TSTP Solution File: SET766+4 by SuperZenon---0.0.1
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%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SET766+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n018.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 05:43:50 EDT 2022
% Result : Theorem 0.19s 0.48s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET766+4 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 07:59:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 (* PROOF-FOUND *)
% 0.19/0.48 (* BEGIN-PROOF *)
% 0.19/0.48 % SZS output start Proof
% 0.19/0.48 1. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom
% 0.19/0.48 2. (member T_0 T_1) (-. (member T_0 T_1)) ### Axiom
% 0.19/0.48 3. (-. (apply T_2 T_0 T_0)) (apply T_2 T_0 T_0) ### Axiom
% 0.19/0.48 4. ((member T_0 T_1) => (apply T_2 T_0 T_0)) (-. (apply T_2 T_0 T_0)) (member T_0 T_1) ### Imply 2 3
% 0.19/0.48 5. (All X, ((member X T_1) => (apply T_2 X X))) (member T_0 T_1) (-. (apply T_2 T_0 T_0)) ### All 4
% 0.19/0.48 6. (-. ((member T_0 T_1) /\ (apply T_2 T_0 T_0))) (All X, ((member X T_1) => (apply T_2 X X))) (member T_0 T_1) ### NotAnd 1 5
% 0.19/0.48 7. (-. (member T_0 (equivalence_class T_0 T_1 T_2))) (member T_0 (equivalence_class T_0 T_1 T_2)) ### Axiom
% 0.19/0.48 8. ((member T_0 (equivalence_class T_0 T_1 T_2)) <=> ((member T_0 T_1) /\ (apply T_2 T_0 T_0))) (-. (member T_0 (equivalence_class T_0 T_1 T_2))) (member T_0 T_1) (All X, ((member X T_1) => (apply T_2 X X))) ### Equiv 6 7
% 0.19/0.48 9. (All X, ((member X (equivalence_class T_0 T_1 T_2)) <=> ((member X T_1) /\ (apply T_2 T_0 X)))) (All X, ((member X T_1) => (apply T_2 X X))) (member T_0 T_1) (-. (member T_0 (equivalence_class T_0 T_1 T_2))) ### All 8
% 0.19/0.48 10. (All A, (All X, ((member X (equivalence_class A T_1 T_2)) <=> ((member X T_1) /\ (apply T_2 A X))))) (-. (member T_0 (equivalence_class T_0 T_1 T_2))) (member T_0 T_1) (All X, ((member X T_1) => (apply T_2 X X))) ### All 9
% 0.19/0.48 11. (All E, (All A, (All X, ((member X (equivalence_class A E T_2)) <=> ((member X E) /\ (apply T_2 A X)))))) (All X, ((member X T_1) => (apply T_2 X X))) (member T_0 T_1) (-. (member T_0 (equivalence_class T_0 T_1 T_2))) ### All 10
% 0.19/0.48 12. (All R, (All E, (All A, (All X, ((member X (equivalence_class A E R)) <=> ((member X E) /\ (apply R A X))))))) (-. (member T_0 (equivalence_class T_0 T_1 T_2))) (member T_0 T_1) (All X, ((member X T_1) => (apply T_2 X X))) ### All 11
% 0.19/0.48 13. ((All X, ((member X T_1) => (apply T_2 X X))) /\ ((All X, (All Y, (((member X T_1) /\ (member Y T_1)) => ((apply T_2 X Y) => (apply T_2 Y X))))) /\ (All X, (All Y, (All Z, (((member X T_1) /\ ((member Y T_1) /\ (member Z T_1))) => (((apply T_2 X Y) /\ (apply T_2 Y Z)) => (apply T_2 X Z)))))))) (member T_0 T_1) (-. (member T_0 (equivalence_class T_0 T_1 T_2))) (All R, (All E, (All A, (All X, ((member X (equivalence_class A E R)) <=> ((member X E) /\ (apply R A X))))))) ### ConjTree 12
% 0.19/0.48 14. (equivalence T_2 T_1) (All R, (All E, (All A, (All X, ((member X (equivalence_class A E R)) <=> ((member X E) /\ (apply R A X))))))) (-. (member T_0 (equivalence_class T_0 T_1 T_2))) (member T_0 T_1) ### Definition-Pseudo(equivalence) 13
% 0.19/0.48 15. (-. (((equivalence T_2 T_1) /\ (member T_0 T_1)) => (member T_0 (equivalence_class T_0 T_1 T_2)))) (All R, (All E, (All A, (All X, ((member X (equivalence_class A E R)) <=> ((member X E) /\ (apply R A X))))))) ### ConjTree 14
% 0.19/0.48 16. (-. (All A, (((equivalence T_2 T_1) /\ (member A T_1)) => (member A (equivalence_class A T_1 T_2))))) (All R, (All E, (All A, (All X, ((member X (equivalence_class A E R)) <=> ((member X E) /\ (apply R A X))))))) ### NotAllEx 15
% 0.19/0.48 17. (-. (All R, (All A, (((equivalence R T_1) /\ (member A T_1)) => (member A (equivalence_class A T_1 R)))))) (All R, (All E, (All A, (All X, ((member X (equivalence_class A E R)) <=> ((member X E) /\ (apply R A X))))))) ### NotAllEx 16
% 0.19/0.48 18. (-. (All E, (All R, (All A, (((equivalence R E) /\ (member A E)) => (member A (equivalence_class A E R))))))) (All R, (All E, (All A, (All X, ((member X (equivalence_class A E R)) <=> ((member X E) /\ (apply R A X))))))) ### NotAllEx 17
% 0.19/0.48 % SZS output end Proof
% 0.19/0.48 (* END-PROOF *)
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