TSTP Solution File: SET928+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET928+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n011.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 06:39:43 EDT 2022
% Result : Theorem 3.70s 3.93s
% Output : Proof 3.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET928+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n011.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 18:44:11 EDT 2022
% 0.12/0.34 % CPUTime :
% 3.70/3.93 (* PROOF-FOUND *)
% 3.70/3.93 % SZS status Theorem
% 3.70/3.93 (* BEGIN-PROOF *)
% 3.70/3.93 % SZS output start Proof
% 3.70/3.93 Theorem t72_zfmisc_1 : (forall A : zenon_U, (forall B : zenon_U, (forall C : zenon_U, (((set_difference (unordered_pair A B) C) = (unordered_pair A B))<->((~(in A C))/\(~(in B C))))))).
% 3.70/3.93 Proof.
% 3.70/3.93 apply NNPP. intro zenon_G.
% 3.70/3.93 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (forall C : zenon_U, (((set_difference (unordered_pair A B) C) = (unordered_pair A B))<->((~(in A C))/\(~(in B C))))))) zenon_G); [ zenon_intro zenon_H9; idtac ].
% 3.70/3.93 elim zenon_H9. zenon_intro zenon_TA_k. zenon_intro zenon_Hb.
% 3.70/3.93 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (((set_difference (unordered_pair zenon_TA_k B) C) = (unordered_pair zenon_TA_k B))<->((~(in zenon_TA_k C))/\(~(in B C)))))) zenon_Hb); [ zenon_intro zenon_Hc; idtac ].
% 3.70/3.93 elim zenon_Hc. zenon_intro zenon_TB_n. zenon_intro zenon_He.
% 3.70/3.93 apply (zenon_notallex_s (fun C : zenon_U => (((set_difference (unordered_pair zenon_TA_k zenon_TB_n) C) = (unordered_pair zenon_TA_k zenon_TB_n))<->((~(in zenon_TA_k C))/\(~(in zenon_TB_n C))))) zenon_He); [ zenon_intro zenon_Hf; idtac ].
% 3.70/3.93 elim zenon_Hf. zenon_intro zenon_TC_q. zenon_intro zenon_H11.
% 3.70/3.93 apply (zenon_notequiv_s _ _ zenon_H11); [ zenon_intro zenon_H15; zenon_intro zenon_H14 | zenon_intro zenon_H13; zenon_intro zenon_H12 ].
% 3.70/3.93 apply (zenon_and_s _ _ zenon_H14). zenon_intro zenon_H17. zenon_intro zenon_H16.
% 3.70/3.93 generalize (t57_zfmisc_1 zenon_TA_k). zenon_intro zenon_H18.
% 3.70/3.93 generalize (zenon_H18 zenon_TC_q). zenon_intro zenon_H19.
% 3.70/3.93 generalize (zenon_H19 zenon_TB_n). zenon_intro zenon_H1a.
% 3.70/3.93 apply (zenon_notand_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ].
% 3.70/3.93 exact (zenon_H1c zenon_H17).
% 3.70/3.93 apply (zenon_notand_s _ _ zenon_H1b); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ].
% 3.70/3.93 exact (zenon_H1e zenon_H16).
% 3.70/3.93 apply zenon_H1d. zenon_intro zenon_H1f.
% 3.70/3.93 generalize (t83_xboole_1 (unordered_pair zenon_TA_k zenon_TB_n)). zenon_intro zenon_H20.
% 3.70/3.93 generalize (zenon_H20 zenon_TC_q). zenon_intro zenon_H21.
% 3.70/3.93 apply (zenon_equiv_s _ _ zenon_H21); [ zenon_intro zenon_H22; zenon_intro zenon_H15 | zenon_intro zenon_H1f; zenon_intro zenon_H13 ].
% 3.70/3.93 exact (zenon_H22 zenon_H1f).
% 3.70/3.93 exact (zenon_H15 zenon_H13).
% 3.70/3.93 apply (zenon_notand_s _ _ zenon_H12); [ zenon_intro zenon_H1c | zenon_intro zenon_H1e ].
% 3.70/3.93 apply zenon_H1c. zenon_intro zenon_H23.
% 3.70/3.93 generalize (t55_zfmisc_1 zenon_TA_k). zenon_intro zenon_H24.
% 3.70/3.93 generalize (zenon_H24 zenon_TB_n). zenon_intro zenon_H25.
% 3.70/3.93 generalize (zenon_H25 zenon_TC_q). zenon_intro zenon_H26.
% 3.70/3.93 apply (zenon_notand_s _ _ zenon_H26); [ zenon_intro zenon_H22 | zenon_intro zenon_H17 ].
% 3.70/3.93 generalize (t83_xboole_1 (unordered_pair zenon_TA_k zenon_TB_n)). zenon_intro zenon_H20.
% 3.70/3.93 generalize (zenon_H20 zenon_TC_q). zenon_intro zenon_H21.
% 3.70/3.93 apply (zenon_equiv_s _ _ zenon_H21); [ zenon_intro zenon_H22; zenon_intro zenon_H15 | zenon_intro zenon_H1f; zenon_intro zenon_H13 ].
% 3.70/3.93 exact (zenon_H15 zenon_H13).
% 3.70/3.93 exact (zenon_H22 zenon_H1f).
% 3.70/3.93 exact (zenon_H17 zenon_H23).
% 3.70/3.93 apply zenon_H1e. zenon_intro zenon_H27.
% 3.70/3.93 generalize (t55_zfmisc_1 zenon_TB_n). zenon_intro zenon_H28.
% 3.70/3.93 generalize (commutativity_k2_tarski zenon_TB_n). zenon_intro zenon_H29.
% 3.70/3.93 generalize (zenon_H29 zenon_TA_k). zenon_intro zenon_H2a.
% 3.70/3.93 generalize (zenon_H28 zenon_TA_k). zenon_intro zenon_H2b.
% 3.70/3.93 generalize (zenon_H2b zenon_TC_q). zenon_intro zenon_H2c.
% 3.70/3.93 apply (zenon_notand_s _ _ zenon_H2c); [ zenon_intro zenon_H2d | zenon_intro zenon_H16 ].
% 3.70/3.93 generalize (t83_xboole_1 (unordered_pair zenon_TB_n zenon_TA_k)). zenon_intro zenon_H2e.
% 3.70/3.93 generalize (zenon_H2e zenon_TC_q). zenon_intro zenon_H2f.
% 3.70/3.93 apply (zenon_equiv_s _ _ zenon_H2f); [ zenon_intro zenon_H2d; zenon_intro zenon_H32 | zenon_intro zenon_H31; zenon_intro zenon_H30 ].
% 3.70/3.93 cut (((set_difference (unordered_pair zenon_TA_k zenon_TB_n) zenon_TC_q) = (unordered_pair zenon_TA_k zenon_TB_n)) = ((set_difference (unordered_pair zenon_TB_n zenon_TA_k) zenon_TC_q) = (unordered_pair zenon_TB_n zenon_TA_k))).
% 3.70/3.93 intro zenon_D_pnotp.
% 3.70/3.93 apply zenon_H32.
% 3.70/3.93 rewrite <- zenon_D_pnotp.
% 3.70/3.93 exact zenon_H13.
% 3.70/3.93 cut (((unordered_pair zenon_TA_k zenon_TB_n) = (unordered_pair zenon_TB_n zenon_TA_k))); [idtac | apply NNPP; zenon_intro zenon_H33].
% 3.76/3.93 cut (((set_difference (unordered_pair zenon_TA_k zenon_TB_n) zenon_TC_q) = (set_difference (unordered_pair zenon_TB_n zenon_TA_k) zenon_TC_q))); [idtac | apply NNPP; zenon_intro zenon_H34].
% 3.76/3.93 congruence.
% 3.76/3.93 elim (classic ((set_difference (unordered_pair zenon_TB_n zenon_TA_k) zenon_TC_q) = (set_difference (unordered_pair zenon_TB_n zenon_TA_k) zenon_TC_q))); [ zenon_intro zenon_H35 | zenon_intro zenon_H36 ].
% 3.76/3.93 cut (((set_difference (unordered_pair zenon_TB_n zenon_TA_k) zenon_TC_q) = (set_difference (unordered_pair zenon_TB_n zenon_TA_k) zenon_TC_q)) = ((set_difference (unordered_pair zenon_TA_k zenon_TB_n) zenon_TC_q) = (set_difference (unordered_pair zenon_TB_n zenon_TA_k) zenon_TC_q))).
% 3.76/3.93 intro zenon_D_pnotp.
% 3.76/3.93 apply zenon_H34.
% 3.76/3.93 rewrite <- zenon_D_pnotp.
% 3.76/3.93 exact zenon_H35.
% 3.76/3.93 cut (((set_difference (unordered_pair zenon_TB_n zenon_TA_k) zenon_TC_q) = (set_difference (unordered_pair zenon_TB_n zenon_TA_k) zenon_TC_q))); [idtac | apply NNPP; zenon_intro zenon_H36].
% 3.76/3.93 cut (((set_difference (unordered_pair zenon_TB_n zenon_TA_k) zenon_TC_q) = (set_difference (unordered_pair zenon_TA_k zenon_TB_n) zenon_TC_q))); [idtac | apply NNPP; zenon_intro zenon_H37].
% 3.76/3.93 congruence.
% 3.76/3.93 cut ((zenon_TC_q = zenon_TC_q)); [idtac | apply NNPP; zenon_intro zenon_H38].
% 3.76/3.93 cut (((unordered_pair zenon_TB_n zenon_TA_k) = (unordered_pair zenon_TA_k zenon_TB_n))); [idtac | apply NNPP; zenon_intro zenon_H39].
% 3.76/3.93 congruence.
% 3.76/3.93 exact (zenon_H39 zenon_H2a).
% 3.76/3.93 apply zenon_H38. apply refl_equal.
% 3.76/3.93 apply zenon_H36. apply refl_equal.
% 3.76/3.93 apply zenon_H36. apply refl_equal.
% 3.76/3.93 apply zenon_H33. apply sym_equal. exact zenon_H2a.
% 3.76/3.93 exact (zenon_H2d zenon_H31).
% 3.76/3.93 exact (zenon_H16 zenon_H27).
% 3.76/3.93 Qed.
% 3.76/3.93 % SZS output end Proof
% 3.76/3.93 (* END-PROOF *)
% 3.76/3.93 nodes searched: 129296
% 3.76/3.93 max branch formulas: 8283
% 3.76/3.93 proof nodes created: 2108
% 3.76/3.93 formulas created: 286993
% 3.76/3.93
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