TSTP Solution File: SET807+4 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SET807+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n009.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 05:44:06 EDT 2022
% Result : Theorem 48.11s 48.35s
% Output : Proof 48.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET807+4 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 11 10:49:52 EDT 2022
% 0.14/0.34 % CPUTime :
% 48.11/48.35 % SZS status Theorem
% 48.11/48.35 (* PROOF-FOUND *)
% 48.11/48.35 (* BEGIN-PROOF *)
% 48.11/48.35 % SZS output start Proof
% 48.11/48.35 1. (-. (member T_0 T_1)) (member T_0 T_1) ### Axiom
% 48.11/48.35 2. (-. ((member T_0 T_1) => (member T_0 T_1))) ### NotImply 1
% 48.11/48.35 3. (-. (All X, ((member X T_1) => (member X T_1)))) ### NotAllEx 2
% 48.11/48.35 4. (-. (subset T_1 T_1)) ### Definition-Pseudo(subset) 3
% 48.11/48.35 5. (-. (apply (subset_predicate) T_1 T_1)) (apply (subset_predicate) T_1 T_1) ### Axiom
% 48.11/48.35 6. ((apply (subset_predicate) T_1 T_1) <=> (subset T_1 T_1)) (-. (apply (subset_predicate) T_1 T_1)) ### Equiv 4 5
% 48.11/48.35 7. (All Y, ((apply (subset_predicate) T_1 Y) <=> (subset T_1 Y))) (-. (apply (subset_predicate) T_1 T_1)) ### All 6
% 48.11/48.35 8. (All X, (All Y, ((apply (subset_predicate) X Y) <=> (subset X Y)))) (-. (apply (subset_predicate) T_1 T_1)) ### All 7
% 48.11/48.35 9. (-. ((member T_1 (power_set T_2)) => (apply (subset_predicate) T_1 T_1))) (All X, (All Y, ((apply (subset_predicate) X Y) <=> (subset X Y)))) ### NotImply 8
% 48.11/48.35 10. (-. (All X, ((member X (power_set T_2)) => (apply (subset_predicate) X X)))) (All X, (All Y, ((apply (subset_predicate) X Y) <=> (subset X Y)))) ### NotAllEx 9
% 48.11/48.35 11. (member T_3 T_4) (-. (member T_3 T_4)) ### Axiom
% 48.11/48.35 12. (apply (subset_predicate) T_5 T_6) (-. (apply (subset_predicate) T_5 T_6)) ### Axiom
% 48.11/48.35 13. (member T_3 T_5) (-. (member T_3 T_5)) ### Axiom
% 48.11/48.35 14. (-. (member T_3 T_6)) (member T_3 T_6) ### Axiom
% 48.11/48.35 15. ((member T_3 T_5) => (member T_3 T_6)) (-. (member T_3 T_6)) (member T_3 T_5) ### Imply 13 14
% 48.11/48.35 16. (All X, ((member X T_5) => (member X T_6))) (member T_3 T_5) (-. (member T_3 T_6)) ### All 15
% 48.11/48.35 17. (subset T_5 T_6) (-. (member T_3 T_6)) (member T_3 T_5) ### Definition-Pseudo(subset) 16
% 48.11/48.35 18. ((apply (subset_predicate) T_5 T_6) <=> (subset T_5 T_6)) (member T_3 T_5) (-. (member T_3 T_6)) (apply (subset_predicate) T_5 T_6) ### Equiv 12 17
% 48.11/48.35 19. (All Y, ((apply (subset_predicate) T_5 Y) <=> (subset T_5 Y))) (apply (subset_predicate) T_5 T_6) (-. (member T_3 T_6)) (member T_3 T_5) ### All 18
% 48.11/48.35 20. (All X, (All Y, ((apply (subset_predicate) X Y) <=> (subset X Y)))) (member T_3 T_5) (-. (member T_3 T_6)) (apply (subset_predicate) T_5 T_6) ### All 19
% 48.11/48.35 21. (-. (-. (member T_3 T_5))) (apply (subset_predicate) T_5 T_6) (-. (member T_3 T_6)) (All X, (All Y, ((apply (subset_predicate) X Y) <=> (subset X Y)))) ### NotNot 20
% 48.11/48.35 22. (-. ((member T_3 T_4) /\ (-. (member T_3 T_5)))) (All X, (All Y, ((apply (subset_predicate) X Y) <=> (subset X Y)))) (-. (member T_3 T_6)) (apply (subset_predicate) T_5 T_6) (member T_3 T_4) ### NotAnd 11 21
% 48.11/48.35 23. (apply (subset_predicate) T_4 T_5) (-. (apply (subset_predicate) T_4 T_5)) ### Axiom
% 48.11/48.35 24. (member T_3 T_4) (-. (member T_3 T_4)) ### Axiom
% 48.11/48.35 25. (-. (member T_3 T_5)) (member T_3 T_5) ### Axiom
% 48.11/48.35 26. ((member T_3 T_4) => (member T_3 T_5)) (-. (member T_3 T_5)) (member T_3 T_4) ### Imply 24 25
% 48.11/48.35 27. (All X, ((member X T_4) => (member X T_5))) (member T_3 T_4) (-. (member T_3 T_5)) ### All 26
% 48.11/48.35 28. (subset T_4 T_5) (-. (member T_3 T_5)) (member T_3 T_4) ### Definition-Pseudo(subset) 27
% 48.11/48.35 29. ((apply (subset_predicate) T_4 T_5) <=> (subset T_4 T_5)) (member T_3 T_4) (-. (member T_3 T_5)) (apply (subset_predicate) T_4 T_5) ### Equiv 23 28
% 48.11/48.35 30. (All Y, ((apply (subset_predicate) T_4 Y) <=> (subset T_4 Y))) (apply (subset_predicate) T_4 T_5) (-. (member T_3 T_5)) (member T_3 T_4) ### All 29
% 48.11/48.35 31. ((member T_3 T_4) /\ (-. (member T_3 T_5))) (member T_3 T_4) (apply (subset_predicate) T_4 T_5) (All Y, ((apply (subset_predicate) T_4 Y) <=> (subset T_4 Y))) ### And 30
% 48.11/48.35 32. ((member T_3 (difference T_4 T_5)) <=> ((member T_3 T_4) /\ (-. (member T_3 T_5)))) (All Y, ((apply (subset_predicate) T_4 Y) <=> (subset T_4 Y))) (apply (subset_predicate) T_4 T_5) (member T_3 T_4) (apply (subset_predicate) T_5 T_6) (-. (member T_3 T_6)) (All X, (All Y, ((apply (subset_predicate) X Y) <=> (subset X Y)))) ### Equiv 22 31
% 48.11/48.35 33. (All E, ((member T_3 (difference E T_5)) <=> ((member T_3 E) /\ (-. (member T_3 T_5))))) (All X, (All Y, ((apply (subset_predicate) X Y) <=> (subset X Y)))) (-. (member T_3 T_6)) (apply (subset_predicate) T_5 T_6) (member T_3 T_4) (apply (subset_predicate) T_4 T_5) (All Y, ((apply (subset_predicate) T_4 Y) <=> (subset T_4 Y))) ### All 32
% 48.11/48.35 34. (All A, (All E, ((member T_3 (difference E A)) <=> ((member T_3 E) /\ (-. (member T_3 A)))))) (All Y, ((apply (subset_predicate) T_4 Y) <=> (subset T_4 Y))) (apply (subset_predicate) T_4 T_5) (member T_3 T_4) (apply (subset_predicate) T_5 T_6) (-. (member T_3 T_6)) (All X, (All Y, ((apply (subset_predicate) X Y) <=> (subset X Y)))) ### All 33
% 48.11/48.35 35. (All B, (All A, (All E, ((member B (difference E A)) <=> ((member B E) /\ (-. (member B A))))))) (All X, (All Y, ((apply (subset_predicate) X Y) <=> (subset X Y)))) (-. (member T_3 T_6)) (apply (subset_predicate) T_5 T_6) (member T_3 T_4) (apply (subset_predicate) T_4 T_5) (All Y, ((apply (subset_predicate) T_4 Y) <=> (subset T_4 Y))) ### All 34
% 48.11/48.35 36. (-. ((member T_3 T_4) => (member T_3 T_6))) (All Y, ((apply (subset_predicate) T_4 Y) <=> (subset T_4 Y))) (apply (subset_predicate) T_4 T_5) (apply (subset_predicate) T_5 T_6) (All X, (All Y, ((apply (subset_predicate) X Y) <=> (subset X Y)))) (All B, (All A, (All E, ((member B (difference E A)) <=> ((member B E) /\ (-. (member B A))))))) ### NotImply 35
% 48.11/48.35 37. (-. (All X, ((member X T_4) => (member X T_6)))) (All B, (All A, (All E, ((member B (difference E A)) <=> ((member B E) /\ (-. (member B A))))))) (All X, (All Y, ((apply (subset_predicate) X Y) <=> (subset X Y)))) (apply (subset_predicate) T_5 T_6) (apply (subset_predicate) T_4 T_5) (All Y, ((apply (subset_predicate) T_4 Y) <=> (subset T_4 Y))) ### NotAllEx 36
% 48.11/48.35 38. (-. (subset T_4 T_6)) (All Y, ((apply (subset_predicate) T_4 Y) <=> (subset T_4 Y))) (apply (subset_predicate) T_4 T_5) (apply (subset_predicate) T_5 T_6) (All X, (All Y, ((apply (subset_predicate) X Y) <=> (subset X Y)))) (All B, (All A, (All E, ((member B (difference E A)) <=> ((member B E) /\ (-. (member B A))))))) ### Definition-Pseudo(subset) 37
% 48.11/48.35 39. (-. (apply (subset_predicate) T_4 T_6)) (apply (subset_predicate) T_4 T_6) ### Axiom
% 48.11/48.35 40. ((apply (subset_predicate) T_4 T_6) <=> (subset T_4 T_6)) (-. (apply (subset_predicate) T_4 T_6)) (All B, (All A, (All E, ((member B (difference E A)) <=> ((member B E) /\ (-. (member B A))))))) (All X, (All Y, ((apply (subset_predicate) X Y) <=> (subset X Y)))) (apply (subset_predicate) T_5 T_6) (apply (subset_predicate) T_4 T_5) (All Y, ((apply (subset_predicate) T_4 Y) <=> (subset T_4 Y))) ### Equiv 38 39
% 48.11/48.35 41. (All Y, ((apply (subset_predicate) T_4 Y) <=> (subset T_4 Y))) (apply (subset_predicate) T_4 T_5) (apply (subset_predicate) T_5 T_6) (All X, (All Y, ((apply (subset_predicate) X Y) <=> (subset X Y)))) (All B, (All A, (All E, ((member B (difference E A)) <=> ((member B E) /\ (-. (member B A))))))) (-. (apply (subset_predicate) T_4 T_6)) ### All 40
% 48.11/48.35 42. (-. (apply (subset_predicate) T_4 T_6)) (All B, (All A, (All E, ((member B (difference E A)) <=> ((member B E) /\ (-. (member B A))))))) (All X, (All Y, ((apply (subset_predicate) X Y) <=> (subset X Y)))) (apply (subset_predicate) T_5 T_6) (apply (subset_predicate) T_4 T_5) ### All 41
% 48.11/48.35 43. (-. (((member T_4 (power_set T_2)) /\ ((member T_5 (power_set T_2)) /\ (member T_6 (power_set T_2)))) => (((apply (subset_predicate) T_4 T_5) /\ (apply (subset_predicate) T_5 T_6)) => (apply (subset_predicate) T_4 T_6)))) (All X, (All Y, ((apply (subset_predicate) X Y) <=> (subset X Y)))) (All B, (All A, (All E, ((member B (difference E A)) <=> ((member B E) /\ (-. (member B A))))))) ### ConjTree 42
% 48.11/48.35 44. (-. (All Z, (((member T_4 (power_set T_2)) /\ ((member T_5 (power_set T_2)) /\ (member Z (power_set T_2)))) => (((apply (subset_predicate) T_4 T_5) /\ (apply (subset_predicate) T_5 Z)) => (apply (subset_predicate) T_4 Z))))) (All B, (All A, (All E, ((member B (difference E A)) <=> ((member B E) /\ (-. (member B A))))))) (All X, (All Y, ((apply (subset_predicate) X Y) <=> (subset X Y)))) ### NotAllEx 43
% 48.11/48.35 45. (-. (All Y, (All Z, (((member T_4 (power_set T_2)) /\ ((member Y (power_set T_2)) /\ (member Z (power_set T_2)))) => (((apply (subset_predicate) T_4 Y) /\ (apply (subset_predicate) Y Z)) => (apply (subset_predicate) T_4 Z)))))) (All X, (All Y, ((apply (subset_predicate) X Y) <=> (subset X Y)))) (All B, (All A, (All E, ((member B (difference E A)) <=> ((member B E) /\ (-. (member B A))))))) ### NotAllEx 44
% 48.19/48.37 46. (-. (All X, (All Y, (All Z, (((member X (power_set T_2)) /\ ((member Y (power_set T_2)) /\ (member Z (power_set T_2)))) => (((apply (subset_predicate) X Y) /\ (apply (subset_predicate) Y Z)) => (apply (subset_predicate) X Z))))))) (All B, (All A, (All E, ((member B (difference E A)) <=> ((member B E) /\ (-. (member B A))))))) (All X, (All Y, ((apply (subset_predicate) X Y) <=> (subset X Y)))) ### NotAllEx 45
% 48.19/48.37 47. (-. ((All X, ((member X (power_set T_2)) => (apply (subset_predicate) X X))) /\ (All X, (All Y, (All Z, (((member X (power_set T_2)) /\ ((member Y (power_set T_2)) /\ (member Z (power_set T_2)))) => (((apply (subset_predicate) X Y) /\ (apply (subset_predicate) Y Z)) => (apply (subset_predicate) X Z)))))))) (All B, (All A, (All E, ((member B (difference E A)) <=> ((member B E) /\ (-. (member B A))))))) (All X, (All Y, ((apply (subset_predicate) X Y) <=> (subset X Y)))) ### NotAnd 10 46
% 48.19/48.37 48. (-. (pre_order (subset_predicate) (power_set T_2))) (All X, (All Y, ((apply (subset_predicate) X Y) <=> (subset X Y)))) (All B, (All A, (All E, ((member B (difference E A)) <=> ((member B E) /\ (-. (member B A))))))) ### Definition-Pseudo(pre_order) 47
% 48.19/48.37 49. (-. (All E, (pre_order (subset_predicate) (power_set E)))) (All B, (All A, (All E, ((member B (difference E A)) <=> ((member B E) /\ (-. (member B A))))))) (All X, (All Y, ((apply (subset_predicate) X Y) <=> (subset X Y)))) ### NotAllEx 48
% 48.19/48.37 % SZS output end Proof
% 48.19/48.37 (* END-PROOF *)
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