TSTP Solution File: SYN345+1 by SuperZenon---0.0.1
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%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SYN345+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 : n012.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 12:42:49 EDT 2022
% Result : Theorem 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYN345+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jul 11 18:40:13 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 (* PROOF-FOUND *)
% 0.20/0.45 (* BEGIN-PROOF *)
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 1. (big_f T_0 T_0 T_1) (-. (big_f T_0 T_0 T_1)) ### Axiom
% 0.20/0.45 2. (-. (big_f T_0 T_2 T_2)) (big_f T_0 T_2 T_2) ### Axiom
% 0.20/0.45 3. (-. ((big_f T_0 T_2 T_2) => (big_f T_2 T_3 T_3))) (-. (big_f T_0 T_2 T_2)) ### NotImply 2
% 0.20/0.45 4. (big_f T_4 T_0 T_0) (-. (big_f T_4 T_0 T_0)) ### Axiom
% 0.20/0.45 5. (-. (big_f T_4 T_4 T_0)) (big_f T_4 T_4 T_0) ### Axiom
% 0.20/0.45 6. (((big_f T_0 T_2 T_2) => (big_f T_2 T_3 T_3)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) (-. (big_f T_4 T_4 T_0)) (big_f T_4 T_0 T_0) (-. (big_f T_0 T_2 T_2)) ### DisjTree 3 4 5
% 0.20/0.45 7. (-. ((((big_f T_4 T_0 T_2) => (big_f T_2 T_2 T_3)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 T_2 T_2) => (big_f T_2 T_3 T_3)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f T_2 T_2 T_3) => ((big_f T_0 T_0 T_2) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0))))))) (-. (big_f T_0 T_2 T_2)) (big_f T_4 T_0 T_0) (-. (big_f T_4 T_4 T_0)) ### ConjTree 6
% 0.20/0.45 8. (-. (All Z, ((((big_f T_4 T_0 T_2) => (big_f T_2 T_2 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 T_2 T_2) => (big_f T_2 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f T_2 T_2 Z) => ((big_f T_0 T_0 T_2) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0)))))))) (-. (big_f T_4 T_4 T_0)) (big_f T_4 T_0 T_0) (-. (big_f T_0 T_2 T_2)) ### NotAllEx 7
% 0.20/0.45 9. (-. (Ex Y2, (All Z, ((((big_f T_4 T_0 T_2) => (big_f Y2 T_2 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 T_2 Y2) => (big_f T_2 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f T_2 Y2 Z) => ((big_f T_0 T_0 T_2) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0))))))))) (-. (big_f T_0 T_2 T_2)) (big_f T_4 T_0 T_0) (-. (big_f T_4 T_4 T_0)) ### NotExists 8
% 0.20/0.45 10. (-. (Ex Y1, (Ex Y2, (All Z, ((((big_f T_4 T_0 Y1) => (big_f Y2 Y1 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 Y1 Y2) => (big_f Y1 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f Y1 Y2 Z) => ((big_f T_0 T_0 Y1) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0)))))))))) (-. (big_f T_4 T_4 T_0)) (big_f T_4 T_0 T_0) (-. (big_f T_0 T_2 T_2)) ### NotExists 9
% 0.20/0.45 11. (-. ((big_f T_0 T_0 zenon_X5) => (big_f T_0 T_2 T_2))) (big_f T_4 T_0 T_0) (-. (big_f T_4 T_4 T_0)) (-. (Ex Y1, (Ex Y2, (All Z, ((((big_f T_4 T_0 Y1) => (big_f Y2 Y1 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 Y1 Y2) => (big_f Y1 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f Y1 Y2 Z) => ((big_f T_0 T_0 Y1) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0)))))))))) ### NotImply 10
% 0.20/0.45 12. (big_f T_4 T_0 T_0) (-. (big_f T_4 T_0 T_0)) ### Axiom
% 0.20/0.45 13. (-. (big_f T_4 T_4 T_0)) (big_f T_4 T_4 T_0) ### Axiom
% 0.20/0.45 14. (((big_f T_0 T_0 zenon_X5) => (big_f T_0 T_2 T_2)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) (-. (Ex Y1, (Ex Y2, (All Z, ((((big_f T_4 T_0 Y1) => (big_f Y2 Y1 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 Y1 Y2) => (big_f Y1 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f Y1 Y2 Z) => ((big_f T_0 T_0 Y1) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0)))))))))) (-. (big_f T_4 T_4 T_0)) (big_f T_4 T_0 T_0) ### DisjTree 11 12 13
% 0.20/0.45 15. (-. ((((big_f T_4 T_0 T_0) => (big_f zenon_X5 T_0 T_2)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 T_0 zenon_X5) => (big_f T_0 T_2 T_2)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f T_0 zenon_X5 T_2) => ((big_f T_0 T_0 T_0) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0))))))) (big_f T_4 T_0 T_0) (-. (big_f T_4 T_4 T_0)) (-. (Ex Y1, (Ex Y2, (All Z, ((((big_f T_4 T_0 Y1) => (big_f Y2 Y1 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 Y1 Y2) => (big_f Y1 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f Y1 Y2 Z) => ((big_f T_0 T_0 Y1) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0)))))))))) ### ConjTree 14
% 0.20/0.45 16. (-. (All Z, ((((big_f T_4 T_0 T_0) => (big_f zenon_X5 T_0 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 T_0 zenon_X5) => (big_f T_0 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f T_0 zenon_X5 Z) => ((big_f T_0 T_0 T_0) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0)))))))) (-. (Ex Y1, (Ex Y2, (All Z, ((((big_f T_4 T_0 Y1) => (big_f Y2 Y1 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 Y1 Y2) => (big_f Y1 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f Y1 Y2 Z) => ((big_f T_0 T_0 Y1) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0)))))))))) (-. (big_f T_4 T_4 T_0)) (big_f T_4 T_0 T_0) ### NotAllEx 15
% 0.20/0.45 17. (-. (Ex Y2, (All Z, ((((big_f T_4 T_0 T_0) => (big_f Y2 T_0 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 T_0 Y2) => (big_f T_0 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f T_0 Y2 Z) => ((big_f T_0 T_0 T_0) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0))))))))) (big_f T_4 T_0 T_0) (-. (big_f T_4 T_4 T_0)) (-. (Ex Y1, (Ex Y2, (All Z, ((((big_f T_4 T_0 Y1) => (big_f Y2 Y1 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 Y1 Y2) => (big_f Y1 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f Y1 Y2 Z) => ((big_f T_0 T_0 Y1) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0)))))))))) ### NotExists 16
% 0.20/0.45 18. (-. (Ex Y1, (Ex Y2, (All Z, ((((big_f T_4 T_0 Y1) => (big_f Y2 Y1 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 Y1 Y2) => (big_f Y1 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f Y1 Y2 Z) => ((big_f T_0 T_0 Y1) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0)))))))))) (-. (big_f T_4 T_4 T_0)) (big_f T_4 T_0 T_0) ### NotExists 17
% 0.20/0.45 19. (big_f T_4 T_0 T_0) (-. (big_f T_4 T_0 T_0)) ### Axiom
% 0.20/0.45 20. (-. ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0))) (big_f T_4 T_0 T_0) (-. (Ex Y1, (Ex Y2, (All Z, ((((big_f T_4 T_0 Y1) => (big_f Y2 Y1 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 Y1 Y2) => (big_f Y1 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f Y1 Y2 Z) => ((big_f T_0 T_0 Y1) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0)))))))))) ### NotEquiv 18 19
% 0.20/0.45 21. (-. (big_f T_4 T_0 T_0)) (big_f T_4 T_0 T_0) ### Axiom
% 0.20/0.45 22. (-. ((big_f T_4 T_0 T_0) => (big_f zenon_X5 T_0 T_2))) (-. (big_f T_4 T_0 T_0)) ### NotImply 21
% 0.20/0.45 23. (big_f T_4 T_4 T_0) (-. (big_f T_4 T_4 T_0)) ### Axiom
% 0.20/0.45 24. (-. (big_f T_4 T_0 T_0)) (big_f T_4 T_0 T_0) ### Axiom
% 0.20/0.45 25. (((big_f T_4 T_0 T_0) => (big_f zenon_X5 T_0 T_2)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) (big_f T_4 T_4 T_0) (-. (big_f T_4 T_0 T_0)) ### DisjTree 22 23 24
% 0.20/0.45 26. (-. ((((big_f T_4 T_0 T_0) => (big_f zenon_X5 T_0 T_2)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 T_0 zenon_X5) => (big_f T_0 T_2 T_2)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f T_0 zenon_X5 T_2) => ((big_f T_0 T_0 T_0) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0))))))) (-. (big_f T_4 T_0 T_0)) (big_f T_4 T_4 T_0) ### ConjTree 25
% 0.20/0.45 27. (-. (All Z, ((((big_f T_4 T_0 T_0) => (big_f zenon_X5 T_0 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 T_0 zenon_X5) => (big_f T_0 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f T_0 zenon_X5 Z) => ((big_f T_0 T_0 T_0) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0)))))))) (big_f T_4 T_4 T_0) (-. (big_f T_4 T_0 T_0)) ### NotAllEx 26
% 0.20/0.45 28. (-. (Ex Y2, (All Z, ((((big_f T_4 T_0 T_0) => (big_f Y2 T_0 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 T_0 Y2) => (big_f T_0 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f T_0 Y2 Z) => ((big_f T_0 T_0 T_0) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0))))))))) (-. (big_f T_4 T_0 T_0)) (big_f T_4 T_4 T_0) ### NotExists 27
% 0.20/0.45 29. (-. (Ex Y1, (Ex Y2, (All Z, ((((big_f T_4 T_0 Y1) => (big_f Y2 Y1 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 Y1 Y2) => (big_f Y1 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f Y1 Y2 Z) => ((big_f T_0 T_0 Y1) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0)))))))))) (big_f T_4 T_4 T_0) (-. (big_f T_4 T_0 T_0)) ### NotExists 28
% 0.20/0.45 30. (-. (Ex Y1, (Ex Y2, (All Z, ((((big_f T_4 T_0 Y1) => (big_f Y2 Y1 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 Y1 Y2) => (big_f Y1 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f Y1 Y2 Z) => ((big_f T_0 T_0 Y1) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0)))))))))) (-. ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0))) ### NotEquiv 20 29
% 0.20/0.46 31. (-. ((big_f T_0 T_0 T_1) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0)))) (-. (Ex Y1, (Ex Y2, (All Z, ((((big_f T_4 T_0 Y1) => (big_f Y2 Y1 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 Y1 Y2) => (big_f Y1 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f Y1 Y2 Z) => ((big_f T_0 T_0 Y1) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0)))))))))) (big_f T_0 T_0 T_1) ### NotAnd 1 30
% 0.20/0.46 32. (-. ((((big_f T_4 T_0 T_1) => (big_f zenon_X6 T_1 T_7)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 T_1 zenon_X6) => (big_f T_1 T_7 T_7)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f T_1 zenon_X6 T_7) => ((big_f T_0 T_0 T_1) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0))))))) (big_f T_0 T_0 T_1) (-. (Ex Y1, (Ex Y2, (All Z, ((((big_f T_4 T_0 Y1) => (big_f Y2 Y1 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 Y1 Y2) => (big_f Y1 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f Y1 Y2 Z) => ((big_f T_0 T_0 Y1) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0)))))))))) ### ConjTree 31
% 0.20/0.46 33. (-. (All Z, ((((big_f T_4 T_0 T_1) => (big_f zenon_X6 T_1 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 T_1 zenon_X6) => (big_f T_1 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f T_1 zenon_X6 Z) => ((big_f T_0 T_0 T_1) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0)))))))) (-. (Ex Y1, (Ex Y2, (All Z, ((((big_f T_4 T_0 Y1) => (big_f Y2 Y1 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 Y1 Y2) => (big_f Y1 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f Y1 Y2 Z) => ((big_f T_0 T_0 Y1) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0)))))))))) (big_f T_0 T_0 T_1) ### NotAllEx 32
% 0.20/0.46 34. (-. (Ex Y2, (All Z, ((((big_f T_4 T_0 T_1) => (big_f Y2 T_1 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 T_1 Y2) => (big_f T_1 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f T_1 Y2 Z) => ((big_f T_0 T_0 T_1) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0))))))))) (big_f T_0 T_0 T_1) (-. (Ex Y1, (Ex Y2, (All Z, ((((big_f T_4 T_0 Y1) => (big_f Y2 Y1 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 Y1 Y2) => (big_f Y1 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f Y1 Y2 Z) => ((big_f T_0 T_0 Y1) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0)))))))))) ### NotExists 33
% 0.20/0.46 35. (-. (Ex Y1, (Ex Y2, (All Z, ((((big_f T_4 T_0 Y1) => (big_f Y2 Y1 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 Y1 Y2) => (big_f Y1 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f Y1 Y2 Z) => ((big_f T_0 T_0 Y1) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0)))))))))) (big_f T_0 T_0 T_1) ### NotExists 34
% 0.20/0.46 36. (-. ((((big_f T_4 T_0 T_0) => (big_f T_0 T_0 T_1)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 T_0 T_0) => (big_f T_0 T_1 T_1)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f T_0 T_0 T_1) => ((big_f T_0 T_0 T_0) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0))))))) (-. (Ex Y1, (Ex Y2, (All Z, ((((big_f T_4 T_0 Y1) => (big_f Y2 Y1 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 Y1 Y2) => (big_f Y1 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f Y1 Y2 Z) => ((big_f T_0 T_0 Y1) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0)))))))))) ### ConjTree 35
% 0.20/0.46 37. (-. (All Z, ((((big_f T_4 T_0 T_0) => (big_f T_0 T_0 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 T_0 T_0) => (big_f T_0 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f T_0 T_0 Z) => ((big_f T_0 T_0 T_0) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0)))))))) (-. (Ex Y1, (Ex Y2, (All Z, ((((big_f T_4 T_0 Y1) => (big_f Y2 Y1 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 Y1 Y2) => (big_f Y1 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f Y1 Y2 Z) => ((big_f T_0 T_0 Y1) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0)))))))))) ### NotAllEx 36
% 0.20/0.46 38. (-. (Ex Y2, (All Z, ((((big_f T_4 T_0 T_0) => (big_f Y2 T_0 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 T_0 Y2) => (big_f T_0 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f T_0 Y2 Z) => ((big_f T_0 T_0 T_0) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0))))))))) (-. (Ex Y1, (Ex Y2, (All Z, ((((big_f T_4 T_0 Y1) => (big_f Y2 Y1 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 Y1 Y2) => (big_f Y1 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f Y1 Y2 Z) => ((big_f T_0 T_0 Y1) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0)))))))))) ### NotExists 37
% 0.20/0.46 39. (-. (Ex Y1, (Ex Y2, (All Z, ((((big_f T_4 T_0 Y1) => (big_f Y2 Y1 Z)) => ((big_f T_4 T_4 T_0) => (big_f T_4 T_0 T_0))) => ((((big_f T_0 Y1 Y2) => (big_f Y1 Z Z)) => ((big_f T_4 T_0 T_0) => (big_f T_4 T_4 T_0))) => ((big_f Y1 Y2 Z) => ((big_f T_0 T_0 Y1) /\ ((big_f T_4 T_4 T_0) <=> (big_f T_4 T_0 T_0)))))))))) ### NotExists 38
% 0.20/0.46 40. (-. (All X2, (Ex Y1, (Ex Y2, (All Z, ((((big_f T_4 X2 Y1) => (big_f Y2 Y1 Z)) => ((big_f T_4 T_4 X2) => (big_f T_4 X2 X2))) => ((((big_f X2 Y1 Y2) => (big_f Y1 Z Z)) => ((big_f T_4 X2 X2) => (big_f T_4 T_4 X2))) => ((big_f Y1 Y2 Z) => ((big_f X2 X2 Y1) /\ ((big_f T_4 T_4 X2) <=> (big_f T_4 X2 X2))))))))))) ### NotAllEx 39
% 0.20/0.46 41. (-. (All X1, (All X2, (Ex Y1, (Ex Y2, (All Z, ((((big_f X1 X2 Y1) => (big_f Y2 Y1 Z)) => ((big_f X1 X1 X2) => (big_f X1 X2 X2))) => ((((big_f X2 Y1 Y2) => (big_f Y1 Z Z)) => ((big_f X1 X2 X2) => (big_f X1 X1 X2))) => ((big_f Y1 Y2 Z) => ((big_f X2 X2 Y1) /\ ((big_f X1 X1 X2) <=> (big_f X1 X2 X2)))))))))))) ### NotAllEx 40
% 0.20/0.46 % SZS output end Proof
% 0.20/0.46 (* END-PROOF *)
%------------------------------------------------------------------------------