TSTP Solution File: KRS098+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : KRS098+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 : n021.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 03:31:53 EDT 2022
% Result : Unsatisfiable 134.01s 134.27s
% Output : Proof 134.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KRS098+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 : n021.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 20:01:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 134.01/134.27 % SZS status Theorem
% 134.01/134.27 (* PROOF-FOUND *)
% 134.01/134.27 (* BEGIN-PROOF *)
% 134.01/134.27 % SZS output start Proof
% 134.01/134.27 1. (rr1 (i2003_11_14_17_20_25524) T_0) (-. (rr1 (i2003_11_14_17_20_25524) T_0)) ### Axiom
% 134.01/134.27 2. (-. (rr (i2003_11_14_17_20_25524) T_0)) (rr (i2003_11_14_17_20_25524) T_0) ### Axiom
% 134.01/134.27 3. ((rr1 (i2003_11_14_17_20_25524) T_0) => (rr (i2003_11_14_17_20_25524) T_0)) (-. (rr (i2003_11_14_17_20_25524) T_0)) (rr1 (i2003_11_14_17_20_25524) T_0) ### Imply 1 2
% 134.01/134.27 4. (All Y, ((rr1 (i2003_11_14_17_20_25524) Y) => (rr (i2003_11_14_17_20_25524) Y))) (rr1 (i2003_11_14_17_20_25524) T_0) (-. (rr (i2003_11_14_17_20_25524) T_0)) ### All 3
% 134.01/134.27 5. (All X, (All Y, ((rr1 X Y) => (rr X Y)))) (-. (rr (i2003_11_14_17_20_25524) T_0)) (rr1 (i2003_11_14_17_20_25524) T_0) ### All 4
% 134.01/134.27 6. (rr3 (i2003_11_14_17_20_25524) T_1) (-. (rr3 (i2003_11_14_17_20_25524) T_1)) ### Axiom
% 134.01/134.27 7. (-. (rr (i2003_11_14_17_20_25524) T_1)) (rr (i2003_11_14_17_20_25524) T_1) ### Axiom
% 134.01/134.27 8. ((rr3 (i2003_11_14_17_20_25524) T_1) => (rr (i2003_11_14_17_20_25524) T_1)) (-. (rr (i2003_11_14_17_20_25524) T_1)) (rr3 (i2003_11_14_17_20_25524) T_1) ### Imply 6 7
% 134.01/134.27 9. (All Y, ((rr3 (i2003_11_14_17_20_25524) Y) => (rr (i2003_11_14_17_20_25524) Y))) (rr3 (i2003_11_14_17_20_25524) T_1) (-. (rr (i2003_11_14_17_20_25524) T_1)) ### All 8
% 134.01/134.27 10. (All X, (All Y, ((rr3 X Y) => (rr X Y)))) (-. (rr (i2003_11_14_17_20_25524) T_1)) (rr3 (i2003_11_14_17_20_25524) T_1) ### All 9
% 134.01/134.27 11. (rt1 T_0 T_2) (-. (rt1 T_0 T_2)) ### Axiom
% 134.01/134.27 12. (-. (rtt T_0 T_2)) (rtt T_0 T_2) ### Axiom
% 134.01/134.27 13. ((rt1 T_0 T_2) => (rtt T_0 T_2)) (-. (rtt T_0 T_2)) (rt1 T_0 T_2) ### Imply 11 12
% 134.01/134.27 14. (All Y, ((rt1 T_0 Y) => (rtt T_0 Y))) (rt1 T_0 T_2) (-. (rtt T_0 T_2)) ### All 13
% 134.01/134.27 15. (All X, (All Y, ((rt1 X Y) => (rtt X Y)))) (-. (rtt T_0 T_2)) (rt1 T_0 T_2) ### All 14
% 134.01/134.27 16. (T_3 != T_3) ### Refl(=)
% 134.01/134.27 17. (rt3 T_1 T_3) (-. (rt3 T_1 T_3)) ### Axiom
% 134.01/134.27 18. (-. (rtt T_1 T_3)) (rtt T_1 T_3) ### Axiom
% 134.01/134.27 19. ((rt3 T_1 T_3) => (rtt T_1 T_3)) (-. (rtt T_1 T_3)) (rt3 T_1 T_3) ### Imply 17 18
% 134.01/134.27 20. (All Y, ((rt3 T_1 Y) => (rtt T_1 Y))) (rt3 T_1 T_3) (-. (rtt T_1 T_3)) ### All 19
% 134.01/134.27 21. (T_0 = T_1) (T_1 != T_0) ### Sym(=)
% 134.01/134.27 22. (rtt T_1 T_3) (-. (rtt T_1 T_3)) ### Axiom
% 134.01/134.27 23. (-. (rtt T_0 T_3)) (rtt T_0 T_3) ### Axiom
% 134.01/134.27 24. (((T_1 = T_0) /\ (rtt T_1 T_3)) => (rtt T_0 T_3)) (-. (rtt T_0 T_3)) (rtt T_1 T_3) (T_0 = T_1) ### DisjTree 21 22 23
% 134.01/134.27 25. (All C, (((T_1 = T_0) /\ (rtt T_1 C)) => (rtt T_0 C))) (T_0 = T_1) (rtt T_1 T_3) (-. (rtt T_0 T_3)) ### All 24
% 134.01/134.27 26. (All B, (All C, (((T_1 = B) /\ (rtt T_1 C)) => (rtt B C)))) (-. (rtt T_0 T_3)) (rtt T_1 T_3) (T_0 = T_1) ### All 25
% 134.01/134.27 27. (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (T_0 = T_1) (rtt T_1 T_3) (-. (rtt T_0 T_3)) ### All 26
% 134.01/134.27 28. (((T_3 = T_3) /\ (rtt T_1 T_3)) => (rtt T_1 T_3)) (-. (rtt T_0 T_3)) (T_0 = T_1) (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (rt3 T_1 T_3) (All Y, ((rt3 T_1 Y) => (rtt T_1 Y))) ### DisjTree 16 20 27
% 134.01/134.27 29. (All C, (((T_3 = T_3) /\ (rtt C T_3)) => (rtt C T_3))) (All Y, ((rt3 T_1 Y) => (rtt T_1 Y))) (rt3 T_1 T_3) (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (T_0 = T_1) (-. (rtt T_0 T_3)) ### All 28
% 134.01/134.27 30. (All B, (All C, (((T_3 = B) /\ (rtt C T_3)) => (rtt C B)))) (-. (rtt T_0 T_3)) (T_0 = T_1) (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (rt3 T_1 T_3) (All Y, ((rt3 T_1 Y) => (rtt T_1 Y))) ### All 29
% 134.01/134.27 31. (All X, (All Y, ((rt3 X Y) => (rtt X Y)))) (rt3 T_1 T_3) (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (T_0 = T_1) (-. (rtt T_0 T_3)) (All B, (All C, (((T_3 = B) /\ (rtt C T_3)) => (rtt C B)))) ### All 30
% 134.01/134.27 32. (T_3 != T_2) (T_2 = T_3) ### Sym(=)
% 134.01/134.27 33. (((rtt T_0 T_2) /\ (rtt T_0 T_3)) => (T_2 = T_3)) (T_3 != T_2) (All B, (All C, (((T_3 = B) /\ (rtt C T_3)) => (rtt C B)))) (T_0 = T_1) (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (rt3 T_1 T_3) (All X, (All Y, ((rt3 X Y) => (rtt X Y)))) (rt1 T_0 T_2) (All X, (All Y, ((rt1 X Y) => (rtt X Y)))) ### DisjTree 15 31 32
% 134.01/134.27 34. (All Z1, (((rtt T_0 T_2) /\ (rtt T_0 Z1)) => (T_2 = Z1))) (All X, (All Y, ((rt1 X Y) => (rtt X Y)))) (rt1 T_0 T_2) (All X, (All Y, ((rt3 X Y) => (rtt X Y)))) (rt3 T_1 T_3) (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (T_0 = T_1) (All B, (All C, (((T_3 = B) /\ (rtt C T_3)) => (rtt C B)))) (T_3 != T_2) ### All 33
% 134.01/134.27 35. (-. ((rr (i2003_11_14_17_20_25524) T_0) /\ ((rr (i2003_11_14_17_20_25524) T_1) /\ (T_0 != T_1)))) (T_3 != T_2) (All B, (All C, (((T_3 = B) /\ (rtt C T_3)) => (rtt C B)))) (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (rt3 T_1 T_3) (All X, (All Y, ((rt3 X Y) => (rtt X Y)))) (rt1 T_0 T_2) (All X, (All Y, ((rt1 X Y) => (rtt X Y)))) (All Z1, (((rtt T_0 T_2) /\ (rtt T_0 Z1)) => (T_2 = Z1))) (rr3 (i2003_11_14_17_20_25524) T_1) (All X, (All Y, ((rr3 X Y) => (rr X Y)))) (rr1 (i2003_11_14_17_20_25524) T_0) (All X, (All Y, ((rr1 X Y) => (rr X Y)))) ### DisjTree 5 10 34
% 134.01/134.27 36. (-. (Ex Y1, ((rr (i2003_11_14_17_20_25524) T_0) /\ ((rr (i2003_11_14_17_20_25524) Y1) /\ (T_0 != Y1))))) (All X, (All Y, ((rr1 X Y) => (rr X Y)))) (rr1 (i2003_11_14_17_20_25524) T_0) (All X, (All Y, ((rr3 X Y) => (rr X Y)))) (rr3 (i2003_11_14_17_20_25524) T_1) (All Z1, (((rtt T_0 T_2) /\ (rtt T_0 Z1)) => (T_2 = Z1))) (All X, (All Y, ((rt1 X Y) => (rtt X Y)))) (rt1 T_0 T_2) (All X, (All Y, ((rt3 X Y) => (rtt X Y)))) (rt3 T_1 T_3) (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (All B, (All C, (((T_3 = B) /\ (rtt C T_3)) => (rtt C B)))) (T_3 != T_2) ### NotExists 35
% 134.01/134.27 37. (ce T_3) (-. (ce T_3)) ### Axiom
% 134.01/134.27 38. (-. (ce T_2)) (ce T_2) ### Axiom
% 134.01/134.27 39. (((T_3 = T_2) /\ (ce T_3)) => (ce T_2)) (-. (ce T_2)) (ce T_3) (All B, (All C, (((T_3 = B) /\ (rtt C T_3)) => (rtt C B)))) (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (rt3 T_1 T_3) (All X, (All Y, ((rt3 X Y) => (rtt X Y)))) (rt1 T_0 T_2) (All X, (All Y, ((rt1 X Y) => (rtt X Y)))) (All Z1, (((rtt T_0 T_2) /\ (rtt T_0 Z1)) => (T_2 = Z1))) (rr3 (i2003_11_14_17_20_25524) T_1) (All X, (All Y, ((rr3 X Y) => (rr X Y)))) (rr1 (i2003_11_14_17_20_25524) T_0) (All X, (All Y, ((rr1 X Y) => (rr X Y)))) (-. (Ex Y1, ((rr (i2003_11_14_17_20_25524) T_0) /\ ((rr (i2003_11_14_17_20_25524) Y1) /\ (T_0 != Y1))))) ### DisjTree 36 37 38
% 134.01/134.27 40. (All B, (((T_3 = B) /\ (ce T_3)) => (ce B))) (-. (Ex Y1, ((rr (i2003_11_14_17_20_25524) T_0) /\ ((rr (i2003_11_14_17_20_25524) Y1) /\ (T_0 != Y1))))) (All X, (All Y, ((rr1 X Y) => (rr X Y)))) (rr1 (i2003_11_14_17_20_25524) T_0) (All X, (All Y, ((rr3 X Y) => (rr X Y)))) (rr3 (i2003_11_14_17_20_25524) T_1) (All Z1, (((rtt T_0 T_2) /\ (rtt T_0 Z1)) => (T_2 = Z1))) (All X, (All Y, ((rt1 X Y) => (rtt X Y)))) (rt1 T_0 T_2) (All X, (All Y, ((rt3 X Y) => (rtt X Y)))) (rt3 T_1 T_3) (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (All B, (All C, (((T_3 = B) /\ (rtt C T_3)) => (rtt C B)))) (ce T_3) (-. (ce T_2)) ### All 39
% 134.01/134.27 41. (All A, (All B, (All C, (((A = B) /\ (rtt C A)) => (rtt C B))))) (-. (ce T_2)) (ce T_3) (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (rt3 T_1 T_3) (All X, (All Y, ((rt3 X Y) => (rtt X Y)))) (rt1 T_0 T_2) (All X, (All Y, ((rt1 X Y) => (rtt X Y)))) (All Z1, (((rtt T_0 T_2) /\ (rtt T_0 Z1)) => (T_2 = Z1))) (rr3 (i2003_11_14_17_20_25524) T_1) (All X, (All Y, ((rr3 X Y) => (rr X Y)))) (rr1 (i2003_11_14_17_20_25524) T_0) (All X, (All Y, ((rr1 X Y) => (rr X Y)))) (-. (Ex Y1, ((rr (i2003_11_14_17_20_25524) T_0) /\ ((rr (i2003_11_14_17_20_25524) Y1) /\ (T_0 != Y1))))) (All B, (((T_3 = B) /\ (ce T_3)) => (ce B))) ### All 40
% 134.01/134.27 42. (All A, (All B, (((A = B) /\ (ce A)) => (ce B)))) (-. (Ex Y1, ((rr (i2003_11_14_17_20_25524) T_0) /\ ((rr (i2003_11_14_17_20_25524) Y1) /\ (T_0 != Y1))))) (All X, (All Y, ((rr1 X Y) => (rr X Y)))) (rr1 (i2003_11_14_17_20_25524) T_0) (All X, (All Y, ((rr3 X Y) => (rr X Y)))) (rr3 (i2003_11_14_17_20_25524) T_1) (All Z1, (((rtt T_0 T_2) /\ (rtt T_0 Z1)) => (T_2 = Z1))) (All X, (All Y, ((rt1 X Y) => (rtt X Y)))) (rt1 T_0 T_2) (All X, (All Y, ((rt3 X Y) => (rtt X Y)))) (rt3 T_1 T_3) (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (ce T_3) (-. (ce T_2)) (All A, (All B, (All C, (((A = B) /\ (rtt C A)) => (rtt C B))))) ### All 41
% 134.01/134.27 43. (-. (Ex Y0, (Ex Y1, ((rr (i2003_11_14_17_20_25524) Y0) /\ ((rr (i2003_11_14_17_20_25524) Y1) /\ (Y0 != Y1)))))) (All A, (All B, (All C, (((A = B) /\ (rtt C A)) => (rtt C B))))) (-. (ce T_2)) (ce T_3) (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (rt3 T_1 T_3) (All X, (All Y, ((rt3 X Y) => (rtt X Y)))) (rt1 T_0 T_2) (All X, (All Y, ((rt1 X Y) => (rtt X Y)))) (All Z1, (((rtt T_0 T_2) /\ (rtt T_0 Z1)) => (T_2 = Z1))) (rr3 (i2003_11_14_17_20_25524) T_1) (All X, (All Y, ((rr3 X Y) => (rr X Y)))) (rr1 (i2003_11_14_17_20_25524) T_0) (All X, (All Y, ((rr1 X Y) => (rr X Y)))) (All A, (All B, (((A = B) /\ (ce A)) => (ce B)))) ### NotExists 42
% 134.09/134.30 44. (All Z0, (All Z1, (((rtt T_0 Z0) /\ (rtt T_0 Z1)) => (Z0 = Z1)))) (All A, (All B, (((A = B) /\ (ce A)) => (ce B)))) (All X, (All Y, ((rr1 X Y) => (rr X Y)))) (rr1 (i2003_11_14_17_20_25524) T_0) (All X, (All Y, ((rr3 X Y) => (rr X Y)))) (rr3 (i2003_11_14_17_20_25524) T_1) (All X, (All Y, ((rt1 X Y) => (rtt X Y)))) (rt1 T_0 T_2) (All X, (All Y, ((rt3 X Y) => (rtt X Y)))) (rt3 T_1 T_3) (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (ce T_3) (-. (ce T_2)) (All A, (All B, (All C, (((A = B) /\ (rtt C A)) => (rtt C B))))) (-. (Ex Y0, (Ex Y1, ((rr (i2003_11_14_17_20_25524) Y0) /\ ((rr (i2003_11_14_17_20_25524) Y1) /\ (Y0 != Y1)))))) ### All 43
% 134.09/134.30 45. (cc T_2) (-. (cc T_2)) ### Axiom
% 134.09/134.30 46. (-. ((ce T_2) /\ (cc T_2))) (cc T_2) (-. (Ex Y0, (Ex Y1, ((rr (i2003_11_14_17_20_25524) Y0) /\ ((rr (i2003_11_14_17_20_25524) Y1) /\ (Y0 != Y1)))))) (All A, (All B, (All C, (((A = B) /\ (rtt C A)) => (rtt C B))))) (ce T_3) (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (rt3 T_1 T_3) (All X, (All Y, ((rt3 X Y) => (rtt X Y)))) (rt1 T_0 T_2) (All X, (All Y, ((rt1 X Y) => (rtt X Y)))) (rr3 (i2003_11_14_17_20_25524) T_1) (All X, (All Y, ((rr3 X Y) => (rr X Y)))) (rr1 (i2003_11_14_17_20_25524) T_0) (All X, (All Y, ((rr1 X Y) => (rr X Y)))) (All A, (All B, (((A = B) /\ (ce A)) => (ce B)))) (All Z0, (All Z1, (((rtt T_0 Z0) /\ (rtt T_0 Z1)) => (Z0 = Z1)))) ### NotAnd 44 45
% 134.09/134.30 47. (All X, (-. ((ce X) /\ (cc X)))) (All Z0, (All Z1, (((rtt T_0 Z0) /\ (rtt T_0 Z1)) => (Z0 = Z1)))) (All A, (All B, (((A = B) /\ (ce A)) => (ce B)))) (All X, (All Y, ((rr1 X Y) => (rr X Y)))) (rr1 (i2003_11_14_17_20_25524) T_0) (All X, (All Y, ((rr3 X Y) => (rr X Y)))) (rr3 (i2003_11_14_17_20_25524) T_1) (All X, (All Y, ((rt1 X Y) => (rtt X Y)))) (rt1 T_0 T_2) (All X, (All Y, ((rt3 X Y) => (rtt X Y)))) (rt3 T_1 T_3) (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (ce T_3) (All A, (All B, (All C, (((A = B) /\ (rtt C A)) => (rtt C B))))) (-. (Ex Y0, (Ex Y1, ((rr (i2003_11_14_17_20_25524) Y0) /\ ((rr (i2003_11_14_17_20_25524) Y1) /\ (Y0 != Y1)))))) (cc T_2) ### All 46
% 134.09/134.30 48. ((rt1 T_0 T_2) /\ (cc T_2)) (-. (Ex Y0, (Ex Y1, ((rr (i2003_11_14_17_20_25524) Y0) /\ ((rr (i2003_11_14_17_20_25524) Y1) /\ (Y0 != Y1)))))) (All A, (All B, (All C, (((A = B) /\ (rtt C A)) => (rtt C B))))) (ce T_3) (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (rt3 T_1 T_3) (All X, (All Y, ((rt3 X Y) => (rtt X Y)))) (All X, (All Y, ((rt1 X Y) => (rtt X Y)))) (rr3 (i2003_11_14_17_20_25524) T_1) (All X, (All Y, ((rr3 X Y) => (rr X Y)))) (rr1 (i2003_11_14_17_20_25524) T_0) (All X, (All Y, ((rr1 X Y) => (rr X Y)))) (All A, (All B, (((A = B) /\ (ce A)) => (ce B)))) (All Z0, (All Z1, (((rtt T_0 Z0) /\ (rtt T_0 Z1)) => (Z0 = Z1)))) (All X, (-. ((ce X) /\ (cc X)))) ### And 47
% 134.09/134.30 49. (Ex Z, ((rt1 T_0 Z) /\ (cc Z))) (All X, (-. ((ce X) /\ (cc X)))) (All Z0, (All Z1, (((rtt T_0 Z0) /\ (rtt T_0 Z1)) => (Z0 = Z1)))) (All A, (All B, (((A = B) /\ (ce A)) => (ce B)))) (All X, (All Y, ((rr1 X Y) => (rr X Y)))) (rr1 (i2003_11_14_17_20_25524) T_0) (All X, (All Y, ((rr3 X Y) => (rr X Y)))) (rr3 (i2003_11_14_17_20_25524) T_1) (All X, (All Y, ((rt1 X Y) => (rtt X Y)))) (All X, (All Y, ((rt3 X Y) => (rtt X Y)))) (rt3 T_1 T_3) (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (ce T_3) (All A, (All B, (All C, (((A = B) /\ (rtt C A)) => (rtt C B))))) (-. (Ex Y0, (Ex Y1, ((rr (i2003_11_14_17_20_25524) Y0) /\ ((rr (i2003_11_14_17_20_25524) Y1) /\ (Y0 != Y1)))))) ### Exists 48
% 134.09/134.31 50. ((rr1 (i2003_11_14_17_20_25524) T_0) /\ ((All Z0, (All Z1, (((rtt T_0 Z0) /\ (rtt T_0 Z1)) => (Z0 = Z1)))) /\ (Ex Z, ((rt1 T_0 Z) /\ (cc Z))))) (-. (Ex Y0, (Ex Y1, ((rr (i2003_11_14_17_20_25524) Y0) /\ ((rr (i2003_11_14_17_20_25524) Y1) /\ (Y0 != Y1)))))) (All A, (All B, (All C, (((A = B) /\ (rtt C A)) => (rtt C B))))) (ce T_3) (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (rt3 T_1 T_3) (All X, (All Y, ((rt3 X Y) => (rtt X Y)))) (All X, (All Y, ((rt1 X Y) => (rtt X Y)))) (rr3 (i2003_11_14_17_20_25524) T_1) (All X, (All Y, ((rr3 X Y) => (rr X Y)))) (All X, (All Y, ((rr1 X Y) => (rr X Y)))) (All A, (All B, (((A = B) /\ (ce A)) => (ce B)))) (All X, (-. ((ce X) /\ (cc X)))) ### ConjTree 49
% 134.09/134.31 51. (Ex Y, ((rr1 (i2003_11_14_17_20_25524) Y) /\ ((All Z0, (All Z1, (((rtt Y Z0) /\ (rtt Y Z1)) => (Z0 = Z1)))) /\ (Ex Z, ((rt1 Y Z) /\ (cc Z)))))) (All X, (-. ((ce X) /\ (cc X)))) (All A, (All B, (((A = B) /\ (ce A)) => (ce B)))) (All X, (All Y, ((rr1 X Y) => (rr X Y)))) (All X, (All Y, ((rr3 X Y) => (rr X Y)))) (rr3 (i2003_11_14_17_20_25524) T_1) (All X, (All Y, ((rt1 X Y) => (rtt X Y)))) (All X, (All Y, ((rt3 X Y) => (rtt X Y)))) (rt3 T_1 T_3) (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (ce T_3) (All A, (All B, (All C, (((A = B) /\ (rtt C A)) => (rtt C B))))) (-. (Ex Y0, (Ex Y1, ((rr (i2003_11_14_17_20_25524) Y0) /\ ((rr (i2003_11_14_17_20_25524) Y1) /\ (Y0 != Y1)))))) ### Exists 50
% 134.09/134.31 52. ((rt3 T_1 T_3) /\ (ce T_3)) (-. (Ex Y0, (Ex Y1, ((rr (i2003_11_14_17_20_25524) Y0) /\ ((rr (i2003_11_14_17_20_25524) Y1) /\ (Y0 != Y1)))))) (All A, (All B, (All C, (((A = B) /\ (rtt C A)) => (rtt C B))))) (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (All X, (All Y, ((rt3 X Y) => (rtt X Y)))) (All X, (All Y, ((rt1 X Y) => (rtt X Y)))) (rr3 (i2003_11_14_17_20_25524) T_1) (All X, (All Y, ((rr3 X Y) => (rr X Y)))) (All X, (All Y, ((rr1 X Y) => (rr X Y)))) (All A, (All B, (((A = B) /\ (ce A)) => (ce B)))) (All X, (-. ((ce X) /\ (cc X)))) (Ex Y, ((rr1 (i2003_11_14_17_20_25524) Y) /\ ((All Z0, (All Z1, (((rtt Y Z0) /\ (rtt Y Z1)) => (Z0 = Z1)))) /\ (Ex Z, ((rt1 Y Z) /\ (cc Z)))))) ### And 51
% 134.09/134.31 53. (Ex Z, ((rt3 T_1 Z) /\ (ce Z))) (Ex Y, ((rr1 (i2003_11_14_17_20_25524) Y) /\ ((All Z0, (All Z1, (((rtt Y Z0) /\ (rtt Y Z1)) => (Z0 = Z1)))) /\ (Ex Z, ((rt1 Y Z) /\ (cc Z)))))) (All X, (-. ((ce X) /\ (cc X)))) (All A, (All B, (((A = B) /\ (ce A)) => (ce B)))) (All X, (All Y, ((rr1 X Y) => (rr X Y)))) (All X, (All Y, ((rr3 X Y) => (rr X Y)))) (rr3 (i2003_11_14_17_20_25524) T_1) (All X, (All Y, ((rt1 X Y) => (rtt X Y)))) (All X, (All Y, ((rt3 X Y) => (rtt X Y)))) (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (All A, (All B, (All C, (((A = B) /\ (rtt C A)) => (rtt C B))))) (-. (Ex Y0, (Ex Y1, ((rr (i2003_11_14_17_20_25524) Y0) /\ ((rr (i2003_11_14_17_20_25524) Y1) /\ (Y0 != Y1)))))) ### Exists 52
% 134.09/134.31 54. ((rr3 (i2003_11_14_17_20_25524) T_1) /\ ((Ex Z, ((rt3 T_1 Z) /\ (ce Z))) /\ (All Z0, (All Z1, (((rtt T_1 Z0) /\ (rtt T_1 Z1)) => (Z0 = Z1)))))) (-. (Ex Y0, (Ex Y1, ((rr (i2003_11_14_17_20_25524) Y0) /\ ((rr (i2003_11_14_17_20_25524) Y1) /\ (Y0 != Y1)))))) (All A, (All B, (All C, (((A = B) /\ (rtt C A)) => (rtt C B))))) (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (All X, (All Y, ((rt3 X Y) => (rtt X Y)))) (All X, (All Y, ((rt1 X Y) => (rtt X Y)))) (All X, (All Y, ((rr3 X Y) => (rr X Y)))) (All X, (All Y, ((rr1 X Y) => (rr X Y)))) (All A, (All B, (((A = B) /\ (ce A)) => (ce B)))) (All X, (-. ((ce X) /\ (cc X)))) (Ex Y, ((rr1 (i2003_11_14_17_20_25524) Y) /\ ((All Z0, (All Z1, (((rtt Y Z0) /\ (rtt Y Z1)) => (Z0 = Z1)))) /\ (Ex Z, ((rt1 Y Z) /\ (cc Z)))))) ### ConjTree 53
% 134.09/134.31 55. (Ex Y, ((rr3 (i2003_11_14_17_20_25524) Y) /\ ((Ex Z, ((rt3 Y Z) /\ (ce Z))) /\ (All Z0, (All Z1, (((rtt Y Z0) /\ (rtt Y Z1)) => (Z0 = Z1))))))) (Ex Y, ((rr1 (i2003_11_14_17_20_25524) Y) /\ ((All Z0, (All Z1, (((rtt Y Z0) /\ (rtt Y Z1)) => (Z0 = Z1)))) /\ (Ex Z, ((rt1 Y Z) /\ (cc Z)))))) (All X, (-. ((ce X) /\ (cc X)))) (All A, (All B, (((A = B) /\ (ce A)) => (ce B)))) (All X, (All Y, ((rr1 X Y) => (rr X Y)))) (All X, (All Y, ((rr3 X Y) => (rr X Y)))) (All X, (All Y, ((rt1 X Y) => (rtt X Y)))) (All X, (All Y, ((rt3 X Y) => (rtt X Y)))) (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (All A, (All B, (All C, (((A = B) /\ (rtt C A)) => (rtt C B))))) (-. (Ex Y0, (Ex Y1, ((rr (i2003_11_14_17_20_25524) Y0) /\ ((rr (i2003_11_14_17_20_25524) Y1) /\ (Y0 != Y1)))))) ### Exists 54
% 134.09/134.31 56. ((Ex Y, ((rr3 (i2003_11_14_17_20_25524) Y) /\ ((Ex Z, ((rt3 Y Z) /\ (ce Z))) /\ (All Z0, (All Z1, (((rtt Y Z0) /\ (rtt Y Z1)) => (Z0 = Z1))))))) /\ ((Ex Y, ((rr2 (i2003_11_14_17_20_25524) Y) /\ ((All Z0, (All Z1, (((rtt Y Z0) /\ (rtt Y Z1)) => (Z0 = Z1)))) /\ (Ex Z, ((rt2 Y Z) /\ (cd Z)))))) /\ ((-. (Ex Y0, (Ex Y1, ((rr (i2003_11_14_17_20_25524) Y0) /\ ((rr (i2003_11_14_17_20_25524) Y1) /\ (Y0 != Y1)))))) /\ (Ex Y, ((rr1 (i2003_11_14_17_20_25524) Y) /\ ((All Z0, (All Z1, (((rtt Y Z0) /\ (rtt Y Z1)) => (Z0 = Z1)))) /\ (Ex Z, ((rt1 Y Z) /\ (cc Z))))))))) (All A, (All B, (All C, (((A = B) /\ (rtt C A)) => (rtt C B))))) (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (All X, (All Y, ((rt3 X Y) => (rtt X Y)))) (All X, (All Y, ((rt1 X Y) => (rtt X Y)))) (All X, (All Y, ((rr3 X Y) => (rr X Y)))) (All X, (All Y, ((rr1 X Y) => (rr X Y)))) (All A, (All B, (((A = B) /\ (ce A)) => (ce B)))) (All X, (-. ((ce X) /\ (cc X)))) ### ConjTree 55
% 134.09/134.31 57. (cUnsatisfiable (i2003_11_14_17_20_25524)) (All X, (-. ((ce X) /\ (cc X)))) (All A, (All B, (((A = B) /\ (ce A)) => (ce B)))) (All X, (All Y, ((rr1 X Y) => (rr X Y)))) (All X, (All Y, ((rr3 X Y) => (rr X Y)))) (All X, (All Y, ((rt1 X Y) => (rtt X Y)))) (All X, (All Y, ((rt3 X Y) => (rtt X Y)))) (All A, (All B, (All C, (((A = B) /\ (rtt A C)) => (rtt B C))))) (All A, (All B, (All C, (((A = B) /\ (rtt C A)) => (rtt C B))))) ### Definition-Pseudo(cUnsatisfiable) 56
% 134.09/134.31 % SZS output end Proof
% 134.09/134.31 (* END-PROOF *)
%------------------------------------------------------------------------------