TSTP Solution File: KLE076+1 by Zenon---0.7.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : KLE076+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n008.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 02:37:32 EDT 2022
% Result : Theorem 0.36s 0.55s
% Output : Proof 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : KLE076+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 10:53:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.36/0.55 (* PROOF-FOUND *)
% 0.36/0.55 % SZS status Theorem
% 0.36/0.55 (* BEGIN-PROOF *)
% 0.36/0.55 % SZS output start Proof
% 0.36/0.55 Theorem goals : (forall X0 : zenon_U, ((domain (multiplication X0 (domain (zero)))) = (zero))).
% 0.36/0.55 Proof.
% 0.36/0.55 assert (zenon_L1_ : (~((zero) = (zero))) -> False).
% 0.36/0.55 do 0 intro. intros zenon_H12.
% 0.36/0.55 apply zenon_H12. apply refl_equal.
% 0.36/0.55 (* end of lemma zenon_L1_ *)
% 0.36/0.55 apply NNPP. intro zenon_G.
% 0.36/0.55 apply (zenon_notallex_s (fun X0 : zenon_U => ((domain (multiplication X0 (domain (zero)))) = (zero))) zenon_G); [ zenon_intro zenon_H13; idtac ].
% 0.36/0.55 elim zenon_H13. zenon_intro zenon_TX0_u. zenon_intro zenon_H15.
% 0.36/0.55 generalize (right_annihilation zenon_E). zenon_intro zenon_H16.
% 0.36/0.55 cut (((domain (zero)) = (zero)) = ((domain (multiplication zenon_TX0_u (domain (zero)))) = (zero))).
% 0.36/0.55 intro zenon_D_pnotp.
% 0.36/0.55 apply zenon_H15.
% 0.36/0.55 rewrite <- zenon_D_pnotp.
% 0.36/0.55 exact domain4.
% 0.36/0.55 cut (((zero) = (zero))); [idtac | apply NNPP; zenon_intro zenon_H12].
% 0.36/0.55 cut (((domain (zero)) = (domain (multiplication zenon_TX0_u (domain (zero)))))); [idtac | apply NNPP; zenon_intro zenon_H17].
% 0.36/0.55 congruence.
% 0.36/0.55 elim (classic ((domain (multiplication zenon_TX0_u (domain (zero)))) = (domain (multiplication zenon_TX0_u (domain (zero)))))); [ zenon_intro zenon_H18 | zenon_intro zenon_H19 ].
% 0.36/0.55 cut (((domain (multiplication zenon_TX0_u (domain (zero)))) = (domain (multiplication zenon_TX0_u (domain (zero))))) = ((domain (zero)) = (domain (multiplication zenon_TX0_u (domain (zero)))))).
% 0.36/0.55 intro zenon_D_pnotp.
% 0.36/0.55 apply zenon_H17.
% 0.36/0.55 rewrite <- zenon_D_pnotp.
% 0.36/0.55 exact zenon_H18.
% 0.36/0.55 cut (((domain (multiplication zenon_TX0_u (domain (zero)))) = (domain (multiplication zenon_TX0_u (domain (zero)))))); [idtac | apply NNPP; zenon_intro zenon_H19].
% 0.36/0.55 cut (((domain (multiplication zenon_TX0_u (domain (zero)))) = (domain (zero)))); [idtac | apply NNPP; zenon_intro zenon_H1a].
% 0.36/0.55 congruence.
% 0.36/0.55 cut (((multiplication zenon_TX0_u (domain (zero))) = (zero))); [idtac | apply NNPP; zenon_intro zenon_H1b].
% 0.36/0.55 congruence.
% 0.36/0.55 cut (((multiplication zenon_E (zero)) = (zero)) = ((multiplication zenon_TX0_u (domain (zero))) = (zero))).
% 0.36/0.55 intro zenon_D_pnotp.
% 0.36/0.55 apply zenon_H1b.
% 0.36/0.55 rewrite <- zenon_D_pnotp.
% 0.36/0.55 exact zenon_H16.
% 0.36/0.55 cut (((zero) = (zero))); [idtac | apply NNPP; zenon_intro zenon_H12].
% 0.36/0.55 cut (((multiplication zenon_E (zero)) = (multiplication zenon_TX0_u (domain (zero))))); [idtac | apply NNPP; zenon_intro zenon_H1c].
% 0.36/0.55 congruence.
% 0.36/0.55 elim (classic ((multiplication zenon_TX0_u (domain (zero))) = (multiplication zenon_TX0_u (domain (zero))))); [ zenon_intro zenon_H1d | zenon_intro zenon_H1e ].
% 0.36/0.55 cut (((multiplication zenon_TX0_u (domain (zero))) = (multiplication zenon_TX0_u (domain (zero)))) = ((multiplication zenon_E (zero)) = (multiplication zenon_TX0_u (domain (zero))))).
% 0.36/0.55 intro zenon_D_pnotp.
% 0.36/0.55 apply zenon_H1c.
% 0.36/0.55 rewrite <- zenon_D_pnotp.
% 0.36/0.55 exact zenon_H1d.
% 0.36/0.55 cut (((multiplication zenon_TX0_u (domain (zero))) = (multiplication zenon_TX0_u (domain (zero))))); [idtac | apply NNPP; zenon_intro zenon_H1e].
% 0.36/0.55 cut (((multiplication zenon_TX0_u (domain (zero))) = (multiplication zenon_E (zero)))); [idtac | apply NNPP; zenon_intro zenon_H1f].
% 0.36/0.55 congruence.
% 0.36/0.55 generalize (right_annihilation zenon_TX0_u). zenon_intro zenon_H20.
% 0.36/0.55 cut (((multiplication zenon_TX0_u (zero)) = (zero)) = ((multiplication zenon_TX0_u (domain (zero))) = (multiplication zenon_E (zero)))).
% 0.36/0.55 intro zenon_D_pnotp.
% 0.36/0.55 apply zenon_H1f.
% 0.36/0.55 rewrite <- zenon_D_pnotp.
% 0.36/0.55 exact zenon_H20.
% 0.36/0.55 cut (((zero) = (multiplication zenon_E (zero)))); [idtac | apply NNPP; zenon_intro zenon_H21].
% 0.36/0.55 cut (((multiplication zenon_TX0_u (zero)) = (multiplication zenon_TX0_u (domain (zero))))); [idtac | apply NNPP; zenon_intro zenon_H22].
% 0.36/0.55 congruence.
% 0.36/0.55 elim (classic ((multiplication zenon_TX0_u (domain (zero))) = (multiplication zenon_TX0_u (domain (zero))))); [ zenon_intro zenon_H1d | zenon_intro zenon_H1e ].
% 0.36/0.55 cut (((multiplication zenon_TX0_u (domain (zero))) = (multiplication zenon_TX0_u (domain (zero)))) = ((multiplication zenon_TX0_u (zero)) = (multiplication zenon_TX0_u (domain (zero))))).
% 0.36/0.55 intro zenon_D_pnotp.
% 0.36/0.55 apply zenon_H22.
% 0.36/0.55 rewrite <- zenon_D_pnotp.
% 0.36/0.55 exact zenon_H1d.
% 0.36/0.55 cut (((multiplication zenon_TX0_u (domain (zero))) = (multiplication zenon_TX0_u (domain (zero))))); [idtac | apply NNPP; zenon_intro zenon_H1e].
% 0.38/0.55 cut (((multiplication zenon_TX0_u (domain (zero))) = (multiplication zenon_TX0_u (zero)))); [idtac | apply NNPP; zenon_intro zenon_H23].
% 0.38/0.55 congruence.
% 0.38/0.55 cut (((domain (zero)) = (zero))); [idtac | apply NNPP; zenon_intro zenon_H24].
% 0.38/0.55 cut ((zenon_TX0_u = zenon_TX0_u)); [idtac | apply NNPP; zenon_intro zenon_H25].
% 0.38/0.55 congruence.
% 0.38/0.55 apply zenon_H25. apply refl_equal.
% 0.38/0.55 exact (zenon_H24 domain4).
% 0.38/0.55 apply zenon_H1e. apply refl_equal.
% 0.38/0.55 apply zenon_H1e. apply refl_equal.
% 0.38/0.55 apply zenon_H21. apply sym_equal. exact zenon_H16.
% 0.38/0.55 apply zenon_H1e. apply refl_equal.
% 0.38/0.55 apply zenon_H1e. apply refl_equal.
% 0.38/0.55 apply zenon_H12. apply refl_equal.
% 0.38/0.55 apply zenon_H19. apply refl_equal.
% 0.38/0.55 apply zenon_H19. apply refl_equal.
% 0.38/0.55 apply zenon_H12. apply refl_equal.
% 0.38/0.55 Qed.
% 0.38/0.55 % SZS output end Proof
% 0.38/0.55 (* END-PROOF *)
% 0.38/0.55 nodes searched: 375
% 0.38/0.55 max branch formulas: 216
% 0.38/0.55 proof nodes created: 24
% 0.38/0.55 formulas created: 4720
% 0.38/0.55
%------------------------------------------------------------------------------