TSTP Solution File: SYN333+1 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SYN333+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n019.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 22:23:01 EDT 2022
% Result : Theorem 0.20s 0.55s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYN333+1 : TPTP v8.1.0. Released v2.0.0.
% 0.10/0.12 % Command : goeland -dmt -presko -proof %s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Sep 5 02:41:35 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 [DMT] DMT loaded with preskolemization
% 0.13/0.34 [EQ] equality loaded.
% 0.13/0.34 [0.000038s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.34 Start search
% 0.13/0.34 nb_step : 1 - limit : 2
% 0.13/0.34 Launch Gotab with destructive = true
% 0.13/0.37 nb_step : 2 - limit : 4
% 0.13/0.37 Launch Gotab with destructive = true
% 0.20/0.54 % SZS output start Proof for theBenchmark.p
% 0.20/0.55 [40] GAMMA_NOT_EXISTS : ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55 -> [41] ~! [Z5_5] : ((big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)) => ((big_f(skolem_Z55(X3_3_0, Y4_3_0), Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)) & big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) => (big_g(skolem_Z55(X3_3_0, Y4_3_0), Z5_5) & big_g(Z5_5, Z5_5))))))
% 0.20/0.55
% 0.20/0.55 [41] DELTA_NOT_FORALL : ~! [Z5_5] : ((big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)) => ((big_f(skolem_Z55(X3_3_0, Y4_3_0), Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)) & big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) => (big_g(skolem_Z55(X3_3_0, Y4_3_0), Z5_5) & big_g(Z5_5, Z5_5))))))
% 0.20/0.55 -> [42] ~(big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)) => ((big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & ((big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)) & big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) => (big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))))))
% 0.20/0.55
% 0.20/0.55 [42] ALPHA_NOT_IMPLY : ~(big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)) => ((big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & ((big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)) & big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) => (big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))))))
% 0.20/0.55 -> [43] big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), ~((big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & ((big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)) & big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) => (big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))))
% 0.20/0.55
% 0.20/0.55 [43] BETA_NOT_AND : ~((big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & ((big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)) & big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) => (big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))))
% 0.20/0.55 -> [44] ~(big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))
% 0.20/0.55 -> [45] ~((big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)) & big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) => (big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))))
% 0.20/0.55
% 0.20/0.55 [44] BETA_NOT_AND : ~(big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))
% 0.20/0.55 -> [46] ~big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))
% 0.20/0.55 -> [47] ~big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))
% 0.20/0.55
% 0.20/0.55 [46] : ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55 -> [50] ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55
% 0.20/0.55 [50] GAMMA_NOT_EXISTS : ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55 -> [52] ~! [Z5_5] : ((big_f(X3_1_0, Y4_1_0) => ((big_f(Y4_1_0, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_1_0, Y4_1_0) & big_g(X3_1_0, Y4_1_0)) => (big_g(X3_1_0, Z5_5) & big_g(Z5_5, Z5_5))))))
% 0.20/0.55
% 0.20/0.55 [52] DELTA_NOT_FORALL : ~! [Z5_5] : ((big_f(X3_1_0, Y4_1_0) => ((big_f(Y4_1_0, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_1_0, Y4_1_0) & big_g(X3_1_0, Y4_1_0)) => (big_g(X3_1_0, Z5_5) & big_g(Z5_5, Z5_5))))))
% 0.20/0.55 -> [56] ~(big_f(X3_1_0, Y4_1_0) => ((big_f(Y4_1_0, skolem_Z55(X3_1_0, Y4_1_0)) & big_f(skolem_Z55(X3_1_0, Y4_1_0), skolem_Z55(X3_1_0, Y4_1_0))) & ((big_f(X3_1_0, Y4_1_0) & big_g(X3_1_0, Y4_1_0)) => (big_g(X3_1_0, skolem_Z55(X3_1_0, Y4_1_0)) & big_g(skolem_Z55(X3_1_0, Y4_1_0), skolem_Z55(X3_1_0, Y4_1_0))))))
% 0.20/0.55
% 0.20/0.55 [56] ALPHA_NOT_IMPLY : ~(big_f(X3_1_0, Y4_1_0) => ((big_f(Y4_1_0, skolem_Z55(X3_1_0, Y4_1_0)) & big_f(skolem_Z55(X3_1_0, Y4_1_0), skolem_Z55(X3_1_0, Y4_1_0))) & ((big_f(X3_1_0, Y4_1_0) & big_g(X3_1_0, Y4_1_0)) => (big_g(X3_1_0, skolem_Z55(X3_1_0, Y4_1_0)) & big_g(skolem_Z55(X3_1_0, Y4_1_0), skolem_Z55(X3_1_0, Y4_1_0))))))
% 0.20/0.55 -> [58] big_f(X3_1_0, Y4_1_0), ~((big_f(Y4_1_0, skolem_Z55(X3_1_0, Y4_1_0)) & big_f(skolem_Z55(X3_1_0, Y4_1_0), skolem_Z55(X3_1_0, Y4_1_0))) & ((big_f(X3_1_0, Y4_1_0) & big_g(X3_1_0, Y4_1_0)) => (big_g(X3_1_0, skolem_Z55(X3_1_0, Y4_1_0)) & big_g(skolem_Z55(X3_1_0, Y4_1_0), skolem_Z55(X3_1_0, Y4_1_0)))))
% 0.20/0.55
% 0.20/0.55 [58] CLOSURE : big_f(X3_1_0, Y4_1_0)
% 0.20/0.55
% 0.20/0.55 [47] : ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55 -> [51] ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55
% 0.20/0.55 [51] GAMMA_NOT_EXISTS : ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55 -> [53] ~! [Z5_5] : ((big_f(X3_2_0, Y4_2_0) => ((big_f(Y4_2_0, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_2_0, Y4_2_0) & big_g(X3_2_0, Y4_2_0)) => (big_g(X3_2_0, Z5_5) & big_g(Z5_5, Z5_5))))))
% 0.20/0.55
% 0.20/0.55 [53] DELTA_NOT_FORALL : ~! [Z5_5] : ((big_f(X3_2_0, Y4_2_0) => ((big_f(Y4_2_0, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_2_0, Y4_2_0) & big_g(X3_2_0, Y4_2_0)) => (big_g(X3_2_0, Z5_5) & big_g(Z5_5, Z5_5))))))
% 0.20/0.55 -> [57] ~(big_f(X3_2_0, Y4_2_0) => ((big_f(Y4_2_0, skolem_Z55(X3_2_0, Y4_2_0)) & big_f(skolem_Z55(X3_2_0, Y4_2_0), skolem_Z55(X3_2_0, Y4_2_0))) & ((big_f(X3_2_0, Y4_2_0) & big_g(X3_2_0, Y4_2_0)) => (big_g(X3_2_0, skolem_Z55(X3_2_0, Y4_2_0)) & big_g(skolem_Z55(X3_2_0, Y4_2_0), skolem_Z55(X3_2_0, Y4_2_0))))))
% 0.20/0.55
% 0.20/0.55 [57] ALPHA_NOT_IMPLY : ~(big_f(X3_2_0, Y4_2_0) => ((big_f(Y4_2_0, skolem_Z55(X3_2_0, Y4_2_0)) & big_f(skolem_Z55(X3_2_0, Y4_2_0), skolem_Z55(X3_2_0, Y4_2_0))) & ((big_f(X3_2_0, Y4_2_0) & big_g(X3_2_0, Y4_2_0)) => (big_g(X3_2_0, skolem_Z55(X3_2_0, Y4_2_0)) & big_g(skolem_Z55(X3_2_0, Y4_2_0), skolem_Z55(X3_2_0, Y4_2_0))))))
% 0.20/0.55 -> [59] big_f(X3_2_0, Y4_2_0), ~((big_f(Y4_2_0, skolem_Z55(X3_2_0, Y4_2_0)) & big_f(skolem_Z55(X3_2_0, Y4_2_0), skolem_Z55(X3_2_0, Y4_2_0))) & ((big_f(X3_2_0, Y4_2_0) & big_g(X3_2_0, Y4_2_0)) => (big_g(X3_2_0, skolem_Z55(X3_2_0, Y4_2_0)) & big_g(skolem_Z55(X3_2_0, Y4_2_0), skolem_Z55(X3_2_0, Y4_2_0)))))
% 0.20/0.55
% 0.20/0.55 [59] CLOSURE : big_f(X3_2_0, Y4_2_0)
% 0.20/0.55
% 0.20/0.55 [45] ALPHA_NOT_IMPLY : ~((big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)) & big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) => (big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))))
% 0.20/0.55 -> [48] (big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)) & big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), ~(big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))
% 0.20/0.55
% 0.20/0.55 [48] ALPHA_AND : (big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)) & big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))
% 0.20/0.55 -> [49] big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))
% 0.20/0.55
% 0.20/0.55 [49] BETA_NOT_AND : ~(big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))
% 0.20/0.55 -> [54] ~big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))
% 0.20/0.55 -> [55] ~big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))
% 0.20/0.55
% 0.20/0.55 [55] : ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55 -> [61] ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55
% 0.20/0.55 [61] GAMMA_NOT_EXISTS : ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55 -> [63] ~! [Z5_5] : ((big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) => ((big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) => (big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), Z5_5) & big_g(Z5_5, Z5_5))))))
% 0.20/0.55
% 0.20/0.55 [63] DELTA_NOT_FORALL : ~! [Z5_5] : ((big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) => ((big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) => (big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), Z5_5) & big_g(Z5_5, Z5_5))))))
% 0.20/0.55 -> [65] ~(big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) => ((big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & big_f(skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))) & ((big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) => (big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & big_g(skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))))))
% 0.20/0.55
% 0.20/0.55 [65] ALPHA_NOT_IMPLY : ~(big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) => ((big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & big_f(skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))) & ((big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) => (big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & big_g(skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))))))
% 0.20/0.55 -> [67] big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), ~((big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & big_f(skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))) & ((big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) => (big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & big_g(skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))))))
% 0.20/0.55
% 0.20/0.55 [67] BETA_NOT_AND : ~((big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & big_f(skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))) & ((big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) => (big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & big_g(skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))))))
% 0.20/0.55 -> [68] ~(big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & big_f(skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))))
% 0.20/0.55 -> [69] ~((big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) => (big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & big_g(skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))))
% 0.20/0.55
% 0.20/0.55 [69] ALPHA_NOT_IMPLY : ~((big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) => (big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & big_g(skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))))
% 0.20/0.55 -> [77] (big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))), ~(big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & big_g(skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))))
% 0.20/0.55
% 0.20/0.55 [77] ALPHA_AND : (big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))
% 0.20/0.55 -> [79] big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))
% 0.20/0.55
% 0.20/0.55 [79] CLOSURE : big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))
% 0.20/0.55
% 0.20/0.55 [68] BETA_NOT_AND : ~(big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & big_f(skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))))
% 0.20/0.55 -> [88] ~big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))
% 0.20/0.55 -> [89] ~big_f(skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))
% 0.20/0.55
% 0.20/0.55 [88] : ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55 -> [92] ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55
% 0.20/0.55 [92] GAMMA_NOT_EXISTS : ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55 -> [94] ~! [Z5_5] : ((big_f(X3_7_0, Y4_7_0) => ((big_f(Y4_7_0, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_7_0, Y4_7_0) & big_g(X3_7_0, Y4_7_0)) => (big_g(X3_7_0, Z5_5) & big_g(Z5_5, Z5_5))))))
% 0.20/0.55
% 0.20/0.55 [94] DELTA_NOT_FORALL : ~! [Z5_5] : ((big_f(X3_7_0, Y4_7_0) => ((big_f(Y4_7_0, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_7_0, Y4_7_0) & big_g(X3_7_0, Y4_7_0)) => (big_g(X3_7_0, Z5_5) & big_g(Z5_5, Z5_5))))))
% 0.20/0.55 -> [97] ~(big_f(X3_7_0, Y4_7_0) => ((big_f(Y4_7_0, skolem_Z55(X3_7_0, Y4_7_0)) & big_f(skolem_Z55(X3_7_0, Y4_7_0), skolem_Z55(X3_7_0, Y4_7_0))) & ((big_f(X3_7_0, Y4_7_0) & big_g(X3_7_0, Y4_7_0)) => (big_g(X3_7_0, skolem_Z55(X3_7_0, Y4_7_0)) & big_g(skolem_Z55(X3_7_0, Y4_7_0), skolem_Z55(X3_7_0, Y4_7_0))))))
% 0.20/0.55
% 0.20/0.55 [97] ALPHA_NOT_IMPLY : ~(big_f(X3_7_0, Y4_7_0) => ((big_f(Y4_7_0, skolem_Z55(X3_7_0, Y4_7_0)) & big_f(skolem_Z55(X3_7_0, Y4_7_0), skolem_Z55(X3_7_0, Y4_7_0))) & ((big_f(X3_7_0, Y4_7_0) & big_g(X3_7_0, Y4_7_0)) => (big_g(X3_7_0, skolem_Z55(X3_7_0, Y4_7_0)) & big_g(skolem_Z55(X3_7_0, Y4_7_0), skolem_Z55(X3_7_0, Y4_7_0))))))
% 0.20/0.55 -> [100] big_f(X3_7_0, Y4_7_0), ~((big_f(Y4_7_0, skolem_Z55(X3_7_0, Y4_7_0)) & big_f(skolem_Z55(X3_7_0, Y4_7_0), skolem_Z55(X3_7_0, Y4_7_0))) & ((big_f(X3_7_0, Y4_7_0) & big_g(X3_7_0, Y4_7_0)) => (big_g(X3_7_0, skolem_Z55(X3_7_0, Y4_7_0)) & big_g(skolem_Z55(X3_7_0, Y4_7_0), skolem_Z55(X3_7_0, Y4_7_0)))))
% 0.20/0.55
% 0.20/0.55 [100] CLOSURE : big_f(X3_7_0, Y4_7_0)
% 0.20/0.55
% 0.20/0.55 [89] : ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55 -> [93] ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55
% 0.20/0.55 [93] GAMMA_NOT_EXISTS : ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55 -> [95] ~! [Z5_5] : ((big_f(X3_8_0, Y4_8_0) => ((big_f(Y4_8_0, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_8_0, Y4_8_0) & big_g(X3_8_0, Y4_8_0)) => (big_g(X3_8_0, Z5_5) & big_g(Z5_5, Z5_5))))))
% 0.20/0.55
% 0.20/0.55 [95] DELTA_NOT_FORALL : ~! [Z5_5] : ((big_f(X3_8_0, Y4_8_0) => ((big_f(Y4_8_0, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_8_0, Y4_8_0) & big_g(X3_8_0, Y4_8_0)) => (big_g(X3_8_0, Z5_5) & big_g(Z5_5, Z5_5))))))
% 0.20/0.55 -> [99] ~(big_f(X3_8_0, Y4_8_0) => ((big_f(Y4_8_0, skolem_Z55(X3_8_0, Y4_8_0)) & big_f(skolem_Z55(X3_8_0, Y4_8_0), skolem_Z55(X3_8_0, Y4_8_0))) & ((big_f(X3_8_0, Y4_8_0) & big_g(X3_8_0, Y4_8_0)) => (big_g(X3_8_0, skolem_Z55(X3_8_0, Y4_8_0)) & big_g(skolem_Z55(X3_8_0, Y4_8_0), skolem_Z55(X3_8_0, Y4_8_0))))))
% 0.20/0.55
% 0.20/0.55 [99] ALPHA_NOT_IMPLY : ~(big_f(X3_8_0, Y4_8_0) => ((big_f(Y4_8_0, skolem_Z55(X3_8_0, Y4_8_0)) & big_f(skolem_Z55(X3_8_0, Y4_8_0), skolem_Z55(X3_8_0, Y4_8_0))) & ((big_f(X3_8_0, Y4_8_0) & big_g(X3_8_0, Y4_8_0)) => (big_g(X3_8_0, skolem_Z55(X3_8_0, Y4_8_0)) & big_g(skolem_Z55(X3_8_0, Y4_8_0), skolem_Z55(X3_8_0, Y4_8_0))))))
% 0.20/0.55 -> [102] big_f(X3_8_0, Y4_8_0), ~((big_f(Y4_8_0, skolem_Z55(X3_8_0, Y4_8_0)) & big_f(skolem_Z55(X3_8_0, Y4_8_0), skolem_Z55(X3_8_0, Y4_8_0))) & ((big_f(X3_8_0, Y4_8_0) & big_g(X3_8_0, Y4_8_0)) => (big_g(X3_8_0, skolem_Z55(X3_8_0, Y4_8_0)) & big_g(skolem_Z55(X3_8_0, Y4_8_0), skolem_Z55(X3_8_0, Y4_8_0)))))
% 0.20/0.55
% 0.20/0.55 [102] CLOSURE : big_f(X3_8_0, Y4_8_0)
% 0.20/0.55
% 0.20/0.55 [54] : ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55 -> [60] ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55
% 0.20/0.55 [60] GAMMA_NOT_EXISTS : ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55 -> [62] ~! [Z5_5] : ((big_f(X3_3_0, Y4_3_0) => ((big_f(Y4_3_0, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3_0, Y4_3_0) & big_g(X3_3_0, Y4_3_0)) => (big_g(X3_3_0, Z5_5) & big_g(Z5_5, Z5_5))))))
% 0.20/0.55
% 0.20/0.55 [62] DELTA_NOT_FORALL : ~! [Z5_5] : ((big_f(X3_3_0, Y4_3_0) => ((big_f(Y4_3_0, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3_0, Y4_3_0) & big_g(X3_3_0, Y4_3_0)) => (big_g(X3_3_0, Z5_5) & big_g(Z5_5, Z5_5))))))
% 0.20/0.55 -> [64] ~(big_f(X3_3_0, Y4_3_0) => ((big_f(Y4_3_0, skolem_Z55(X3_3_0, Y4_3_0)) & big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & ((big_f(X3_3_0, Y4_3_0) & big_g(X3_3_0, Y4_3_0)) => (big_g(X3_3_0, skolem_Z55(X3_3_0, Y4_3_0)) & big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))))
% 0.20/0.55
% 0.20/0.55 [64] ALPHA_NOT_IMPLY : ~(big_f(X3_3_0, Y4_3_0) => ((big_f(Y4_3_0, skolem_Z55(X3_3_0, Y4_3_0)) & big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & ((big_f(X3_3_0, Y4_3_0) & big_g(X3_3_0, Y4_3_0)) => (big_g(X3_3_0, skolem_Z55(X3_3_0, Y4_3_0)) & big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))))
% 0.20/0.55 -> [66] big_f(X3_3_0, Y4_3_0), ~((big_f(Y4_3_0, skolem_Z55(X3_3_0, Y4_3_0)) & big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & ((big_f(X3_3_0, Y4_3_0) & big_g(X3_3_0, Y4_3_0)) => (big_g(X3_3_0, skolem_Z55(X3_3_0, Y4_3_0)) & big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))))
% 0.20/0.55
% 0.20/0.55 [66] BETA_NOT_AND : ~((big_f(Y4_3_0, skolem_Z55(X3_3_0, Y4_3_0)) & big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & ((big_f(X3_3_0, Y4_3_0) & big_g(X3_3_0, Y4_3_0)) => (big_g(X3_3_0, skolem_Z55(X3_3_0, Y4_3_0)) & big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))))
% 0.20/0.55 -> [70] ~(big_f(Y4_3_0, skolem_Z55(X3_3_0, Y4_3_0)) & big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))
% 0.20/0.55 -> [71] ~((big_f(X3_3_0, Y4_3_0) & big_g(X3_3_0, Y4_3_0)) => (big_g(X3_3_0, skolem_Z55(X3_3_0, Y4_3_0)) & big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))
% 0.20/0.55
% 0.20/0.55 [70] BETA_NOT_AND : ~(big_f(Y4_3_0, skolem_Z55(X3_3_0, Y4_3_0)) & big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))
% 0.20/0.55 -> [74] ~big_f(Y4_3_0, skolem_Z55(X3_3_0, Y4_3_0))
% 0.20/0.55 -> [75] ~big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))
% 0.20/0.55
% 0.20/0.55 [75] CLOSURE : ~big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))
% 0.20/0.55
% 0.20/0.55 [74] : ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55 -> [80] ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55
% 0.20/0.55 [80] GAMMA_NOT_EXISTS : ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55 -> [82] ~! [Z5_5] : ((big_f(X3_5_0, Y4_5_0) => ((big_f(Y4_5_0, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_5_0, Y4_5_0) & big_g(X3_5_0, Y4_5_0)) => (big_g(X3_5_0, Z5_5) & big_g(Z5_5, Z5_5))))))
% 0.20/0.55
% 0.20/0.55 [82] DELTA_NOT_FORALL : ~! [Z5_5] : ((big_f(X3_5_0, Y4_5_0) => ((big_f(Y4_5_0, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_5_0, Y4_5_0) & big_g(X3_5_0, Y4_5_0)) => (big_g(X3_5_0, Z5_5) & big_g(Z5_5, Z5_5))))))
% 0.20/0.55 -> [84] ~(big_f(X3_5_0, Y4_5_0) => ((big_f(Y4_5_0, skolem_Z55(X3_5_0, Y4_5_0)) & big_f(skolem_Z55(X3_5_0, Y4_5_0), skolem_Z55(X3_5_0, Y4_5_0))) & ((big_f(X3_5_0, Y4_5_0) & big_g(X3_5_0, Y4_5_0)) => (big_g(X3_5_0, skolem_Z55(X3_5_0, Y4_5_0)) & big_g(skolem_Z55(X3_5_0, Y4_5_0), skolem_Z55(X3_5_0, Y4_5_0))))))
% 0.20/0.55
% 0.20/0.55 [84] ALPHA_NOT_IMPLY : ~(big_f(X3_5_0, Y4_5_0) => ((big_f(Y4_5_0, skolem_Z55(X3_5_0, Y4_5_0)) & big_f(skolem_Z55(X3_5_0, Y4_5_0), skolem_Z55(X3_5_0, Y4_5_0))) & ((big_f(X3_5_0, Y4_5_0) & big_g(X3_5_0, Y4_5_0)) => (big_g(X3_5_0, skolem_Z55(X3_5_0, Y4_5_0)) & big_g(skolem_Z55(X3_5_0, Y4_5_0), skolem_Z55(X3_5_0, Y4_5_0))))))
% 0.20/0.55 -> [86] big_f(X3_5_0, Y4_5_0), ~((big_f(Y4_5_0, skolem_Z55(X3_5_0, Y4_5_0)) & big_f(skolem_Z55(X3_5_0, Y4_5_0), skolem_Z55(X3_5_0, Y4_5_0))) & ((big_f(X3_5_0, Y4_5_0) & big_g(X3_5_0, Y4_5_0)) => (big_g(X3_5_0, skolem_Z55(X3_5_0, Y4_5_0)) & big_g(skolem_Z55(X3_5_0, Y4_5_0), skolem_Z55(X3_5_0, Y4_5_0)))))
% 0.20/0.55
% 0.20/0.55 [86] CLOSURE : big_f(X3_5_0, Y4_5_0)
% 0.20/0.55
% 0.20/0.55 [78] BETA_NOT_AND : ~(big_g(X3_3_0, skolem_Z55(X3_3_0, Y4_3_0)) & big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))
% 0.20/0.55 -> [90] ~big_g(X3_3_0, skolem_Z55(X3_3_0, Y4_3_0))
% 0.20/0.55 -> [91] ~big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))
% 0.20/0.55
% 0.20/0.55 [91] CLOSURE : ~big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))
% 0.20/0.55
% 0.20/0.55 [90] : ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55 -> [96] ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55
% 0.20/0.55 [96] GAMMA_NOT_EXISTS : ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55 -> [98] ~! [Z5_5] : ((big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) => ((big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) => (big_g(skolem_Z55(X3_3_0, Y4_3_0), Z5_5) & big_g(Z5_5, Z5_5))))))
% 0.20/0.55
% 0.20/0.55 [98] DELTA_NOT_FORALL : ~! [Z5_5] : ((big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) => ((big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) => (big_g(skolem_Z55(X3_3_0, Y4_3_0), Z5_5) & big_g(Z5_5, Z5_5))))))
% 0.20/0.55 -> [101] ~(big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) => ((big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))) & ((big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) => (big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))))))
% 0.20/0.55
% 0.20/0.55 [101] ALPHA_NOT_IMPLY : ~(big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) => ((big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))) & ((big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) => (big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))))))
% 0.20/0.55 -> [103] big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), ~((big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))) & ((big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) => (big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))))))
% 0.20/0.55
% 0.20/0.55 [103] BETA_NOT_AND : ~((big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))) & ((big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) => (big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))))))
% 0.20/0.55 -> [104] ~(big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))))
% 0.20/0.55 -> [105] ~((big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) => (big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))))
% 0.20/0.55
% 0.20/0.55 [105] ALPHA_NOT_IMPLY : ~((big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) => (big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))))
% 0.20/0.55 -> [108] (big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))), ~(big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & big_g(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))))
% 0.20/0.55
% 0.20/0.55 [108] ALPHA_AND : (big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))) & big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))
% 0.20/0.55 -> [109] big_f(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))
% 0.20/0.55
% 0.20/0.55 [109] CLOSURE : big_g(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))
% 0.20/0.55
% 0.20/0.55 [104] BETA_NOT_AND : ~(big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))) & big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)))))
% 0.20/0.55 -> [114] ~big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0)), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))
% 0.20/0.55 -> [115] ~big_f(skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(skolem_Z55(X3_3_0, Y4_3_0), skolem_Z55(X3_3_0, Y4_3_0))))
% 0.20/0.55
% 0.20/0.55 [114] : ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55 -> [116] ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55
% 0.20/0.55 [116] GAMMA_NOT_EXISTS : ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55 -> [118] ~! [Z5_5] : ((big_f(X3_11_0, Y4_11_0) => ((big_f(Y4_11_0, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_11_0, Y4_11_0) & big_g(X3_11_0, Y4_11_0)) => (big_g(X3_11_0, Z5_5) & big_g(Z5_5, Z5_5))))))
% 0.20/0.55
% 0.20/0.55 [118] DELTA_NOT_FORALL : ~! [Z5_5] : ((big_f(X3_11_0, Y4_11_0) => ((big_f(Y4_11_0, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_11_0, Y4_11_0) & big_g(X3_11_0, Y4_11_0)) => (big_g(X3_11_0, Z5_5) & big_g(Z5_5, Z5_5))))))
% 0.20/0.55 -> [120] ~(big_f(X3_11_0, Y4_11_0) => ((big_f(Y4_11_0, skolem_Z55(X3_11_0, Y4_11_0)) & big_f(skolem_Z55(X3_11_0, Y4_11_0), skolem_Z55(X3_11_0, Y4_11_0))) & ((big_f(X3_11_0, Y4_11_0) & big_g(X3_11_0, Y4_11_0)) => (big_g(X3_11_0, skolem_Z55(X3_11_0, Y4_11_0)) & big_g(skolem_Z55(X3_11_0, Y4_11_0), skolem_Z55(X3_11_0, Y4_11_0))))))
% 0.20/0.55
% 0.20/0.55 [120] ALPHA_NOT_IMPLY : ~(big_f(X3_11_0, Y4_11_0) => ((big_f(Y4_11_0, skolem_Z55(X3_11_0, Y4_11_0)) & big_f(skolem_Z55(X3_11_0, Y4_11_0), skolem_Z55(X3_11_0, Y4_11_0))) & ((big_f(X3_11_0, Y4_11_0) & big_g(X3_11_0, Y4_11_0)) => (big_g(X3_11_0, skolem_Z55(X3_11_0, Y4_11_0)) & big_g(skolem_Z55(X3_11_0, Y4_11_0), skolem_Z55(X3_11_0, Y4_11_0))))))
% 0.20/0.55 -> [122] big_f(X3_11_0, Y4_11_0), ~((big_f(Y4_11_0, skolem_Z55(X3_11_0, Y4_11_0)) & big_f(skolem_Z55(X3_11_0, Y4_11_0), skolem_Z55(X3_11_0, Y4_11_0))) & ((big_f(X3_11_0, Y4_11_0) & big_g(X3_11_0, Y4_11_0)) => (big_g(X3_11_0, skolem_Z55(X3_11_0, Y4_11_0)) & big_g(skolem_Z55(X3_11_0, Y4_11_0), skolem_Z55(X3_11_0, Y4_11_0)))))
% 0.20/0.55
% 0.20/0.55 [122] CLOSURE : big_f(X3_11_0, Y4_11_0)
% 0.20/0.55
% 0.20/0.55 [115] : ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55 -> [117] ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55
% 0.20/0.55 [117] GAMMA_NOT_EXISTS : ~? [X3_3, Y4_4] : (! [Z5_5] : ((big_f(X3_3, Y4_4) => ((big_f(Y4_4, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_3, Y4_4) & big_g(X3_3, Y4_4)) => (big_g(X3_3, Z5_5) & big_g(Z5_5, Z5_5)))))))
% 0.20/0.55 -> [119] ~! [Z5_5] : ((big_f(X3_12_0, Y4_12_0) => ((big_f(Y4_12_0, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_12_0, Y4_12_0) & big_g(X3_12_0, Y4_12_0)) => (big_g(X3_12_0, Z5_5) & big_g(Z5_5, Z5_5))))))
% 0.20/0.55
% 0.20/0.55 [119] DELTA_NOT_FORALL : ~! [Z5_5] : ((big_f(X3_12_0, Y4_12_0) => ((big_f(Y4_12_0, Z5_5) & big_f(Z5_5, Z5_5)) & ((big_f(X3_12_0, Y4_12_0) & big_g(X3_12_0, Y4_12_0)) => (big_g(X3_12_0, Z5_5) & big_g(Z5_5, Z5_5))))))
% 0.20/0.55 -> [121] ~(big_f(X3_12_0, Y4_12_0) => ((big_f(Y4_12_0, skolem_Z55(X3_12_0, Y4_12_0)) & big_f(skolem_Z55(X3_12_0, Y4_12_0), skolem_Z55(X3_12_0, Y4_12_0))) & ((big_f(X3_12_0, Y4_12_0) & big_g(X3_12_0, Y4_12_0)) => (big_g(X3_12_0, skolem_Z55(X3_12_0, Y4_12_0)) & big_g(skolem_Z55(X3_12_0, Y4_12_0), skolem_Z55(X3_12_0, Y4_12_0))))))
% 0.20/0.55
% 0.20/0.55 [121] ALPHA_NOT_IMPLY : ~(big_f(X3_12_0, Y4_12_0) => ((big_f(Y4_12_0, skolem_Z55(X3_12_0, Y4_12_0)) & big_f(skolem_Z55(X3_12_0, Y4_12_0), skolem_Z55(X3_12_0, Y4_12_0))) & ((big_f(X3_12_0, Y4_12_0) & big_g(X3_12_0, Y4_12_0)) => (big_g(X3_12_0, skolem_Z55(X3_12_0, Y4_12_0)) & big_g(skolem_Z55(X3_12_0, Y4_12_0), skolem_Z55(X3_12_0, Y4_12_0))))))
% 0.20/0.55 -> [123] big_f(X3_12_0, Y4_12_0), ~((big_f(Y4_12_0, skolem_Z55(X3_12_0, Y4_12_0)) & big_f(skolem_Z55(X3_12_0, Y4_12_0), skolem_Z55(X3_12_0, Y4_12_0))) & ((big_f(X3_12_0, Y4_12_0) & big_g(X3_12_0, Y4_12_0)) => (big_g(X3_12_0, skolem_Z55(X3_12_0, Y4_12_0)) & big_g(skolem_Z55(X3_12_0, Y4_12_0), skolem_Z55(X3_12_0, Y4_12_0)))))
% 0.20/0.55
% 0.20/0.55 [123] CLOSURE : big_f(X3_12_0, Y4_12_0)
% 0.20/0.55
% 0.20/0.55 % SZS output end Proof for theBenchmark.p
% 0.20/0.55 [0.215242s][1][Res] 215 goroutines created
% 0.20/0.55 ==== Result ====
% 0.20/0.55 [0.215283s][1][Res] VALID
% 0.20/0.55 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------