TSTP Solution File: SET874+1 by SuperZenon---0.0.1
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%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SET874+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 : n027.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 05:44:44 EDT 2022
% Result : Theorem 23.28s 23.48s
% Output : Proof 23.28s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET874+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.34 % Computer : n027.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 : Mon Jul 11 07:03:48 EDT 2022
% 0.13/0.35 % CPUTime :
% 23.28/23.48 % SZS status Theorem
% 23.28/23.48 (* PROOF-FOUND *)
% 23.28/23.48 (* BEGIN-PROOF *)
% 23.28/23.48 % SZS output start Proof
% 23.28/23.48 1. ((unordered_pair T_0 T_1) != (unordered_pair T_0 T_1)) ### Refl(=)
% 23.28/23.48 2. (T_0 != T_0) ### Refl(=)
% 23.28/23.48 3. (-. ((T_0 = T_0) \/ (T_0 = T_1))) ### NotOr 2
% 23.28/23.48 4. (-. (in T_0 (unordered_pair T_0 T_1))) (in T_0 (unordered_pair T_0 T_1)) ### Axiom
% 23.28/23.48 5. ((in T_0 (unordered_pair T_0 T_1)) <=> ((T_0 = T_0) \/ (T_0 = T_1))) (-. (in T_0 (unordered_pair T_0 T_1))) ### Equiv 3 4
% 23.28/23.48 6. (All D, ((in D (unordered_pair T_0 T_1)) <=> ((D = T_0) \/ (D = T_1)))) (-. (in T_0 (unordered_pair T_0 T_1))) ### All 5
% 23.28/23.48 7. ((set_union2 (singleton T_0) (unordered_pair T_0 T_1)) != (unordered_pair T_0 T_1)) ((set_union2 (singleton T_0) (unordered_pair T_0 T_1)) = (unordered_pair T_0 T_1)) ### Axiom
% 23.28/23.48 8. ((in T_0 (unordered_pair T_0 T_1)) => ((set_union2 (singleton T_0) (unordered_pair T_0 T_1)) = (unordered_pair T_0 T_1))) ((set_union2 (singleton T_0) (unordered_pair T_0 T_1)) != (unordered_pair T_0 T_1)) (All D, ((in D (unordered_pair T_0 T_1)) <=> ((D = T_0) \/ (D = T_1)))) ### Imply 6 7
% 23.28/23.48 9. (All B, ((in T_0 B) => ((set_union2 (singleton T_0) B) = B))) (All D, ((in D (unordered_pair T_0 T_1)) <=> ((D = T_0) \/ (D = T_1)))) ((set_union2 (singleton T_0) (unordered_pair T_0 T_1)) != (unordered_pair T_0 T_1)) ### All 8
% 23.28/23.48 10. (All A, (All B, ((in A B) => ((set_union2 (singleton A) B) = B)))) ((set_union2 (singleton T_0) (unordered_pair T_0 T_1)) != (unordered_pair T_0 T_1)) (All D, ((in D (unordered_pair T_0 T_1)) <=> ((D = T_0) \/ (D = T_1)))) ### All 9
% 23.28/23.48 11. (((unordered_pair T_0 T_1) = (unordered_pair T_0 T_1)) <=> (All D, ((in D (unordered_pair T_0 T_1)) <=> ((D = T_0) \/ (D = T_1))))) ((set_union2 (singleton T_0) (unordered_pair T_0 T_1)) != (unordered_pair T_0 T_1)) (All A, (All B, ((in A B) => ((set_union2 (singleton A) B) = B)))) ### Equiv 1 10
% 23.28/23.48 12. (All C, ((C = (unordered_pair T_0 T_1)) <=> (All D, ((in D C) <=> ((D = T_0) \/ (D = T_1)))))) (All A, (All B, ((in A B) => ((set_union2 (singleton A) B) = B)))) ((set_union2 (singleton T_0) (unordered_pair T_0 T_1)) != (unordered_pair T_0 T_1)) ### All 11
% 23.28/23.48 13. (All B, (All C, ((C = (unordered_pair T_0 B)) <=> (All D, ((in D C) <=> ((D = T_0) \/ (D = B))))))) ((set_union2 (singleton T_0) (unordered_pair T_0 T_1)) != (unordered_pair T_0 T_1)) (All A, (All B, ((in A B) => ((set_union2 (singleton A) B) = B)))) ### All 12
% 23.28/23.48 14. (All A, (All B, (All C, ((C = (unordered_pair A B)) <=> (All D, ((in D C) <=> ((D = A) \/ (D = B)))))))) (All A, (All B, ((in A B) => ((set_union2 (singleton A) B) = B)))) ((set_union2 (singleton T_0) (unordered_pair T_0 T_1)) != (unordered_pair T_0 T_1)) ### All 13
% 23.28/23.48 15. (-. (All B, ((set_union2 (singleton T_0) (unordered_pair T_0 B)) = (unordered_pair T_0 B)))) (All A, (All B, ((in A B) => ((set_union2 (singleton A) B) = B)))) (All A, (All B, (All C, ((C = (unordered_pair A B)) <=> (All D, ((in D C) <=> ((D = A) \/ (D = B)))))))) ### NotAllEx 14
% 23.28/23.48 16. (-. (All A, (All B, ((set_union2 (singleton A) (unordered_pair A B)) = (unordered_pair A B))))) (All A, (All B, (All C, ((C = (unordered_pair A B)) <=> (All D, ((in D C) <=> ((D = A) \/ (D = B)))))))) (All A, (All B, ((in A B) => ((set_union2 (singleton A) B) = B)))) ### NotAllEx 15
% 23.28/23.48 % SZS output end Proof
% 23.28/23.48 (* END-PROOF *)
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