TSTP Solution File: SEU355+1 by SuperZenon---0.0.1
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%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SEU355+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 : n024.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 14:50:30 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU355+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 19 10:36:47 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 (* PROOF-FOUND *)
% 0.20/0.41 (* BEGIN-PROOF *)
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 1. (rel_str T_0) (-. (rel_str T_0)) ### Axiom
% 0.20/0.41 2. (element T_1 (the_carrier T_0)) (-. (element T_1 (the_carrier T_0))) ### Axiom
% 0.20/0.41 3. (in T_2 (empty_set)) (-. (in T_2 (empty_set))) ### Axiom
% 0.20/0.41 4. (empty (empty_set)) (-. (empty (empty_set))) ### Axiom
% 0.20/0.41 5. (-. ((in T_2 (empty_set)) /\ (empty (empty_set)))) (empty (empty_set)) (in T_2 (empty_set)) ### NotAnd 3 4
% 0.20/0.41 6. (All B, (-. ((in T_2 B) /\ (empty B)))) (in T_2 (empty_set)) (empty (empty_set)) ### All 5
% 0.20/0.41 7. (All A, (All B, (-. ((in A B) /\ (empty B))))) (empty (empty_set)) (in T_2 (empty_set)) ### All 6
% 0.20/0.41 8. (-. ((element T_2 (the_carrier T_0)) => ((in T_2 (empty_set)) => (related T_0 T_2 T_1)))) (empty (empty_set)) (All A, (All B, (-. ((in A B) /\ (empty B))))) ### ConjTree 7
% 0.20/0.41 9. (-. (All D, ((element D (the_carrier T_0)) => ((in D (empty_set)) => (related T_0 D T_1))))) (All A, (All B, (-. ((in A B) /\ (empty B))))) (empty (empty_set)) ### NotAllEx 8
% 0.20/0.41 10. (-. (relstr_set_smaller T_0 (empty_set) T_1)) (relstr_set_smaller T_0 (empty_set) T_1) ### Axiom
% 0.20/0.41 11. ((relstr_set_smaller T_0 (empty_set) T_1) <=> (All D, ((element D (the_carrier T_0)) => ((in D (empty_set)) => (related T_0 D T_1))))) (-. (relstr_set_smaller T_0 (empty_set) T_1)) (empty (empty_set)) (All A, (All B, (-. ((in A B) /\ (empty B))))) ### Equiv 9 10
% 0.20/0.41 12. ((element T_1 (the_carrier T_0)) => ((relstr_set_smaller T_0 (empty_set) T_1) <=> (All D, ((element D (the_carrier T_0)) => ((in D (empty_set)) => (related T_0 D T_1)))))) (All A, (All B, (-. ((in A B) /\ (empty B))))) (empty (empty_set)) (-. (relstr_set_smaller T_0 (empty_set) T_1)) (element T_1 (the_carrier T_0)) ### Imply 2 11
% 0.20/0.41 13. (All C, ((element C (the_carrier T_0)) => ((relstr_set_smaller T_0 (empty_set) C) <=> (All D, ((element D (the_carrier T_0)) => ((in D (empty_set)) => (related T_0 D C))))))) (element T_1 (the_carrier T_0)) (-. (relstr_set_smaller T_0 (empty_set) T_1)) (empty (empty_set)) (All A, (All B, (-. ((in A B) /\ (empty B))))) ### All 12
% 0.20/0.41 14. (All B, (All C, ((element C (the_carrier T_0)) => ((relstr_set_smaller T_0 B C) <=> (All D, ((element D (the_carrier T_0)) => ((in D B) => (related T_0 D C)))))))) (All A, (All B, (-. ((in A B) /\ (empty B))))) (empty (empty_set)) (-. (relstr_set_smaller T_0 (empty_set) T_1)) (element T_1 (the_carrier T_0)) ### All 13
% 0.20/0.41 15. ((rel_str T_0) => (All B, (All C, ((element C (the_carrier T_0)) => ((relstr_set_smaller T_0 B C) <=> (All D, ((element D (the_carrier T_0)) => ((in D B) => (related T_0 D C))))))))) (element T_1 (the_carrier T_0)) (-. (relstr_set_smaller T_0 (empty_set) T_1)) (empty (empty_set)) (All A, (All B, (-. ((in A B) /\ (empty B))))) (rel_str T_0) ### Imply 1 14
% 0.20/0.41 16. (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((relstr_set_smaller A B C) <=> (All D, ((element D (the_carrier A)) => ((in D B) => (related A D C)))))))))) (rel_str T_0) (All A, (All B, (-. ((in A B) /\ (empty B))))) (empty (empty_set)) (-. (relstr_set_smaller T_0 (empty_set) T_1)) (element T_1 (the_carrier T_0)) ### All 15
% 0.20/0.41 17. (rel_str T_0) (-. (rel_str T_0)) ### Axiom
% 0.20/0.41 18. (element T_1 (the_carrier T_0)) (-. (element T_1 (the_carrier T_0))) ### Axiom
% 0.20/0.41 19. (in T_3 (empty_set)) (-. (in T_3 (empty_set))) ### Axiom
% 0.20/0.41 20. (empty (empty_set)) (-. (empty (empty_set))) ### Axiom
% 0.20/0.41 21. (-. ((in T_3 (empty_set)) /\ (empty (empty_set)))) (empty (empty_set)) (in T_3 (empty_set)) ### NotAnd 19 20
% 0.20/0.41 22. (All B, (-. ((in T_3 B) /\ (empty B)))) (in T_3 (empty_set)) (empty (empty_set)) ### All 21
% 0.20/0.41 23. (All A, (All B, (-. ((in A B) /\ (empty B))))) (empty (empty_set)) (in T_3 (empty_set)) ### All 22
% 0.20/0.41 24. (-. ((element T_3 (the_carrier T_0)) => ((in T_3 (empty_set)) => (related T_0 T_1 T_3)))) (empty (empty_set)) (All A, (All B, (-. ((in A B) /\ (empty B))))) ### ConjTree 23
% 0.20/0.41 25. (-. (All D, ((element D (the_carrier T_0)) => ((in D (empty_set)) => (related T_0 T_1 D))))) (All A, (All B, (-. ((in A B) /\ (empty B))))) (empty (empty_set)) ### NotAllEx 24
% 0.20/0.41 26. (-. (relstr_element_smaller T_0 (empty_set) T_1)) (relstr_element_smaller T_0 (empty_set) T_1) ### Axiom
% 0.20/0.41 27. ((relstr_element_smaller T_0 (empty_set) T_1) <=> (All D, ((element D (the_carrier T_0)) => ((in D (empty_set)) => (related T_0 T_1 D))))) (-. (relstr_element_smaller T_0 (empty_set) T_1)) (empty (empty_set)) (All A, (All B, (-. ((in A B) /\ (empty B))))) ### Equiv 25 26
% 0.20/0.41 28. ((element T_1 (the_carrier T_0)) => ((relstr_element_smaller T_0 (empty_set) T_1) <=> (All D, ((element D (the_carrier T_0)) => ((in D (empty_set)) => (related T_0 T_1 D)))))) (All A, (All B, (-. ((in A B) /\ (empty B))))) (empty (empty_set)) (-. (relstr_element_smaller T_0 (empty_set) T_1)) (element T_1 (the_carrier T_0)) ### Imply 18 27
% 0.20/0.41 29. (All C, ((element C (the_carrier T_0)) => ((relstr_element_smaller T_0 (empty_set) C) <=> (All D, ((element D (the_carrier T_0)) => ((in D (empty_set)) => (related T_0 C D))))))) (element T_1 (the_carrier T_0)) (-. (relstr_element_smaller T_0 (empty_set) T_1)) (empty (empty_set)) (All A, (All B, (-. ((in A B) /\ (empty B))))) ### All 28
% 0.20/0.41 30. (All B, (All C, ((element C (the_carrier T_0)) => ((relstr_element_smaller T_0 B C) <=> (All D, ((element D (the_carrier T_0)) => ((in D B) => (related T_0 C D)))))))) (All A, (All B, (-. ((in A B) /\ (empty B))))) (empty (empty_set)) (-. (relstr_element_smaller T_0 (empty_set) T_1)) (element T_1 (the_carrier T_0)) ### All 29
% 0.20/0.41 31. ((rel_str T_0) => (All B, (All C, ((element C (the_carrier T_0)) => ((relstr_element_smaller T_0 B C) <=> (All D, ((element D (the_carrier T_0)) => ((in D B) => (related T_0 C D))))))))) (element T_1 (the_carrier T_0)) (-. (relstr_element_smaller T_0 (empty_set) T_1)) (empty (empty_set)) (All A, (All B, (-. ((in A B) /\ (empty B))))) (rel_str T_0) ### Imply 17 30
% 0.20/0.41 32. (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((relstr_element_smaller A B C) <=> (All D, ((element D (the_carrier A)) => ((in D B) => (related A C D)))))))))) (rel_str T_0) (All A, (All B, (-. ((in A B) /\ (empty B))))) (empty (empty_set)) (-. (relstr_element_smaller T_0 (empty_set) T_1)) (element T_1 (the_carrier T_0)) ### All 31
% 0.20/0.41 33. (-. ((relstr_set_smaller T_0 (empty_set) T_1) /\ (relstr_element_smaller T_0 (empty_set) T_1))) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((relstr_element_smaller A B C) <=> (All D, ((element D (the_carrier A)) => ((in D B) => (related A C D)))))))))) (element T_1 (the_carrier T_0)) (empty (empty_set)) (All A, (All B, (-. ((in A B) /\ (empty B))))) (rel_str T_0) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((relstr_set_smaller A B C) <=> (All D, ((element D (the_carrier A)) => ((in D B) => (related A D C)))))))))) ### NotAnd 16 32
% 0.20/0.41 34. (-. ((element T_1 (the_carrier T_0)) => ((relstr_set_smaller T_0 (empty_set) T_1) /\ (relstr_element_smaller T_0 (empty_set) T_1)))) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((relstr_set_smaller A B C) <=> (All D, ((element D (the_carrier A)) => ((in D B) => (related A D C)))))))))) (rel_str T_0) (All A, (All B, (-. ((in A B) /\ (empty B))))) (empty (empty_set)) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((relstr_element_smaller A B C) <=> (All D, ((element D (the_carrier A)) => ((in D B) => (related A C D)))))))))) ### NotImply 33
% 0.20/0.41 35. (-. (All B, ((element B (the_carrier T_0)) => ((relstr_set_smaller T_0 (empty_set) B) /\ (relstr_element_smaller T_0 (empty_set) B))))) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((relstr_element_smaller A B C) <=> (All D, ((element D (the_carrier A)) => ((in D B) => (related A C D)))))))))) (empty (empty_set)) (All A, (All B, (-. ((in A B) /\ (empty B))))) (rel_str T_0) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((relstr_set_smaller A B C) <=> (All D, ((element D (the_carrier A)) => ((in D B) => (related A D C)))))))))) ### NotAllEx 34
% 0.20/0.41 36. (-. ((rel_str T_0) => (All B, ((element B (the_carrier T_0)) => ((relstr_set_smaller T_0 (empty_set) B) /\ (relstr_element_smaller T_0 (empty_set) B)))))) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((relstr_set_smaller A B C) <=> (All D, ((element D (the_carrier A)) => ((in D B) => (related A D C)))))))))) (All A, (All B, (-. ((in A B) /\ (empty B))))) (empty (empty_set)) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((relstr_element_smaller A B C) <=> (All D, ((element D (the_carrier A)) => ((in D B) => (related A C D)))))))))) ### NotImply 35
% 0.20/0.42 37. (-. (All A, ((rel_str A) => (All B, ((element B (the_carrier A)) => ((relstr_set_smaller A (empty_set) B) /\ (relstr_element_smaller A (empty_set) B))))))) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((relstr_element_smaller A B C) <=> (All D, ((element D (the_carrier A)) => ((in D B) => (related A C D)))))))))) (empty (empty_set)) (All A, (All B, (-. ((in A B) /\ (empty B))))) (All A, ((rel_str A) => (All B, (All C, ((element C (the_carrier A)) => ((relstr_set_smaller A B C) <=> (All D, ((element D (the_carrier A)) => ((in D B) => (related A D C)))))))))) ### NotAllEx 36
% 0.20/0.42 % SZS output end Proof
% 0.20/0.42 (* END-PROOF *)
%------------------------------------------------------------------------------