zenon_TX_t : zenon_U) (zenon_TY_u : zenon_U), (forall Y : zenon_U, ((rsymProp zenon_TY_u Y)->((Y = (ia))\/(Y = (ib))))) -> (rsymProp zenon_TX_t zenon_TY_u) -> (~(rsymProp zenon_TX_t zenon_TZ_bh)) -> (rsymProp zenon_TY_u zenon_TZ_bh) -> (zenon_TY_u = (ia)) -> (~((ib) = zenon_TX_t)) -> False). % 0.40/0.62 do 3 intro. intros zenon_Hf zenon_H10 zenon_H2a zenon_H1e zenon_H28 zenon_H12. % 0.40/0.62 generalize (zenon_Hf zenon_TX_t). zenon_intro zenon_H15. % 0.40/0.62 apply (zenon_imply_s _ _ zenon_H15); [ zenon_intro zenon_H17 | zenon_intro zenon_H16 ]. % 0.40/0.62 generalize (axiom_3 zenon_TX_t). zenon_intro zenon_H18. % 0.40/0.62 generalize (zenon_H18 zenon_TY_u). zenon_intro zenon_H19. % 0.40/0.62 apply (zenon_imply_s _ _ zenon_H19); [ zenon_intro zenon_H1b | zenon_intro zenon_H1a ]. % 0.40/0.62 exact (zenon_H1b zenon_H10). % 0.40/0.62 exact (zenon_H17 zenon_H1a). % 0.40/0.62 apply (zenon_or_s _ _ zenon_H16); [ zenon_intro zenon_H1d | zenon_intro zenon_H1c ]. % 0.40/0.62 cut ((rsymProp zenon_TY_u zenon_TZ_bh) = (rsymProp zenon_TX_t zenon_TZ_bh)). % 0.40/0.62 intro zenon_D_pnotp. % 0.40/0.62 apply zenon_H2a. % 0.40/0.62 rewrite <- zenon_D_pnotp. % 0.40/0.62 exact zenon_H1e. % 0.40/0.62 cut ((zenon_TZ_bh = zenon_TZ_bh)); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 0.40/0.62 cut ((zenon_TY_u = zenon_TX_t)); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 0.40/0.62 congruence. % 0.40/0.62 cut ((zenon_TY_u = (ia)) = (zenon_TY_u = zenon_TX_t)). % 0.40/0.62 intro zenon_D_pnotp. % 0.40/0.62 apply zenon_H2e. % 0.40/0.62 rewrite <- zenon_D_pnotp. % 0.40/0.62 exact zenon_H28. % 0.40/0.62 cut (((ia) = zenon_TX_t)); [idtac | apply NNPP; zenon_intro zenon_H11]. % 0.40/0.62 cut ((zenon_TY_u = zenon_TY_u)); [idtac | apply NNPP; zenon_intro zenon_H29]. % 0.40/0.62 congruence. % 0.40/0.62 apply zenon_H29. apply refl_equal. % 0.40/0.62 apply zenon_H11. apply sym_equal. exact zenon_H1d. % 0.40/0.62 apply zenon_H2d. apply refl_equal. % 0.40/0.62 apply zenon_H12. apply sym_equal. exact zenon_H1c. % 0.40/0.62 (* end of lemma zenon_L9_ *) % 0.40/0.62 assert (zenon_L10_ : forall (zenon_TY_u : zenon_U) (zenon_TZ_bh : zenon_U) (zenon_TX_t : zenon_U), (~(rsymProp zenon_TX_t zenon_TZ_bh)) -> (rsymProp zenon_TX_t zenon_TY_u) -> (zenon_TZ_bh = (ib)) -> (zenon_TY_u = (ib)) -> False). % 0.40/0.62 do 3 intro. intros zenon_H2a zenon_H10 zenon_H25 zenon_H2c. % 0.40/0.62 cut ((rsymProp zenon_TX_t zenon_TY_u) = (rsymProp zenon_TX_t zenon_TZ_bh)). % 0.40/0.62 intro zenon_D_pnotp. % 0.40/0.62 apply zenon_H2a. % 0.40/0.62 rewrite <- zenon_D_pnotp. % 0.40/0.62 exact zenon_H10. % 0.40/0.62 cut ((zenon_TY_u = zenon_TZ_bh)); [idtac | apply NNPP; zenon_intro zenon_H27]. % 0.40/0.62 cut ((zenon_TX_t = zenon_TX_t)); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 0.40/0.62 congruence. % 0.40/0.62 apply zenon_H2b. apply refl_equal. % 0.40/0.62 cut ((zenon_TY_u = (ib)) = (zenon_TY_u = zenon_TZ_bh)). % 0.40/0.62 intro zenon_D_pnotp. % 0.40/0.62 apply zenon_H27. % 0.40/0.62 rewrite <- zenon_D_pnotp. % 0.40/0.62 exact zenon_H2c. % 0.40/0.62 cut (((ib) = zenon_TZ_bh)); [idtac | apply NNPP; zenon_intro zenon_H20]. % 0.40/0.62 cut ((zenon_TY_u = zenon_TY_u)); [idtac | apply NNPP; zenon_intro zenon_H29]. % 0.40/0.62 congruence. % 0.40/0.62 apply zenon_H29. apply refl_equal. % 0.40/0.62 apply zenon_H20. apply sym_equal. exact zenon_H25. % 0.40/0.62 (* end of lemma zenon_L10_ *) % 0.40/0.62 assert (zenon_L11_ : forall (zenon_TZ_bh : zenon_U) (zenon_TY_u : zenon_U) (zenon_TX_t : zenon_U), (forall Y : zenon_U, ((rsymProp zenon_TX_t Y)->((Y = (ia))\/(Y = (ib))))) -> (rsymProp zenon_TX_t zenon_TY_u) -> (forall Y : zenon_U, ((rsymProp zenon_TY_u Y)->((Y = (ia))\/(Y = (ib))))) -> (~(rsymProp zenon_TX_t zenon_TZ_bh)) -> (rsymProp zenon_TY_u zenon_TZ_bh) -> (~((ib) = zenon_TX_t)) -> (zenon_TZ_bh = (ib)) -> False). % 0.40/0.62 do 3 intro. intros zenon_H2f zenon_H10 zenon_Hf zenon_H2a zenon_H1e zenon_H12 zenon_H25. % 0.40/0.62 generalize (zenon_H2f zenon_TY_u). zenon_intro zenon_H30. % 0.40/0.62 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H1b | zenon_intro zenon_H31 ]. % 0.40/0.62 exact (zenon_H1b zenon_H10). % 0.40/0.62 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H28 | zenon_intro zenon_H2c ]. % 0.40/0.62 apply (zenon_L9_ zenon_TZ_bh zenon_TX_t zenon_TY_u); trivial. % 0.40/0.62 apply (zenon_L10_ zenon_TY_u zenon_TZ_bh zenon_TX_t); trivial. % 0.40/0.62 (* end of lemma zenon_L11_ *) % 0.40/0.62 assert (zenon_L12_ : forall (zenon_TZ_bh : zenon_U) (zenon_TY_u : zenon_U) (zenon_TX_t : zenon_U), (rsymProp zenon_TX_t zenon_TY_u) -> (~(rsymProp zenon_TX_t zenon_TZ_bh)) -> (forall Y : zenon_U, ((rsymProp zenon_TY_u Y)->((Y = (ia))\/(Y = (ib))))) -> (rsymProp zenon_TY_u zenon_TZ_bh) -> (~((ia) = zenon_TZ_bh)) -> False). % 0.40/0.62 do 3 intro. intros zenon_H10 zenon_H2a zenon_Hf zenon_H1e zenon_H1f. % 0.40/0.62 cut ((rsymProp (ib) (ib)) = (rsymProp zenon_TX_t zenon_TZ_bh)). % 0.40/0.62 intro zenon_D_pnotp. % 0.40/0.62 apply zenon_H2a. % 0.40/0.62 rewrite <- zenon_D_pnotp. % 0.40/0.62 exact axiom_7. % 0.40/0.62 cut (((ib) = zenon_TZ_bh)); [idtac | apply NNPP; zenon_intro zenon_H20]. % 0.40/0.62 cut (((ib) = zenon_TX_t)); [idtac | apply NNPP; zenon_intro zenon_H12]. % 0.40/0.62 congruence. % 0.40/0.62 generalize (axiom_2 zenon_TX_t). zenon_intro zenon_H2f. % 0.40/0.62 generalize (zenon_Hf zenon_TZ_bh). zenon_intro zenon_H22. % 0.40/0.62 apply (zenon_imply_s _ _ zenon_H22); [ zenon_intro zenon_H24 | zenon_intro zenon_H23 ]. % 0.40/0.62 exact (zenon_H24 zenon_H1e). % 0.40/0.62 apply (zenon_or_s _ _ zenon_H23); [ zenon_intro zenon_H26 | zenon_intro zenon_H25 ]. % 0.40/0.62 apply zenon_H1f. apply sym_equal. exact zenon_H26. % 0.40/0.62 apply (zenon_L11_ zenon_TZ_bh zenon_TY_u zenon_TX_t); trivial. % 0.40/0.62 apply (zenon_L3_ zenon_TZ_bh zenon_TY_u); trivial. % 0.40/0.62 (* end of lemma zenon_L12_ *) % 0.40/0.62 assert (zenon_L13_ : forall (zenon_TZ_bh : zenon_U) (zenon_TY_u : zenon_U) (zenon_TX_t : zenon_U), (rsymProp zenon_TX_t zenon_TY_u) -> (~(rsymProp zenon_TX_t zenon_TZ_bh)) -> (rsymProp zenon_TY_u zenon_TZ_bh) -> (zenon_TY_u = (ib)) -> False). % 0.40/0.62 do 3 intro. intros zenon_H10 zenon_H2a zenon_H1e zenon_H2c. % 0.40/0.62 generalize (axiom_2 zenon_TY_u). zenon_intro zenon_Hf. % 0.40/0.62 cut ((rsymProp (ia) (ia)) = (rsymProp zenon_TX_t zenon_TZ_bh)). % 0.40/0.62 intro zenon_D_pnotp. % 0.40/0.62 apply zenon_H2a. % 0.40/0.62 rewrite <- zenon_D_pnotp. % 0.40/0.62 exact axiom_5. % 0.40/0.62 cut (((ia) = zenon_TZ_bh)); [idtac | apply NNPP; zenon_intro zenon_H1f]. % 0.40/0.62 cut (((ia) = zenon_TX_t)); [idtac | apply NNPP; zenon_intro zenon_H11]. % 0.40/0.62 congruence. % 0.40/0.62 apply (zenon_L8_ zenon_TZ_bh zenon_TX_t zenon_TY_u); trivial. % 0.40/0.62 apply (zenon_L12_ zenon_TZ_bh zenon_TY_u zenon_TX_t); trivial. % 0.40/0.62 (* end of lemma zenon_L13_ *) % 0.40/0.62 assert (zenon_L14_ : forall (zenon_TX_t : zenon_U) (zenon_TY_u : zenon_U) (zenon_TZ_bh : zenon_U), (forall Y : zenon_U, ((rsymProp zenon_TZ_bh Y)->((Y = (ia))\/(Y = (ib))))) -> (rsymProp zenon_TY_u zenon_TZ_bh) -> (~(rsymProp zenon_TX_t zenon_TZ_bh)) -> (rsymProp zenon_TX_t zenon_TY_u) -> (forall Y : zenon_U, ((rsymProp zenon_TY_u Y)->((Y = (ia))\/(Y = (ib))))) -> (~((ib) = zenon_TZ_bh)) -> False). % 0.40/0.62 do 3 intro. intros zenon_H32 zenon_H1e zenon_H2a zenon_H10 zenon_Hf zenon_H20. % 0.40/0.62 generalize (zenon_H32 zenon_TY_u). zenon_intro zenon_H33. % 0.40/0.62 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H34 | zenon_intro zenon_H31 ]. % 0.40/0.62 generalize (axiom_3 zenon_TY_u). zenon_intro zenon_H35. % 0.40/0.62 generalize (zenon_H35 zenon_TZ_bh). zenon_intro zenon_H36. % 0.40/0.62 apply (zenon_imply_s _ _ zenon_H36); [ zenon_intro zenon_H24 | zenon_intro zenon_H37 ]. % 0.40/0.62 exact (zenon_H24 zenon_H1e). % 0.40/0.62 exact (zenon_H34 zenon_H37). % 0.40/0.62 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H28 | zenon_intro zenon_H2c ]. % 0.40/0.62 apply (zenon_L5_ zenon_TY_u zenon_TZ_bh zenon_TX_t); trivial. % 0.40/0.62 apply (zenon_L13_ zenon_TZ_bh zenon_TY_u zenon_TX_t); trivial. % 0.40/0.62 (* end of lemma zenon_L14_ *) % 0.40/0.62 apply NNPP. intro zenon_G. % 0.40/0.62 apply (zenon_notand_s _ _ zenon_G); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ]. % 0.40/0.62 exact (zenon_H39 axiom_0). % 0.40/0.62 apply (zenon_notand_s _ _ zenon_H38); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ]. % 0.40/0.62 exact (zenon_H3b axiom_1). % 0.40/0.62 apply (zenon_notand_s _ _ zenon_H3a); [ zenon_intro zenon_H3d | zenon_intro zenon_H3c ]. % 0.40/0.62 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((rsymProp X Y)/\(rsymProp Y Z))->(rsymProp X Z))))) zenon_H3d); [ zenon_intro zenon_H3e; idtac ]. % 0.40/0.62 elim zenon_H3e. zenon_intro zenon_TX_t. zenon_intro zenon_H3f. % 0.40/0.62 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((rsymProp zenon_TX_t Y)/\(rsymProp Y Z))->(rsymProp zenon_TX_t Z)))) zenon_H3f); [ zenon_intro zenon_H40; idtac ]. % 0.40/0.62 elim zenon_H40. zenon_intro zenon_TY_u. zenon_intro zenon_H41. % 0.40/0.62 apply (zenon_notallex_s (fun Z : zenon_U => (((rsymProp zenon_TX_t zenon_TY_u)/\(rsymProp zenon_TY_u Z))->(rsymProp zenon_TX_t Z))) zenon_H41); [ zenon_intro zenon_H42; idtac ]. % 0.40/0.62 elim zenon_H42. zenon_intro zenon_TZ_bh. zenon_intro zenon_H43. % 0.40/0.62 apply (zenon_notimply_s _ _ zenon_H43). zenon_intro zenon_H44. zenon_intro zenon_H2a. % 0.40/0.62 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H10. zenon_intro zenon_H1e. % 0.40/0.62 generalize (axiom_2 zenon_TZ_bh). zenon_intro zenon_H32. % 0.40/0.62 generalize (axiom_2 zenon_TY_u). zenon_intro zenon_Hf. % 0.40/0.62 cut ((rsymProp (ia) (ia)) = (rsymProp zenon_TX_t zenon_TZ_bh)). % 0.40/0.62 intro zenon_D_pnotp. % 0.40/0.62 apply zenon_H2a. % 0.40/0.62 rewrite <- zenon_D_pnotp. % 0.40/0.62 exact axiom_5. % 0.40/0.62 cut (((ia) = zenon_TZ_bh)); [idtac | apply NNPP; zenon_intro zenon_H1f]. % 0.40/0.62 cut (((ia) = zenon_TX_t)); [idtac | apply NNPP; zenon_intro zenon_H11]. % 0.40/0.62 congruence. % 0.40/0.62 cut ((rsymProp (ib) (ib)) = (rsymProp zenon_TX_t zenon_TZ_bh)). % 0.40/0.62 intro zenon_D_pnotp. % 0.40/0.62 apply zenon_H2a. % 0.40/0.62 rewrite <- zenon_D_pnotp. % 0.40/0.62 exact axiom_7. % 0.40/0.62 cut (((ib) = zenon_TZ_bh)); [idtac | apply NNPP; zenon_intro zenon_H20]. % 0.40/0.62 cut (((ib) = zenon_TX_t)); [idtac | apply NNPP; zenon_intro zenon_H12]. % 0.40/0.62 congruence. % 0.40/0.62 apply (zenon_L2_ zenon_TY_u zenon_TX_t); trivial. % 0.40/0.62 apply (zenon_L14_ zenon_TX_t zenon_TY_u zenon_TZ_bh); trivial. % 0.40/0.62 apply (zenon_L12_ zenon_TZ_bh zenon_TY_u zenon_TX_t); trivial. % 0.40/0.62 apply zenon_H3c. exists (ia). apply NNPP. zenon_intro zenon_H45. % 0.40/0.62 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 0.40/0.62 exact (zenon_H47 axiom_5). % 0.40/0.62 exact (zenon_H46 axiom_4). % 0.40/0.62 Qed. % 0.40/0.62 % SZS output end Proof % 0.40/0.62 (* END-PROOF *) % 0.40/0.62 nodes searched: 7919 % 0.40/0.62 max branch formulas: 575 % 0.40/0.62 proof nodes created: 329 % 0.40/0.62 formulas created: 15839 % 0.40/0.62 %------------------------------------------------------------------------------