TSTP Solution File: SYN334+1 by SuperZenon---0.0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SYN334+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n023.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 21 12:42:41 EDT 2022
% Result : Theorem 0.19s 0.47s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SYN334+1 : TPTP v8.1.0. Released v2.0.0.
% 0.09/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.32 % Computer : n023.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 600
% 0.13/0.32 % DateTime : Mon Jul 11 20:43:24 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 (* PROOF-FOUND *)
% 0.19/0.47 (* BEGIN-PROOF *)
% 0.19/0.47 % SZS output start Proof
% 0.19/0.47 1. (big_f T_0 T_0) (-. (big_f T_0 T_0)) ### Axiom
% 0.19/0.47 2. (-. (big_g T_1 T_1)) (big_g T_1 T_1) ### Axiom
% 0.19/0.47 3. (-. (big_g T_0 T_2)) (big_g T_0 T_2) ### Axiom
% 0.19/0.47 4. (-. ((big_g T_0 T_2) <=> (big_g T_1 T_1))) (-. (big_g T_0 T_2)) (-. (big_g T_1 T_1)) ### NotEquiv 2 3
% 0.19/0.47 5. (-. ((big_f T_1 T_1) => (big_g T_1 T_1))) (-. (big_g T_0 T_2)) (-. ((big_g T_0 T_2) <=> (big_g T_1 T_1))) ### NotImply 4
% 0.19/0.47 6. (-. (big_f T_0 T_2)) (big_f T_0 T_2) ### Axiom
% 0.19/0.47 7. ((big_f T_0 T_2) <=> ((big_f T_1 T_1) => (big_g T_1 T_1))) (-. (big_f T_0 T_2)) (-. ((big_g T_0 T_2) <=> (big_g T_1 T_1))) (-. (big_g T_0 T_2)) ### Equiv 5 6
% 0.19/0.47 8. (-. (((big_f T_0 T_2) => ((big_f T_0 T_1) <=> (big_g T_2 T_1))) => (((big_f T_0 T_2) <=> ((big_f T_1 T_1) => (big_g T_1 T_1))) => ((big_g T_0 T_2) <=> (big_g T_1 T_1))))) (-. (big_g T_0 T_2)) (-. (big_f T_0 T_2)) ### ConjTree 7
% 0.19/0.47 9. (-. (All Z, (((big_f T_0 T_2) => ((big_f T_0 Z) <=> (big_g T_2 Z))) => (((big_f T_0 T_2) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g T_0 T_2) <=> (big_g Z Z)))))) (-. (big_f T_0 T_2)) (-. (big_g T_0 T_2)) ### NotAllEx 8
% 0.19/0.47 10. (-. (Ex Y, (All Z, (((big_f T_0 Y) => ((big_f T_0 Z) <=> (big_g Y Z))) => (((big_f T_0 Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g T_0 Y) <=> (big_g Z Z))))))) (-. (big_g T_0 T_2)) (-. (big_f T_0 T_2)) ### NotExists 9
% 0.19/0.47 11. (big_f T_0 T_2) (-. (big_f T_0 T_2)) ### Axiom
% 0.19/0.47 12. (big_g T_0 T_2) (-. (big_g T_0 T_2)) ### Axiom
% 0.19/0.47 13. (-. (big_g T_3 T_3)) (big_g T_3 T_3) ### Axiom
% 0.19/0.47 14. (-. (big_g T_1 T_1)) (big_g T_1 T_1) ### Axiom
% 0.19/0.47 15. (-. ((big_g T_1 T_1) <=> (big_g T_3 T_3))) (-. (big_g T_1 T_1)) (-. (big_g T_3 T_3)) ### NotEquiv 13 14
% 0.19/0.47 16. (-. ((big_f T_3 T_3) => (big_g T_3 T_3))) (-. (big_g T_1 T_1)) (-. ((big_g T_1 T_1) <=> (big_g T_3 T_3))) ### NotImply 15
% 0.19/0.47 17. (-. (big_f T_1 T_1)) (big_f T_1 T_1) ### Axiom
% 0.19/0.47 18. ((big_f T_1 T_1) <=> ((big_f T_3 T_3) => (big_g T_3 T_3))) (-. (big_f T_1 T_1)) (-. ((big_g T_1 T_1) <=> (big_g T_3 T_3))) (-. (big_g T_1 T_1)) ### Equiv 16 17
% 0.19/0.47 19. (-. (((big_f T_1 T_1) => ((big_f T_1 T_3) <=> (big_g T_1 T_3))) => (((big_f T_1 T_1) <=> ((big_f T_3 T_3) => (big_g T_3 T_3))) => ((big_g T_1 T_1) <=> (big_g T_3 T_3))))) (-. (big_g T_1 T_1)) (-. (big_f T_1 T_1)) ### ConjTree 18
% 0.19/0.47 20. (-. (All Z, (((big_f T_1 T_1) => ((big_f T_1 Z) <=> (big_g T_1 Z))) => (((big_f T_1 T_1) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g T_1 T_1) <=> (big_g Z Z)))))) (-. (big_f T_1 T_1)) (-. (big_g T_1 T_1)) ### NotAllEx 19
% 0.19/0.47 21. (-. (Ex Y, (All Z, (((big_f T_1 Y) => ((big_f T_1 Z) <=> (big_g Y Z))) => (((big_f T_1 Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g T_1 Y) <=> (big_g Z Z))))))) (-. (big_g T_1 T_1)) (-. (big_f T_1 T_1)) ### NotExists 20
% 0.19/0.47 22. (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) (-. (big_f T_1 T_1)) (-. (big_g T_1 T_1)) ### NotExists 21
% 0.19/0.47 23. (-. ((big_g T_0 T_2) <=> (big_g T_1 T_1))) (-. (big_f T_1 T_1)) (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) (big_g T_0 T_2) ### NotEquiv 12 22
% 0.19/0.47 24. (big_g T_0 T_2) (-. (big_g T_0 T_2)) ### Axiom
% 0.19/0.47 25. (big_g T_1 T_1) (-. (big_g T_1 T_1)) ### Axiom
% 0.19/0.47 26. (-. ((big_g T_0 T_2) <=> (big_g T_1 T_1))) (big_g T_1 T_1) (big_g T_0 T_2) ### NotEquiv 24 25
% 0.19/0.47 27. ((big_f T_1 T_1) => (big_g T_1 T_1)) (big_g T_0 T_2) (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) (-. ((big_g T_0 T_2) <=> (big_g T_1 T_1))) ### Imply 23 26
% 0.19/0.47 28. ((big_f T_0 T_2) <=> ((big_f T_1 T_1) => (big_g T_1 T_1))) (-. ((big_g T_0 T_2) <=> (big_g T_1 T_1))) (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) (big_g T_0 T_2) (big_f T_0 T_2) ### Equiv 11 27
% 0.19/0.47 29. (-. (((big_f T_0 T_2) => ((big_f T_0 T_1) <=> (big_g T_2 T_1))) => (((big_f T_0 T_2) <=> ((big_f T_1 T_1) => (big_g T_1 T_1))) => ((big_g T_0 T_2) <=> (big_g T_1 T_1))))) (big_f T_0 T_2) (big_g T_0 T_2) (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) ### ConjTree 28
% 0.19/0.47 30. (-. (All Z, (((big_f T_0 T_2) => ((big_f T_0 Z) <=> (big_g T_2 Z))) => (((big_f T_0 T_2) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g T_0 T_2) <=> (big_g Z Z)))))) (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) (big_g T_0 T_2) (big_f T_0 T_2) ### NotAllEx 29
% 0.19/0.47 31. (-. (Ex Y, (All Z, (((big_f T_0 Y) => ((big_f T_0 Z) <=> (big_g Y Z))) => (((big_f T_0 Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g T_0 Y) <=> (big_g Z Z))))))) (big_f T_0 T_2) (big_g T_0 T_2) (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) ### NotExists 30
% 0.19/0.47 32. ((big_f T_0 T_2) <=> (big_g T_0 T_2)) (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) (-. (Ex Y, (All Z, (((big_f T_0 Y) => ((big_f T_0 Z) <=> (big_g Y Z))) => (((big_f T_0 Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g T_0 Y) <=> (big_g Z Z))))))) ### Equiv 10 31
% 0.19/0.47 33. ((big_f T_0 T_0) => ((big_f T_0 T_2) <=> (big_g T_0 T_2))) (-. (Ex Y, (All Z, (((big_f T_0 Y) => ((big_f T_0 Z) <=> (big_g Y Z))) => (((big_f T_0 Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g T_0 Y) <=> (big_g Z Z))))))) (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) (big_f T_0 T_0) ### Imply 1 32
% 0.19/0.47 34. (-. (((big_f T_0 T_0) => ((big_f T_0 T_2) <=> (big_g T_0 T_2))) => (((big_f T_0 T_0) <=> ((big_f T_2 T_2) => (big_g T_2 T_2))) => ((big_g T_0 T_0) <=> (big_g T_2 T_2))))) (big_f T_0 T_0) (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) (-. (Ex Y, (All Z, (((big_f T_0 Y) => ((big_f T_0 Z) <=> (big_g Y Z))) => (((big_f T_0 Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g T_0 Y) <=> (big_g Z Z))))))) ### ConjTree 33
% 0.19/0.47 35. (-. (All Z, (((big_f T_0 T_0) => ((big_f T_0 Z) <=> (big_g T_0 Z))) => (((big_f T_0 T_0) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g T_0 T_0) <=> (big_g Z Z)))))) (-. (Ex Y, (All Z, (((big_f T_0 Y) => ((big_f T_0 Z) <=> (big_g Y Z))) => (((big_f T_0 Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g T_0 Y) <=> (big_g Z Z))))))) (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) (big_f T_0 T_0) ### NotAllEx 34
% 0.19/0.47 36. (big_f T_0 T_0) (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) (-. (Ex Y, (All Z, (((big_f T_0 Y) => ((big_f T_0 Z) <=> (big_g Y Z))) => (((big_f T_0 Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g T_0 Y) <=> (big_g Z Z))))))) ### NotExists 35
% 0.19/0.47 37. (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) (big_f T_0 T_0) ### NotExists 36
% 0.19/0.47 38. (-. ((big_f T_0 T_0) => (big_g T_0 T_0))) (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) ### NotImply 37
% 0.19/0.47 39. (-. (big_f zenon_X4 zenon_X4)) (big_f zenon_X4 zenon_X4) ### Axiom
% 0.19/0.47 40. ((big_f zenon_X4 zenon_X4) <=> ((big_f T_0 T_0) => (big_g T_0 T_0))) (-. (big_f zenon_X4 zenon_X4)) (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) ### Equiv 38 39
% 0.19/0.48 41. (-. (big_g T_5 T_5)) (big_g T_5 T_5) ### Axiom
% 0.19/0.48 42. (-. (big_g zenon_X4 T_0)) (big_g zenon_X4 T_0) ### Axiom
% 0.19/0.48 43. (-. ((big_g zenon_X4 T_0) <=> (big_g T_5 T_5))) (-. (big_g zenon_X4 T_0)) (-. (big_g T_5 T_5)) ### NotEquiv 41 42
% 0.19/0.48 44. (-. ((big_f T_5 T_5) => (big_g T_5 T_5))) (-. (big_g zenon_X4 T_0)) (-. ((big_g zenon_X4 T_0) <=> (big_g T_5 T_5))) ### NotImply 43
% 0.19/0.48 45. (-. (big_f zenon_X4 T_0)) (big_f zenon_X4 T_0) ### Axiom
% 0.19/0.48 46. ((big_f zenon_X4 T_0) <=> ((big_f T_5 T_5) => (big_g T_5 T_5))) (-. (big_f zenon_X4 T_0)) (-. ((big_g zenon_X4 T_0) <=> (big_g T_5 T_5))) (-. (big_g zenon_X4 T_0)) ### Equiv 44 45
% 0.19/0.48 47. (-. (((big_f zenon_X4 T_0) => ((big_f zenon_X4 T_5) <=> (big_g T_0 T_5))) => (((big_f zenon_X4 T_0) <=> ((big_f T_5 T_5) => (big_g T_5 T_5))) => ((big_g zenon_X4 T_0) <=> (big_g T_5 T_5))))) (-. (big_g zenon_X4 T_0)) (-. (big_f zenon_X4 T_0)) ### ConjTree 46
% 0.19/0.48 48. (-. (All Z, (((big_f zenon_X4 T_0) => ((big_f zenon_X4 Z) <=> (big_g T_0 Z))) => (((big_f zenon_X4 T_0) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g zenon_X4 T_0) <=> (big_g Z Z)))))) (-. (big_f zenon_X4 T_0)) (-. (big_g zenon_X4 T_0)) ### NotAllEx 47
% 0.19/0.48 49. (-. (Ex Y, (All Z, (((big_f zenon_X4 Y) => ((big_f zenon_X4 Z) <=> (big_g Y Z))) => (((big_f zenon_X4 Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g zenon_X4 Y) <=> (big_g Z Z))))))) (-. (big_g zenon_X4 T_0)) (-. (big_f zenon_X4 T_0)) ### NotExists 48
% 0.19/0.48 50. (big_f zenon_X4 T_0) (-. (big_f zenon_X4 T_0)) ### Axiom
% 0.19/0.48 51. (big_g zenon_X4 T_0) (-. (big_g zenon_X4 T_0)) ### Axiom
% 0.19/0.48 52. (-. (big_g T_6 T_6)) (big_g T_6 T_6) ### Axiom
% 0.19/0.48 53. (-. (big_g T_5 T_5)) (big_g T_5 T_5) ### Axiom
% 0.19/0.48 54. (-. ((big_g T_5 T_5) <=> (big_g T_6 T_6))) (-. (big_g T_5 T_5)) (-. (big_g T_6 T_6)) ### NotEquiv 52 53
% 0.19/0.48 55. (-. ((big_f T_6 T_6) => (big_g T_6 T_6))) (-. (big_g T_5 T_5)) (-. ((big_g T_5 T_5) <=> (big_g T_6 T_6))) ### NotImply 54
% 0.19/0.48 56. (-. (big_f T_5 T_5)) (big_f T_5 T_5) ### Axiom
% 0.19/0.48 57. ((big_f T_5 T_5) <=> ((big_f T_6 T_6) => (big_g T_6 T_6))) (-. (big_f T_5 T_5)) (-. ((big_g T_5 T_5) <=> (big_g T_6 T_6))) (-. (big_g T_5 T_5)) ### Equiv 55 56
% 0.19/0.48 58. (-. (((big_f T_5 T_5) => ((big_f T_5 T_6) <=> (big_g T_5 T_6))) => (((big_f T_5 T_5) <=> ((big_f T_6 T_6) => (big_g T_6 T_6))) => ((big_g T_5 T_5) <=> (big_g T_6 T_6))))) (-. (big_g T_5 T_5)) (-. (big_f T_5 T_5)) ### ConjTree 57
% 0.19/0.48 59. (-. (All Z, (((big_f T_5 T_5) => ((big_f T_5 Z) <=> (big_g T_5 Z))) => (((big_f T_5 T_5) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g T_5 T_5) <=> (big_g Z Z)))))) (-. (big_f T_5 T_5)) (-. (big_g T_5 T_5)) ### NotAllEx 58
% 0.19/0.48 60. (-. (Ex Y, (All Z, (((big_f T_5 Y) => ((big_f T_5 Z) <=> (big_g Y Z))) => (((big_f T_5 Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g T_5 Y) <=> (big_g Z Z))))))) (-. (big_g T_5 T_5)) (-. (big_f T_5 T_5)) ### NotExists 59
% 0.19/0.48 61. (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) (-. (big_f T_5 T_5)) (-. (big_g T_5 T_5)) ### NotExists 60
% 0.19/0.48 62. (-. ((big_g zenon_X4 T_0) <=> (big_g T_5 T_5))) (-. (big_f T_5 T_5)) (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) (big_g zenon_X4 T_0) ### NotEquiv 51 61
% 0.19/0.48 63. (big_g zenon_X4 T_0) (-. (big_g zenon_X4 T_0)) ### Axiom
% 0.19/0.48 64. (big_g T_5 T_5) (-. (big_g T_5 T_5)) ### Axiom
% 0.19/0.48 65. (-. ((big_g zenon_X4 T_0) <=> (big_g T_5 T_5))) (big_g T_5 T_5) (big_g zenon_X4 T_0) ### NotEquiv 63 64
% 0.19/0.48 66. ((big_f T_5 T_5) => (big_g T_5 T_5)) (big_g zenon_X4 T_0) (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) (-. ((big_g zenon_X4 T_0) <=> (big_g T_5 T_5))) ### Imply 62 65
% 0.19/0.48 67. ((big_f zenon_X4 T_0) <=> ((big_f T_5 T_5) => (big_g T_5 T_5))) (-. ((big_g zenon_X4 T_0) <=> (big_g T_5 T_5))) (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) (big_g zenon_X4 T_0) (big_f zenon_X4 T_0) ### Equiv 50 66
% 0.19/0.48 68. (-. (((big_f zenon_X4 T_0) => ((big_f zenon_X4 T_5) <=> (big_g T_0 T_5))) => (((big_f zenon_X4 T_0) <=> ((big_f T_5 T_5) => (big_g T_5 T_5))) => ((big_g zenon_X4 T_0) <=> (big_g T_5 T_5))))) (big_f zenon_X4 T_0) (big_g zenon_X4 T_0) (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) ### ConjTree 67
% 0.19/0.48 69. (-. (All Z, (((big_f zenon_X4 T_0) => ((big_f zenon_X4 Z) <=> (big_g T_0 Z))) => (((big_f zenon_X4 T_0) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g zenon_X4 T_0) <=> (big_g Z Z)))))) (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) (big_g zenon_X4 T_0) (big_f zenon_X4 T_0) ### NotAllEx 68
% 0.19/0.48 70. (-. (Ex Y, (All Z, (((big_f zenon_X4 Y) => ((big_f zenon_X4 Z) <=> (big_g Y Z))) => (((big_f zenon_X4 Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g zenon_X4 Y) <=> (big_g Z Z))))))) (big_f zenon_X4 T_0) (big_g zenon_X4 T_0) (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) ### NotExists 69
% 0.19/0.48 71. ((big_f zenon_X4 T_0) <=> (big_g zenon_X4 T_0)) (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) (-. (Ex Y, (All Z, (((big_f zenon_X4 Y) => ((big_f zenon_X4 Z) <=> (big_g Y Z))) => (((big_f zenon_X4 Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g zenon_X4 Y) <=> (big_g Z Z))))))) ### Equiv 49 70
% 0.19/0.48 72. ((big_f zenon_X4 zenon_X4) => ((big_f zenon_X4 T_0) <=> (big_g zenon_X4 T_0))) (-. (Ex Y, (All Z, (((big_f zenon_X4 Y) => ((big_f zenon_X4 Z) <=> (big_g Y Z))) => (((big_f zenon_X4 Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g zenon_X4 Y) <=> (big_g Z Z))))))) (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) ((big_f zenon_X4 zenon_X4) <=> ((big_f T_0 T_0) => (big_g T_0 T_0))) ### Imply 40 71
% 0.19/0.48 73. (-. (((big_f zenon_X4 zenon_X4) => ((big_f zenon_X4 T_0) <=> (big_g zenon_X4 T_0))) => (((big_f zenon_X4 zenon_X4) <=> ((big_f T_0 T_0) => (big_g T_0 T_0))) => ((big_g zenon_X4 zenon_X4) <=> (big_g T_0 T_0))))) (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) (-. (Ex Y, (All Z, (((big_f zenon_X4 Y) => ((big_f zenon_X4 Z) <=> (big_g Y Z))) => (((big_f zenon_X4 Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g zenon_X4 Y) <=> (big_g Z Z))))))) ### ConjTree 72
% 0.19/0.48 74. (-. (All Z, (((big_f zenon_X4 zenon_X4) => ((big_f zenon_X4 Z) <=> (big_g zenon_X4 Z))) => (((big_f zenon_X4 zenon_X4) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g zenon_X4 zenon_X4) <=> (big_g Z Z)))))) (-. (Ex Y, (All Z, (((big_f zenon_X4 Y) => ((big_f zenon_X4 Z) <=> (big_g Y Z))) => (((big_f zenon_X4 Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g zenon_X4 Y) <=> (big_g Z Z))))))) (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) ### NotAllEx 73
% 0.19/0.48 75. (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) (-. (Ex Y, (All Z, (((big_f zenon_X4 Y) => ((big_f zenon_X4 Z) <=> (big_g Y Z))) => (((big_f zenon_X4 Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g zenon_X4 Y) <=> (big_g Z Z))))))) ### NotExists 74
% 0.19/0.48 76. (-. (Ex X, (Ex Y, (All Z, (((big_f X Y) => ((big_f X Z) <=> (big_g Y Z))) => (((big_f X Y) <=> ((big_f Z Z) => (big_g Z Z))) => ((big_g X Y) <=> (big_g Z Z)))))))) ### NotExists 75
% 0.19/0.48 % SZS output end Proof
% 0.19/0.48 (* END-PROOF *)
%------------------------------------------------------------------------------