TSTP Solution File: SYN319+1 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SYN319+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n005.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 : 300s
% DateTime : Thu Sep 29 22:22:56 EDT 2022
% Result : Theorem 0.19s 0.51s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN319+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n005.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Sep 5 02:32:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 [DMT] DMT loaded with preskolemization
% 0.12/0.34 [EQ] equality loaded.
% 0.12/0.34 [0.000040s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.34 Start search
% 0.12/0.34 nb_step : 1 - limit : 2
% 0.12/0.34 Launch Gotab with destructive = true
% 0.19/0.50 % SZS output start Proof for theBenchmark.p
% 0.19/0.51 [0] GAMMA_NOT_EXISTS : ~? [X4_4, Y5_5] : (! [Z16_6, Z27_7] : ((((big_f(Y5_5) => big_g(Z16_6)) => (big_g(X4_4) & ~big_f(Z16_6))) => (((big_f(X4_4) | big_g(X4_4)) => big_h(X4_4)) => (big_h(Z27_7) & (big_h(Y5_5) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7))))))))
% 0.19/0.51 -> [1] ~! [Z16_6, Z27_7] : ((((big_f(X4_0_0) => big_g(Z16_6)) => (big_g(X4_0_0) & ~big_f(Z16_6))) => (((big_f(X4_0_0) | big_g(X4_0_0)) => big_h(X4_0_0)) => (big_h(Z27_7) & (big_h(X4_0_0) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7)))))))
% 0.19/0.51
% 0.19/0.51 [1] DELTA_NOT_FORALL : ~! [Z16_6, Z27_7] : ((((big_f(X4_0_0) => big_g(Z16_6)) => (big_g(X4_0_0) & ~big_f(Z16_6))) => (((big_f(X4_0_0) | big_g(X4_0_0)) => big_h(X4_0_0)) => (big_h(Z27_7) & (big_h(X4_0_0) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7)))))))
% 0.19/0.51 -> [2] ~(((big_f(X4_0_0) => big_g(skolem_Z166(X4_0_0, X4_0_0))) => (big_g(X4_0_0) & ~big_f(skolem_Z166(X4_0_0, X4_0_0)))) => (((big_f(X4_0_0) | big_g(X4_0_0)) => big_h(X4_0_0)) => (big_h(skolem_Z277(X4_0_0, X4_0_0)) & (big_h(X4_0_0) => ((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0)))))))
% 0.19/0.51
% 0.19/0.51 [2] ALPHA_NOT_IMPLY : ~(((big_f(X4_0_0) => big_g(skolem_Z166(X4_0_0, X4_0_0))) => (big_g(X4_0_0) & ~big_f(skolem_Z166(X4_0_0, X4_0_0)))) => (((big_f(X4_0_0) | big_g(X4_0_0)) => big_h(X4_0_0)) => (big_h(skolem_Z277(X4_0_0, X4_0_0)) & (big_h(X4_0_0) => ((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0)))))))
% 0.19/0.51 -> [3] ((big_f(X4_0_0) => big_g(skolem_Z166(X4_0_0, X4_0_0))) => (big_g(X4_0_0) & ~big_f(skolem_Z166(X4_0_0, X4_0_0)))), ~(((big_f(X4_0_0) | big_g(X4_0_0)) => big_h(X4_0_0)) => (big_h(skolem_Z277(X4_0_0, X4_0_0)) & (big_h(X4_0_0) => ((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))))))
% 0.19/0.51
% 0.19/0.51 [3] ALPHA_NOT_IMPLY : ~(((big_f(X4_0_0) | big_g(X4_0_0)) => big_h(X4_0_0)) => (big_h(skolem_Z277(X4_0_0, X4_0_0)) & (big_h(X4_0_0) => ((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))))))
% 0.19/0.51 -> [4] ((big_f(X4_0_0) | big_g(X4_0_0)) => big_h(X4_0_0)), ~(big_h(skolem_Z277(X4_0_0, X4_0_0)) & (big_h(X4_0_0) => ((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0)))))
% 0.19/0.51
% 0.19/0.51 [4] BETA_IMPLY : ((big_f(X4_0_0) => big_g(skolem_Z166(X4_0_0, X4_0_0))) => (big_g(X4_0_0) & ~big_f(skolem_Z166(X4_0_0, X4_0_0))))
% 0.19/0.51 -> [5] ~(big_f(X4_0_0) => big_g(skolem_Z166(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [6] (big_g(X4_0_0) & ~big_f(skolem_Z166(X4_0_0, X4_0_0)))
% 0.19/0.51
% 0.19/0.51 [6] ALPHA_AND : (big_g(X4_0_0) & ~big_f(skolem_Z166(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [8] big_g(X4_0_0), ~big_f(skolem_Z166(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [8] BETA_IMPLY : ((big_f(X4_0_0) | big_g(X4_0_0)) => big_h(X4_0_0))
% 0.19/0.51 -> [11] ~(big_f(X4_0_0) | big_g(X4_0_0))
% 0.19/0.51 -> [12] big_h(X4_0_0)
% 0.19/0.51
% 0.19/0.51 [11] ALPHA_NOT_OR : ~(big_f(X4_0_0) | big_g(X4_0_0))
% 0.19/0.51 -> [14] ~big_f(X4_0_0), ~big_g(X4_0_0)
% 0.19/0.51
% 0.19/0.51 [14] CLOSURE : ~big_g(X4_0_0)
% 0.19/0.51
% 0.19/0.51 [12] BETA_NOT_AND : ~(big_h(skolem_Z277(X4_0_0, X4_0_0)) & (big_h(X4_0_0) => ((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0)))))
% 0.19/0.51 -> [15] ~big_h(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51 -> [16] ~(big_h(X4_0_0) => ((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))))
% 0.19/0.51
% 0.19/0.51 [15] : ~? [X4_4, Y5_5] : (! [Z16_6, Z27_7] : ((((big_f(Y5_5) => big_g(Z16_6)) => (big_g(X4_4) & ~big_f(Z16_6))) => (((big_f(X4_4) | big_g(X4_4)) => big_h(X4_4)) => (big_h(Z27_7) & (big_h(Y5_5) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7))))))))
% 0.19/0.51 -> [21] ~? [X4_4, Y5_5] : (! [Z16_6, Z27_7] : ((((big_f(Y5_5) => big_g(Z16_6)) => (big_g(X4_4) & ~big_f(Z16_6))) => (((big_f(X4_4) | big_g(X4_4)) => big_h(X4_4)) => (big_h(Z27_7) & (big_h(Y5_5) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7))))))))
% 0.19/0.51
% 0.19/0.51 [21] GAMMA_NOT_EXISTS : ~? [X4_4, Y5_5] : (! [Z16_6, Z27_7] : ((((big_f(Y5_5) => big_g(Z16_6)) => (big_g(X4_4) & ~big_f(Z16_6))) => (((big_f(X4_4) | big_g(X4_4)) => big_h(X4_4)) => (big_h(Z27_7) & (big_h(Y5_5) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7))))))))
% 0.19/0.51 -> [25] ~! [Z16_6, Z27_7] : ((((big_f(skolem_Z166(X4_0_0, X4_0_0)) => big_g(Z16_6)) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(Z16_6))) => (((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(Z27_7) & (big_h(skolem_Z166(X4_0_0, X4_0_0)) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7)))))))
% 0.19/0.51
% 0.19/0.51 [25] DELTA_NOT_FORALL : ~! [Z16_6, Z27_7] : ((((big_f(skolem_Z166(X4_0_0, X4_0_0)) => big_g(Z16_6)) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(Z16_6))) => (((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(Z27_7) & (big_h(skolem_Z166(X4_0_0, X4_0_0)) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7)))))))
% 0.19/0.51 -> [27] ~(((big_f(skolem_Z166(X4_0_0, X4_0_0)) => big_g(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))) => (((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) & (big_h(skolem_Z166(X4_0_0, X4_0_0)) => ((big_f(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))))))
% 0.19/0.51
% 0.19/0.51 [27] ALPHA_NOT_IMPLY : ~(((big_f(skolem_Z166(X4_0_0, X4_0_0)) => big_g(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))) => (((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) & (big_h(skolem_Z166(X4_0_0, X4_0_0)) => ((big_f(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))))))
% 0.19/0.51 -> [31] ((big_f(skolem_Z166(X4_0_0, X4_0_0)) => big_g(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))), ~(((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) & (big_h(skolem_Z166(X4_0_0, X4_0_0)) => ((big_f(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))))))
% 0.19/0.51
% 0.19/0.51 [31] ALPHA_NOT_IMPLY : ~(((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) & (big_h(skolem_Z166(X4_0_0, X4_0_0)) => ((big_f(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))))))
% 0.19/0.51 -> [35] ((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))), ~(big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) & (big_h(skolem_Z166(X4_0_0, X4_0_0)) => ((big_f(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))))
% 0.19/0.51
% 0.19/0.51 [35] BETA_IMPLY : ((big_f(skolem_Z166(X4_0_0, X4_0_0)) => big_g(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))))
% 0.19/0.51 -> [37] ~(big_f(skolem_Z166(X4_0_0, X4_0_0)) => big_g(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))
% 0.19/0.51 -> [38] (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))
% 0.19/0.51
% 0.19/0.51 [37] ALPHA_NOT_IMPLY : ~(big_f(skolem_Z166(X4_0_0, X4_0_0)) => big_g(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))
% 0.19/0.51 -> [41] big_f(skolem_Z166(X4_0_0, X4_0_0)), ~big_g(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51
% 0.19/0.51 [41] CLOSURE : ~big_g(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51
% 0.19/0.51 [47] BETA_IMPLY : ((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [98] ~(big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [99] big_h(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [99] CLOSURE : big_h(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [98] ALPHA_NOT_OR : ~(big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [100] ~big_f(skolem_Z277(X4_0_0, X4_0_0)), ~big_g(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [100] CLOSURE : ~big_g(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [16] ALPHA_NOT_IMPLY : ~(big_h(X4_0_0) => ((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))))
% 0.19/0.51 -> [19] big_h(X4_0_0), ~((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51
% 0.19/0.51 [19] ALPHA_NOT_IMPLY : ~((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [23] (big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))), ~big_h(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [23] BETA_OR : (big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [29] big_f(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51 -> [30] big_g(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [30] : ~? [X4_4, Y5_5] : (! [Z16_6, Z27_7] : ((((big_f(Y5_5) => big_g(Z16_6)) => (big_g(X4_4) & ~big_f(Z16_6))) => (((big_f(X4_4) | big_g(X4_4)) => big_h(X4_4)) => (big_h(Z27_7) & (big_h(Y5_5) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7))))))))
% 0.19/0.51 -> [44] ~? [X4_4, Y5_5] : (! [Z16_6, Z27_7] : ((((big_f(Y5_5) => big_g(Z16_6)) => (big_g(X4_4) & ~big_f(Z16_6))) => (((big_f(X4_4) | big_g(X4_4)) => big_h(X4_4)) => (big_h(Z27_7) & (big_h(Y5_5) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7))))))))
% 0.19/0.51
% 0.19/0.51 [44] GAMMA_NOT_EXISTS : ~? [X4_4, Y5_5] : (! [Z16_6, Z27_7] : ((((big_f(Y5_5) => big_g(Z16_6)) => (big_g(X4_4) & ~big_f(Z16_6))) => (((big_f(X4_4) | big_g(X4_4)) => big_h(X4_4)) => (big_h(Z27_7) & (big_h(Y5_5) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7))))))))
% 0.19/0.51 -> [48] ~! [Z16_6, Z27_7] : ((((big_f(skolem_Z166(X4_0_0, X4_0_0)) => big_g(Z16_6)) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(Z16_6))) => (((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(Z27_7) & (big_h(skolem_Z166(X4_0_0, X4_0_0)) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7)))))))
% 0.19/0.51
% 0.19/0.51 [48] DELTA_NOT_FORALL : ~! [Z16_6, Z27_7] : ((((big_f(skolem_Z166(X4_0_0, X4_0_0)) => big_g(Z16_6)) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(Z16_6))) => (((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(Z27_7) & (big_h(skolem_Z166(X4_0_0, X4_0_0)) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7)))))))
% 0.19/0.51 -> [52] ~(((big_f(skolem_Z166(X4_0_0, X4_0_0)) => big_g(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))) => (((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) & (big_h(skolem_Z166(X4_0_0, X4_0_0)) => ((big_f(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))))))
% 0.19/0.51
% 0.19/0.51 [52] ALPHA_NOT_IMPLY : ~(((big_f(skolem_Z166(X4_0_0, X4_0_0)) => big_g(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))) => (((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) & (big_h(skolem_Z166(X4_0_0, X4_0_0)) => ((big_f(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))))))
% 0.19/0.51 -> [56] ((big_f(skolem_Z166(X4_0_0, X4_0_0)) => big_g(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))), ~(((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) & (big_h(skolem_Z166(X4_0_0, X4_0_0)) => ((big_f(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))))))
% 0.19/0.51
% 0.19/0.51 [56] ALPHA_NOT_IMPLY : ~(((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) & (big_h(skolem_Z166(X4_0_0, X4_0_0)) => ((big_f(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))))))
% 0.19/0.51 -> [60] ((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))), ~(big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) & (big_h(skolem_Z166(X4_0_0, X4_0_0)) => ((big_f(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))))
% 0.19/0.51
% 0.19/0.51 [60] BETA_IMPLY : ((big_f(skolem_Z166(X4_0_0, X4_0_0)) => big_g(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))))
% 0.19/0.51 -> [69] ~(big_f(skolem_Z166(X4_0_0, X4_0_0)) => big_g(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))
% 0.19/0.51 -> [70] (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))
% 0.19/0.51
% 0.19/0.51 [69] ALPHA_NOT_IMPLY : ~(big_f(skolem_Z166(X4_0_0, X4_0_0)) => big_g(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))
% 0.19/0.51 -> [82] big_f(skolem_Z166(X4_0_0, X4_0_0)), ~big_g(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51
% 0.19/0.51 [82] CLOSURE : ~big_g(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51
% 0.19/0.51 [75] BETA_IMPLY : ((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [105] ~(big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [106] big_h(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [106] CLOSURE : big_h(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [105] ALPHA_NOT_OR : ~(big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [109] ~big_f(skolem_Z277(X4_0_0, X4_0_0)), ~big_g(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [109] CLOSURE : ~big_g(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [29] : ~? [X4_4, Y5_5] : (! [Z16_6, Z27_7] : ((((big_f(Y5_5) => big_g(Z16_6)) => (big_g(X4_4) & ~big_f(Z16_6))) => (((big_f(X4_4) | big_g(X4_4)) => big_h(X4_4)) => (big_h(Z27_7) & (big_h(Y5_5) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7))))))))
% 0.19/0.51 -> [43] ~? [X4_4, Y5_5] : (! [Z16_6, Z27_7] : ((((big_f(Y5_5) => big_g(Z16_6)) => (big_g(X4_4) & ~big_f(Z16_6))) => (((big_f(X4_4) | big_g(X4_4)) => big_h(X4_4)) => (big_h(Z27_7) & (big_h(Y5_5) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7))))))))
% 0.19/0.51
% 0.19/0.51 [43] GAMMA_NOT_EXISTS : ~? [X4_4, Y5_5] : (! [Z16_6, Z27_7] : ((((big_f(Y5_5) => big_g(Z16_6)) => (big_g(X4_4) & ~big_f(Z16_6))) => (((big_f(X4_4) | big_g(X4_4)) => big_h(X4_4)) => (big_h(Z27_7) & (big_h(Y5_5) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7))))))))
% 0.19/0.51 -> [45] ~! [Z16_6, Z27_7] : ((((big_f(skolem_Z166(X4_0_0, X4_0_0)) => big_g(Z16_6)) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(Z16_6))) => (((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(Z27_7) & (big_h(skolem_Z166(X4_0_0, X4_0_0)) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7)))))))
% 0.19/0.51
% 0.19/0.51 [45] DELTA_NOT_FORALL : ~! [Z16_6, Z27_7] : ((((big_f(skolem_Z166(X4_0_0, X4_0_0)) => big_g(Z16_6)) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(Z16_6))) => (((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(Z27_7) & (big_h(skolem_Z166(X4_0_0, X4_0_0)) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7)))))))
% 0.19/0.51 -> [49] ~(((big_f(skolem_Z166(X4_0_0, X4_0_0)) => big_g(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))) => (((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) & (big_h(skolem_Z166(X4_0_0, X4_0_0)) => ((big_f(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))))))
% 0.19/0.51
% 0.19/0.51 [49] ALPHA_NOT_IMPLY : ~(((big_f(skolem_Z166(X4_0_0, X4_0_0)) => big_g(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))) => (((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) & (big_h(skolem_Z166(X4_0_0, X4_0_0)) => ((big_f(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))))))
% 0.19/0.51 -> [53] ((big_f(skolem_Z166(X4_0_0, X4_0_0)) => big_g(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))), ~(((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) & (big_h(skolem_Z166(X4_0_0, X4_0_0)) => ((big_f(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))))))
% 0.19/0.51
% 0.19/0.51 [53] ALPHA_NOT_IMPLY : ~(((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) & (big_h(skolem_Z166(X4_0_0, X4_0_0)) => ((big_f(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))))))
% 0.19/0.51 -> [57] ((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))), ~(big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) & (big_h(skolem_Z166(X4_0_0, X4_0_0)) => ((big_f(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))))
% 0.19/0.51
% 0.19/0.51 [57] BETA_IMPLY : ((big_f(skolem_Z166(X4_0_0, X4_0_0)) => big_g(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))))
% 0.19/0.51 -> [63] ~(big_f(skolem_Z166(X4_0_0, X4_0_0)) => big_g(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))
% 0.19/0.51 -> [64] (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))
% 0.19/0.51
% 0.19/0.51 [63] ALPHA_NOT_IMPLY : ~(big_f(skolem_Z166(X4_0_0, X4_0_0)) => big_g(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))
% 0.19/0.51 -> [73] big_f(skolem_Z166(X4_0_0, X4_0_0)), ~big_g(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51
% 0.19/0.51 [73] CLOSURE : ~big_g(skolem_Z166(skolem_Z166(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51
% 0.19/0.51 [76] BETA_IMPLY : ((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [107] ~(big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [108] big_h(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [108] CLOSURE : big_h(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [107] ALPHA_NOT_OR : ~(big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [110] ~big_f(skolem_Z277(X4_0_0, X4_0_0)), ~big_g(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [110] CLOSURE : ~big_g(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [5] ALPHA_NOT_IMPLY : ~(big_f(X4_0_0) => big_g(skolem_Z166(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [7] big_f(X4_0_0), ~big_g(skolem_Z166(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [7] BETA_IMPLY : ((big_f(X4_0_0) | big_g(X4_0_0)) => big_h(X4_0_0))
% 0.19/0.51 -> [9] ~(big_f(X4_0_0) | big_g(X4_0_0))
% 0.19/0.51 -> [10] big_h(X4_0_0)
% 0.19/0.51
% 0.19/0.51 [9] ALPHA_NOT_OR : ~(big_f(X4_0_0) | big_g(X4_0_0))
% 0.19/0.51 -> [13] ~big_f(X4_0_0), ~big_g(X4_0_0)
% 0.19/0.51
% 0.19/0.51 [13] CLOSURE : ~big_f(X4_0_0)
% 0.19/0.51
% 0.19/0.51 [10] BETA_NOT_AND : ~(big_h(skolem_Z277(X4_0_0, X4_0_0)) & (big_h(X4_0_0) => ((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0)))))
% 0.19/0.51 -> [17] ~big_h(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51 -> [18] ~(big_h(X4_0_0) => ((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))))
% 0.19/0.51
% 0.19/0.51 [17] : ~? [X4_4, Y5_5] : (! [Z16_6, Z27_7] : ((((big_f(Y5_5) => big_g(Z16_6)) => (big_g(X4_4) & ~big_f(Z16_6))) => (((big_f(X4_4) | big_g(X4_4)) => big_h(X4_4)) => (big_h(Z27_7) & (big_h(Y5_5) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7))))))))
% 0.19/0.51 -> [22] ~? [X4_4, Y5_5] : (! [Z16_6, Z27_7] : ((((big_f(Y5_5) => big_g(Z16_6)) => (big_g(X4_4) & ~big_f(Z16_6))) => (((big_f(X4_4) | big_g(X4_4)) => big_h(X4_4)) => (big_h(Z27_7) & (big_h(Y5_5) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7))))))))
% 0.19/0.51
% 0.19/0.51 [22] GAMMA_NOT_EXISTS : ~? [X4_4, Y5_5] : (! [Z16_6, Z27_7] : ((((big_f(Y5_5) => big_g(Z16_6)) => (big_g(X4_4) & ~big_f(Z16_6))) => (((big_f(X4_4) | big_g(X4_4)) => big_h(X4_4)) => (big_h(Z27_7) & (big_h(Y5_5) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7))))))))
% 0.19/0.51 -> [26] ~! [Z16_6, Z27_7] : ((((big_f(skolem_Z277(X4_0_0, X4_0_0)) => big_g(Z16_6)) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(Z16_6))) => (((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(Z27_7) & (big_h(skolem_Z277(X4_0_0, X4_0_0)) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7)))))))
% 0.19/0.51
% 0.19/0.51 [26] DELTA_NOT_FORALL : ~! [Z16_6, Z27_7] : ((((big_f(skolem_Z277(X4_0_0, X4_0_0)) => big_g(Z16_6)) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(Z16_6))) => (((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(Z27_7) & (big_h(skolem_Z277(X4_0_0, X4_0_0)) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7)))))))
% 0.19/0.51 -> [28] ~(((big_f(skolem_Z277(X4_0_0, X4_0_0)) => big_g(skolem_Z166(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))) => (((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(skolem_Z277(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) & (big_h(skolem_Z277(X4_0_0, X4_0_0)) => ((big_f(skolem_Z277(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))))))
% 0.19/0.51
% 0.19/0.51 [28] ALPHA_NOT_IMPLY : ~(((big_f(skolem_Z277(X4_0_0, X4_0_0)) => big_g(skolem_Z166(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))) => (((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(skolem_Z277(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) & (big_h(skolem_Z277(X4_0_0, X4_0_0)) => ((big_f(skolem_Z277(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))))))
% 0.19/0.51 -> [34] ((big_f(skolem_Z277(X4_0_0, X4_0_0)) => big_g(skolem_Z166(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))), ~(((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(skolem_Z277(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) & (big_h(skolem_Z277(X4_0_0, X4_0_0)) => ((big_f(skolem_Z277(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))))))
% 0.19/0.51
% 0.19/0.51 [34] ALPHA_NOT_IMPLY : ~(((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(skolem_Z277(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) & (big_h(skolem_Z277(X4_0_0, X4_0_0)) => ((big_f(skolem_Z277(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))))))
% 0.19/0.51 -> [36] ((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))), ~(big_h(skolem_Z277(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) & (big_h(skolem_Z277(X4_0_0, X4_0_0)) => ((big_f(skolem_Z277(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))))
% 0.19/0.51
% 0.19/0.51 [36] BETA_IMPLY : ((big_f(skolem_Z277(X4_0_0, X4_0_0)) => big_g(skolem_Z166(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))))
% 0.19/0.51 -> [39] ~(big_f(skolem_Z277(X4_0_0, X4_0_0)) => big_g(skolem_Z166(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))
% 0.19/0.51 -> [40] (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))
% 0.19/0.51
% 0.19/0.51 [39] ALPHA_NOT_IMPLY : ~(big_f(skolem_Z277(X4_0_0, X4_0_0)) => big_g(skolem_Z166(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0))))
% 0.19/0.51 -> [42] big_f(skolem_Z277(X4_0_0, X4_0_0)), ~big_g(skolem_Z166(skolem_Z277(X4_0_0, X4_0_0), skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51
% 0.19/0.51 [42] BETA_IMPLY : ((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [61] ~(big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [62] big_h(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [61] ALPHA_NOT_OR : ~(big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [71] ~big_f(skolem_Z277(X4_0_0, X4_0_0)), ~big_g(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [71] CLOSURE : ~big_f(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [62] CLOSURE : big_h(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [46] BETA_IMPLY : ((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [129] ~(big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [130] big_h(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [130] CLOSURE : big_h(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [129] ALPHA_NOT_OR : ~(big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [131] ~big_f(skolem_Z277(X4_0_0, X4_0_0)), ~big_g(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [131] CLOSURE : ~big_g(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [18] ALPHA_NOT_IMPLY : ~(big_h(X4_0_0) => ((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))))
% 0.19/0.51 -> [20] big_h(X4_0_0), ~((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51
% 0.19/0.51 [20] ALPHA_NOT_IMPLY : ~((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [24] (big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))), ~big_h(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [24] BETA_OR : (big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [32] big_f(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51 -> [33] big_g(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [32] : ~? [X4_4, Y5_5] : (! [Z16_6, Z27_7] : ((((big_f(Y5_5) => big_g(Z16_6)) => (big_g(X4_4) & ~big_f(Z16_6))) => (((big_f(X4_4) | big_g(X4_4)) => big_h(X4_4)) => (big_h(Z27_7) & (big_h(Y5_5) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7))))))))
% 0.19/0.51 -> [50] ~? [X4_4, Y5_5] : (! [Z16_6, Z27_7] : ((((big_f(Y5_5) => big_g(Z16_6)) => (big_g(X4_4) & ~big_f(Z16_6))) => (((big_f(X4_4) | big_g(X4_4)) => big_h(X4_4)) => (big_h(Z27_7) & (big_h(Y5_5) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7))))))))
% 0.19/0.51
% 0.19/0.51 [50] GAMMA_NOT_EXISTS : ~? [X4_4, Y5_5] : (! [Z16_6, Z27_7] : ((((big_f(Y5_5) => big_g(Z16_6)) => (big_g(X4_4) & ~big_f(Z16_6))) => (((big_f(X4_4) | big_g(X4_4)) => big_h(X4_4)) => (big_h(Z27_7) & (big_h(Y5_5) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7))))))))
% 0.19/0.51 -> [55] ~! [Z16_6, Z27_7] : ((((big_f(Y5_6_0) => big_g(Z16_6)) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(Z16_6))) => (((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(Z27_7) & (big_h(Y5_6_0) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7)))))))
% 0.19/0.51
% 0.19/0.51 [55] DELTA_NOT_FORALL : ~! [Z16_6, Z27_7] : ((((big_f(Y5_6_0) => big_g(Z16_6)) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(Z16_6))) => (((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(Z27_7) & (big_h(Y5_6_0) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7)))))))
% 0.19/0.51 -> [59] ~(((big_f(Y5_6_0) => big_g(skolem_Z166(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0)))) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0))))) => (((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(skolem_Z277(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0))) & (big_h(Y5_6_0) => ((big_f(skolem_Z277(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0))))))))
% 0.19/0.51
% 0.19/0.51 [59] ALPHA_NOT_IMPLY : ~(((big_f(Y5_6_0) => big_g(skolem_Z166(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0)))) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0))))) => (((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(skolem_Z277(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0))) & (big_h(Y5_6_0) => ((big_f(skolem_Z277(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0))))))))
% 0.19/0.51 -> [68] ((big_f(Y5_6_0) => big_g(skolem_Z166(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0)))) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0))))), ~(((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(skolem_Z277(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0))) & (big_h(Y5_6_0) => ((big_f(skolem_Z277(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0)))))))
% 0.19/0.51
% 0.19/0.51 [68] ALPHA_NOT_IMPLY : ~(((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(skolem_Z277(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0))) & (big_h(Y5_6_0) => ((big_f(skolem_Z277(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0)))))))
% 0.19/0.51 -> [77] ((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))), ~(big_h(skolem_Z277(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0))) & (big_h(Y5_6_0) => ((big_f(skolem_Z277(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0))))))
% 0.19/0.51
% 0.19/0.51 [77] BETA_IMPLY : ((big_f(Y5_6_0) => big_g(skolem_Z166(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0)))) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0)))))
% 0.19/0.51 -> [80] ~(big_f(Y5_6_0) => big_g(skolem_Z166(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0))))
% 0.19/0.51 -> [81] (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0))))
% 0.19/0.51
% 0.19/0.51 [80] ALPHA_NOT_IMPLY : ~(big_f(Y5_6_0) => big_g(skolem_Z166(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0))))
% 0.19/0.51 -> [85] big_f(Y5_6_0), ~big_g(skolem_Z166(Y5_6_0, skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51
% 0.19/0.51 [85] BETA_IMPLY : ((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [93] ~(big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [94] big_h(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [94] CLOSURE : big_h(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [93] ALPHA_NOT_OR : ~(big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [95] ~big_f(skolem_Z277(X4_0_0, X4_0_0)), ~big_g(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [95] CLOSURE : ~big_f(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [83] BETA_IMPLY : ((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [132] ~(big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [133] big_h(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [133] CLOSURE : big_h(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [132] ALPHA_NOT_OR : ~(big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [134] ~big_f(skolem_Z277(X4_0_0, X4_0_0)), ~big_g(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [134] CLOSURE : ~big_f(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [33] : ~? [X4_4, Y5_5] : (! [Z16_6, Z27_7] : ((((big_f(Y5_5) => big_g(Z16_6)) => (big_g(X4_4) & ~big_f(Z16_6))) => (((big_f(X4_4) | big_g(X4_4)) => big_h(X4_4)) => (big_h(Z27_7) & (big_h(Y5_5) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7))))))))
% 0.19/0.51 -> [51] ~? [X4_4, Y5_5] : (! [Z16_6, Z27_7] : ((((big_f(Y5_5) => big_g(Z16_6)) => (big_g(X4_4) & ~big_f(Z16_6))) => (((big_f(X4_4) | big_g(X4_4)) => big_h(X4_4)) => (big_h(Z27_7) & (big_h(Y5_5) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7))))))))
% 0.19/0.51
% 0.19/0.51 [51] GAMMA_NOT_EXISTS : ~? [X4_4, Y5_5] : (! [Z16_6, Z27_7] : ((((big_f(Y5_5) => big_g(Z16_6)) => (big_g(X4_4) & ~big_f(Z16_6))) => (((big_f(X4_4) | big_g(X4_4)) => big_h(X4_4)) => (big_h(Z27_7) & (big_h(Y5_5) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7))))))))
% 0.19/0.51 -> [54] ~! [Z16_6, Z27_7] : ((((big_f(Y5_5_0) => big_g(Z16_6)) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(Z16_6))) => (((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(Z27_7) & (big_h(Y5_5_0) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7)))))))
% 0.19/0.51
% 0.19/0.51 [54] DELTA_NOT_FORALL : ~! [Z16_6, Z27_7] : ((((big_f(Y5_5_0) => big_g(Z16_6)) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(Z16_6))) => (((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(Z27_7) & (big_h(Y5_5_0) => ((big_f(Z27_7) | big_g(Z27_7)) => big_h(Z27_7)))))))
% 0.19/0.51 -> [58] ~(((big_f(Y5_5_0) => big_g(skolem_Z166(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0)))) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0))))) => (((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(skolem_Z277(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0))) & (big_h(Y5_5_0) => ((big_f(skolem_Z277(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0))))))))
% 0.19/0.51
% 0.19/0.51 [58] ALPHA_NOT_IMPLY : ~(((big_f(Y5_5_0) => big_g(skolem_Z166(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0)))) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0))))) => (((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(skolem_Z277(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0))) & (big_h(Y5_5_0) => ((big_f(skolem_Z277(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0))))))))
% 0.19/0.51 -> [67] ((big_f(Y5_5_0) => big_g(skolem_Z166(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0)))) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0))))), ~(((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(skolem_Z277(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0))) & (big_h(Y5_5_0) => ((big_f(skolem_Z277(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0)))))))
% 0.19/0.51
% 0.19/0.51 [67] ALPHA_NOT_IMPLY : ~(((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))) => (big_h(skolem_Z277(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0))) & (big_h(Y5_5_0) => ((big_f(skolem_Z277(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0)))))))
% 0.19/0.51 -> [74] ((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0))), ~(big_h(skolem_Z277(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0))) & (big_h(Y5_5_0) => ((big_f(skolem_Z277(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0))) | big_g(skolem_Z277(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0)))) => big_h(skolem_Z277(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0))))))
% 0.19/0.51
% 0.19/0.51 [74] BETA_IMPLY : ((big_f(Y5_5_0) => big_g(skolem_Z166(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0)))) => (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0)))))
% 0.19/0.51 -> [78] ~(big_f(Y5_5_0) => big_g(skolem_Z166(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0))))
% 0.19/0.51 -> [79] (big_g(skolem_Z277(X4_0_0, X4_0_0)) & ~big_f(skolem_Z166(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0))))
% 0.19/0.51
% 0.19/0.51 [78] ALPHA_NOT_IMPLY : ~(big_f(Y5_5_0) => big_g(skolem_Z166(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0))))
% 0.19/0.51 -> [86] big_f(Y5_5_0), ~big_g(skolem_Z166(Y5_5_0, skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51
% 0.19/0.51 [86] BETA_IMPLY : ((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [96] ~(big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [97] big_h(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [97] CLOSURE : big_h(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [96] ALPHA_NOT_OR : ~(big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [101] ~big_f(skolem_Z277(X4_0_0, X4_0_0)), ~big_g(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [101] CLOSURE : ~big_g(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [84] BETA_IMPLY : ((big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0))) => big_h(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [135] ~(big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [136] big_h(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [136] CLOSURE : big_h(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [135] ALPHA_NOT_OR : ~(big_f(skolem_Z277(X4_0_0, X4_0_0)) | big_g(skolem_Z277(X4_0_0, X4_0_0)))
% 0.19/0.51 -> [137] ~big_f(skolem_Z277(X4_0_0, X4_0_0)), ~big_g(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 [137] CLOSURE : ~big_g(skolem_Z277(X4_0_0, X4_0_0))
% 0.19/0.51
% 0.19/0.51 % SZS output end Proof for theBenchmark.p
% 0.19/0.51 [0.167434s][1][Res] 664 goroutines created
% 0.19/0.51 ==== Result ====
% 0.19/0.51 [0.167473s][1][Res] VALID
% 0.19/0.51 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------