TSTP Solution File: ALG138+1 by SuperZenon---0.0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : ALG138+1 : TPTP v8.1.0. Released v2.7.0.
% 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 : Thu Jul 14 18:05:35 EDT 2022
% Result : Unsatisfiable 0.86s 1.07s
% Output : Proof 0.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG138+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.34 % Computer : n024.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 : Wed Jun 8 11:22:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.86/1.07 % SZS status Theorem
% 0.86/1.07 (* PROOF-FOUND *)
% 0.86/1.07 (* BEGIN-PROOF *)
% 0.86/1.07 % SZS output start Proof
% 0.86/1.07 1. ((op (e0) (e0)) = (e1)) ((e1) != (op (e0) (e0))) ### Sym(=)
% 0.86/1.07 2. ((op (e0) (e0)) = (e1)) ((e1) != (op (e0) (e0))) ### Sym(=)
% 0.86/1.07 3. ((e0) != (e0)) ### NotEqual
% 0.86/1.07 4. ((e0) != (e1)) ((op (e0) (e0)) = (e0)) ((op (e0) (e0)) = (e1)) ### TransEq-sym 1 2 3
% 0.86/1.07 5. ((op (e1) (e1)) != (op (e1) (e1))) ### Refl(=)
% 0.86/1.07 6. ((op (e1) (e1)) != (op (e1) (e1))) ### Refl(=)
% 0.86/1.07 7. ((op (e0) (e1)) = (e1)) ((e1) != (op (e0) (e1))) ### Sym(=)
% 0.86/1.07 8. ((op (e0) (e1)) != (op (e1) (e1))) ((op (e1) (e1)) = (e1)) ((op (e0) (e1)) = (e1)) ### TransEq-sym 5 6 7
% 0.86/1.07 9. ((op (e3) (e2)) = (e0)) ((e0) != (op (e3) (e2))) ### Sym(=)
% 0.86/1.07 10. ((op (e3) (e2)) = (e0)) ((op (e3) (e2)) != (e0)) ### Axiom
% 0.86/1.07 11. ((e2) != (e2)) ### NotEqual
% 0.86/1.07 12. ((op (op (e3) (e2)) (e2)) != (op (e0) (e2))) ((op (e3) (e2)) = (e0)) ### NotEqual 10 11
% 0.86/1.07 13. ((e1) != (e1)) ### NotEqual
% 0.86/1.07 14. ((e1) != (op (op (e3) (e2)) (e2))) ((op (e0) (e2)) = (e1)) ((op (e3) (e2)) = (e0)) ### Trans-sym 12 13
% 0.86/1.07 15. (-. (((e0) = (op (e3) (e2))) /\ ((e1) = (op (op (e3) (e2)) (e2))))) ((op (e0) (e2)) = (e1)) ((op (e3) (e2)) = (e0)) ### NotAnd 9 14
% 0.86/1.07 16. ((op (e0) (e2)) != (op (e0) (e2))) ### Refl(=)
% 0.86/1.07 17. ((op (e0) (e2)) != (op (e0) (e2))) ### Refl(=)
% 0.86/1.07 18. ((op (e3) (e2)) = (e1)) ((e1) != (op (e3) (e2))) ### Sym(=)
% 0.86/1.07 19. ((op (e0) (e2)) != (op (e3) (e2))) ((op (e0) (e2)) = (e1)) ((op (e3) (e2)) = (e1)) ### TransEq 16 17 18
% 0.86/1.07 20. ((op (e2) (e2)) != (op (e2) (e2))) ### Refl(=)
% 0.86/1.07 21. ((op (e2) (e2)) != (op (e2) (e2))) ### Refl(=)
% 0.86/1.07 22. ((op (e3) (e2)) = (e2)) ((e2) != (op (e3) (e2))) ### Sym(=)
% 0.86/1.07 23. ((op (e2) (e2)) != (op (e3) (e2))) ((op (e2) (e2)) = (e2)) ((op (e3) (e2)) = (e2)) ### TransEq 20 21 22
% 0.86/1.07 24. ((op (e3) (e3)) != (op (e3) (e3))) ### Refl(=)
% 0.86/1.07 25. ((op (e3) (e3)) != (op (e3) (e3))) ### Refl(=)
% 0.86/1.07 26. ((op (e3) (e2)) = (e3)) ((e3) != (op (e3) (e2))) ### Sym(=)
% 0.86/1.07 27. ((op (e3) (e2)) != (op (e3) (e3))) ((op (e3) (e3)) = (e3)) ((op (e3) (e2)) = (e3)) ### TransEq-sym 24 25 26
% 0.86/1.07 28. (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e3) (e3)) = (e3)) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e2) (e2)) = (e2)) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e0) (e2)) = (e1)) (-. (((e0) = (op (e3) (e2))) /\ ((e1) = (op (op (e3) (e2)) (e2))))) ### DisjTree 15 19 23 27
% 0.86/1.07 29. ((op (e2) (e3)) = (e0)) ((e0) != (op (e2) (e3))) ### Sym(=)
% 0.86/1.07 30. ((op (e2) (e3)) = (e0)) ((op (e2) (e3)) != (e0)) ### Axiom
% 0.86/1.07 31. ((e3) != (e3)) ### NotEqual
% 0.86/1.07 32. ((op (op (e2) (e3)) (e3)) != (op (e0) (e3))) ((op (e2) (e3)) = (e0)) ### NotEqual 30 31
% 0.86/1.07 33. ((e1) != (op (op (e2) (e3)) (e3))) ((op (e0) (e3)) = (e1)) ((op (e2) (e3)) = (e0)) ### Trans-sym 32 13
% 0.86/1.07 34. (-. (((e0) = (op (e2) (e3))) /\ ((e1) = (op (op (e2) (e3)) (e3))))) ((op (e0) (e3)) = (e1)) ((op (e2) (e3)) = (e0)) ### NotAnd 29 33
% 0.86/1.07 35. ((op (e0) (e3)) != (op (e0) (e3))) ### Refl(=)
% 0.86/1.07 36. ((op (e0) (e3)) != (op (e0) (e3))) ### Refl(=)
% 0.86/1.07 37. ((op (e2) (e3)) = (e1)) ((e1) != (op (e2) (e3))) ### Sym(=)
% 0.86/1.07 38. ((op (e0) (e3)) != (op (e2) (e3))) ((op (e0) (e3)) = (e1)) ((op (e2) (e3)) = (e1)) ### TransEq 35 36 37
% 0.86/1.07 39. ((op (e2) (e2)) != (op (e2) (e2))) ### Refl(=)
% 0.86/1.07 40. ((op (e2) (e2)) != (op (e2) (e2))) ### Refl(=)
% 0.86/1.07 41. ((op (e2) (e3)) = (e2)) ((e2) != (op (e2) (e3))) ### Sym(=)
% 0.86/1.07 42. ((op (e2) (e2)) != (op (e2) (e3))) ((op (e2) (e2)) = (e2)) ((op (e2) (e3)) = (e2)) ### TransEq 39 40 41
% 0.86/1.07 43. ((op (e3) (e3)) != (op (e3) (e3))) ### Refl(=)
% 0.86/1.07 44. ((op (e3) (e3)) != (op (e3) (e3))) ### Refl(=)
% 0.86/1.07 45. ((op (e2) (e3)) = (e3)) ((e3) != (op (e2) (e3))) ### Sym(=)
% 0.86/1.07 46. ((op (e2) (e3)) != (op (e3) (e3))) ((op (e3) (e3)) = (e3)) ((op (e2) (e3)) = (e3)) ### TransEq-sym 43 44 45
% 0.86/1.07 47. (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e3) (e3)) = (e3)) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e2) (e2)) = (e2)) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e0) (e3)) = (e1)) (-. (((e0) = (op (e2) (e3))) /\ ((e1) = (op (op (e2) (e3)) (e3))))) ### DisjTree 34 38 42 46
% 0.86/1.07 48. (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) (-. (((e0) = (op (e2) (e3))) /\ ((e1) = (op (op (e2) (e3)) (e3))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) (-. (((e0) = (op (e3) (e2))) /\ ((e1) = (op (op (e3) (e2)) (e2))))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e2) (e2)) = (e2)) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e3) (e3)) = (e3)) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e1) (e1)) = (e1)) ((op (e0) (e1)) != (op (e1) (e1))) ((op (e0) (e0)) = (e0)) ((e0) != (e1)) ### DisjTree 4 8 28 47
% 0.86/1.07 49. (((op (e0) (e0)) = (e0)) /\ (((op (e1) (e1)) = (e1)) /\ (((op (e2) (e2)) = (e2)) /\ ((op (e3) (e3)) = (e3))))) ((e0) != (e1)) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e3) (e2)) != (op (e3) (e3))) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e0) (e2)) != (op (e3) (e2))) (-. (((e0) = (op (e3) (e2))) /\ ((e1) = (op (op (e3) (e2)) (e2))))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) ((op (e2) (e3)) != (op (e3) (e3))) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e0) (e3)) != (op (e2) (e3))) (-. (((e0) = (op (e2) (e3))) /\ ((e1) = (op (op (e2) (e3)) (e3))))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) ### ConjTree 48
% 0.86/1.07 50. (((e0) != (e1)) /\ (((e0) != (e2)) /\ (((e0) != (e3)) /\ (((e1) != (e2)) /\ (((e1) != (e3)) /\ ((e2) != (e3))))))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) (-. (((e0) = (op (e2) (e3))) /\ ((e1) = (op (op (e2) (e3)) (e3))))) ((op (e0) (e3)) != (op (e2) (e3))) ((op (e2) (e2)) != (op (e2) (e3))) ((op (e2) (e3)) != (op (e3) (e3))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) (-. (((e0) = (op (e3) (e2))) /\ ((e1) = (op (op (e3) (e2)) (e2))))) ((op (e0) (e2)) != (op (e3) (e2))) ((op (e2) (e2)) != (op (e3) (e2))) ((op (e3) (e2)) != (op (e3) (e3))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) ((op (e0) (e1)) != (op (e1) (e1))) (((op (e0) (e0)) = (e0)) /\ (((op (e1) (e1)) = (e1)) /\ (((op (e2) (e2)) = (e2)) /\ ((op (e3) (e3)) = (e3))))) ### ConjTree 49
% 0.86/1.07 51. (((op (e0) (e0)) != (op (e1) (e0))) /\ (((op (e0) (e0)) != (op (e2) (e0))) /\ (((op (e0) (e0)) != (op (e3) (e0))) /\ (((op (e1) (e0)) != (op (e2) (e0))) /\ (((op (e1) (e0)) != (op (e3) (e0))) /\ (((op (e2) (e0)) != (op (e3) (e0))) /\ (((op (e0) (e1)) != (op (e1) (e1))) /\ (((op (e0) (e1)) != (op (e2) (e1))) /\ (((op (e0) (e1)) != (op (e3) (e1))) /\ (((op (e1) (e1)) != (op (e2) (e1))) /\ (((op (e1) (e1)) != (op (e3) (e1))) /\ (((op (e2) (e1)) != (op (e3) (e1))) /\ (((op (e0) (e2)) != (op (e1) (e2))) /\ (((op (e0) (e2)) != (op (e2) (e2))) /\ (((op (e0) (e2)) != (op (e3) (e2))) /\ (((op (e1) (e2)) != (op (e2) (e2))) /\ (((op (e1) (e2)) != (op (e3) (e2))) /\ (((op (e2) (e2)) != (op (e3) (e2))) /\ (((op (e0) (e3)) != (op (e1) (e3))) /\ (((op (e0) (e3)) != (op (e2) (e3))) /\ (((op (e0) (e3)) != (op (e3) (e3))) /\ (((op (e1) (e3)) != (op (e2) (e3))) /\ (((op (e1) (e3)) != (op (e3) (e3))) /\ (((op (e2) (e3)) != (op (e3) (e3))) /\ (((op (e0) (e0)) != (op (e0) (e1))) /\ (((op (e0) (e0)) != (op (e0) (e2))) /\ (((op (e0) (e0)) != (op (e0) (e3))) /\ (((op (e0) (e1)) != (op (e0) (e2))) /\ (((op (e0) (e1)) != (op (e0) (e3))) /\ (((op (e0) (e2)) != (op (e0) (e3))) /\ (((op (e1) (e0)) != (op (e1) (e1))) /\ (((op (e1) (e0)) != (op (e1) (e2))) /\ (((op (e1) (e0)) != (op (e1) (e3))) /\ (((op (e1) (e1)) != (op (e1) (e2))) /\ (((op (e1) (e1)) != (op (e1) (e3))) /\ (((op (e1) (e2)) != (op (e1) (e3))) /\ (((op (e2) (e0)) != (op (e2) (e1))) /\ (((op (e2) (e0)) != (op (e2) (e2))) /\ (((op (e2) (e0)) != (op (e2) (e3))) /\ (((op (e2) (e1)) != (op (e2) (e2))) /\ (((op (e2) (e1)) != (op (e2) (e3))) /\ (((op (e2) (e2)) != (op (e2) (e3))) /\ (((op (e3) (e0)) != (op (e3) (e1))) /\ (((op (e3) (e0)) != (op (e3) (e2))) /\ (((op (e3) (e0)) != (op (e3) (e3))) /\ (((op (e3) (e1)) != (op (e3) (e2))) /\ (((op (e3) (e1)) != (op (e3) (e3))) /\ ((op (e3) (e2)) != (op (e3) (e3)))))))))))))))))))))))))))))))))))))))))))))))))) (((op (e0) (e0)) = (e0)) /\ (((op (e1) (e1)) = (e1)) /\ (((op (e2) (e2)) = (e2)) /\ ((op (e3) (e3)) = (e3))))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) (-. (((e0) = (op (e3) (e2))) /\ ((e1) = (op (op (e3) (e2)) (e2))))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) (-. (((e0) = (op (e2) (e3))) /\ ((e1) = (op (op (e2) (e3)) (e3))))) (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) (((e0) != (e1)) /\ (((e0) != (e2)) /\ (((e0) != (e3)) /\ (((e1) != (e2)) /\ (((e1) != (e3)) /\ ((e2) != (e3))))))) ### ConjTree 50
% 0.86/1.07 52. 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(((e0) = (op (e2) (e3))) /\ ((e1) = (op (op (e2) (e3)) (e3))))) (((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) (-. (((e0) = (op (e3) (e2))) /\ ((e1) = (op (op (e3) (e2)) (e2))))) (((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) (((op (e0) (e0)) = (e0)) /\ (((op (e1) (e1)) = (e1)) /\ (((op (e2) (e2)) = (e2)) /\ ((op (e3) (e3)) = (e3))))) (((op (e0) (e0)) != (op (e1) (e0))) /\ (((op (e0) (e0)) != (op (e2) (e0))) /\ (((op (e0) (e0)) != (op (e3) (e0))) /\ (((op (e1) (e0)) != (op (e2) (e0))) /\ (((op (e1) (e0)) != (op (e3) (e0))) /\ (((op (e2) (e0)) != (op (e3) (e0))) /\ (((op (e0) (e1)) != (op (e1) (e1))) /\ (((op (e0) (e1)) != (op (e2) (e1))) /\ (((op (e0) (e1)) != (op (e3) (e1))) /\ (((op (e1) (e1)) != (op (e2) (e1))) /\ (((op (e1) (e1)) != (op (e3) (e1))) /\ (((op (e2) (e1)) != (op (e3) (e1))) /\ (((op (e0) (e2)) != (op (e1) (e2))) /\ (((op (e0) (e2)) != (op (e2) (e2))) /\ (((op (e0) (e2)) != (op (e3) (e2))) /\ (((op (e1) (e2)) != (op (e2) (e2))) /\ (((op (e1) (e2)) != (op (e3) (e2))) /\ (((op (e2) (e2)) != (op (e3) (e2))) /\ (((op (e0) (e3)) != (op (e1) (e3))) /\ (((op (e0) (e3)) != (op (e2) (e3))) /\ (((op (e0) (e3)) != (op (e3) (e3))) /\ (((op (e1) (e3)) != (op (e2) (e3))) /\ (((op (e1) (e3)) != (op (e3) (e3))) /\ (((op (e2) (e3)) != (op (e3) (e3))) /\ (((op (e0) (e0)) != (op (e0) (e1))) /\ (((op (e0) (e0)) != (op (e0) (e2))) /\ (((op (e0) (e0)) != (op (e0) (e3))) /\ (((op (e0) (e1)) != (op (e0) (e2))) /\ (((op (e0) (e1)) != (op (e0) (e3))) /\ (((op (e0) (e2)) != (op (e0) (e3))) /\ (((op (e1) (e0)) != (op (e1) (e1))) /\ (((op (e1) (e0)) != (op (e1) (e2))) /\ (((op (e1) (e0)) != (op (e1) (e3))) /\ (((op (e1) (e1)) != (op (e1) (e2))) /\ (((op (e1) (e1)) != (op (e1) (e3))) /\ (((op (e1) (e2)) != (op (e1) (e3))) /\ (((op (e2) (e0)) != (op (e2) (e1))) /\ (((op (e2) (e0)) != (op (e2) (e2))) /\ (((op (e2) (e0)) != (op (e2) (e3))) /\ (((op (e2) (e1)) != (op (e2) (e2))) /\ (((op (e2) (e1)) != (op (e2) (e3))) /\ (((op (e2) (e2)) != (op (e2) (e3))) /\ (((op (e3) (e0)) != (op (e3) (e1))) /\ (((op (e3) (e0)) != (op (e3) (e2))) /\ (((op (e3) (e0)) != (op (e3) (e3))) /\ (((op (e3) (e1)) != (op (e3) (e2))) /\ (((op (e3) (e1)) != (op (e3) (e3))) /\ ((op (e3) (e2)) != (op (e3) (e3)))))))))))))))))))))))))))))))))))))))))))))))))) ### ConjTree 51
% 0.86/1.07 53. ((((op (e0) (e0)) = (e0)) \/ (((op (e0) (e0)) = (e1)) \/ (((op (e0) (e0)) = (e2)) \/ ((op (e0) (e0)) = (e3))))) /\ ((((op (e0) (e1)) = (e0)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e1)) = (e2)) \/ ((op (e0) (e1)) = (e3))))) /\ ((((op (e0) (e2)) = (e0)) \/ (((op (e0) (e2)) = (e1)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e2)) = (e3))))) /\ ((((op (e0) (e3)) = (e0)) \/ (((op (e0) (e3)) = (e1)) \/ (((op (e0) (e3)) = (e2)) \/ ((op (e0) (e3)) = (e3))))) /\ ((((op (e1) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e2)) \/ ((op (e1) (e0)) = (e3))))) /\ ((((op (e1) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e2)) \/ ((op (e1) (e1)) = (e3))))) /\ ((((op (e1) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e2)) = (e3))))) /\ ((((op (e1) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e2)) \/ ((op (e1) (e3)) = (e3))))) /\ ((((op (e2) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e2) (e0)) = (e3))))) /\ ((((op (e2) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e2)) \/ ((op (e2) (e1)) = (e3))))) /\ ((((op (e2) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e2)) = (e3))))) /\ ((((op (e2) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e2) (e3)) = (e3))))) /\ ((((op (e3) (e0)) = (e0)) \/ (((op (e3) (e0)) = (e1)) \/ (((op (e3) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e3))))) /\ ((((op (e3) (e1)) = (e0)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e3))))) /\ ((((op (e3) (e2)) = (e0)) \/ (((op (e3) (e2)) = (e1)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e3))))) /\ (((op (e3) (e3)) = (e0)) \/ (((op (e3) (e3)) = (e1)) \/ (((op (e3) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e3)))))))))))))))))))) (((op (e0) (e0)) != (op (e1) (e0))) /\ (((op (e0) (e0)) != (op (e2) (e0))) /\ (((op (e0) (e0)) != (op (e3) (e0))) /\ (((op (e1) (e0)) != (op (e2) (e0))) /\ (((op (e1) (e0)) != (op (e3) (e0))) /\ (((op (e2) (e0)) != (op (e3) (e0))) /\ (((op (e0) (e1)) != (op (e1) (e1))) /\ (((op (e0) (e1)) != (op (e2) (e1))) /\ (((op (e0) (e1)) != (op (e3) (e1))) /\ (((op (e1) (e1)) != (op (e2) (e1))) /\ (((op (e1) (e1)) != (op (e3) (e1))) /\ (((op (e2) (e1)) != (op (e3) (e1))) /\ (((op (e0) (e2)) != (op (e1) (e2))) /\ (((op (e0) (e2)) != (op (e2) (e2))) /\ (((op (e0) (e2)) != (op (e3) (e2))) /\ (((op (e1) (e2)) != (op (e2) (e2))) /\ (((op (e1) (e2)) != (op (e3) (e2))) /\ (((op (e2) (e2)) != (op (e3) (e2))) /\ (((op (e0) (e3)) != (op (e1) (e3))) /\ (((op (e0) (e3)) != (op (e2) (e3))) /\ (((op (e0) (e3)) != (op (e3) (e3))) /\ (((op (e1) (e3)) != (op (e2) (e3))) /\ (((op (e1) (e3)) != (op (e3) (e3))) /\ (((op (e2) (e3)) != (op (e3) (e3))) /\ (((op (e0) (e0)) != (op (e0) (e1))) /\ (((op (e0) (e0)) != (op (e0) (e2))) /\ (((op (e0) (e0)) != (op (e0) (e3))) /\ (((op (e0) (e1)) != (op (e0) (e2))) /\ (((op (e0) (e1)) != (op (e0) (e3))) /\ (((op (e0) (e2)) != (op (e0) (e3))) /\ (((op (e1) (e0)) != (op (e1) (e1))) /\ (((op (e1) (e0)) != (op (e1) (e2))) /\ (((op (e1) (e0)) != (op (e1) (e3))) /\ (((op (e1) (e1)) != (op (e1) (e2))) /\ (((op (e1) (e1)) != (op (e1) (e3))) /\ (((op (e1) (e2)) != (op (e1) (e3))) /\ (((op (e2) (e0)) != (op (e2) (e1))) /\ (((op (e2) (e0)) != (op (e2) (e2))) /\ (((op (e2) (e0)) != (op (e2) (e3))) /\ (((op (e2) (e1)) != (op (e2) (e2))) /\ (((op (e2) (e1)) != (op (e2) (e3))) /\ (((op (e2) (e2)) != (op (e2) (e3))) /\ (((op (e3) (e0)) != (op (e3) (e1))) /\ (((op (e3) (e0)) != (op (e3) (e2))) /\ (((op (e3) (e0)) != (op (e3) (e3))) /\ (((op (e3) (e1)) != (op (e3) (e2))) /\ (((op (e3) (e1)) != (op (e3) (e3))) /\ ((op (e3) (e2)) != (op (e3) (e3)))))))))))))))))))))))))))))))))))))))))))))))))) (((op (e0) (e0)) = (e0)) /\ (((op (e1) (e1)) = (e1)) /\ (((op (e2) (e2)) = (e2)) /\ ((op (e3) (e3)) = (e3))))) (-. (((e0) = (op (e3) (e2))) /\ ((e1) = (op (op (e3) (e2)) (e2))))) (-. (((e0) = (op (e2) (e3))) /\ ((e1) = (op (op (e2) (e3)) (e3))))) (((e0) != (e1)) /\ (((e0) != (e2)) /\ (((e0) != (e3)) /\ (((e1) != (e2)) /\ (((e1) != (e3)) /\ ((e2) != (e3))))))) ((((op (e0) (e0)) = (e0)) \/ (((op (e0) (e1)) = (e0)) \/ (((op (e0) (e2)) = (e0)) \/ ((op (e0) (e3)) = (e0))))) /\ ((((op (e0) (e0)) = (e0)) \/ (((op (e1) (e0)) = (e0)) \/ (((op (e2) (e0)) = (e0)) \/ ((op (e3) (e0)) = (e0))))) /\ ((((op (e0) (e0)) = (e1)) \/ (((op (e0) (e1)) = (e1)) \/ (((op (e0) (e2)) = (e1)) \/ ((op (e0) (e3)) = (e1))))) /\ ((((op (e0) (e0)) = (e1)) \/ (((op (e1) (e0)) = (e1)) \/ (((op (e2) (e0)) = (e1)) \/ ((op (e3) (e0)) = (e1))))) /\ ((((op (e0) (e0)) = (e2)) \/ (((op (e0) (e1)) = (e2)) \/ (((op (e0) (e2)) = (e2)) \/ ((op (e0) (e3)) = (e2))))) /\ ((((op (e0) (e0)) = (e2)) \/ (((op (e1) (e0)) = (e2)) \/ (((op (e2) (e0)) = (e2)) \/ ((op (e3) (e0)) = (e2))))) /\ ((((op (e0) (e0)) = (e3)) \/ (((op (e0) (e1)) = (e3)) \/ (((op (e0) (e2)) = (e3)) \/ ((op (e0) (e3)) = (e3))))) /\ ((((op (e0) (e0)) = (e3)) \/ (((op (e1) (e0)) = (e3)) \/ (((op (e2) (e0)) = (e3)) \/ ((op (e3) (e0)) = (e3))))) /\ ((((op (e1) (e0)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ ((op (e1) (e3)) = (e0))))) /\ ((((op (e0) (e1)) = (e0)) \/ (((op (e1) (e1)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ ((op (e3) (e1)) = (e0))))) /\ ((((op (e1) (e0)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ ((op (e1) (e3)) = (e1))))) /\ ((((op (e0) (e1)) = (e1)) \/ (((op (e1) (e1)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ ((op (e3) (e1)) = (e1))))) /\ ((((op (e1) (e0)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ ((op (e1) (e3)) = (e2))))) /\ ((((op (e0) (e1)) = (e2)) \/ (((op (e1) (e1)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ ((op (e3) (e1)) = (e2))))) /\ ((((op (e1) (e0)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ ((op (e1) (e3)) = (e3))))) /\ ((((op (e0) (e1)) = (e3)) \/ (((op (e1) (e1)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ ((op (e3) (e1)) = (e3))))) /\ ((((op (e2) (e0)) = (e0)) \/ (((op (e2) (e1)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e2) (e3)) = (e0))))) /\ ((((op (e0) (e2)) = (e0)) \/ (((op (e1) (e2)) = (e0)) \/ (((op (e2) (e2)) = (e0)) \/ ((op (e3) (e2)) = (e0))))) /\ ((((op (e2) (e0)) = (e1)) \/ (((op (e2) (e1)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e2) (e3)) = (e1))))) /\ ((((op (e0) (e2)) = (e1)) \/ (((op (e1) (e2)) = (e1)) \/ (((op (e2) (e2)) = (e1)) \/ ((op (e3) (e2)) = (e1))))) /\ ((((op (e2) (e0)) = (e2)) \/ (((op (e2) (e1)) = (e2)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e2) (e3)) = (e2))))) /\ ((((op (e0) (e2)) = (e2)) \/ (((op (e1) (e2)) = (e2)) \/ (((op (e2) (e2)) = (e2)) \/ ((op (e3) (e2)) = (e2))))) /\ ((((op (e2) (e0)) = (e3)) \/ (((op (e2) (e1)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e2) (e3)) = (e3))))) /\ ((((op (e0) (e2)) = (e3)) \/ (((op (e1) (e2)) = (e3)) \/ (((op (e2) (e2)) = (e3)) \/ ((op (e3) (e2)) = (e3))))) /\ ((((op (e3) (e0)) = (e0)) \/ (((op (e3) (e1)) = (e0)) \/ (((op (e3) (e2)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) /\ ((((op (e0) (e3)) = (e0)) \/ (((op (e1) (e3)) = (e0)) \/ (((op (e2) (e3)) = (e0)) \/ ((op (e3) (e3)) = (e0))))) /\ ((((op (e3) (e0)) = (e1)) \/ (((op (e3) (e1)) = (e1)) \/ (((op (e3) (e2)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) /\ ((((op (e0) (e3)) = (e1)) \/ (((op (e1) (e3)) = (e1)) \/ (((op (e2) (e3)) = (e1)) \/ ((op (e3) (e3)) = (e1))))) /\ ((((op (e3) (e0)) = (e2)) \/ (((op (e3) (e1)) = (e2)) \/ (((op (e3) (e2)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) /\ ((((op (e0) (e3)) = (e2)) \/ (((op (e1) (e3)) = (e2)) \/ (((op (e2) (e3)) = (e2)) \/ ((op (e3) (e3)) = (e2))))) /\ ((((op (e3) (e0)) = (e3)) \/ (((op (e3) (e1)) = (e3)) \/ (((op (e3) (e2)) = (e3)) \/ ((op (e3) (e3)) = (e3))))) /\ (((op (e0) (e3)) = (e3)) \/ (((op (e1) (e3)) = (e3)) \/ (((op (e2) (e3)) = (e3)) \/ ((op (e3) (e3)) = (e3)))))))))))))))))))))))))))))))))))) ### ConjTree 52
% 0.86/1.07 % SZS output end Proof
% 0.86/1.07 (* END-PROOF *)
%------------------------------------------------------------------------------