TSTP Solution File: SEU243+1 by Zenon---0.7.1
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% File : Zenon---0.7.1
% Problem : SEU243+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n010.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 16:00:33 EDT 2022
% Result : Theorem 2.94s 3.15s
% Output : Proof 2.94s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SEU243+1 : TPTP v8.1.0. Released v3.3.0.
% 0.13/0.14 % Command : run_zenon %s %d
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jun 19 20:11:07 EDT 2022
% 0.13/0.35 % CPUTime :
% 2.94/3.15 Zenon warning: unused variable (B : zenon_U) in idempotence_k2_xboole_0
% 2.94/3.15 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski
% 2.94/3.15 (* PROOF-FOUND *)
% 2.94/3.15 % SZS status Theorem
% 2.94/3.15 (* BEGIN-PROOF *)
% 2.94/3.15 % SZS output start Proof
% 2.94/3.15 Theorem t5_wellord1 : (forall A : zenon_U, ((relation A)->((well_founded_relation A)<->(is_well_founded_in A (relation_field A))))).
% 2.94/3.15 Proof.
% 2.94/3.15 apply NNPP. intro zenon_G.
% 2.94/3.15 apply (zenon_notallex_s (fun A : zenon_U => ((relation A)->((well_founded_relation A)<->(is_well_founded_in A (relation_field A))))) zenon_G); [ zenon_intro zenon_H1e; idtac ].
% 2.94/3.15 elim zenon_H1e. zenon_intro zenon_TA_bf. zenon_intro zenon_H20.
% 2.94/3.15 apply (zenon_notimply_s _ _ zenon_H20). zenon_intro zenon_H22. zenon_intro zenon_H21.
% 2.94/3.15 apply (zenon_notequiv_s _ _ zenon_H21); [ zenon_intro zenon_H26; zenon_intro zenon_H25 | zenon_intro zenon_H24; zenon_intro zenon_H23 ].
% 2.94/3.15 generalize (d2_wellord1 zenon_TA_bf). zenon_intro zenon_H27.
% 2.94/3.15 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ].
% 2.94/3.15 exact (zenon_H29 zenon_H22).
% 2.94/3.15 apply (zenon_equiv_s _ _ zenon_H28); [ zenon_intro zenon_H26; zenon_intro zenon_H2b | zenon_intro zenon_H24; zenon_intro zenon_H2a ].
% 2.94/3.15 generalize (d3_wellord1 zenon_TA_bf). zenon_intro zenon_H2c.
% 2.94/3.15 apply (zenon_imply_s _ _ zenon_H2c); [ zenon_intro zenon_H29 | zenon_intro zenon_H2d ].
% 2.94/3.15 exact (zenon_H29 zenon_H22).
% 2.94/3.15 generalize (zenon_H2d (relation_field zenon_TA_bf)). zenon_intro zenon_H2e.
% 2.94/3.15 apply (zenon_equiv_s _ _ zenon_H2e); [ zenon_intro zenon_H23; zenon_intro zenon_H2b | zenon_intro zenon_H25; zenon_intro zenon_H2a ].
% 2.94/3.15 exact (zenon_H23 zenon_H25).
% 2.94/3.15 exact (zenon_H2b zenon_H2a).
% 2.94/3.15 exact (zenon_H26 zenon_H24).
% 2.94/3.15 generalize (d3_wellord1 zenon_TA_bf). zenon_intro zenon_H2c.
% 2.94/3.15 apply (zenon_imply_s _ _ zenon_H2c); [ zenon_intro zenon_H29 | zenon_intro zenon_H2d ].
% 2.94/3.15 exact (zenon_H29 zenon_H22).
% 2.94/3.15 generalize (zenon_H2d (relation_field zenon_TA_bf)). zenon_intro zenon_H2e.
% 2.94/3.15 apply (zenon_equiv_s _ _ zenon_H2e); [ zenon_intro zenon_H23; zenon_intro zenon_H2b | zenon_intro zenon_H25; zenon_intro zenon_H2a ].
% 2.94/3.15 generalize (d2_wellord1 zenon_TA_bf). zenon_intro zenon_H27.
% 2.94/3.15 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ].
% 2.94/3.15 exact (zenon_H29 zenon_H22).
% 2.94/3.15 apply (zenon_equiv_s _ _ zenon_H28); [ zenon_intro zenon_H26; zenon_intro zenon_H2b | zenon_intro zenon_H24; zenon_intro zenon_H2a ].
% 2.94/3.15 exact (zenon_H26 zenon_H24).
% 2.94/3.15 exact (zenon_H2b zenon_H2a).
% 2.94/3.15 exact (zenon_H23 zenon_H25).
% 2.94/3.15 Qed.
% 2.94/3.15 % SZS output end Proof
% 2.94/3.15 (* END-PROOF *)
% 2.94/3.15 nodes searched: 69222
% 2.94/3.15 max branch formulas: 6525
% 2.94/3.15 proof nodes created: 2284
% 2.94/3.15 formulas created: 219411
% 2.94/3.15
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