%------------------------------------------------------------------------------ % File : SuperZenon---0.0.1 % Problem : KRS115+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 : n019.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 03:31:57 EDT 2022 % Result : Unsatisfiable 22.96s 23.18s % Output : Proof 23.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : KRS115+1 : TPTP v8.1.0. Released v3.1.0. % 0.04/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s % 0.13/0.34 % Computer : n019.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 : Tue Jun 7 15:44:40 EDT 2022 % 0.13/0.34 % CPUTime : % 22.96/23.18 % SZS status Theorem % 22.96/23.18 (* PROOF-FOUND *) % 22.96/23.18 (* BEGIN-PROOF *) % 22.96/23.18 % SZS output start Proof % 22.96/23.18 1. (-. (cowlThing (i2003_11_14_17_21_30578))) (cowlThing (i2003_11_14_17_21_30578)) ### Axiom % 22.96/23.18 2. ((cowlThing (i2003_11_14_17_21_30578)) /\ (-. (cowlNothing (i2003_11_14_17_21_30578)))) (-. (cowlThing (i2003_11_14_17_21_30578))) ### And 1 % 22.96/23.18 3. (All X, ((cowlThing X) /\ (-. (cowlNothing X)))) (-. (cowlThing (i2003_11_14_17_21_30578))) ### All 2 % 22.96/23.18 4. (rr (i2003_11_14_17_21_30578) T_0) (-. (rr (i2003_11_14_17_21_30578) T_0)) ### Axiom % 22.96/23.18 5. (-. (rf2 (i2003_11_14_17_21_30578) T_0)) (rf2 (i2003_11_14_17_21_30578) T_0) ### Axiom % 22.96/23.18 6. ((rr (i2003_11_14_17_21_30578) T_0) => (rf2 (i2003_11_14_17_21_30578) T_0)) (-. (rf2 (i2003_11_14_17_21_30578) T_0)) (rr (i2003_11_14_17_21_30578) T_0) ### Imply 4 5 % 22.96/23.18 7. (All Y, ((rr (i2003_11_14_17_21_30578) Y) => (rf2 (i2003_11_14_17_21_30578) Y))) (rr (i2003_11_14_17_21_30578) T_0) (-. (rf2 (i2003_11_14_17_21_30578) T_0)) ### All 6 % 22.96/23.18 8. (All X, (All Y, ((rr X Y) => (rf2 X Y)))) (-. (rf2 (i2003_11_14_17_21_30578) T_0)) (rr (i2003_11_14_17_21_30578) T_0) ### All 7 % 22.96/23.18 9. (rf2 (i2003_11_14_17_21_30578) T_1) (-. (rf2 (i2003_11_14_17_21_30578) T_1)) ### Axiom % 22.96/23.18 10. (rf1 (i2003_11_14_17_21_30578) T_2) (-. (rf1 (i2003_11_14_17_21_30578) T_2)) ### Axiom % 22.96/23.18 11. (rr (i2003_11_14_17_21_30578) T_0) (-. (rr (i2003_11_14_17_21_30578) T_0)) ### Axiom % 22.96/23.18 12. (-. (rf1 (i2003_11_14_17_21_30578) T_0)) (rf1 (i2003_11_14_17_21_30578) T_0) ### Axiom % 22.96/23.18 13. ((rr (i2003_11_14_17_21_30578) T_0) => (rf1 (i2003_11_14_17_21_30578) T_0)) (-. (rf1 (i2003_11_14_17_21_30578) T_0)) (rr (i2003_11_14_17_21_30578) T_0) ### Imply 11 12 % 22.96/23.18 14. (All Y, ((rr (i2003_11_14_17_21_30578) Y) => (rf1 (i2003_11_14_17_21_30578) Y))) (rr (i2003_11_14_17_21_30578) T_0) (-. (rf1 (i2003_11_14_17_21_30578) T_0)) ### All 13 % 22.96/23.18 15. (All X, (All Y, ((rr X Y) => (rf1 X Y)))) (-. (rf1 (i2003_11_14_17_21_30578) T_0)) (rr (i2003_11_14_17_21_30578) T_0) ### All 14 % 22.96/23.18 16. (rf1 (i2003_11_14_17_21_30578) T_2) (-. (rf1 (i2003_11_14_17_21_30578) T_2)) ### Axiom % 22.96/23.18 17. (T_2 != T_2) ### Refl(=) % 22.96/23.18 18. (T_0 = T_1) (T_0 != T_1) ### Axiom % 22.96/23.18 19. (T_2 != T_1) (T_2 = T_0) (T_0 = T_1) ### Trans 17 18 % 22.96/23.18 20. (rf1 (i2003_11_14_17_21_30578) T_2) (-. (rf1 (i2003_11_14_17_21_30578) T_2)) ### Axiom % 22.96/23.18 21. (-. (rf1 (i2003_11_14_17_21_30578) T_1)) (rf1 (i2003_11_14_17_21_30578) T_1) ### Axiom % 22.96/23.18 22. (((T_2 = T_1) /\ (rf1 (i2003_11_14_17_21_30578) T_2)) => (rf1 (i2003_11_14_17_21_30578) T_1)) (-. (rf1 (i2003_11_14_17_21_30578) T_1)) (rf1 (i2003_11_14_17_21_30578) T_2) (T_0 = T_1) (T_2 = T_0) ### DisjTree 19 20 21 % 22.96/23.18 23. (All C, (((T_2 = T_1) /\ (rf1 C T_2)) => (rf1 C T_1))) (T_2 = T_0) (T_0 = T_1) (rf1 (i2003_11_14_17_21_30578) T_2) (-. (rf1 (i2003_11_14_17_21_30578) T_1)) ### All 22 % 22.96/23.18 24. (All B, (All C, (((T_2 = B) /\ (rf1 C T_2)) => (rf1 C B)))) (-. (rf1 (i2003_11_14_17_21_30578) T_1)) (rf1 (i2003_11_14_17_21_30578) T_2) (T_0 = T_1) (T_2 = T_0) ### All 23 % 22.96/23.18 25. (T_2 = T_1) (T_2 != T_1) ### Axiom % 22.96/23.18 26. (cp1 T_2) (-. (cp1 T_2)) ### Axiom % 22.96/23.18 27. (-. (cp1 T_1)) (cp1 T_1) ### Axiom % 22.96/23.18 28. (((T_2 = T_1) /\ (cp1 T_2)) => (cp1 T_1)) (-. (cp1 T_1)) (cp1 T_2) (T_2 = T_1) ### DisjTree 25 26 27 % 22.96/23.18 29. (All B, (((T_2 = B) /\ (cp1 T_2)) => (cp1 B))) (T_2 = T_1) (cp1 T_2) (-. (cp1 T_1)) ### All 28 % 22.96/23.18 30. (All A, (All B, (((A = B) /\ (cp1 A)) => (cp1 B)))) (-. (cp1 T_1)) (cp1 T_2) (T_2 = T_1) ### All 29 % 22.96/23.18 31. (-. (Ex Y, (ra_Px1 T_1 Y))) (Ex Y, (ra_Px1 T_1 Y)) ### Axiom % 22.96/23.18 32. (cp2xcomp T_1) (-. (Ex Y, (ra_Px1 T_1 Y))) ### Definition-Pseudo(cp2xcomp) 31 % 22.96/23.18 33. ((cp1 T_1) => (cp2xcomp T_1)) (-. (Ex Y, (ra_Px1 T_1 Y))) (T_2 = T_1) (cp1 T_2) (All A, (All B, (((A = B) /\ (cp1 A)) => (cp1 B)))) ### Imply 30 32 % 22.96/23.18 34. (All X, ((cp1 X) => (cp2xcomp X))) (All A, (All B, (((A = B) /\ (cp1 A)) => (cp1 B)))) (cp1 T_2) (T_2 = T_1) (-. (Ex Y, (ra_Px1 T_1 Y))) ### All 33 % 22.96/23.18 35. (((rf1 (i2003_11_14_17_21_30578) T_2) /\ (rf1 (i2003_11_14_17_21_30578) T_1)) => (T_2 = T_1)) (-. (Ex Y, (ra_Px1 T_1 Y))) (cp1 T_2) (All A, (All B, (((A = B) /\ (cp1 A)) => (cp1 B)))) (All X, ((cp1 X) => (cp2xcomp X))) (T_2 = T_0) (T_0 = T_1) (All B, (All C, (((T_2 = B) /\ (rf1 C T_2)) => (rf1 C B)))) (rf1 (i2003_11_14_17_21_30578) T_2) ### DisjTree 16 24 34 % 22.96/23.18 36. (All Y1, (((rf1 (i2003_11_14_17_21_30578) T_2) /\ (rf1 (i2003_11_14_17_21_30578) Y1)) => (T_2 = Y1))) (rf1 (i2003_11_14_17_21_30578) T_2) (All B, (All C, (((T_2 = B) /\ (rf1 C T_2)) => (rf1 C B)))) (T_0 = T_1) (T_2 = T_0) (All X, ((cp1 X) => (cp2xcomp X))) (All A, (All B, (((A = B) /\ (cp1 A)) => (cp1 B)))) (cp1 T_2) (-. (Ex Y, (ra_Px1 T_1 Y))) ### All 35 % 22.96/23.18 37. (((rf1 (i2003_11_14_17_21_30578) T_2) /\ (rf1 (i2003_11_14_17_21_30578) T_0)) => (T_2 = T_0)) (-. (Ex Y, (ra_Px1 T_1 Y))) (cp1 T_2) (All A, (All B, (((A = B) /\ (cp1 A)) => (cp1 B)))) (All X, ((cp1 X) => (cp2xcomp X))) (T_0 = T_1) (All B, (All C, (((T_2 = B) /\ (rf1 C T_2)) => (rf1 C B)))) (All Y1, (((rf1 (i2003_11_14_17_21_30578) T_2) /\ (rf1 (i2003_11_14_17_21_30578) Y1)) => (T_2 = Y1))) (rr (i2003_11_14_17_21_30578) T_0) (All X, (All Y, ((rr X Y) => (rf1 X Y)))) (rf1 (i2003_11_14_17_21_30578) T_2) ### DisjTree 10 15 36 % 22.96/23.18 38. (rf1 (i2003_11_14_17_21_30578) T_2) (All X, (All Y, ((rr X Y) => (rf1 X Y)))) (rr (i2003_11_14_17_21_30578) T_0) (All Y1, (((rf1 (i2003_11_14_17_21_30578) T_2) /\ (rf1 (i2003_11_14_17_21_30578) Y1)) => (T_2 = Y1))) (All B, (All C, (((T_2 = B) /\ (rf1 C T_2)) => (rf1 C B)))) (T_0 = T_1) (All X, ((cp1 X) => (cp2xcomp X))) (All A, (All B, (((A = B) /\ (cp1 A)) => (cp1 B)))) (cp1 T_2) (-. (Ex Y, (ra_Px1 T_1 Y))) ### All 37 % 22.96/23.18 39. (((rf2 (i2003_11_14_17_21_30578) T_0) /\ (rf2 (i2003_11_14_17_21_30578) T_1)) => (T_0 = T_1)) (-. (Ex Y, (ra_Px1 T_1 Y))) (cp1 T_2) (All A, (All B, (((A = B) /\ (cp1 A)) => (cp1 B)))) (All X, ((cp1 X) => (cp2xcomp X))) (All B, (All C, (((T_2 = B) /\ (rf1 C T_2)) => (rf1 C B)))) (All Y1, (((rf1 (i2003_11_14_17_21_30578) T_2) /\ (rf1 (i2003_11_14_17_21_30578) Y1)) => (T_2 = Y1))) (All X, (All Y, ((rr X Y) => (rf1 X Y)))) (rf1 (i2003_11_14_17_21_30578) T_2) (rf2 (i2003_11_14_17_21_30578) T_1) (rr (i2003_11_14_17_21_30578) T_0) (All X, (All Y, ((rr X Y) => (rf2 X Y)))) ### DisjTree 8 9 38 % 22.96/23.18 40. (All Y1, (((rf2 (i2003_11_14_17_21_30578) T_0) /\ (rf2 (i2003_11_14_17_21_30578) Y1)) => (T_0 = Y1))) (All X, (All Y, ((rr X Y) => (rf2 X Y)))) (rr (i2003_11_14_17_21_30578) T_0) (rf2 (i2003_11_14_17_21_30578) T_1) (rf1 (i2003_11_14_17_21_30578) T_2) (All X, (All Y, ((rr X Y) => (rf1 X Y)))) (All Y1, (((rf1 (i2003_11_14_17_21_30578) T_2) /\ (rf1 (i2003_11_14_17_21_30578) Y1)) => (T_2 = Y1))) (All B, (All C, (((T_2 = B) /\ (rf1 C T_2)) => (rf1 C B)))) (All X, ((cp1 X) => (cp2xcomp X))) (All A, (All B, (((A = B) /\ (cp1 A)) => (cp1 B)))) (cp1 T_2) (-. (Ex Y, (ra_Px1 T_1 Y))) ### All 39 % 22.96/23.18 41. (All Y0, (All Y1, (((rf2 (i2003_11_14_17_21_30578) Y0) /\ (rf2 (i2003_11_14_17_21_30578) Y1)) => (Y0 = Y1)))) (-. (Ex Y, (ra_Px1 T_1 Y))) (cp1 T_2) (All A, (All B, (((A = B) /\ (cp1 A)) => (cp1 B)))) (All X, ((cp1 X) => (cp2xcomp X))) (All B, (All C, (((T_2 = B) /\ (rf1 C T_2)) => (rf1 C B)))) (All Y1, (((rf1 (i2003_11_14_17_21_30578) T_2) /\ (rf1 (i2003_11_14_17_21_30578) Y1)) => (T_2 = Y1))) (All X, (All Y, ((rr X Y) => (rf1 X Y)))) (rf1 (i2003_11_14_17_21_30578) T_2) (rf2 (i2003_11_14_17_21_30578) T_1) (rr (i2003_11_14_17_21_30578) T_0) (All X, (All Y, ((rr X Y) => (rf2 X Y)))) ### All 40 % 22.96/23.18 42. (All Y0, (All Y1, (((rf1 (i2003_11_14_17_21_30578) Y0) /\ (rf1 (i2003_11_14_17_21_30578) Y1)) => (Y0 = Y1)))) (All X, (All Y, ((rr X Y) => (rf2 X Y)))) (rr (i2003_11_14_17_21_30578) T_0) (rf2 (i2003_11_14_17_21_30578) T_1) (rf1 (i2003_11_14_17_21_30578) T_2) (All X, (All Y, ((rr X Y) => (rf1 X Y)))) (All B, (All C, (((T_2 = B) /\ (rf1 C T_2)) => (rf1 C B)))) (All X, ((cp1 X) => (cp2xcomp X))) (All A, (All B, (((A = B) /\ (cp1 A)) => (cp1 B)))) (cp1 T_2) (-. (Ex Y, (ra_Px1 T_1 Y))) (All Y0, (All Y1, (((rf2 (i2003_11_14_17_21_30578) Y0) /\ (rf2 (i2003_11_14_17_21_30578) Y1)) => (Y0 = Y1)))) ### All 41 % 22.96/23.18 43. ((cowlThing (i2003_11_14_17_21_30578)) => (All Y0, (All Y1, (((rf2 (i2003_11_14_17_21_30578) Y0) /\ (rf2 (i2003_11_14_17_21_30578) Y1)) => (Y0 = Y1))))) (-. (Ex Y, (ra_Px1 T_1 Y))) (cp1 T_2) (All A, (All B, (((A = B) /\ (cp1 A)) => (cp1 B)))) (All X, ((cp1 X) => (cp2xcomp X))) (All B, (All C, (((T_2 = B) /\ (rf1 C T_2)) => (rf1 C B)))) (All X, (All Y, ((rr X Y) => (rf1 X Y)))) (rf1 (i2003_11_14_17_21_30578) T_2) (rf2 (i2003_11_14_17_21_30578) T_1) (rr (i2003_11_14_17_21_30578) T_0) (All X, (All Y, ((rr X Y) => (rf2 X Y)))) (All Y0, (All Y1, (((rf1 (i2003_11_14_17_21_30578) Y0) /\ (rf1 (i2003_11_14_17_21_30578) Y1)) => (Y0 = Y1)))) (All X, ((cowlThing X) /\ (-. (cowlNothing X)))) ### Imply 3 42 % 22.96/23.19 44. (All X, ((cowlThing X) => (All Y0, (All Y1, (((rf2 X Y0) /\ (rf2 X Y1)) => (Y0 = Y1)))))) (All X, ((cowlThing X) /\ (-. (cowlNothing X)))) (All Y0, (All Y1, (((rf1 (i2003_11_14_17_21_30578) Y0) /\ (rf1 (i2003_11_14_17_21_30578) Y1)) => (Y0 = Y1)))) (All X, (All Y, ((rr X Y) => (rf2 X Y)))) (rr (i2003_11_14_17_21_30578) T_0) (rf2 (i2003_11_14_17_21_30578) T_1) (rf1 (i2003_11_14_17_21_30578) T_2) (All X, (All Y, ((rr X Y) => (rf1 X Y)))) (All B, (All C, (((T_2 = B) /\ (rf1 C T_2)) => (rf1 C B)))) (All X, ((cp1 X) => (cp2xcomp X))) (All A, (All B, (((A = B) /\ (cp1 A)) => (cp1 B)))) (cp1 T_2) (-. (Ex Y, (ra_Px1 T_1 Y))) ### All 43 % 22.96/23.19 45. ((cowlThing (i2003_11_14_17_21_30578)) => (All Y0, (All Y1, (((rf1 (i2003_11_14_17_21_30578) Y0) /\ (rf1 (i2003_11_14_17_21_30578) Y1)) => (Y0 = Y1))))) (-. (Ex Y, (ra_Px1 T_1 Y))) (cp1 T_2) (All A, (All B, (((A = B) /\ (cp1 A)) => (cp1 B)))) (All X, ((cp1 X) => (cp2xcomp X))) (All B, (All C, (((T_2 = B) /\ (rf1 C T_2)) => (rf1 C B)))) (All X, (All Y, ((rr X Y) => (rf1 X Y)))) (rf1 (i2003_11_14_17_21_30578) T_2) (rf2 (i2003_11_14_17_21_30578) T_1) (rr (i2003_11_14_17_21_30578) T_0) (All X, (All Y, ((rr X Y) => (rf2 X Y)))) (All X, ((cowlThing X) => (All Y0, (All Y1, (((rf2 X Y0) /\ (rf2 X Y1)) => (Y0 = Y1)))))) (All X, ((cowlThing X) /\ (-. (cowlNothing X)))) ### Imply 3 44 % 22.96/23.19 46. (All X, ((cowlThing X) => (All Y0, (All Y1, (((rf1 X Y0) /\ (rf1 X Y1)) => (Y0 = Y1)))))) (All X, ((cowlThing X) /\ (-. (cowlNothing X)))) (All X, ((cowlThing X) => (All Y0, (All Y1, (((rf2 X Y0) /\ (rf2 X Y1)) => (Y0 = Y1)))))) (All X, (All Y, ((rr X Y) => (rf2 X Y)))) (rr (i2003_11_14_17_21_30578) T_0) (rf2 (i2003_11_14_17_21_30578) T_1) (rf1 (i2003_11_14_17_21_30578) T_2) (All X, (All Y, ((rr X Y) => (rf1 X Y)))) (All B, (All C, (((T_2 = B) /\ (rf1 C T_2)) => (rf1 C B)))) (All X, ((cp1 X) => (cp2xcomp X))) (All A, (All B, (((A = B) /\ (cp1 A)) => (cp1 B)))) (cp1 T_2) (-. (Ex Y, (ra_Px1 T_1 Y))) ### All 45 % 22.96/23.19 47. (All A, (All B, (All C, (((A = B) /\ (rf1 C A)) => (rf1 C B))))) (-. (Ex Y, (ra_Px1 T_1 Y))) (cp1 T_2) (All A, (All B, (((A = B) /\ (cp1 A)) => (cp1 B)))) (All X, ((cp1 X) => (cp2xcomp X))) (All X, (All Y, ((rr X Y) => (rf1 X Y)))) (rf1 (i2003_11_14_17_21_30578) T_2) (rf2 (i2003_11_14_17_21_30578) T_1) (rr (i2003_11_14_17_21_30578) T_0) (All X, (All Y, ((rr X Y) => (rf2 X Y)))) (All X, ((cowlThing X) => (All Y0, (All Y1, (((rf2 X Y0) /\ (rf2 X Y1)) => (Y0 = Y1)))))) (All X, ((cowlThing X) /\ (-. (cowlNothing X)))) (All X, ((cowlThing X) => (All Y0, (All Y1, (((rf1 X Y0) /\ (rf1 X Y1)) => (Y0 = Y1)))))) ### All 46 % 22.96/23.19 48. ((rr (i2003_11_14_17_21_30578) T_0) /\ (cowlThing T_0)) (All X, ((cowlThing X) => (All Y0, (All Y1, (((rf1 X Y0) /\ (rf1 X Y1)) => (Y0 = Y1)))))) (All X, ((cowlThing X) /\ (-. (cowlNothing X)))) (All X, ((cowlThing X) => (All Y0, (All Y1, (((rf2 X Y0) /\ (rf2 X Y1)) => (Y0 = Y1)))))) (All X, (All Y, ((rr X Y) => (rf2 X Y)))) (rf2 (i2003_11_14_17_21_30578) T_1) (rf1 (i2003_11_14_17_21_30578) T_2) (All X, (All Y, ((rr X Y) => (rf1 X Y)))) (All X, ((cp1 X) => (cp2xcomp X))) (All A, (All B, (((A = B) /\ (cp1 A)) => (cp1 B)))) (cp1 T_2) (-. (Ex Y, (ra_Px1 T_1 Y))) (All A, (All B, (All C, (((A = B) /\ (rf1 C A)) => (rf1 C B))))) ### And 47 % 22.96/23.19 49. (Ex Y, ((rr (i2003_11_14_17_21_30578) Y) /\ (cowlThing Y))) (All A, (All B, (All C, (((A = B) /\ (rf1 C A)) => (rf1 C B))))) (-. (Ex Y, (ra_Px1 T_1 Y))) (cp1 T_2) (All A, (All B, (((A = B) /\ (cp1 A)) => (cp1 B)))) (All X, ((cp1 X) => (cp2xcomp X))) (All X, (All Y, ((rr X Y) => (rf1 X Y)))) (rf1 (i2003_11_14_17_21_30578) T_2) (rf2 (i2003_11_14_17_21_30578) T_1) (All X, (All Y, ((rr X Y) => (rf2 X Y)))) (All X, ((cowlThing X) => (All Y0, (All Y1, (((rf2 X Y0) /\ (rf2 X Y1)) => (Y0 = Y1)))))) (All X, ((cowlThing X) /\ (-. (cowlNothing X)))) (All X, ((cowlThing X) => (All Y0, (All Y1, (((rf1 X Y0) /\ (rf1 X Y1)) => (Y0 = Y1)))))) ### Exists 48 % 22.96/23.19 50. ((rf1 (i2003_11_14_17_21_30578) T_2) /\ (cp1 T_2)) (All X, ((cowlThing X) => (All Y0, (All Y1, (((rf1 X Y0) /\ (rf1 X Y1)) => (Y0 = Y1)))))) (All X, ((cowlThing X) /\ (-. (cowlNothing X)))) (All X, ((cowlThing X) => (All Y0, (All Y1, (((rf2 X Y0) /\ (rf2 X Y1)) => (Y0 = Y1)))))) (All X, (All Y, ((rr X Y) => (rf2 X Y)))) (rf2 (i2003_11_14_17_21_30578) T_1) (All X, (All Y, ((rr X Y) => (rf1 X Y)))) (All X, ((cp1 X) => (cp2xcomp X))) (All A, (All B, (((A = B) /\ (cp1 A)) => (cp1 B)))) (-. (Ex Y, (ra_Px1 T_1 Y))) (All A, (All B, (All C, (((A = B) /\ (rf1 C A)) => (rf1 C B))))) (Ex Y, ((rr (i2003_11_14_17_21_30578) Y) /\ (cowlThing Y))) ### And 49 % 22.96/23.19 51. (Ex Y, ((rf1 (i2003_11_14_17_21_30578) Y) /\ (cp1 Y))) (Ex Y, ((rr (i2003_11_14_17_21_30578) Y) /\ (cowlThing Y))) (All A, (All B, (All C, (((A = B) /\ (rf1 C A)) => (rf1 C B))))) (-. (Ex Y, (ra_Px1 T_1 Y))) (All A, (All B, (((A = B) /\ (cp1 A)) => (cp1 B)))) (All X, ((cp1 X) => (cp2xcomp X))) (All X, (All Y, ((rr X Y) => (rf1 X Y)))) (rf2 (i2003_11_14_17_21_30578) T_1) (All X, (All Y, ((rr X Y) => (rf2 X Y)))) (All X, ((cowlThing X) => (All Y0, (All Y1, (((rf2 X Y0) /\ (rf2 X Y1)) => (Y0 = Y1)))))) (All X, ((cowlThing X) /\ (-. (cowlNothing X)))) (All X, ((cowlThing X) => (All Y0, (All Y1, (((rf1 X Y0) /\ (rf1 X Y1)) => (Y0 = Y1)))))) ### Exists 50 % 22.96/23.19 52. (cp2 T_1) (All X, ((cowlThing X) => (All Y0, (All Y1, (((rf1 X Y0) /\ (rf1 X Y1)) => (Y0 = Y1)))))) (All X, ((cowlThing X) /\ (-. (cowlNothing X)))) (All X, ((cowlThing X) => (All Y0, (All Y1, (((rf2 X Y0) /\ (rf2 X Y1)) => (Y0 = Y1)))))) (All X, (All Y, ((rr X Y) => (rf2 X Y)))) (rf2 (i2003_11_14_17_21_30578) T_1) (All X, (All Y, ((rr X Y) => (rf1 X Y)))) (All X, ((cp1 X) => (cp2xcomp X))) (All A, (All B, (((A = B) /\ (cp1 A)) => (cp1 B)))) (All A, (All B, (All C, (((A = B) /\ (rf1 C A)) => (rf1 C B))))) (Ex Y, ((rr (i2003_11_14_17_21_30578) Y) /\ (cowlThing Y))) (Ex Y, ((rf1 (i2003_11_14_17_21_30578) Y) /\ (cp1 Y))) ### Definition-Pseudo(cp2) 51 % 22.96/23.19 53. ((rf2 (i2003_11_14_17_21_30578) T_1) /\ (cp2 T_1)) (Ex Y, ((rf1 (i2003_11_14_17_21_30578) Y) /\ (cp1 Y))) (Ex Y, ((rr (i2003_11_14_17_21_30578) Y) /\ (cowlThing Y))) (All A, (All B, (All C, (((A = B) /\ (rf1 C A)) => (rf1 C B))))) (All A, (All B, (((A = B) /\ (cp1 A)) => (cp1 B)))) (All X, ((cp1 X) => (cp2xcomp X))) (All X, (All Y, ((rr X Y) => (rf1 X Y)))) (All X, (All Y, ((rr X Y) => (rf2 X Y)))) (All X, ((cowlThing X) => (All Y0, (All Y1, (((rf2 X Y0) /\ (rf2 X Y1)) => (Y0 = Y1)))))) (All X, ((cowlThing X) /\ (-. (cowlNothing X)))) (All X, ((cowlThing X) => (All Y0, (All Y1, (((rf1 X Y0) /\ (rf1 X Y1)) => (Y0 = Y1)))))) ### And 52 % 22.96/23.19 54. (Ex Y, ((rf2 (i2003_11_14_17_21_30578) Y) /\ (cp2 Y))) (All X, ((cowlThing X) => (All Y0, (All Y1, (((rf1 X Y0) /\ (rf1 X Y1)) => (Y0 = Y1)))))) (All X, ((cowlThing X) /\ (-. (cowlNothing X)))) (All X, ((cowlThing X) => (All Y0, (All Y1, (((rf2 X Y0) /\ (rf2 X Y1)) => (Y0 = Y1)))))) (All X, (All Y, ((rr X Y) => (rf2 X Y)))) (All X, (All Y, ((rr X Y) => (rf1 X Y)))) (All X, ((cp1 X) => (cp2xcomp X))) (All A, (All B, (((A = B) /\ (cp1 A)) => (cp1 B)))) (All A, (All B, (All C, (((A = B) /\ (rf1 C A)) => (rf1 C B))))) (Ex Y, ((rr (i2003_11_14_17_21_30578) Y) /\ (cowlThing Y))) (Ex Y, ((rf1 (i2003_11_14_17_21_30578) Y) /\ (cp1 Y))) ### Exists 53 % 22.96/23.19 55. ((Ex Y, ((rf2 (i2003_11_14_17_21_30578) Y) /\ (cp2 Y))) /\ ((Ex Y, ((rf1 (i2003_11_14_17_21_30578) Y) /\ (cp1 Y))) /\ (Ex Y, ((rr (i2003_11_14_17_21_30578) Y) /\ (cowlThing Y))))) (All A, (All B, (All C, (((A = B) /\ (rf1 C A)) => (rf1 C B))))) (All A, (All B, (((A = B) /\ (cp1 A)) => (cp1 B)))) (All X, ((cp1 X) => (cp2xcomp X))) (All X, (All Y, ((rr X Y) => (rf1 X Y)))) (All X, (All Y, ((rr X Y) => (rf2 X Y)))) (All X, ((cowlThing X) => (All Y0, (All Y1, (((rf2 X Y0) /\ (rf2 X Y1)) => (Y0 = Y1)))))) (All X, ((cowlThing X) /\ (-. (cowlNothing X)))) (All X, ((cowlThing X) => (All Y0, (All Y1, (((rf1 X Y0) /\ (rf1 X Y1)) => (Y0 = Y1)))))) ### ConjTree 54 % 23.00/23.20 56. (cUnsatisfiable (i2003_11_14_17_21_30578)) (All X, ((cowlThing X) => (All Y0, (All Y1, (((rf1 X Y0) /\ (rf1 X Y1)) => (Y0 = Y1)))))) (All X, ((cowlThing X) /\ (-. (cowlNothing X)))) (All X, ((cowlThing X) => (All Y0, (All Y1, (((rf2 X Y0) /\ (rf2 X Y1)) => (Y0 = Y1)))))) (All X, (All Y, ((rr X Y) => (rf2 X Y)))) (All X, (All Y, ((rr X Y) => (rf1 X Y)))) (All X, ((cp1 X) => (cp2xcomp X))) (All A, (All B, (((A = B) /\ (cp1 A)) => (cp1 B)))) (All A, (All B, (All C, (((A = B) /\ (rf1 C A)) => (rf1 C B))))) ### Definition-Pseudo(cUnsatisfiable) 55 % 23.00/23.20 % SZS output end Proof % 23.00/23.20 (* END-PROOF *) %------------------------------------------------------------------------------