TSTP Solution File: SEU359+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SEU359+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n021.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 14:50:32 EDT 2022
% Result : Theorem 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU359+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n021.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 Jun 19 09:31:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 (* PROOF-FOUND *)
% 0.19/0.42 (* BEGIN-PROOF *)
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 1. (rel_str T_0) (-. (rel_str T_0)) ### Axiom
% 0.19/0.42 2. (element T_1 (the_carrier T_0)) (-. (element T_1 (the_carrier T_0))) ### Axiom
% 0.19/0.42 3. (ex_sup_of_relstr_set T_0 T_2) (-. (ex_sup_of_relstr_set T_0 T_2)) ### Axiom
% 0.19/0.42 4. (T_1 = (join_on_relstr T_0 T_2)) (T_1 != (join_on_relstr T_0 T_2)) ### Axiom
% 0.19/0.42 5. (-. (relstr_set_smaller T_0 T_2 T_1)) (relstr_set_smaller T_0 T_2 T_1) ### Axiom
% 0.19/0.42 6. ((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) (-. (relstr_set_smaller T_0 T_2 T_1)) ### And 5
% 0.19/0.42 7. ((T_1 = (join_on_relstr T_0 T_2)) <=> ((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))))) (-. (relstr_set_smaller T_0 T_2 T_1)) (T_1 = (join_on_relstr T_0 T_2)) ### Equiv 4 6
% 0.19/0.42 8. ((element T_1 (the_carrier T_0)) => ((ex_sup_of_relstr_set T_0 T_2) => ((T_1 = (join_on_relstr T_0 T_2)) <=> ((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))))))) (T_1 = (join_on_relstr T_0 T_2)) (-. (relstr_set_smaller T_0 T_2 T_1)) (ex_sup_of_relstr_set T_0 T_2) (element T_1 (the_carrier T_0)) ### DisjTree 2 3 7
% 0.19/0.42 9. (All C, ((element C (the_carrier T_0)) => ((ex_sup_of_relstr_set T_0 T_2) => ((C = (join_on_relstr T_0 T_2)) <=> ((relstr_set_smaller T_0 T_2 C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 C D))))))))) (element T_1 (the_carrier T_0)) (ex_sup_of_relstr_set T_0 T_2) (-. (relstr_set_smaller T_0 T_2 T_1)) (T_1 = (join_on_relstr T_0 T_2)) ### All 8
% 0.19/0.42 10. (All B, (All C, ((element C (the_carrier T_0)) => ((ex_sup_of_relstr_set T_0 B) => ((C = (join_on_relstr T_0 B)) <=> ((relstr_set_smaller T_0 B C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 B D) => (related T_0 C D)))))))))) (T_1 = (join_on_relstr T_0 T_2)) (-. (relstr_set_smaller T_0 T_2 T_1)) (ex_sup_of_relstr_set T_0 T_2) (element T_1 (the_carrier T_0)) ### All 9
% 0.19/0.42 11. ((rel_str T_0) => (All B, (All C, ((element C (the_carrier T_0)) => ((ex_sup_of_relstr_set T_0 B) => ((C = (join_on_relstr T_0 B)) <=> ((relstr_set_smaller T_0 B C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 B D) => (related T_0 C D))))))))))) (element T_1 (the_carrier T_0)) (ex_sup_of_relstr_set T_0 T_2) (-. (relstr_set_smaller T_0 T_2 T_1)) (T_1 = (join_on_relstr T_0 T_2)) (rel_str T_0) ### Imply 1 10
% 0.19/0.42 12. (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((ex_sup_of_relstr_set A B) => ((C = (join_on_relstr A B)) <=> ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D)))))))))))) (rel_str T_0) (T_1 = (join_on_relstr T_0 T_2)) (-. (relstr_set_smaller T_0 T_2 T_1)) (ex_sup_of_relstr_set T_0 T_2) (element T_1 (the_carrier T_0)) ### All 11
% 0.19/0.42 13. (rel_str T_0) (-. (rel_str T_0)) ### Axiom
% 0.19/0.42 14. (element T_1 (the_carrier T_0)) (-. (element T_1 (the_carrier T_0))) ### Axiom
% 0.19/0.42 15. (ex_sup_of_relstr_set T_0 T_2) (-. (ex_sup_of_relstr_set T_0 T_2)) ### Axiom
% 0.19/0.42 16. (T_1 = (join_on_relstr T_0 T_2)) (T_1 != (join_on_relstr T_0 T_2)) ### Axiom
% 0.19/0.42 17. (-. (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) ### Axiom
% 0.19/0.42 18. ((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) (-. (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) ### And 17
% 0.19/0.42 19. ((T_1 = (join_on_relstr T_0 T_2)) <=> ((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))))) (-. (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) (T_1 = (join_on_relstr T_0 T_2)) ### Equiv 16 18
% 0.19/0.42 20. ((element T_1 (the_carrier T_0)) => ((ex_sup_of_relstr_set T_0 T_2) => ((T_1 = (join_on_relstr T_0 T_2)) <=> ((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))))))) (T_1 = (join_on_relstr T_0 T_2)) (-. (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) (ex_sup_of_relstr_set T_0 T_2) (element T_1 (the_carrier T_0)) ### DisjTree 14 15 19
% 0.19/0.42 21. (All C, ((element C (the_carrier T_0)) => ((ex_sup_of_relstr_set T_0 T_2) => ((C = (join_on_relstr T_0 T_2)) <=> ((relstr_set_smaller T_0 T_2 C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 C D))))))))) (element T_1 (the_carrier T_0)) (ex_sup_of_relstr_set T_0 T_2) (-. (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) (T_1 = (join_on_relstr T_0 T_2)) ### All 20
% 0.19/0.42 22. (All B, (All C, ((element C (the_carrier T_0)) => ((ex_sup_of_relstr_set T_0 B) => ((C = (join_on_relstr T_0 B)) <=> ((relstr_set_smaller T_0 B C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 B D) => (related T_0 C D)))))))))) (T_1 = (join_on_relstr T_0 T_2)) (-. (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) (ex_sup_of_relstr_set T_0 T_2) (element T_1 (the_carrier T_0)) ### All 21
% 0.19/0.42 23. ((rel_str T_0) => (All B, (All C, ((element C (the_carrier T_0)) => ((ex_sup_of_relstr_set T_0 B) => ((C = (join_on_relstr T_0 B)) <=> ((relstr_set_smaller T_0 B C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 B D) => (related T_0 C D))))))))))) (element T_1 (the_carrier T_0)) (ex_sup_of_relstr_set T_0 T_2) (-. (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) (T_1 = (join_on_relstr T_0 T_2)) (rel_str T_0) ### Imply 13 22
% 0.19/0.42 24. (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((ex_sup_of_relstr_set A B) => ((C = (join_on_relstr A B)) <=> ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D)))))))))))) (rel_str T_0) (T_1 = (join_on_relstr T_0 T_2)) (-. (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) (ex_sup_of_relstr_set T_0 T_2) (element T_1 (the_carrier T_0)) ### All 23
% 0.19/0.42 25. (-. ((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))))) (element T_1 (the_carrier T_0)) (ex_sup_of_relstr_set T_0 T_2) (T_1 = (join_on_relstr T_0 T_2)) (rel_str T_0) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((ex_sup_of_relstr_set A B) => ((C = (join_on_relstr A B)) <=> ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D)))))))))))) ### NotAnd 12 24
% 0.19/0.42 26. (-. (((T_1 = (join_on_relstr T_0 T_2)) /\ (ex_sup_of_relstr_set T_0 T_2)) => ((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))))) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((ex_sup_of_relstr_set A B) => ((C = (join_on_relstr A B)) <=> ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D)))))))))))) (rel_str T_0) (element T_1 (the_carrier T_0)) ### ConjTree 25
% 0.19/0.42 27. (rel_str T_0) (-. (rel_str T_0)) ### Axiom
% 0.19/0.42 28. (element T_1 (the_carrier T_0)) (-. (element T_1 (the_carrier T_0))) ### Axiom
% 0.19/0.42 29. (antisymmetric_relstr T_0) (-. (antisymmetric_relstr T_0)) ### Axiom
% 0.19/0.42 30. (rel_str T_0) (-. (rel_str T_0)) ### Axiom
% 0.19/0.42 31. (element T_1 (the_carrier T_0)) (-. (element T_1 (the_carrier T_0))) ### Axiom
% 0.19/0.42 32. (relstr_set_smaller T_0 T_2 T_1) (-. (relstr_set_smaller T_0 T_2 T_1)) ### Axiom
% 0.19/0.42 33. (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (-. (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) ### Axiom
% 0.19/0.43 34. (-. ((element T_1 (the_carrier T_0)) /\ ((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))))) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (relstr_set_smaller T_0 T_2 T_1) (element T_1 (the_carrier T_0)) ### DisjTree 31 32 33
% 0.19/0.43 35. (-. (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_set_smaller T_0 T_2 C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 C D)))))))) (element T_1 (the_carrier T_0)) (relstr_set_smaller T_0 T_2 T_1) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) ### NotExists 34
% 0.19/0.43 36. (-. (ex_sup_of_relstr_set T_0 T_2)) (ex_sup_of_relstr_set T_0 T_2) ### Axiom
% 0.19/0.43 37. ((ex_sup_of_relstr_set T_0 T_2) <=> (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_set_smaller T_0 T_2 C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 C D)))))))) (-. (ex_sup_of_relstr_set T_0 T_2)) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (relstr_set_smaller T_0 T_2 T_1) (element T_1 (the_carrier T_0)) ### Equiv 35 36
% 0.19/0.43 38. (All B, ((ex_sup_of_relstr_set T_0 B) <=> (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_set_smaller T_0 B C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 B D) => (related T_0 C D))))))))) (element T_1 (the_carrier T_0)) (relstr_set_smaller T_0 T_2 T_1) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (-. (ex_sup_of_relstr_set T_0 T_2)) ### All 37
% 0.19/0.43 39. (((antisymmetric_relstr T_0) /\ (rel_str T_0)) => (All B, ((ex_sup_of_relstr_set T_0 B) <=> (Ex C, ((element C (the_carrier T_0)) /\ ((relstr_set_smaller T_0 B C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 B D) => (related T_0 C D)))))))))) (-. (ex_sup_of_relstr_set T_0 T_2)) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (relstr_set_smaller T_0 T_2 T_1) (element T_1 (the_carrier T_0)) (rel_str T_0) (antisymmetric_relstr T_0) ### DisjTree 29 30 38
% 0.19/0.43 40. (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) (antisymmetric_relstr T_0) (rel_str T_0) (element T_1 (the_carrier T_0)) (relstr_set_smaller T_0 T_2 T_1) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (-. (ex_sup_of_relstr_set T_0 T_2)) ### All 39
% 0.19/0.43 41. (relstr_set_smaller T_0 T_2 T_1) (-. (relstr_set_smaller T_0 T_2 T_1)) ### Axiom
% 0.19/0.43 42. (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (-. (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) ### Axiom
% 0.19/0.43 43. (-. ((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))))) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (relstr_set_smaller T_0 T_2 T_1) ### NotAnd 41 42
% 0.19/0.43 44. (T_1 != (join_on_relstr T_0 T_2)) (T_1 = (join_on_relstr T_0 T_2)) ### Axiom
% 0.19/0.43 45. ((T_1 = (join_on_relstr T_0 T_2)) <=> ((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))))) (T_1 != (join_on_relstr T_0 T_2)) (relstr_set_smaller T_0 T_2 T_1) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) ### Equiv 43 44
% 0.19/0.43 46. ((element T_1 (the_carrier T_0)) => ((ex_sup_of_relstr_set T_0 T_2) => ((T_1 = (join_on_relstr T_0 T_2)) <=> ((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))))))) (T_1 != (join_on_relstr T_0 T_2)) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (relstr_set_smaller T_0 T_2 T_1) (rel_str T_0) (antisymmetric_relstr T_0) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) (element T_1 (the_carrier T_0)) ### DisjTree 28 40 45
% 0.19/0.43 47. (All C, ((element C (the_carrier T_0)) => ((ex_sup_of_relstr_set T_0 T_2) => ((C = (join_on_relstr T_0 T_2)) <=> ((relstr_set_smaller T_0 T_2 C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 C D))))))))) (element T_1 (the_carrier T_0)) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) (antisymmetric_relstr T_0) (rel_str T_0) (relstr_set_smaller T_0 T_2 T_1) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (T_1 != (join_on_relstr T_0 T_2)) ### All 46
% 0.19/0.43 48. (All B, (All C, ((element C (the_carrier T_0)) => ((ex_sup_of_relstr_set T_0 B) => ((C = (join_on_relstr T_0 B)) <=> ((relstr_set_smaller T_0 B C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 B D) => (related T_0 C D)))))))))) (T_1 != (join_on_relstr T_0 T_2)) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (relstr_set_smaller T_0 T_2 T_1) (rel_str T_0) (antisymmetric_relstr T_0) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) (element T_1 (the_carrier T_0)) ### All 47
% 0.19/0.43 49. ((rel_str T_0) => (All B, (All C, ((element C (the_carrier T_0)) => ((ex_sup_of_relstr_set T_0 B) => ((C = (join_on_relstr T_0 B)) <=> ((relstr_set_smaller T_0 B C) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 B D) => (related T_0 C D))))))))))) (element T_1 (the_carrier T_0)) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) (antisymmetric_relstr T_0) (relstr_set_smaller T_0 T_2 T_1) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (T_1 != (join_on_relstr T_0 T_2)) (rel_str T_0) ### Imply 27 48
% 0.19/0.43 50. (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((ex_sup_of_relstr_set A B) => ((C = (join_on_relstr A B)) <=> ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D)))))))))))) (rel_str T_0) (T_1 != (join_on_relstr T_0 T_2)) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (relstr_set_smaller T_0 T_2 T_1) (antisymmetric_relstr T_0) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) (element T_1 (the_carrier T_0)) ### All 49
% 0.19/0.43 51. (-. ((T_1 = (join_on_relstr T_0 T_2)) /\ (ex_sup_of_relstr_set T_0 T_2))) (element T_1 (the_carrier T_0)) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) (antisymmetric_relstr T_0) (relstr_set_smaller T_0 T_2 T_1) (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))) (rel_str T_0) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((ex_sup_of_relstr_set A B) => ((C = (join_on_relstr A B)) <=> ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D)))))))))))) ### NotAnd 50 40
% 0.19/0.44 52. (-. (((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) => ((T_1 = (join_on_relstr T_0 T_2)) /\ (ex_sup_of_relstr_set T_0 T_2)))) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((ex_sup_of_relstr_set A B) => ((C = (join_on_relstr A B)) <=> ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D)))))))))))) (rel_str T_0) (antisymmetric_relstr T_0) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) (element T_1 (the_carrier T_0)) ### ConjTree 51
% 0.19/0.44 53. (-. ((((T_1 = (join_on_relstr T_0 T_2)) /\ (ex_sup_of_relstr_set T_0 T_2)) => ((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D)))))) /\ (((relstr_set_smaller T_0 T_2 T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 T_2 D) => (related T_0 T_1 D))))) => ((T_1 = (join_on_relstr T_0 T_2)) /\ (ex_sup_of_relstr_set T_0 T_2))))) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) (antisymmetric_relstr T_0) (element T_1 (the_carrier T_0)) (rel_str T_0) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((ex_sup_of_relstr_set A B) => ((C = (join_on_relstr A B)) <=> ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D)))))))))))) ### NotAnd 26 52
% 0.19/0.44 54. (-. (All C, ((((T_1 = (join_on_relstr T_0 C)) /\ (ex_sup_of_relstr_set T_0 C)) => ((relstr_set_smaller T_0 C T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 C D) => (related T_0 T_1 D)))))) /\ (((relstr_set_smaller T_0 C T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 C D) => (related T_0 T_1 D))))) => ((T_1 = (join_on_relstr T_0 C)) /\ (ex_sup_of_relstr_set T_0 C)))))) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((ex_sup_of_relstr_set A B) => ((C = (join_on_relstr A B)) <=> ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D)))))))))))) (rel_str T_0) (element T_1 (the_carrier T_0)) (antisymmetric_relstr T_0) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) ### NotAllEx 53
% 0.19/0.44 55. (-. ((element T_1 (the_carrier T_0)) => (All C, ((((T_1 = (join_on_relstr T_0 C)) /\ (ex_sup_of_relstr_set T_0 C)) => ((relstr_set_smaller T_0 C T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 C D) => (related T_0 T_1 D)))))) /\ (((relstr_set_smaller T_0 C T_1) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 C D) => (related T_0 T_1 D))))) => ((T_1 = (join_on_relstr T_0 C)) /\ (ex_sup_of_relstr_set T_0 C))))))) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) (antisymmetric_relstr T_0) (rel_str T_0) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((ex_sup_of_relstr_set A B) => ((C = (join_on_relstr A B)) <=> ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D)))))))))))) ### NotImply 54
% 0.19/0.44 56. (-. (All B, ((element B (the_carrier T_0)) => (All C, ((((B = (join_on_relstr T_0 C)) /\ (ex_sup_of_relstr_set T_0 C)) => ((relstr_set_smaller T_0 C B) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 C D) => (related T_0 B D)))))) /\ (((relstr_set_smaller T_0 C B) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 C D) => (related T_0 B D))))) => ((B = (join_on_relstr T_0 C)) /\ (ex_sup_of_relstr_set T_0 C)))))))) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((ex_sup_of_relstr_set A B) => ((C = (join_on_relstr A B)) <=> ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D)))))))))))) (rel_str T_0) (antisymmetric_relstr T_0) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) ### NotAllEx 55
% 0.19/0.44 57. (-. (((antisymmetric_relstr T_0) /\ (rel_str T_0)) => (All B, ((element B (the_carrier T_0)) => (All C, ((((B = (join_on_relstr T_0 C)) /\ (ex_sup_of_relstr_set T_0 C)) => ((relstr_set_smaller T_0 C B) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 C D) => (related T_0 B D)))))) /\ (((relstr_set_smaller T_0 C B) /\ (All D, ((element D (the_carrier T_0)) => ((relstr_set_smaller T_0 C D) => (related T_0 B D))))) => ((B = (join_on_relstr T_0 C)) /\ (ex_sup_of_relstr_set T_0 C))))))))) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((ex_sup_of_relstr_set A B) => ((C = (join_on_relstr A B)) <=> ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D)))))))))))) ### ConjTree 56
% 0.19/0.44 58. (-. (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((element B (the_carrier A)) => (All C, ((((B = (join_on_relstr A C)) /\ (ex_sup_of_relstr_set A C)) => ((relstr_set_smaller A C B) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A C D) => (related A B D)))))) /\ (((relstr_set_smaller A C B) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A C D) => (related A B D))))) => ((B = (join_on_relstr A C)) /\ (ex_sup_of_relstr_set A C)))))))))) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((ex_sup_of_relstr_set A B) => ((C = (join_on_relstr A B)) <=> ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D)))))))))))) (All A, (((antisymmetric_relstr A) /\ (rel_str A)) => (All B, ((ex_sup_of_relstr_set A B) <=> (Ex C, ((element C (the_carrier A)) /\ ((relstr_set_smaller A B C) /\ (All D, ((element D (the_carrier A)) => ((relstr_set_smaller A B D) => (related A C D))))))))))) ### NotAllEx 57
% 0.19/0.44 % SZS output end Proof
% 0.19/0.44 (* END-PROOF *)
%------------------------------------------------------------------------------