TSTP Solution File: SET618+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET618+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n014.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 : Tue Jul 19 06:37:25 EDT 2022
% Result : Theorem 0.46s 0.64s
% Output : Proof 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET618+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n014.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 : Sun Jul 10 06:45:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.46/0.64 (* PROOF-FOUND *)
% 0.46/0.64 % SZS status Theorem
% 0.46/0.64 (* BEGIN-PROOF *)
% 0.46/0.64 % SZS output start Proof
% 0.46/0.64 Theorem prove_th93 : (forall B : zenon_U, ((symmetric_difference B B) = (empty_set))).
% 0.46/0.64 Proof.
% 0.46/0.64 assert (zenon_L1_ : forall (zenon_TB_n : zenon_U), (~((difference zenon_TB_n zenon_TB_n) = (empty_set))) -> False).
% 0.46/0.64 do 1 intro. intros zenon_Hc.
% 0.46/0.64 generalize (self_difference_is_empty_set zenon_TB_n). zenon_intro zenon_He.
% 0.46/0.64 exact (zenon_Hc zenon_He).
% 0.46/0.64 (* end of lemma zenon_L1_ *)
% 0.46/0.64 assert (zenon_L2_ : (~((empty_set) = (empty_set))) -> False).
% 0.46/0.64 do 0 intro. intros zenon_Hf.
% 0.46/0.64 apply zenon_Hf. apply refl_equal.
% 0.46/0.64 (* end of lemma zenon_L2_ *)
% 0.46/0.64 apply NNPP. intro zenon_G.
% 0.46/0.64 apply (zenon_notallex_s (fun B : zenon_U => ((symmetric_difference B B) = (empty_set))) zenon_G); [ zenon_intro zenon_H10; idtac ].
% 0.46/0.64 elim zenon_H10. zenon_intro zenon_TB_n. zenon_intro zenon_H11.
% 0.46/0.64 generalize (symmetric_difference_defn zenon_TB_n). zenon_intro zenon_H12.
% 0.46/0.64 generalize (zenon_H12 zenon_TB_n). zenon_intro zenon_H13.
% 0.46/0.64 apply (zenon_congruence_lr_s _ (fun zenon_Vg : _ => (~(zenon_Vg = (empty_set)))) _ _ zenon_H11 zenon_H13). zenon_intro zenon_H14.
% 0.46/0.64 generalize (self_difference_is_empty_set zenon_E). zenon_intro zenon_H15.
% 0.46/0.64 cut (((difference zenon_E zenon_E) = (empty_set)) = ((union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)) = (empty_set))).
% 0.46/0.64 intro zenon_D_pnotp.
% 0.46/0.64 apply zenon_H14.
% 0.46/0.64 rewrite <- zenon_D_pnotp.
% 0.46/0.64 exact zenon_H15.
% 0.46/0.64 cut (((empty_set) = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_Hf].
% 0.46/0.64 cut (((difference zenon_E zenon_E) = (union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)))); [idtac | apply NNPP; zenon_intro zenon_H16].
% 0.46/0.64 congruence.
% 0.46/0.64 elim (classic ((union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)) = (union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)))); [ zenon_intro zenon_H17 | zenon_intro zenon_H18 ].
% 0.46/0.64 cut (((union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)) = (union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n))) = ((difference zenon_E zenon_E) = (union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)))).
% 0.46/0.64 intro zenon_D_pnotp.
% 0.46/0.64 apply zenon_H16.
% 0.46/0.64 rewrite <- zenon_D_pnotp.
% 0.46/0.64 exact zenon_H17.
% 0.46/0.64 cut (((union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)) = (union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)))); [idtac | apply NNPP; zenon_intro zenon_H18].
% 0.46/0.64 cut (((union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)) = (difference zenon_E zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H19].
% 0.46/0.64 congruence.
% 0.46/0.64 generalize (idempotency_of_union (empty_set)). zenon_intro zenon_H1a.
% 0.46/0.64 cut (((union (empty_set) (empty_set)) = (empty_set)) = ((union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)) = (difference zenon_E zenon_E))).
% 0.46/0.64 intro zenon_D_pnotp.
% 0.46/0.64 apply zenon_H19.
% 0.46/0.64 rewrite <- zenon_D_pnotp.
% 0.46/0.64 exact zenon_H1a.
% 0.46/0.64 cut (((empty_set) = (difference zenon_E zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H1b].
% 0.46/0.64 cut (((union (empty_set) (empty_set)) = (union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)))); [idtac | apply NNPP; zenon_intro zenon_H1c].
% 0.46/0.64 congruence.
% 0.46/0.64 elim (classic ((union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)) = (union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)))); [ zenon_intro zenon_H17 | zenon_intro zenon_H18 ].
% 0.46/0.64 cut (((union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)) = (union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n))) = ((union (empty_set) (empty_set)) = (union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)))).
% 0.46/0.64 intro zenon_D_pnotp.
% 0.46/0.64 apply zenon_H1c.
% 0.46/0.64 rewrite <- zenon_D_pnotp.
% 0.46/0.64 exact zenon_H17.
% 0.46/0.64 cut (((union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)) = (union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)))); [idtac | apply NNPP; zenon_intro zenon_H18].
% 0.46/0.64 cut (((union (difference zenon_TB_n zenon_TB_n) (difference zenon_TB_n zenon_TB_n)) = (union (empty_set) (empty_set)))); [idtac | apply NNPP; zenon_intro zenon_H1d].
% 0.46/0.64 congruence.
% 0.46/0.64 cut (((difference zenon_TB_n zenon_TB_n) = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_Hc].
% 0.46/0.64 cut (((difference zenon_TB_n zenon_TB_n) = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_Hc].
% 0.46/0.64 congruence.
% 0.46/0.64 apply (zenon_L1_ zenon_TB_n); trivial.
% 0.46/0.64 apply (zenon_L1_ zenon_TB_n); trivial.
% 0.46/0.64 apply zenon_H18. apply refl_equal.
% 0.46/0.64 apply zenon_H18. apply refl_equal.
% 0.46/0.64 apply zenon_H1b. apply sym_equal. exact zenon_H15.
% 0.46/0.64 apply zenon_H18. apply refl_equal.
% 0.46/0.64 apply zenon_H18. apply refl_equal.
% 0.46/0.64 apply zenon_Hf. apply refl_equal.
% 0.46/0.64 Qed.
% 0.46/0.64 % SZS output end Proof
% 0.46/0.64 (* END-PROOF *)
% 0.46/0.64 nodes searched: 3123
% 0.46/0.64 max branch formulas: 408
% 0.46/0.64 proof nodes created: 252
% 0.46/0.64 formulas created: 10132
% 0.46/0.64
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