%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : KRS106+1 : TPTP v8.1.0. Released v3.1.0. % 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 : Sun Jul 17 03:31:55 EDT 2022 % Result : Unsatisfiable 10.27s 10.48s % Output : Proof 10.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : KRS106+1 : TPTP v8.1.0. Released v3.1.0. % 0.06/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.12/0.33 % Computer : n024.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 : Tue Jun 7 14:12:49 EDT 2022 % 0.12/0.33 % CPUTime : % 10.27/10.48 % SZS status Theorem % 10.27/10.48 (* PROOF-FOUND *) % 10.27/10.48 (* BEGIN-PROOF *) % 10.27/10.48 % SZS output start Proof % 10.27/10.48 1. (rf3 (i2003_11_14_17_20_57644) T_0) (-. (rf3 (i2003_11_14_17_20_57644) T_0)) ### Axiom % 10.27/10.48 2. (-. (rf2 (i2003_11_14_17_20_57644) T_0)) (rf2 (i2003_11_14_17_20_57644) T_0) ### Axiom % 10.27/10.48 3. ((rf3 (i2003_11_14_17_20_57644) T_0) => (rf2 (i2003_11_14_17_20_57644) T_0)) (-. (rf2 (i2003_11_14_17_20_57644) T_0)) (rf3 (i2003_11_14_17_20_57644) T_0) ### Imply 1 2 % 10.27/10.48 4. (All Y, ((rf3 (i2003_11_14_17_20_57644) Y) => (rf2 (i2003_11_14_17_20_57644) Y))) (rf3 (i2003_11_14_17_20_57644) T_0) (-. (rf2 (i2003_11_14_17_20_57644) T_0)) ### All 3 % 10.27/10.48 5. (All X, (All Y, ((rf3 X Y) => (rf2 X Y)))) (-. (rf2 (i2003_11_14_17_20_57644) T_0)) (rf3 (i2003_11_14_17_20_57644) T_0) ### All 4 % 10.27/10.48 6. (rf2 (i2003_11_14_17_20_57644) T_1) (-. (rf2 (i2003_11_14_17_20_57644) T_1)) ### Axiom % 10.27/10.48 7. (rf1 (i2003_11_14_17_20_57644) T_2) (-. (rf1 (i2003_11_14_17_20_57644) T_2)) ### Axiom % 10.27/10.48 8. (T_0 = T_1) (T_0 != T_1) ### Axiom % 10.27/10.48 9. (rf3 (i2003_11_14_17_20_57644) T_0) (-. (rf3 (i2003_11_14_17_20_57644) T_0)) ### Axiom % 10.27/10.48 10. (-. (rf1 (i2003_11_14_17_20_57644) T_0)) (rf1 (i2003_11_14_17_20_57644) T_0) ### Axiom % 10.27/10.48 11. ((rf3 (i2003_11_14_17_20_57644) T_0) => (rf1 (i2003_11_14_17_20_57644) T_0)) (-. (rf1 (i2003_11_14_17_20_57644) T_0)) (rf3 (i2003_11_14_17_20_57644) T_0) ### Imply 9 10 % 10.27/10.48 12. (All Y, ((rf3 (i2003_11_14_17_20_57644) Y) => (rf1 (i2003_11_14_17_20_57644) Y))) (rf3 (i2003_11_14_17_20_57644) T_0) (-. (rf1 (i2003_11_14_17_20_57644) T_0)) ### All 11 % 10.27/10.48 13. (-. (rf1 (i2003_11_14_17_20_57644) T_1)) (rf1 (i2003_11_14_17_20_57644) T_1) ### Axiom % 10.27/10.48 14. (((T_0 = T_1) /\ (rf1 (i2003_11_14_17_20_57644) T_0)) => (rf1 (i2003_11_14_17_20_57644) T_1)) (-. (rf1 (i2003_11_14_17_20_57644) T_1)) (rf3 (i2003_11_14_17_20_57644) T_0) (All Y, ((rf3 (i2003_11_14_17_20_57644) Y) => (rf1 (i2003_11_14_17_20_57644) Y))) (T_0 = T_1) ### DisjTree 8 12 13 % 10.27/10.48 15. (All C, (((T_0 = T_1) /\ (rf1 C T_0)) => (rf1 C T_1))) (T_0 = T_1) (All Y, ((rf3 (i2003_11_14_17_20_57644) Y) => (rf1 (i2003_11_14_17_20_57644) Y))) (rf3 (i2003_11_14_17_20_57644) T_0) (-. (rf1 (i2003_11_14_17_20_57644) T_1)) ### All 14 % 10.27/10.48 16. (All X, (All Y, ((rf3 X Y) => (rf1 X Y)))) (-. (rf1 (i2003_11_14_17_20_57644) T_1)) (rf3 (i2003_11_14_17_20_57644) T_0) (T_0 = T_1) (All C, (((T_0 = T_1) /\ (rf1 C T_0)) => (rf1 C T_1))) ### All 15 % 10.27/10.48 17. (T_2 = T_1) (T_1 != T_2) ### Sym(=) % 10.27/10.48 18. (ra_Px1 T_1 T_3) (-. (ra_Px1 T_1 T_3)) ### Axiom % 10.27/10.48 19. (-. (ra_Px1 T_2 T_3)) (ra_Px1 T_2 T_3) ### Axiom % 10.27/10.48 20. (((T_1 = T_2) /\ (ra_Px1 T_1 T_3)) => (ra_Px1 T_2 T_3)) (-. (ra_Px1 T_2 T_3)) (ra_Px1 T_1 T_3) (T_2 = T_1) ### DisjTree 17 18 19 % 10.27/10.48 21. (All C, (((T_1 = T_2) /\ (ra_Px1 T_1 C)) => (ra_Px1 T_2 C))) (T_2 = T_1) (ra_Px1 T_1 T_3) (-. (ra_Px1 T_2 T_3)) ### All 20 % 10.27/10.48 22. (All B, (All C, (((T_1 = B) /\ (ra_Px1 T_1 C)) => (ra_Px1 B C)))) (-. (ra_Px1 T_2 T_3)) (ra_Px1 T_1 T_3) (T_2 = T_1) ### All 21 % 10.27/10.48 23. (All A, (All B, (All C, (((A = B) /\ (ra_Px1 A C)) => (ra_Px1 B C))))) (T_2 = T_1) (ra_Px1 T_1 T_3) (-. (ra_Px1 T_2 T_3)) ### All 22 % 10.27/10.48 24. (((rf1 (i2003_11_14_17_20_57644) T_2) /\ (rf1 (i2003_11_14_17_20_57644) T_1)) => (T_2 = T_1)) (-. (ra_Px1 T_2 T_3)) (ra_Px1 T_1 T_3) (All A, (All B, (All C, (((A = B) /\ (ra_Px1 A C)) => (ra_Px1 B C))))) (All C, (((T_0 = T_1) /\ (rf1 C T_0)) => (rf1 C T_1))) (T_0 = T_1) (rf3 (i2003_11_14_17_20_57644) T_0) (All X, (All Y, ((rf3 X Y) => (rf1 X Y)))) (rf1 (i2003_11_14_17_20_57644) T_2) ### DisjTree 7 16 23 % 10.27/10.48 25. (All Z, (((rf1 (i2003_11_14_17_20_57644) T_2) /\ (rf1 (i2003_11_14_17_20_57644) Z)) => (T_2 = Z))) (rf1 (i2003_11_14_17_20_57644) T_2) (All X, (All Y, ((rf3 X Y) => (rf1 X Y)))) (rf3 (i2003_11_14_17_20_57644) T_0) (T_0 = T_1) (All C, (((T_0 = T_1) /\ (rf1 C T_0)) => (rf1 C T_1))) (All A, (All B, (All C, (((A = B) /\ (ra_Px1 A C)) => (ra_Px1 B C))))) (ra_Px1 T_1 T_3) (-. (ra_Px1 T_2 T_3)) ### All 24 % 10.27/10.48 26. (All B, (All C, (((T_0 = B) /\ (rf1 C T_0)) => (rf1 C B)))) (-. (ra_Px1 T_2 T_3)) (ra_Px1 T_1 T_3) (All A, (All B, (All C, (((A = B) /\ (ra_Px1 A C)) => (ra_Px1 B C))))) (T_0 = T_1) (rf3 (i2003_11_14_17_20_57644) T_0) (All X, (All Y, ((rf3 X Y) => (rf1 X Y)))) (rf1 (i2003_11_14_17_20_57644) T_2) (All Z, (((rf1 (i2003_11_14_17_20_57644) T_2) /\ (rf1 (i2003_11_14_17_20_57644) Z)) => (T_2 = Z))) ### All 25 % 10.27/10.48 27. (All Y, (All Z, (((rf1 (i2003_11_14_17_20_57644) Y) /\ (rf1 (i2003_11_14_17_20_57644) Z)) => (Y = Z)))) (rf1 (i2003_11_14_17_20_57644) T_2) (All X, (All Y, ((rf3 X Y) => (rf1 X Y)))) (rf3 (i2003_11_14_17_20_57644) T_0) (T_0 = T_1) (All A, (All B, (All C, (((A = B) /\ (ra_Px1 A C)) => (ra_Px1 B C))))) (ra_Px1 T_1 T_3) (-. (ra_Px1 T_2 T_3)) (All B, (All C, (((T_0 = B) /\ (rf1 C T_0)) => (rf1 C B)))) ### All 26 % 10.27/10.48 28. (((rf2 (i2003_11_14_17_20_57644) T_0) /\ (rf2 (i2003_11_14_17_20_57644) T_1)) => (T_0 = T_1)) (All B, (All C, (((T_0 = B) /\ (rf1 C T_0)) => (rf1 C B)))) (-. (ra_Px1 T_2 T_3)) (ra_Px1 T_1 T_3) (All A, (All B, (All C, (((A = B) /\ (ra_Px1 A C)) => (ra_Px1 B C))))) (All X, (All Y, ((rf3 X Y) => (rf1 X Y)))) (rf1 (i2003_11_14_17_20_57644) T_2) (All Y, (All Z, (((rf1 (i2003_11_14_17_20_57644) Y) /\ (rf1 (i2003_11_14_17_20_57644) Z)) => (Y = Z)))) (rf2 (i2003_11_14_17_20_57644) T_1) (rf3 (i2003_11_14_17_20_57644) T_0) (All X, (All Y, ((rf3 X Y) => (rf2 X Y)))) ### DisjTree 5 6 27 % 10.27/10.48 29. (All Z, (((rf2 (i2003_11_14_17_20_57644) T_0) /\ (rf2 (i2003_11_14_17_20_57644) Z)) => (T_0 = Z))) (All X, (All Y, ((rf3 X Y) => (rf2 X Y)))) (rf3 (i2003_11_14_17_20_57644) T_0) (rf2 (i2003_11_14_17_20_57644) T_1) (All Y, (All Z, (((rf1 (i2003_11_14_17_20_57644) Y) /\ (rf1 (i2003_11_14_17_20_57644) Z)) => (Y = Z)))) (rf1 (i2003_11_14_17_20_57644) T_2) (All X, (All Y, ((rf3 X Y) => (rf1 X Y)))) (All A, (All B, (All C, (((A = B) /\ (ra_Px1 A C)) => (ra_Px1 B C))))) (ra_Px1 T_1 T_3) (-. (ra_Px1 T_2 T_3)) (All B, (All C, (((T_0 = B) /\ (rf1 C T_0)) => (rf1 C B)))) ### All 28 % 10.27/10.48 30. (All A, (All B, (All C, (((A = B) /\ (rf1 C A)) => (rf1 C B))))) (-. (ra_Px1 T_2 T_3)) (ra_Px1 T_1 T_3) (All A, (All B, (All C, (((A = B) /\ (ra_Px1 A C)) => (ra_Px1 B C))))) (All X, (All Y, ((rf3 X Y) => (rf1 X Y)))) (rf1 (i2003_11_14_17_20_57644) T_2) (All Y, (All Z, (((rf1 (i2003_11_14_17_20_57644) Y) /\ (rf1 (i2003_11_14_17_20_57644) Z)) => (Y = Z)))) (rf2 (i2003_11_14_17_20_57644) T_1) (rf3 (i2003_11_14_17_20_57644) T_0) (All X, (All Y, ((rf3 X Y) => (rf2 X Y)))) (All Z, (((rf2 (i2003_11_14_17_20_57644) T_0) /\ (rf2 (i2003_11_14_17_20_57644) Z)) => (T_0 = Z))) ### All 29 % 10.27/10.48 31. (-. (Ex Y, (ra_Px1 T_2 Y))) (All Z, (((rf2 (i2003_11_14_17_20_57644) T_0) /\ (rf2 (i2003_11_14_17_20_57644) Z)) => (T_0 = Z))) (All X, (All Y, ((rf3 X Y) => (rf2 X Y)))) (rf3 (i2003_11_14_17_20_57644) T_0) (rf2 (i2003_11_14_17_20_57644) T_1) (All Y, (All Z, (((rf1 (i2003_11_14_17_20_57644) Y) /\ (rf1 (i2003_11_14_17_20_57644) Z)) => (Y = Z)))) (rf1 (i2003_11_14_17_20_57644) T_2) (All X, (All Y, ((rf3 X Y) => (rf1 X Y)))) (All A, (All B, (All C, (((A = B) /\ (ra_Px1 A C)) => (ra_Px1 B C))))) (ra_Px1 T_1 T_3) (All A, (All B, (All C, (((A = B) /\ (rf1 C A)) => (rf1 C B))))) ### NotExists 30 % 10.27/10.48 32. (All X, (All Y, (All Z, (((rf1 X Y) /\ (rf1 X Z)) => (Y = Z))))) (All A, (All B, (All C, (((A = B) /\ (rf1 C A)) => (rf1 C B))))) (ra_Px1 T_1 T_3) (All A, (All B, (All C, (((A = B) /\ (ra_Px1 A C)) => (ra_Px1 B C))))) (All X, (All Y, ((rf3 X Y) => (rf1 X Y)))) (rf1 (i2003_11_14_17_20_57644) T_2) (rf2 (i2003_11_14_17_20_57644) T_1) (rf3 (i2003_11_14_17_20_57644) T_0) (All X, (All Y, ((rf3 X Y) => (rf2 X Y)))) (All Z, (((rf2 (i2003_11_14_17_20_57644) T_0) /\ (rf2 (i2003_11_14_17_20_57644) Z)) => (T_0 = Z))) (-. (Ex Y, (ra_Px1 T_2 Y))) ### All 31 % 10.27/10.48 33. (All Y, (All Z, (((rf2 (i2003_11_14_17_20_57644) Y) /\ (rf2 (i2003_11_14_17_20_57644) Z)) => (Y = Z)))) (-. (Ex Y, (ra_Px1 T_2 Y))) (All X, (All Y, ((rf3 X Y) => (rf2 X Y)))) (rf3 (i2003_11_14_17_20_57644) T_0) (rf2 (i2003_11_14_17_20_57644) T_1) (rf1 (i2003_11_14_17_20_57644) T_2) (All X, (All Y, ((rf3 X Y) => (rf1 X Y)))) (All A, (All B, (All C, (((A = B) /\ (ra_Px1 A C)) => (ra_Px1 B C))))) (ra_Px1 T_1 T_3) (All A, (All B, (All C, (((A = B) /\ (rf1 C A)) => (rf1 C B))))) (All X, (All Y, (All Z, (((rf1 X Y) /\ (rf1 X Z)) => (Y = Z))))) ### All 32 % 10.27/10.48 34. (All X, (All Y, (All Z, (((rf2 X Y) /\ (rf2 X Z)) => (Y = Z))))) (All X, (All Y, (All Z, (((rf1 X Y) /\ (rf1 X Z)) => (Y = Z))))) (All A, (All B, (All C, (((A = B) /\ (rf1 C A)) => (rf1 C B))))) (ra_Px1 T_1 T_3) (All A, (All B, (All C, (((A = B) /\ (ra_Px1 A C)) => (ra_Px1 B C))))) (All X, (All Y, ((rf3 X Y) => (rf1 X Y)))) (rf1 (i2003_11_14_17_20_57644) T_2) (rf2 (i2003_11_14_17_20_57644) T_1) (rf3 (i2003_11_14_17_20_57644) T_0) (All X, (All Y, ((rf3 X Y) => (rf2 X Y)))) (-. (Ex Y, (ra_Px1 T_2 Y))) ### All 33 % 10.27/10.49 35. (Ex Y, (ra_Px1 T_1 Y)) (-. (Ex Y, (ra_Px1 T_2 Y))) (All X, (All Y, ((rf3 X Y) => (rf2 X Y)))) (rf3 (i2003_11_14_17_20_57644) T_0) (rf2 (i2003_11_14_17_20_57644) T_1) (rf1 (i2003_11_14_17_20_57644) T_2) (All X, (All Y, ((rf3 X Y) => (rf1 X Y)))) (All A, (All B, (All C, (((A = B) /\ (ra_Px1 A C)) => (ra_Px1 B C))))) (All A, (All B, (All C, (((A = B) /\ (rf1 C A)) => (rf1 C B))))) (All X, (All Y, (All Z, (((rf1 X Y) /\ (rf1 X Z)) => (Y = Z))))) (All X, (All Y, (All Z, (((rf2 X Y) /\ (rf2 X Z)) => (Y = Z))))) ### Exists 34 % 10.27/10.49 36. (cp1xcomp T_1) (All X, (All Y, (All Z, (((rf2 X Y) /\ (rf2 X Z)) => (Y = Z))))) (All X, (All Y, (All Z, (((rf1 X Y) /\ (rf1 X Z)) => (Y = Z))))) (All A, (All B, (All C, (((A = B) /\ (rf1 C A)) => (rf1 C B))))) (All A, (All B, (All C, (((A = B) /\ (ra_Px1 A C)) => (ra_Px1 B C))))) (All X, (All Y, ((rf3 X Y) => (rf1 X Y)))) (rf1 (i2003_11_14_17_20_57644) T_2) (rf2 (i2003_11_14_17_20_57644) T_1) (rf3 (i2003_11_14_17_20_57644) T_0) (All X, (All Y, ((rf3 X Y) => (rf2 X Y)))) (-. (Ex Y, (ra_Px1 T_2 Y))) ### Definition-Pseudo(cp1xcomp) 35 % 10.27/10.49 37. ((rf2 (i2003_11_14_17_20_57644) T_1) /\ (cp1xcomp T_1)) (-. (Ex Y, (ra_Px1 T_2 Y))) (All X, (All Y, ((rf3 X Y) => (rf2 X Y)))) (rf3 (i2003_11_14_17_20_57644) T_0) (rf1 (i2003_11_14_17_20_57644) T_2) (All X, (All Y, ((rf3 X Y) => (rf1 X Y)))) (All A, (All B, (All C, (((A = B) /\ (ra_Px1 A C)) => (ra_Px1 B C))))) (All A, (All B, (All C, (((A = B) /\ (rf1 C A)) => (rf1 C B))))) (All X, (All Y, (All Z, (((rf1 X Y) /\ (rf1 X Z)) => (Y = Z))))) (All X, (All Y, (All Z, (((rf2 X Y) /\ (rf2 X Z)) => (Y = Z))))) ### And 36 % 10.27/10.49 38. (Ex Y, ((rf2 (i2003_11_14_17_20_57644) Y) /\ (cp1xcomp Y))) (All X, (All Y, (All Z, (((rf2 X Y) /\ (rf2 X Z)) => (Y = Z))))) (All X, (All Y, (All Z, (((rf1 X Y) /\ (rf1 X Z)) => (Y = Z))))) (All A, (All B, (All C, (((A = B) /\ (rf1 C A)) => (rf1 C B))))) (All A, (All B, (All C, (((A = B) /\ (ra_Px1 A C)) => (ra_Px1 B C))))) (All X, (All Y, ((rf3 X Y) => (rf1 X Y)))) (rf1 (i2003_11_14_17_20_57644) T_2) (rf3 (i2003_11_14_17_20_57644) T_0) (All X, (All Y, ((rf3 X Y) => (rf2 X Y)))) (-. (Ex Y, (ra_Px1 T_2 Y))) ### Exists 37 % 10.27/10.49 39. (cp1 T_2) (All X, (All Y, ((rf3 X Y) => (rf2 X Y)))) (rf3 (i2003_11_14_17_20_57644) T_0) (rf1 (i2003_11_14_17_20_57644) T_2) (All X, (All Y, ((rf3 X Y) => (rf1 X Y)))) (All A, (All B, (All C, (((A = B) /\ (ra_Px1 A C)) => (ra_Px1 B C))))) (All A, (All B, (All C, (((A = B) /\ (rf1 C A)) => (rf1 C B))))) (All X, (All Y, (All Z, (((rf1 X Y) /\ (rf1 X Z)) => (Y = Z))))) (All X, (All Y, (All Z, (((rf2 X Y) /\ (rf2 X Z)) => (Y = Z))))) (Ex Y, ((rf2 (i2003_11_14_17_20_57644) Y) /\ (cp1xcomp Y))) ### Definition-Pseudo(cp1) 38 % 10.27/10.49 40. ((rf1 (i2003_11_14_17_20_57644) T_2) /\ (cp1 T_2)) (Ex Y, ((rf2 (i2003_11_14_17_20_57644) Y) /\ (cp1xcomp Y))) (All X, (All Y, (All Z, (((rf2 X Y) /\ (rf2 X Z)) => (Y = Z))))) (All X, (All Y, (All Z, (((rf1 X Y) /\ (rf1 X Z)) => (Y = Z))))) (All A, (All B, (All C, (((A = B) /\ (rf1 C A)) => (rf1 C B))))) (All A, (All B, (All C, (((A = B) /\ (ra_Px1 A C)) => (ra_Px1 B C))))) (All X, (All Y, ((rf3 X Y) => (rf1 X Y)))) (rf3 (i2003_11_14_17_20_57644) T_0) (All X, (All Y, ((rf3 X Y) => (rf2 X Y)))) ### And 39 % 10.27/10.49 41. (Ex Y, ((rf1 (i2003_11_14_17_20_57644) Y) /\ (cp1 Y))) (All X, (All Y, ((rf3 X Y) => (rf2 X Y)))) (rf3 (i2003_11_14_17_20_57644) T_0) (All X, (All Y, ((rf3 X Y) => (rf1 X Y)))) (All A, (All B, (All C, (((A = B) /\ (ra_Px1 A C)) => (ra_Px1 B C))))) (All A, (All B, (All C, (((A = B) /\ (rf1 C A)) => (rf1 C B))))) (All X, (All Y, (All Z, (((rf1 X Y) /\ (rf1 X Z)) => (Y = Z))))) (All X, (All Y, (All Z, (((rf2 X Y) /\ (rf2 X Z)) => (Y = Z))))) (Ex Y, ((rf2 (i2003_11_14_17_20_57644) Y) /\ (cp1xcomp Y))) ### Exists 40 % 10.27/10.49 42. ((rf3 (i2003_11_14_17_20_57644) T_0) /\ (cp2 T_0)) (Ex Y, ((rf2 (i2003_11_14_17_20_57644) Y) /\ (cp1xcomp Y))) (All X, (All Y, (All Z, (((rf2 X Y) /\ (rf2 X Z)) => (Y = Z))))) (All X, (All Y, (All Z, (((rf1 X Y) /\ (rf1 X Z)) => (Y = Z))))) (All A, (All B, (All C, (((A = B) /\ (rf1 C A)) => (rf1 C B))))) (All A, (All B, (All C, (((A = B) /\ (ra_Px1 A C)) => (ra_Px1 B C))))) (All X, (All Y, ((rf3 X Y) => (rf1 X Y)))) (All X, (All Y, ((rf3 X Y) => (rf2 X Y)))) (Ex Y, ((rf1 (i2003_11_14_17_20_57644) Y) /\ (cp1 Y))) ### And 41 % 10.27/10.49 43. (Ex Y, ((rf3 (i2003_11_14_17_20_57644) Y) /\ (cp2 Y))) (Ex Y, ((rf1 (i2003_11_14_17_20_57644) Y) /\ (cp1 Y))) (All X, (All Y, ((rf3 X Y) => (rf2 X Y)))) (All X, (All Y, ((rf3 X Y) => (rf1 X Y)))) (All A, (All B, (All C, (((A = B) /\ (ra_Px1 A C)) => (ra_Px1 B C))))) (All A, (All B, (All C, (((A = B) /\ (rf1 C A)) => (rf1 C B))))) (All X, (All Y, (All Z, (((rf1 X Y) /\ (rf1 X Z)) => (Y = Z))))) (All X, (All Y, (All Z, (((rf2 X Y) /\ (rf2 X Z)) => (Y = Z))))) (Ex Y, ((rf2 (i2003_11_14_17_20_57644) Y) /\ (cp1xcomp Y))) ### Exists 42 % 10.27/10.49 44. ((Ex Y, ((rf3 (i2003_11_14_17_20_57644) Y) /\ (cp2 Y))) /\ ((Ex Y, ((rf1 (i2003_11_14_17_20_57644) Y) /\ (cp1 Y))) /\ (Ex Y, ((rf2 (i2003_11_14_17_20_57644) Y) /\ (cp1xcomp Y))))) (All X, (All Y, (All Z, (((rf2 X Y) /\ (rf2 X Z)) => (Y = Z))))) (All X, (All Y, (All Z, (((rf1 X Y) /\ (rf1 X Z)) => (Y = Z))))) (All A, (All B, (All C, (((A = B) /\ (rf1 C A)) => (rf1 C B))))) (All A, (All B, (All C, (((A = B) /\ (ra_Px1 A C)) => (ra_Px1 B C))))) (All X, (All Y, ((rf3 X Y) => (rf1 X Y)))) (All X, (All Y, ((rf3 X Y) => (rf2 X Y)))) ### ConjTree 43 % 10.27/10.49 45. (cUnsatisfiable (i2003_11_14_17_20_57644)) (All X, (All Y, ((rf3 X Y) => (rf2 X Y)))) (All X, (All Y, ((rf3 X Y) => (rf1 X Y)))) (All A, (All B, (All C, (((A = B) /\ (ra_Px1 A C)) => (ra_Px1 B C))))) (All A, (All B, (All C, (((A = B) /\ (rf1 C A)) => (rf1 C B))))) (All X, (All Y, (All Z, (((rf1 X Y) /\ (rf1 X Z)) => (Y = Z))))) (All X, (All Y, (All Z, (((rf2 X Y) /\ (rf2 X Z)) => (Y = Z))))) ### Definition-Pseudo(cUnsatisfiable) 44 % 10.27/10.49 % SZS output end Proof % 10.27/10.49 (* END-PROOF *) %------------------------------------------------------------------------------