TSTP Solution File: NUM383+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : NUM383+1 : 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 : n023.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 : Mon Jul 18 14:42:05 EDT 2022
% Result : Theorem 67.73s 67.93s
% Output : Proof 67.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM383+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jul 7 01:00:11 EDT 2022
% 0.12/0.34 % CPUTime :
% 67.73/67.93 % SZS status Theorem
% 67.73/67.93 (* PROOF-FOUND *)
% 67.73/67.93 (* BEGIN-PROOF *)
% 67.73/67.93 % SZS output start Proof
% 67.73/67.93 1. (empty T_0) (-. (empty T_0)) ### Axiom
% 67.73/67.93 2. (T_0 != T_0) ### Refl(=)
% 67.73/67.93 3. (in T_1 T_2) (-. (in T_1 T_2)) ### Axiom
% 67.73/67.93 4. (subset T_2 T_1) (-. (subset T_2 T_1)) ### Axiom
% 67.73/67.93 5. (-. (element T_2 (powerset T_1))) (element T_2 (powerset T_1)) ### Axiom
% 67.73/67.93 6. ((element T_2 (powerset T_1)) <=> (subset T_2 T_1)) (-. (element T_2 (powerset T_1))) (subset T_2 T_1) ### Equiv 4 5
% 67.73/67.93 7. (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (subset T_2 T_1) (-. (element T_2 (powerset T_1))) ### All 6
% 67.73/67.93 8. (-. (element T_1 T_1)) (element T_1 T_1) ### Axiom
% 67.73/67.93 9. (((in T_1 T_2) /\ (element T_2 (powerset T_1))) => (element T_1 T_1)) (-. (element T_1 T_1)) (subset T_2 T_1) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (in T_1 T_2) ### DisjTree 3 7 8
% 67.73/67.93 10. (All C, (((in T_1 T_2) /\ (element T_2 (powerset C))) => (element T_1 C))) (in T_1 T_2) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (subset T_2 T_1) (-. (element T_1 T_1)) ### All 9
% 67.73/67.93 11. (empty T_1) (-. (empty T_1)) ### Axiom
% 67.73/67.93 12. ((empty_set) != T_1) (T_1 = (empty_set)) ### Sym(=)
% 67.73/67.93 13. ((empty T_1) => (T_1 = (empty_set))) ((empty_set) != T_1) (empty T_1) ### Imply 11 12
% 67.73/67.93 14. (All A, ((empty A) => (A = (empty_set)))) (empty T_1) ((empty_set) != T_1) ### All 13
% 67.73/67.93 15. (in T_1 T_1) (-. (in T_1 T_1)) ### Axiom
% 67.73/67.93 16. (in T_1 T_1) (-. (in T_1 T_1)) ### Axiom
% 67.73/67.93 17. ((in T_1 T_1) => (-. (in T_1 T_1))) (in T_1 T_1) ### Imply 15 16
% 67.73/67.93 18. (All B, ((in T_1 B) => (-. (in B T_1)))) (in T_1 T_1) ### All 17
% 67.73/67.93 19. (All A, (All B, ((in A B) => (-. (in B A))))) (in T_1 T_1) ### All 18
% 67.73/67.93 20. ((element T_1 T_1) => ((empty T_1) \/ (in T_1 T_1))) (All A, (All B, ((in A B) => (-. (in B A))))) ((empty_set) != T_1) (All A, ((empty A) => (A = (empty_set)))) (subset T_2 T_1) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (in T_1 T_2) (All C, (((in T_1 T_2) /\ (element T_2 (powerset C))) => (element T_1 C))) ### DisjTree 10 14 19
% 67.73/67.93 21. (All B, ((element T_1 B) => ((empty B) \/ (in T_1 B)))) (All C, (((in T_1 T_2) /\ (element T_2 (powerset C))) => (element T_1 C))) (in T_1 T_2) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (subset T_2 T_1) (All A, ((empty A) => (A = (empty_set)))) ((empty_set) != T_1) (All A, (All B, ((in A B) => (-. (in B A))))) ### All 20
% 67.73/67.93 22. (T_1 != T_0) (T_0 = (empty_set)) (All A, (All B, ((in A B) => (-. (in B A))))) (All A, ((empty A) => (A = (empty_set)))) (subset T_2 T_1) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (in T_1 T_2) (All C, (((in T_1 T_2) /\ (element T_2 (powerset C))) => (element T_1 C))) (All B, ((element T_1 B) => ((empty B) \/ (in T_1 B)))) ### Trans-sym 2 21
% 67.73/67.93 23. (-. (subset T_1 T_0)) (All B, ((element T_1 B) => ((empty B) \/ (in T_1 B)))) (All C, (((in T_1 T_2) /\ (element T_2 (powerset C))) => (element T_1 C))) (in T_1 T_2) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (subset T_2 T_1) (All A, ((empty A) => (A = (empty_set)))) (All A, (All B, ((in A B) => (-. (in B A))))) (T_0 = (empty_set)) ### Refl(subset) 22
% 67.73/67.93 24. (in T_1 T_2) (-. (in T_1 T_2)) ### Axiom
% 67.73/67.93 25. (-. (empty T_1)) (empty T_1) ### Axiom
% 67.73/67.93 26. (in T_1 T_1) (-. (in T_1 T_1)) ### Axiom
% 67.73/67.93 27. (element T_1 (powerset T_0)) (-. (element T_1 (powerset T_0))) ### Axiom
% 67.73/67.93 28. (empty T_0) (-. (empty T_0)) ### Axiom
% 67.73/67.93 29. (-. ((in T_1 T_1) /\ ((element T_1 (powerset T_0)) /\ (empty T_0)))) (empty T_0) (element T_1 (powerset T_0)) (in T_1 T_1) ### DisjTree 26 27 28
% 67.73/67.93 30. (All C, (-. ((in T_1 T_1) /\ ((element T_1 (powerset C)) /\ (empty C))))) (in T_1 T_1) (element T_1 (powerset T_0)) (empty T_0) ### All 29
% 67.73/67.93 31. (All B, (All C, (-. ((in T_1 B) /\ ((element B (powerset C)) /\ (empty C)))))) (empty T_0) (element T_1 (powerset T_0)) (in T_1 T_1) ### All 30
% 67.73/67.93 32. ((element T_1 T_1) => ((empty T_1) \/ (in T_1 T_1))) (element T_1 (powerset T_0)) (empty T_0) (All B, (All C, (-. ((in T_1 B) /\ ((element B (powerset C)) /\ (empty C)))))) (-. (empty T_1)) (subset T_2 T_1) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (in T_1 T_2) (All C, (((in T_1 T_2) /\ (element T_2 (powerset C))) => (element T_1 C))) ### DisjTree 10 25 31
% 67.73/67.93 33. (All B, ((element T_1 B) => ((empty B) \/ (in T_1 B)))) (All C, (((in T_1 T_2) /\ (element T_2 (powerset C))) => (element T_1 C))) (in T_1 T_2) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (subset T_2 T_1) (-. (empty T_1)) (All B, (All C, (-. ((in T_1 B) /\ ((element B (powerset C)) /\ (empty C)))))) (empty T_0) (element T_1 (powerset T_0)) ### All 32
% 67.73/67.93 34. (-. ((in T_1 T_2) /\ ((element T_2 (powerset T_1)) /\ (empty T_1)))) (element T_1 (powerset T_0)) (empty T_0) (All B, (All C, (-. ((in T_1 B) /\ ((element B (powerset C)) /\ (empty C)))))) (All C, (((in T_1 T_2) /\ (element T_2 (powerset C))) => (element T_1 C))) (All B, ((element T_1 B) => ((empty B) \/ (in T_1 B)))) (subset T_2 T_1) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (in T_1 T_2) ### DisjTree 24 7 33
% 67.73/67.93 35. (All C, (-. ((in T_1 T_2) /\ ((element T_2 (powerset C)) /\ (empty C))))) (in T_1 T_2) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (subset T_2 T_1) (All B, ((element T_1 B) => ((empty B) \/ (in T_1 B)))) (All C, (((in T_1 T_2) /\ (element T_2 (powerset C))) => (element T_1 C))) (All B, (All C, (-. ((in T_1 B) /\ ((element B (powerset C)) /\ (empty C)))))) (empty T_0) (element T_1 (powerset T_0)) ### All 34
% 67.73/67.93 36. ((element T_1 (powerset T_0)) <=> (subset T_1 T_0)) (empty T_0) (All B, (All C, (-. ((in T_1 B) /\ ((element B (powerset C)) /\ (empty C)))))) (All C, (-. ((in T_1 T_2) /\ ((element T_2 (powerset C)) /\ (empty C))))) (T_0 = (empty_set)) (All A, (All B, ((in A B) => (-. (in B A))))) (All A, ((empty A) => (A = (empty_set)))) (subset T_2 T_1) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (in T_1 T_2) (All C, (((in T_1 T_2) /\ (element T_2 (powerset C))) => (element T_1 C))) (All B, ((element T_1 B) => ((empty B) \/ (in T_1 B)))) ### Equiv 23 35
% 67.73/67.93 37. (All B, ((element T_1 (powerset B)) <=> (subset T_1 B))) (All B, ((element T_1 B) => ((empty B) \/ (in T_1 B)))) (All C, (((in T_1 T_2) /\ (element T_2 (powerset C))) => (element T_1 C))) (in T_1 T_2) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (subset T_2 T_1) (All A, ((empty A) => (A = (empty_set)))) (All A, (All B, ((in A B) => (-. (in B A))))) (T_0 = (empty_set)) (All C, (-. ((in T_1 T_2) /\ ((element T_2 (powerset C)) /\ (empty C))))) (All B, (All C, (-. ((in T_1 B) /\ ((element B (powerset C)) /\ (empty C)))))) (empty T_0) ### All 36
% 67.73/67.93 38. (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (empty T_0) (All B, (All C, (-. ((in T_1 B) /\ ((element B (powerset C)) /\ (empty C)))))) (All C, (-. ((in T_1 T_2) /\ ((element T_2 (powerset C)) /\ (empty C))))) (T_0 = (empty_set)) (All A, (All B, ((in A B) => (-. (in B A))))) (All A, ((empty A) => (A = (empty_set)))) (subset T_2 T_1) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (in T_1 T_2) (All C, (((in T_1 T_2) /\ (element T_2 (powerset C))) => (element T_1 C))) (All B, ((element T_1 B) => ((empty B) \/ (in T_1 B)))) ### All 37
% 67.73/67.93 39. ((empty T_0) => (T_0 = (empty_set))) (All B, ((element T_1 B) => ((empty B) \/ (in T_1 B)))) (All C, (((in T_1 T_2) /\ (element T_2 (powerset C))) => (element T_1 C))) (in T_1 T_2) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (subset T_2 T_1) (All A, ((empty A) => (A = (empty_set)))) (All A, (All B, ((in A B) => (-. (in B A))))) (All C, (-. ((in T_1 T_2) /\ ((element T_2 (powerset C)) /\ (empty C))))) (All B, (All C, (-. ((in T_1 B) /\ ((element B (powerset C)) /\ (empty C)))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (empty T_0) ### Imply 1 38
% 67.73/67.93 40. (empty T_0) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All B, (All C, (-. ((in T_1 B) /\ ((element B (powerset C)) /\ (empty C)))))) (All C, (-. ((in T_1 T_2) /\ ((element T_2 (powerset C)) /\ (empty C))))) (All A, (All B, ((in A B) => (-. (in B A))))) (All A, ((empty A) => (A = (empty_set)))) (subset T_2 T_1) (All B, ((element T_2 (powerset B)) <=> (subset T_2 B))) (in T_1 T_2) (All C, (((in T_1 T_2) /\ (element T_2 (powerset C))) => (element T_1 C))) (All B, ((element T_1 B) => ((empty B) \/ (in T_1 B)))) ### All 39
% 67.73/67.95 41. (All B, ((element T_1 B) => ((empty B) \/ (in T_1 B)))) (All C, (((in T_1 T_2) /\ (element T_2 (powerset C))) => (element T_1 C))) (in T_1 T_2) (subset T_2 T_1) (All A, ((empty A) => (A = (empty_set)))) (All A, (All B, ((in A B) => (-. (in B A))))) (All C, (-. ((in T_1 T_2) /\ ((element T_2 (powerset C)) /\ (empty C))))) (All B, (All C, (-. ((in T_1 B) /\ ((element B (powerset C)) /\ (empty C)))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (empty T_0) ### All 40
% 67.73/67.95 42. (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (empty T_0) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All B, (All C, (-. ((in T_1 B) /\ ((element B (powerset C)) /\ (empty C)))))) (All C, (-. ((in T_1 T_2) /\ ((element T_2 (powerset C)) /\ (empty C))))) (All A, (All B, ((in A B) => (-. (in B A))))) (All A, ((empty A) => (A = (empty_set)))) (subset T_2 T_1) (in T_1 T_2) (All C, (((in T_1 T_2) /\ (element T_2 (powerset C))) => (element T_1 C))) ### All 41
% 67.73/67.95 43. (All C, (((in T_1 T_2) /\ (element T_2 (powerset C))) => (element T_1 C))) (in T_1 T_2) (subset T_2 T_1) (All A, ((empty A) => (A = (empty_set)))) (All A, (All B, ((in A B) => (-. (in B A))))) (All B, (All C, (-. ((in T_1 B) /\ ((element B (powerset C)) /\ (empty C)))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (empty T_0) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) ### All 42
% 67.73/67.95 44. (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (empty T_0) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, (All B, ((in A B) => (-. (in B A))))) (All A, ((empty A) => (A = (empty_set)))) (subset T_2 T_1) (in T_1 T_2) (All C, (((in T_1 T_2) /\ (element T_2 (powerset C))) => (element T_1 C))) ### All 43
% 67.73/67.95 45. (All B, (All C, (((in T_1 B) /\ (element B (powerset C))) => (element T_1 C)))) (in T_1 T_2) (subset T_2 T_1) (All A, ((empty A) => (A = (empty_set)))) (All A, (All B, ((in A B) => (-. (in B A))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (empty T_0) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) ### All 44
% 67.73/67.95 46. (All A, (All B, (All C, (((in A B) /\ (element B (powerset C))) => (element A C))))) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (empty T_0) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, (All B, ((in A B) => (-. (in B A))))) (All A, ((empty A) => (A = (empty_set)))) (subset T_2 T_1) (in T_1 T_2) ### All 45
% 67.73/67.95 47. (Ex A, (empty A)) (in T_1 T_2) (subset T_2 T_1) (All A, ((empty A) => (A = (empty_set)))) (All A, (All B, ((in A B) => (-. (in B A))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (All A, (All B, (All C, (((in A B) /\ (element B (powerset C))) => (element A C))))) ### Exists 46
% 67.73/67.95 48. ((in T_1 T_2) /\ (subset T_2 T_1)) (All A, (All B, (All C, (((in A B) /\ (element B (powerset C))) => (element A C))))) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, (All B, ((in A B) => (-. (in B A))))) (All A, ((empty A) => (A = (empty_set)))) (Ex A, (empty A)) ### And 47
% 67.73/67.95 49. (-. (-. ((in T_1 T_2) /\ (subset T_2 T_1)))) (Ex A, (empty A)) (All A, ((empty A) => (A = (empty_set)))) (All A, (All B, ((in A B) => (-. (in B A))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (All A, (All B, (All C, (((in A B) /\ (element B (powerset C))) => (element A C))))) ### NotNot 48
% 67.73/67.95 50. (-. (All B, (-. ((in T_1 B) /\ (subset B T_1))))) (All A, (All B, (All C, (((in A B) /\ (element B (powerset C))) => (element A C))))) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, (All B, ((in A B) => (-. (in B A))))) (All A, ((empty A) => (A = (empty_set)))) (Ex A, (empty A)) ### NotAllEx 49
% 67.73/67.95 51. (-. (All A, (All B, (-. ((in A B) /\ (subset B A)))))) (Ex A, (empty A)) (All A, ((empty A) => (A = (empty_set)))) (All A, (All B, ((in A B) => (-. (in B A))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, (All B, ((element A B) => ((empty B) \/ (in A B))))) (All A, (All B, (All C, (-. ((in A B) /\ ((element B (powerset C)) /\ (empty C))))))) (All A, (All B, (All C, (((in A B) /\ (element B (powerset C))) => (element A C))))) ### NotAllEx 50
% 67.73/67.95 % SZS output end Proof
% 67.73/67.95 (* END-PROOF *)
%------------------------------------------------------------------------------