%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : SET929+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 : n003.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 05:45:06 EDT 2022 % Result : Theorem 0.20s 0.48s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET929+1 : TPTP v8.1.0. Released v3.2.0. % 0.07/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.14/0.34 % Computer : n003.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 : Sat Jul 9 21:46:59 EDT 2022 % 0.14/0.34 % CPUTime : % 0.20/0.48 % SZS status Theorem % 0.20/0.48 (* PROOF-FOUND *) % 0.20/0.48 (* BEGIN-PROOF *) % 0.20/0.48 % SZS output start Proof % 0.20/0.48 1. ((in T_0 T_1) /\ (in T_2 T_1)) (-. ((in T_0 T_1) /\ (in T_2 T_1))) ### Axiom % 0.20/0.48 2. ((set_difference (unordered_pair T_0 T_2) T_1) != (empty_set)) ((set_difference (unordered_pair T_0 T_2) T_1) = (empty_set)) ### Axiom % 0.20/0.48 3. (subset (unordered_pair T_0 T_2) T_1) ((set_difference (unordered_pair T_0 T_2) T_1) != (empty_set)) ### Definition-Pseudo(subset) 2 % 0.20/0.48 4. ((subset (unordered_pair T_0 T_2) T_1) <=> ((in T_0 T_1) /\ (in T_2 T_1))) ((set_difference (unordered_pair T_0 T_2) T_1) != (empty_set)) ((in T_0 T_1) /\ (in T_2 T_1)) ### Equiv 1 3 % 0.20/0.48 5. (All C, ((subset (unordered_pair T_0 T_2) C) <=> ((in T_0 C) /\ (in T_2 C)))) ((in T_0 T_1) /\ (in T_2 T_1)) ((set_difference (unordered_pair T_0 T_2) T_1) != (empty_set)) ### All 4 % 0.20/0.48 6. (All B, (All C, ((subset (unordered_pair T_0 B) C) <=> ((in T_0 C) /\ (in B C))))) ((set_difference (unordered_pair T_0 T_2) T_1) != (empty_set)) ((in T_0 T_1) /\ (in T_2 T_1)) ### All 5 % 0.20/0.48 7. (All A, (All B, (All C, ((subset (unordered_pair A B) C) <=> ((in A C) /\ (in B C)))))) ((in T_0 T_1) /\ (in T_2 T_1)) ((set_difference (unordered_pair T_0 T_2) T_1) != (empty_set)) ### All 6 % 0.20/0.48 8. ((set_difference (unordered_pair T_0 T_2) T_1) = (empty_set)) ((set_difference (unordered_pair T_0 T_2) T_1) != (empty_set)) ### Axiom % 0.20/0.48 9. (-. (subset (unordered_pair T_0 T_2) T_1)) ((set_difference (unordered_pair T_0 T_2) T_1) = (empty_set)) ### Definition-Pseudo(subset) 8 % 0.20/0.48 10. (-. (in T_0 T_1)) (in T_0 T_1) ### Axiom % 0.20/0.48 11. ((in T_0 T_1) /\ (in T_2 T_1)) (-. (in T_0 T_1)) ### And 10 % 0.20/0.48 12. ((subset (unordered_pair T_0 T_2) T_1) <=> ((in T_0 T_1) /\ (in T_2 T_1))) (-. (in T_0 T_1)) ((set_difference (unordered_pair T_0 T_2) T_1) = (empty_set)) ### Equiv 9 11 % 0.20/0.48 13. (All C, ((subset (unordered_pair T_0 T_2) C) <=> ((in T_0 C) /\ (in T_2 C)))) ((set_difference (unordered_pair T_0 T_2) T_1) = (empty_set)) (-. (in T_0 T_1)) ### All 12 % 0.20/0.48 14. (All B, (All C, ((subset (unordered_pair T_0 B) C) <=> ((in T_0 C) /\ (in B C))))) (-. (in T_0 T_1)) ((set_difference (unordered_pair T_0 T_2) T_1) = (empty_set)) ### All 13 % 0.20/0.48 15. (All A, (All B, (All C, ((subset (unordered_pair A B) C) <=> ((in A C) /\ (in B C)))))) ((set_difference (unordered_pair T_0 T_2) T_1) = (empty_set)) (-. (in T_0 T_1)) ### All 14 % 0.20/0.48 16. (-. (in T_2 T_1)) (in T_2 T_1) ### Axiom % 0.20/0.48 17. ((in T_0 T_1) /\ (in T_2 T_1)) (-. (in T_2 T_1)) ### And 16 % 0.20/0.48 18. ((subset (unordered_pair T_0 T_2) T_1) <=> ((in T_0 T_1) /\ (in T_2 T_1))) (-. (in T_2 T_1)) ((set_difference (unordered_pair T_0 T_2) T_1) = (empty_set)) ### Equiv 9 17 % 0.20/0.48 19. (All C, ((subset (unordered_pair T_0 T_2) C) <=> ((in T_0 C) /\ (in T_2 C)))) ((set_difference (unordered_pair T_0 T_2) T_1) = (empty_set)) (-. (in T_2 T_1)) ### All 18 % 0.20/0.48 20. (All B, (All C, ((subset (unordered_pair T_0 B) C) <=> ((in T_0 C) /\ (in B C))))) (-. (in T_2 T_1)) ((set_difference (unordered_pair T_0 T_2) T_1) = (empty_set)) ### All 19 % 0.20/0.48 21. (All A, (All B, (All C, ((subset (unordered_pair A B) C) <=> ((in A C) /\ (in B C)))))) ((set_difference (unordered_pair T_0 T_2) T_1) = (empty_set)) (-. (in T_2 T_1)) ### All 20 % 0.20/0.48 22. (-. ((in T_0 T_1) /\ (in T_2 T_1))) ((set_difference (unordered_pair T_0 T_2) T_1) = (empty_set)) (All A, (All B, (All C, ((subset (unordered_pair A B) C) <=> ((in A C) /\ (in B C)))))) ### NotAnd 15 21 % 0.20/0.48 23. (-. (((set_difference (unordered_pair T_0 T_2) T_1) = (empty_set)) <=> ((in T_0 T_1) /\ (in T_2 T_1)))) (All A, (All B, (All C, ((subset (unordered_pair A B) C) <=> ((in A C) /\ (in B C)))))) ### NotEquiv 7 22 % 0.20/0.48 24. (-. (All C, (((set_difference (unordered_pair T_0 T_2) C) = (empty_set)) <=> ((in T_0 C) /\ (in T_2 C))))) (All A, (All B, (All C, ((subset (unordered_pair A B) C) <=> ((in A C) /\ (in B C)))))) ### NotAllEx 23 % 0.20/0.48 25. (-. (All B, (All C, (((set_difference (unordered_pair T_0 B) C) = (empty_set)) <=> ((in T_0 C) /\ (in B C)))))) (All A, (All B, (All C, ((subset (unordered_pair A B) C) <=> ((in A C) /\ (in B C)))))) ### NotAllEx 24 % 0.20/0.48 26. (-. (All A, (All B, (All C, (((set_difference (unordered_pair A B) C) = (empty_set)) <=> ((in A C) /\ (in B C))))))) (All A, (All B, (All C, ((subset (unordered_pair A B) C) <=> ((in A C) /\ (in B C)))))) ### NotAllEx 25 % 0.20/0.48 % SZS output end Proof % 0.20/0.48 (* END-PROOF *) %------------------------------------------------------------------------------