TSTP Solution File: SYN067+1 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SYN067+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n004.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 22:22:17 EDT 2022
% Result : Theorem 0.19s 0.56s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYN067+1 : TPTP v8.1.0. Released v2.0.0.
% 0.10/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n004.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 01:28:34 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 [DMT] DMT loaded with preskolemization
% 0.12/0.34 [EQ] equality loaded.
% 0.12/0.34 [0.000038s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.34 Start search
% 0.12/0.34 nb_step : 1 - limit : 7
% 0.12/0.34 Launch Gotab with destructive = true
% 0.19/0.55 % SZS output start Proof for theBenchmark.p
% 0.19/0.56 [0] BETA_NOT_EQUIV : ~(! [X10_10] : (((big_p(a) & (big_p(X10_10) => ? [Y11_11] : ((big_p(Y11_11) & big_r(X10_10, Y11_11))))) => ? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(X10_10, W13_13)) & big_r(W13_13, Z12_12))))) <=> ! [X114_14] : ((((~big_p(a) | big_p(X114_14)) | ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(X114_14, W116_16)) & big_r(W116_16, Z115_15)))) & ((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(X114_14, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(X114_14, W219_19)) & big_r(W219_19, Z218_18)))))))
% 0.19/0.56 -> [1] ~! [X10_10] : (((big_p(a) & (big_p(X10_10) => ? [Y11_11] : ((big_p(Y11_11) & big_r(X10_10, Y11_11))))) => ? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(X10_10, W13_13)) & big_r(W13_13, Z12_12))))), ! [X114_14] : ((((~big_p(a) | big_p(X114_14)) | ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(X114_14, W116_16)) & big_r(W116_16, Z115_15)))) & ((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(X114_14, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(X114_14, W219_19)) & big_r(W219_19, Z218_18))))))
% 0.19/0.56 -> [2] ! [X10_10] : (((big_p(a) & (big_p(X10_10) => ? [Y11_11] : ((big_p(Y11_11) & big_r(X10_10, Y11_11))))) => ? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(X10_10, W13_13)) & big_r(W13_13, Z12_12))))), ~! [X114_14] : ((((~big_p(a) | big_p(X114_14)) | ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(X114_14, W116_16)) & big_r(W116_16, Z115_15)))) & ((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(X114_14, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(X114_14, W219_19)) & big_r(W219_19, Z218_18))))))
% 0.19/0.56
% 0.19/0.56 [2] DELTA_NOT_FORALL : ~! [X114_14] : ((((~big_p(a) | big_p(X114_14)) | ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(X114_14, W116_16)) & big_r(W116_16, Z115_15)))) & ((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(X114_14, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(X114_14, W219_19)) & big_r(W219_19, Z218_18))))))
% 0.19/0.56 -> [5] ~(((~big_p(a) | big_p(skolem_X11414)) | ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(skolem_X11414, W116_16)) & big_r(W116_16, Z115_15)))) & ((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X11414, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X11414, W219_19)) & big_r(W219_19, Z218_18)))))
% 0.19/0.56
% 0.19/0.56 [5] BETA_NOT_AND : ~(((~big_p(a) | big_p(skolem_X11414)) | ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(skolem_X11414, W116_16)) & big_r(W116_16, Z115_15)))) & ((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X11414, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X11414, W219_19)) & big_r(W219_19, Z218_18)))))
% 0.19/0.56 -> [7] ~((~big_p(a) | big_p(skolem_X11414)) | ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(skolem_X11414, W116_16)) & big_r(W116_16, Z115_15))))
% 0.19/0.56 -> [8] ~((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X11414, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X11414, W219_19)) & big_r(W219_19, Z218_18))))
% 0.19/0.56
% 0.19/0.56 [7] ALPHA_NOT_OR : ~((~big_p(a) | big_p(skolem_X11414)) | ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(skolem_X11414, W116_16)) & big_r(W116_16, Z115_15))))
% 0.19/0.56 -> [12] ~(~big_p(a) | big_p(skolem_X11414)), ~? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(skolem_X11414, W116_16)) & big_r(W116_16, Z115_15)))
% 0.19/0.56
% 0.19/0.56 [12] ALPHA_NOT_OR : ~(~big_p(a) | big_p(skolem_X11414))
% 0.19/0.56 -> [13] ~~big_p(a), ~big_p(skolem_X11414)
% 0.19/0.56
% 0.19/0.56 [13] ALPHA_NOT_NOT : ~~big_p(a)
% 0.19/0.56 -> [17] big_p(a)
% 0.19/0.56
% 0.19/0.56 [17] GAMMA_FORALL : ! [X10_10] : (((big_p(a) & (big_p(X10_10) => ? [Y11_11] : ((big_p(Y11_11) & big_r(X10_10, Y11_11))))) => ? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(X10_10, W13_13)) & big_r(W13_13, Z12_12)))))
% 0.19/0.56 -> [22] ((big_p(a) & (big_p(skolem_X11414) => ? [Y11_11] : ((big_p(Y11_11) & big_r(skolem_X11414, Y11_11))))) => ? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(skolem_X11414, W13_13)) & big_r(W13_13, Z12_12))))
% 0.19/0.56
% 0.19/0.56 [22] BETA_IMPLY : ((big_p(a) & (big_p(skolem_X11414) => ? [Y11_11] : ((big_p(Y11_11) & big_r(skolem_X11414, Y11_11))))) => ? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(skolem_X11414, W13_13)) & big_r(W13_13, Z12_12))))
% 0.19/0.56 -> [24] ~(big_p(a) & (big_p(skolem_X11414) => ? [Y11_11] : ((big_p(Y11_11) & big_r(skolem_X11414, Y11_11)))))
% 0.19/0.56 -> [25] ? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(skolem_X11414, W13_13)) & big_r(W13_13, Z12_12)))
% 0.19/0.56
% 0.19/0.56 [24] BETA_NOT_AND : ~(big_p(a) & (big_p(skolem_X11414) => ? [Y11_11] : ((big_p(Y11_11) & big_r(skolem_X11414, Y11_11)))))
% 0.19/0.56 -> [28] ~big_p(a)
% 0.19/0.56 -> [29] ~(big_p(skolem_X11414) => ? [Y11_11] : ((big_p(Y11_11) & big_r(skolem_X11414, Y11_11))))
% 0.19/0.56
% 0.19/0.56 [28] CLOSURE : ~big_p(a)
% 0.19/0.56
% 0.19/0.56 [29] ALPHA_NOT_IMPLY : ~(big_p(skolem_X11414) => ? [Y11_11] : ((big_p(Y11_11) & big_r(skolem_X11414, Y11_11))))
% 0.19/0.56 -> [33] big_p(skolem_X11414), ~? [Y11_11] : ((big_p(Y11_11) & big_r(skolem_X11414, Y11_11)))
% 0.19/0.56
% 0.19/0.56 [33] CLOSURE : big_p(skolem_X11414)
% 0.19/0.56
% 0.19/0.56 [25] DELTA_EXISTS : ? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(skolem_X11414, W13_13)) & big_r(W13_13, Z12_12)))
% 0.19/0.56 -> [30] ((big_p(skolem_Z1212(skolem_X11414)) & big_r(skolem_X11414, skolem_W1313(skolem_X11414))) & big_r(skolem_W1313(skolem_X11414), skolem_Z1212(skolem_X11414)))
% 0.19/0.56
% 0.19/0.56 [30] ALPHA_AND : ((big_p(skolem_Z1212(skolem_X11414)) & big_r(skolem_X11414, skolem_W1313(skolem_X11414))) & big_r(skolem_W1313(skolem_X11414), skolem_Z1212(skolem_X11414)))
% 0.19/0.56 -> [34] (big_p(skolem_Z1212(skolem_X11414)) & big_r(skolem_X11414, skolem_W1313(skolem_X11414))), big_r(skolem_W1313(skolem_X11414), skolem_Z1212(skolem_X11414))
% 0.19/0.56
% 0.19/0.56 [34] ALPHA_AND : (big_p(skolem_Z1212(skolem_X11414)) & big_r(skolem_X11414, skolem_W1313(skolem_X11414)))
% 0.19/0.56 -> [49] big_p(skolem_Z1212(skolem_X11414)), big_r(skolem_X11414, skolem_W1313(skolem_X11414))
% 0.19/0.56
% 0.19/0.56 [49] GAMMA_NOT_EXISTS : ~? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(skolem_X11414, W116_16)) & big_r(W116_16, Z115_15)))
% 0.19/0.56 -> [71] ~((big_p(skolem_Z1212(skolem_X11414)) & big_r(skolem_X11414, skolem_W1313(skolem_X11414))) & big_r(skolem_W1313(skolem_X11414), skolem_Z1212(skolem_X11414)))
% 0.19/0.56
% 0.19/0.56 [71] BETA_NOT_AND : ~((big_p(skolem_Z1212(skolem_X11414)) & big_r(skolem_X11414, skolem_W1313(skolem_X11414))) & big_r(skolem_W1313(skolem_X11414), skolem_Z1212(skolem_X11414)))
% 0.19/0.56 -> [76] ~(big_p(skolem_Z1212(skolem_X11414)) & big_r(skolem_X11414, skolem_W1313(skolem_X11414)))
% 0.19/0.56 -> [77] ~big_r(skolem_W1313(skolem_X11414), skolem_Z1212(skolem_X11414))
% 0.19/0.56
% 0.19/0.56 [77] CLOSURE : ~big_r(skolem_W1313(skolem_X11414), skolem_Z1212(skolem_X11414))
% 0.19/0.56
% 0.19/0.56 [76] BETA_NOT_AND : ~(big_p(skolem_Z1212(skolem_X11414)) & big_r(skolem_X11414, skolem_W1313(skolem_X11414)))
% 0.19/0.56 -> [147] ~big_p(skolem_Z1212(skolem_X11414))
% 0.19/0.56 -> [148] ~big_r(skolem_X11414, skolem_W1313(skolem_X11414))
% 0.19/0.56
% 0.19/0.56 [148] CLOSURE : ~big_r(skolem_X11414, skolem_W1313(skolem_X11414))
% 0.19/0.56
% 0.19/0.56 [147] CLOSURE : ~big_p(skolem_Z1212(skolem_X11414))
% 0.19/0.56
% 0.19/0.56 [8] ALPHA_NOT_OR : ~((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X11414, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X11414, W219_19)) & big_r(W219_19, Z218_18))))
% 0.19/0.56 -> [11] ~(~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X11414, Y117_17)))), ~? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X11414, W219_19)) & big_r(W219_19, Z218_18)))
% 0.19/0.56
% 0.19/0.56 [11] ALPHA_NOT_OR : ~(~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X11414, Y117_17))))
% 0.19/0.56 -> [14] ~~big_p(a), ~~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X11414, Y117_17)))
% 0.19/0.56
% 0.19/0.56 [14] ALPHA_NOT_NOT : ~~big_p(a)
% 0.19/0.56 -> [16] big_p(a)
% 0.19/0.56
% 0.19/0.56 [16] ALPHA_NOT_NOT : ~~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X11414, Y117_17)))
% 0.19/0.56 -> [19] ? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X11414, Y117_17)))
% 0.19/0.56
% 0.19/0.56 [19] DELTA_EXISTS : ? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X11414, Y117_17)))
% 0.19/0.56 -> [21] (big_p(skolem_Y11717) & big_r(skolem_X11414, skolem_Y11717))
% 0.19/0.56
% 0.19/0.56 [21] ALPHA_AND : (big_p(skolem_Y11717) & big_r(skolem_X11414, skolem_Y11717))
% 0.19/0.56 -> [23] big_p(skolem_Y11717), big_r(skolem_X11414, skolem_Y11717)
% 0.19/0.56
% 0.19/0.56 [23] GAMMA_FORALL : ! [X10_10] : (((big_p(a) & (big_p(X10_10) => ? [Y11_11] : ((big_p(Y11_11) & big_r(X10_10, Y11_11))))) => ? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(X10_10, W13_13)) & big_r(W13_13, Z12_12)))))
% 0.19/0.56 -> [38] ((big_p(a) & (big_p(skolem_X11414) => ? [Y11_11] : ((big_p(Y11_11) & big_r(skolem_X11414, Y11_11))))) => ? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(skolem_X11414, W13_13)) & big_r(W13_13, Z12_12))))
% 0.19/0.56
% 0.19/0.56 [38] BETA_IMPLY : ((big_p(a) & (big_p(skolem_X11414) => ? [Y11_11] : ((big_p(Y11_11) & big_r(skolem_X11414, Y11_11))))) => ? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(skolem_X11414, W13_13)) & big_r(W13_13, Z12_12))))
% 0.19/0.56 -> [45] ~(big_p(a) & (big_p(skolem_X11414) => ? [Y11_11] : ((big_p(Y11_11) & big_r(skolem_X11414, Y11_11)))))
% 0.19/0.56 -> [46] ? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(skolem_X11414, W13_13)) & big_r(W13_13, Z12_12)))
% 0.19/0.56
% 0.19/0.56 [45] BETA_NOT_AND : ~(big_p(a) & (big_p(skolem_X11414) => ? [Y11_11] : ((big_p(Y11_11) & big_r(skolem_X11414, Y11_11)))))
% 0.19/0.56 -> [53] ~big_p(a)
% 0.19/0.56 -> [54] ~(big_p(skolem_X11414) => ? [Y11_11] : ((big_p(Y11_11) & big_r(skolem_X11414, Y11_11))))
% 0.19/0.56
% 0.19/0.56 [53] CLOSURE : ~big_p(a)
% 0.19/0.56
% 0.19/0.56 [54] ALPHA_NOT_IMPLY : ~(big_p(skolem_X11414) => ? [Y11_11] : ((big_p(Y11_11) & big_r(skolem_X11414, Y11_11))))
% 0.19/0.56 -> [60] big_p(skolem_X11414), ~? [Y11_11] : ((big_p(Y11_11) & big_r(skolem_X11414, Y11_11)))
% 0.19/0.56
% 0.19/0.56 [60] GAMMA_NOT_EXISTS : ~? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X11414, W219_19)) & big_r(W219_19, Z218_18)))
% 0.19/0.56 -> [72] ~((big_p(skolem_Y11717) & big_r(skolem_X11414, skolem_X11414)) & big_r(skolem_X11414, skolem_Y11717))
% 0.19/0.56
% 0.19/0.56 [72] BETA_NOT_AND : ~((big_p(skolem_Y11717) & big_r(skolem_X11414, skolem_X11414)) & big_r(skolem_X11414, skolem_Y11717))
% 0.19/0.56 -> [78] ~(big_p(skolem_Y11717) & big_r(skolem_X11414, skolem_X11414))
% 0.19/0.56 -> [79] ~big_r(skolem_X11414, skolem_Y11717)
% 0.19/0.56
% 0.19/0.56 [79] CLOSURE : ~big_r(skolem_X11414, skolem_Y11717)
% 0.19/0.56
% 0.19/0.56 [78] BETA_NOT_AND : ~(big_p(skolem_Y11717) & big_r(skolem_X11414, skolem_X11414))
% 0.19/0.56 -> [126] ~big_p(skolem_Y11717)
% 0.19/0.56 -> [127] ~big_r(skolem_X11414, skolem_X11414)
% 0.19/0.56
% 0.19/0.56 [126] CLOSURE : ~big_p(skolem_Y11717)
% 0.19/0.56
% 0.19/0.56 [127] GAMMA_NOT_EXISTS : ~? [Y11_11] : ((big_p(Y11_11) & big_r(skolem_X11414, Y11_11)))
% 0.19/0.56 -> [135] ~(big_p(skolem_Y11717) & big_r(skolem_X11414, skolem_Y11717))
% 0.19/0.56
% 0.19/0.56 [135] BETA_NOT_AND : ~(big_p(skolem_Y11717) & big_r(skolem_X11414, skolem_Y11717))
% 0.19/0.56 -> [136] ~big_p(skolem_Y11717)
% 0.19/0.56 -> [137] ~big_r(skolem_X11414, skolem_Y11717)
% 0.19/0.56
% 0.19/0.56 [136] CLOSURE : ~big_p(skolem_Y11717)
% 0.19/0.56
% 0.19/0.56 [137] CLOSURE : ~big_r(skolem_X11414, skolem_Y11717)
% 0.19/0.56
% 0.19/0.56 [46] DELTA_EXISTS : ? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(skolem_X11414, W13_13)) & big_r(W13_13, Z12_12)))
% 0.19/0.56 -> [63] ((big_p(skolem_Z1212(skolem_X11414)) & big_r(skolem_X11414, skolem_W1313(skolem_X11414))) & big_r(skolem_W1313(skolem_X11414), skolem_Z1212(skolem_X11414)))
% 0.19/0.56
% 0.19/0.56 [63] ALPHA_AND : ((big_p(skolem_Z1212(skolem_X11414)) & big_r(skolem_X11414, skolem_W1313(skolem_X11414))) & big_r(skolem_W1313(skolem_X11414), skolem_Z1212(skolem_X11414)))
% 0.19/0.56 -> [64] (big_p(skolem_Z1212(skolem_X11414)) & big_r(skolem_X11414, skolem_W1313(skolem_X11414))), big_r(skolem_W1313(skolem_X11414), skolem_Z1212(skolem_X11414))
% 0.19/0.56
% 0.19/0.56 [64] ALPHA_AND : (big_p(skolem_Z1212(skolem_X11414)) & big_r(skolem_X11414, skolem_W1313(skolem_X11414)))
% 0.19/0.56 -> [67] big_p(skolem_Z1212(skolem_X11414)), big_r(skolem_X11414, skolem_W1313(skolem_X11414))
% 0.19/0.56
% 0.19/0.56 [67] GAMMA_NOT_EXISTS : ~? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X11414, W219_19)) & big_r(W219_19, Z218_18)))
% 0.19/0.56 -> [93] ~((big_p(skolem_Z1212(skolem_X11414)) & big_r(skolem_X11414, skolem_W1313(skolem_X11414))) & big_r(skolem_W1313(skolem_X11414), skolem_Z1212(skolem_X11414)))
% 0.19/0.56
% 0.19/0.56 [93] BETA_NOT_AND : ~((big_p(skolem_Z1212(skolem_X11414)) & big_r(skolem_X11414, skolem_W1313(skolem_X11414))) & big_r(skolem_W1313(skolem_X11414), skolem_Z1212(skolem_X11414)))
% 0.19/0.56 -> [96] ~(big_p(skolem_Z1212(skolem_X11414)) & big_r(skolem_X11414, skolem_W1313(skolem_X11414)))
% 0.19/0.56 -> [97] ~big_r(skolem_W1313(skolem_X11414), skolem_Z1212(skolem_X11414))
% 0.19/0.56
% 0.19/0.56 [97] CLOSURE : ~big_r(skolem_W1313(skolem_X11414), skolem_Z1212(skolem_X11414))
% 0.19/0.56
% 0.19/0.56 [96] BETA_NOT_AND : ~(big_p(skolem_Z1212(skolem_X11414)) & big_r(skolem_X11414, skolem_W1313(skolem_X11414)))
% 0.19/0.56 -> [145] ~big_p(skolem_Z1212(skolem_X11414))
% 0.19/0.56 -> [146] ~big_r(skolem_X11414, skolem_W1313(skolem_X11414))
% 0.19/0.56
% 0.19/0.56 [146] CLOSURE : ~big_r(skolem_X11414, skolem_W1313(skolem_X11414))
% 0.19/0.56
% 0.19/0.56 [145] CLOSURE : ~big_p(skolem_Z1212(skolem_X11414))
% 0.19/0.56
% 0.19/0.56 [1] DELTA_NOT_FORALL : ~! [X10_10] : (((big_p(a) & (big_p(X10_10) => ? [Y11_11] : ((big_p(Y11_11) & big_r(X10_10, Y11_11))))) => ? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(X10_10, W13_13)) & big_r(W13_13, Z12_12)))))
% 0.19/0.56 -> [3] ~((big_p(a) & (big_p(skolem_X1010) => ? [Y11_11] : ((big_p(Y11_11) & big_r(skolem_X1010, Y11_11))))) => ? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(skolem_X1010, W13_13)) & big_r(W13_13, Z12_12))))
% 0.19/0.56
% 0.19/0.56 [3] ALPHA_NOT_IMPLY : ~((big_p(a) & (big_p(skolem_X1010) => ? [Y11_11] : ((big_p(Y11_11) & big_r(skolem_X1010, Y11_11))))) => ? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(skolem_X1010, W13_13)) & big_r(W13_13, Z12_12))))
% 0.19/0.56 -> [4] (big_p(a) & (big_p(skolem_X1010) => ? [Y11_11] : ((big_p(Y11_11) & big_r(skolem_X1010, Y11_11))))), ~? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(skolem_X1010, W13_13)) & big_r(W13_13, Z12_12)))
% 0.19/0.56
% 0.19/0.56 [4] ALPHA_AND : (big_p(a) & (big_p(skolem_X1010) => ? [Y11_11] : ((big_p(Y11_11) & big_r(skolem_X1010, Y11_11)))))
% 0.19/0.56 -> [6] big_p(a), (big_p(skolem_X1010) => ? [Y11_11] : ((big_p(Y11_11) & big_r(skolem_X1010, Y11_11))))
% 0.19/0.56
% 0.19/0.56 [6] BETA_IMPLY : (big_p(skolem_X1010) => ? [Y11_11] : ((big_p(Y11_11) & big_r(skolem_X1010, Y11_11))))
% 0.19/0.56 -> [9] ~big_p(skolem_X1010)
% 0.19/0.56 -> [10] ? [Y11_11] : ((big_p(Y11_11) & big_r(skolem_X1010, Y11_11)))
% 0.19/0.56
% 0.19/0.56 [9] GAMMA_FORALL : ! [X114_14] : ((((~big_p(a) | big_p(X114_14)) | ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(X114_14, W116_16)) & big_r(W116_16, Z115_15)))) & ((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(X114_14, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(X114_14, W219_19)) & big_r(W219_19, Z218_18))))))
% 0.19/0.56 -> [20] (((~big_p(a) | big_p(skolem_X1010)) | ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(skolem_X1010, W116_16)) & big_r(W116_16, Z115_15)))) & ((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X1010, W219_19)) & big_r(W219_19, Z218_18)))))
% 0.19/0.56
% 0.19/0.56 [20] ALPHA_AND : (((~big_p(a) | big_p(skolem_X1010)) | ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(skolem_X1010, W116_16)) & big_r(W116_16, Z115_15)))) & ((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X1010, W219_19)) & big_r(W219_19, Z218_18)))))
% 0.19/0.56 -> [26] ((~big_p(a) | big_p(skolem_X1010)) | ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(skolem_X1010, W116_16)) & big_r(W116_16, Z115_15)))), ((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X1010, W219_19)) & big_r(W219_19, Z218_18))))
% 0.19/0.56
% 0.19/0.56 [26] BETA_OR : ((~big_p(a) | big_p(skolem_X1010)) | ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(skolem_X1010, W116_16)) & big_r(W116_16, Z115_15))))
% 0.19/0.56 -> [31] (~big_p(a) | big_p(skolem_X1010))
% 0.19/0.56 -> [32] ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(skolem_X1010, W116_16)) & big_r(W116_16, Z115_15)))
% 0.19/0.56
% 0.19/0.56 [31] BETA_OR : ((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X1010, W219_19)) & big_r(W219_19, Z218_18))))
% 0.19/0.56 -> [36] (~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17))))
% 0.19/0.56 -> [37] ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X1010, W219_19)) & big_r(W219_19, Z218_18)))
% 0.19/0.56
% 0.19/0.56 [36] BETA_OR : (~big_p(a) | big_p(skolem_X1010))
% 0.19/0.56 -> [40] ~big_p(a)
% 0.19/0.56 -> [41] big_p(skolem_X1010)
% 0.19/0.56
% 0.19/0.56 [41] CLOSURE : big_p(skolem_X1010)
% 0.19/0.56
% 0.19/0.56 [40] CLOSURE : ~big_p(a)
% 0.19/0.56
% 0.19/0.56 [37] DELTA_EXISTS : ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X1010, W219_19)) & big_r(W219_19, Z218_18)))
% 0.19/0.56 -> [39] ((big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010))) & big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010)))
% 0.19/0.56
% 0.19/0.56 [39] ALPHA_AND : ((big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010))) & big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010)))
% 0.19/0.56 -> [44] (big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010))), big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [44] ALPHA_AND : (big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010)))
% 0.19/0.56 -> [59] big_p(skolem_Z21818(skolem_X1010)), big_r(skolem_X1010, skolem_W21919(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [59] BETA_OR : (~big_p(a) | big_p(skolem_X1010))
% 0.19/0.56 -> [88] ~big_p(a)
% 0.19/0.56 -> [89] big_p(skolem_X1010)
% 0.19/0.56
% 0.19/0.56 [88] CLOSURE : ~big_p(a)
% 0.19/0.56
% 0.19/0.56 [89] CLOSURE : big_p(skolem_X1010)
% 0.19/0.56
% 0.19/0.56 [32] DELTA_EXISTS : ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(skolem_X1010, W116_16)) & big_r(W116_16, Z115_15)))
% 0.19/0.56 -> [47] ((big_p(skolem_Z11515(skolem_X1010)) & big_r(skolem_X1010, skolem_W11616(skolem_X1010))) & big_r(skolem_W11616(skolem_X1010), skolem_Z11515(skolem_X1010)))
% 0.19/0.56
% 0.19/0.56 [47] ALPHA_AND : ((big_p(skolem_Z11515(skolem_X1010)) & big_r(skolem_X1010, skolem_W11616(skolem_X1010))) & big_r(skolem_W11616(skolem_X1010), skolem_Z11515(skolem_X1010)))
% 0.19/0.56 -> [48] (big_p(skolem_Z11515(skolem_X1010)) & big_r(skolem_X1010, skolem_W11616(skolem_X1010))), big_r(skolem_W11616(skolem_X1010), skolem_Z11515(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [48] ALPHA_AND : (big_p(skolem_Z11515(skolem_X1010)) & big_r(skolem_X1010, skolem_W11616(skolem_X1010)))
% 0.19/0.56 -> [58] big_p(skolem_Z11515(skolem_X1010)), big_r(skolem_X1010, skolem_W11616(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [58] BETA_OR : ((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X1010, W219_19)) & big_r(W219_19, Z218_18))))
% 0.19/0.56 -> [65] (~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17))))
% 0.19/0.56 -> [66] ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X1010, W219_19)) & big_r(W219_19, Z218_18)))
% 0.19/0.56
% 0.19/0.56 [65] BETA_OR : (~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17))))
% 0.19/0.56 -> [69] ~big_p(a)
% 0.19/0.56 -> [70] ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17)))
% 0.19/0.56
% 0.19/0.56 [69] CLOSURE : ~big_p(a)
% 0.19/0.56
% 0.19/0.56 [70] GAMMA_NOT_EXISTS : ~? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(skolem_X1010, W13_13)) & big_r(W13_13, Z12_12)))
% 0.19/0.56 -> [81] ~((big_p(skolem_Z11515(skolem_X1010)) & big_r(skolem_X1010, skolem_W11616(skolem_X1010))) & big_r(skolem_W11616(skolem_X1010), skolem_Z11515(skolem_X1010)))
% 0.19/0.56
% 0.19/0.56 [81] BETA_NOT_AND : ~((big_p(skolem_Z11515(skolem_X1010)) & big_r(skolem_X1010, skolem_W11616(skolem_X1010))) & big_r(skolem_W11616(skolem_X1010), skolem_Z11515(skolem_X1010)))
% 0.19/0.56 -> [82] ~(big_p(skolem_Z11515(skolem_X1010)) & big_r(skolem_X1010, skolem_W11616(skolem_X1010)))
% 0.19/0.56 -> [83] ~big_r(skolem_W11616(skolem_X1010), skolem_Z11515(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [83] CLOSURE : ~big_r(skolem_W11616(skolem_X1010), skolem_Z11515(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [82] BETA_NOT_AND : ~(big_p(skolem_Z11515(skolem_X1010)) & big_r(skolem_X1010, skolem_W11616(skolem_X1010)))
% 0.19/0.56 -> [143] ~big_p(skolem_Z11515(skolem_X1010))
% 0.19/0.56 -> [144] ~big_r(skolem_X1010, skolem_W11616(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [143] CLOSURE : ~big_p(skolem_Z11515(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [144] CLOSURE : ~big_r(skolem_X1010, skolem_W11616(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [66] DELTA_EXISTS : ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X1010, W219_19)) & big_r(W219_19, Z218_18)))
% 0.19/0.56 -> [75] ((big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010))) & big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010)))
% 0.19/0.56
% 0.19/0.56 [75] ALPHA_AND : ((big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010))) & big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010)))
% 0.19/0.56 -> [80] (big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010))), big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [80] ALPHA_AND : (big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010)))
% 0.19/0.56 -> [92] big_p(skolem_Z21818(skolem_X1010)), big_r(skolem_X1010, skolem_W21919(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [92] GAMMA_NOT_EXISTS : ~? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(skolem_X1010, W13_13)) & big_r(W13_13, Z12_12)))
% 0.19/0.56 -> [112] ~((big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010))) & big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010)))
% 0.19/0.56
% 0.19/0.56 [112] BETA_NOT_AND : ~((big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010))) & big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010)))
% 0.19/0.56 -> [116] ~(big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010)))
% 0.19/0.56 -> [117] ~big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [117] CLOSURE : ~big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [116] BETA_NOT_AND : ~(big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010)))
% 0.19/0.56 -> [155] ~big_p(skolem_Z21818(skolem_X1010))
% 0.19/0.56 -> [156] ~big_r(skolem_X1010, skolem_W21919(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [155] CLOSURE : ~big_p(skolem_Z21818(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [156] CLOSURE : ~big_r(skolem_X1010, skolem_W21919(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [10] DELTA_EXISTS : ? [Y11_11] : ((big_p(Y11_11) & big_r(skolem_X1010, Y11_11)))
% 0.19/0.56 -> [15] (big_p(skolem_Y1111) & big_r(skolem_X1010, skolem_Y1111))
% 0.19/0.56
% 0.19/0.56 [15] ALPHA_AND : (big_p(skolem_Y1111) & big_r(skolem_X1010, skolem_Y1111))
% 0.19/0.56 -> [18] big_p(skolem_Y1111), big_r(skolem_X1010, skolem_Y1111)
% 0.19/0.56
% 0.19/0.56 [18] GAMMA_FORALL : ! [X114_14] : ((((~big_p(a) | big_p(X114_14)) | ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(X114_14, W116_16)) & big_r(W116_16, Z115_15)))) & ((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(X114_14, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(X114_14, W219_19)) & big_r(W219_19, Z218_18))))))
% 0.19/0.56 -> [27] (((~big_p(a) | big_p(skolem_X1010)) | ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(skolem_X1010, W116_16)) & big_r(W116_16, Z115_15)))) & ((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X1010, W219_19)) & big_r(W219_19, Z218_18)))))
% 0.19/0.56
% 0.19/0.56 [27] ALPHA_AND : (((~big_p(a) | big_p(skolem_X1010)) | ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(skolem_X1010, W116_16)) & big_r(W116_16, Z115_15)))) & ((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X1010, W219_19)) & big_r(W219_19, Z218_18)))))
% 0.19/0.56 -> [35] ((~big_p(a) | big_p(skolem_X1010)) | ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(skolem_X1010, W116_16)) & big_r(W116_16, Z115_15)))), ((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X1010, W219_19)) & big_r(W219_19, Z218_18))))
% 0.19/0.56
% 0.19/0.56 [35] BETA_OR : ((~big_p(a) | big_p(skolem_X1010)) | ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(skolem_X1010, W116_16)) & big_r(W116_16, Z115_15))))
% 0.19/0.56 -> [42] (~big_p(a) | big_p(skolem_X1010))
% 0.19/0.56 -> [43] ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(skolem_X1010, W116_16)) & big_r(W116_16, Z115_15)))
% 0.19/0.56
% 0.19/0.56 [43] DELTA_EXISTS : ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(skolem_X1010, W116_16)) & big_r(W116_16, Z115_15)))
% 0.19/0.56 -> [52] ((big_p(skolem_Z11515(skolem_X1010)) & big_r(skolem_X1010, skolem_W11616(skolem_X1010))) & big_r(skolem_W11616(skolem_X1010), skolem_Z11515(skolem_X1010)))
% 0.19/0.56
% 0.19/0.56 [52] ALPHA_AND : ((big_p(skolem_Z11515(skolem_X1010)) & big_r(skolem_X1010, skolem_W11616(skolem_X1010))) & big_r(skolem_W11616(skolem_X1010), skolem_Z11515(skolem_X1010)))
% 0.19/0.56 -> [55] (big_p(skolem_Z11515(skolem_X1010)) & big_r(skolem_X1010, skolem_W11616(skolem_X1010))), big_r(skolem_W11616(skolem_X1010), skolem_Z11515(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [55] ALPHA_AND : (big_p(skolem_Z11515(skolem_X1010)) & big_r(skolem_X1010, skolem_W11616(skolem_X1010)))
% 0.19/0.56 -> [68] big_p(skolem_Z11515(skolem_X1010)), big_r(skolem_X1010, skolem_W11616(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [68] BETA_OR : ((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X1010, W219_19)) & big_r(W219_19, Z218_18))))
% 0.19/0.56 -> [104] (~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17))))
% 0.19/0.56 -> [105] ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X1010, W219_19)) & big_r(W219_19, Z218_18)))
% 0.19/0.56
% 0.19/0.56 [104] BETA_OR : (~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17))))
% 0.19/0.56 -> [110] ~big_p(a)
% 0.19/0.56 -> [111] ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17)))
% 0.19/0.56
% 0.19/0.56 [110] CLOSURE : ~big_p(a)
% 0.19/0.56
% 0.19/0.56 [111] GAMMA_NOT_EXISTS : ~? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(skolem_X1010, W13_13)) & big_r(W13_13, Z12_12)))
% 0.19/0.56 -> [113] ~((big_p(skolem_Z11515(skolem_X1010)) & big_r(skolem_X1010, skolem_W11616(skolem_X1010))) & big_r(skolem_W11616(skolem_X1010), skolem_Z11515(skolem_X1010)))
% 0.19/0.56
% 0.19/0.56 [113] BETA_NOT_AND : ~((big_p(skolem_Z11515(skolem_X1010)) & big_r(skolem_X1010, skolem_W11616(skolem_X1010))) & big_r(skolem_W11616(skolem_X1010), skolem_Z11515(skolem_X1010)))
% 0.19/0.56 -> [114] ~(big_p(skolem_Z11515(skolem_X1010)) & big_r(skolem_X1010, skolem_W11616(skolem_X1010)))
% 0.19/0.56 -> [115] ~big_r(skolem_W11616(skolem_X1010), skolem_Z11515(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [115] CLOSURE : ~big_r(skolem_W11616(skolem_X1010), skolem_Z11515(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [114] BETA_NOT_AND : ~(big_p(skolem_Z11515(skolem_X1010)) & big_r(skolem_X1010, skolem_W11616(skolem_X1010)))
% 0.19/0.56 -> [149] ~big_p(skolem_Z11515(skolem_X1010))
% 0.19/0.56 -> [150] ~big_r(skolem_X1010, skolem_W11616(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [149] CLOSURE : ~big_p(skolem_Z11515(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [150] CLOSURE : ~big_r(skolem_X1010, skolem_W11616(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [105] DELTA_EXISTS : ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X1010, W219_19)) & big_r(W219_19, Z218_18)))
% 0.19/0.56 -> [108] ((big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010))) & big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010)))
% 0.19/0.56
% 0.19/0.56 [108] ALPHA_AND : ((big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010))) & big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010)))
% 0.19/0.56 -> [109] (big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010))), big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [109] ALPHA_AND : (big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010)))
% 0.19/0.56 -> [121] big_p(skolem_Z21818(skolem_X1010)), big_r(skolem_X1010, skolem_W21919(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [121] GAMMA_NOT_EXISTS : ~? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(skolem_X1010, W13_13)) & big_r(W13_13, Z12_12)))
% 0.19/0.56 -> [128] ~((big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010))) & big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010)))
% 0.19/0.56
% 0.19/0.56 [128] BETA_NOT_AND : ~((big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010))) & big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010)))
% 0.19/0.56 -> [131] ~(big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010)))
% 0.19/0.56 -> [132] ~big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [132] CLOSURE : ~big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [131] BETA_NOT_AND : ~(big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010)))
% 0.19/0.56 -> [153] ~big_p(skolem_Z21818(skolem_X1010))
% 0.19/0.56 -> [154] ~big_r(skolem_X1010, skolem_W21919(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [153] CLOSURE : ~big_p(skolem_Z21818(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [154] CLOSURE : ~big_r(skolem_X1010, skolem_W21919(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [42] BETA_OR : ((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X1010, W219_19)) & big_r(W219_19, Z218_18))))
% 0.19/0.56 -> [50] (~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17))))
% 0.19/0.56 -> [51] ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X1010, W219_19)) & big_r(W219_19, Z218_18)))
% 0.19/0.56
% 0.19/0.56 [50] BETA_OR : (~big_p(a) | big_p(skolem_X1010))
% 0.19/0.56 -> [56] ~big_p(a)
% 0.19/0.56 -> [57] big_p(skolem_X1010)
% 0.19/0.56
% 0.19/0.56 [56] CLOSURE : ~big_p(a)
% 0.19/0.56
% 0.19/0.56 [57] BETA_OR : (~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17))))
% 0.19/0.56 -> [73] ~big_p(a)
% 0.19/0.56 -> [74] ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17)))
% 0.19/0.56
% 0.19/0.56 [73] CLOSURE : ~big_p(a)
% 0.19/0.56
% 0.19/0.56 [74] GAMMA_NOT_EXISTS : ~? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(skolem_X1010, W13_13)) & big_r(W13_13, Z12_12)))
% 0.19/0.56 -> [85] ~((big_p(skolem_Y1111) & big_r(skolem_X1010, skolem_X1010)) & big_r(skolem_X1010, skolem_Y1111))
% 0.19/0.56
% 0.19/0.56 [85] BETA_NOT_AND : ~((big_p(skolem_Y1111) & big_r(skolem_X1010, skolem_X1010)) & big_r(skolem_X1010, skolem_Y1111))
% 0.19/0.56 -> [86] ~(big_p(skolem_Y1111) & big_r(skolem_X1010, skolem_X1010))
% 0.19/0.56 -> [87] ~big_r(skolem_X1010, skolem_Y1111)
% 0.19/0.56
% 0.19/0.56 [87] CLOSURE : ~big_r(skolem_X1010, skolem_Y1111)
% 0.19/0.56
% 0.19/0.56 [86] BETA_NOT_AND : ~(big_p(skolem_Y1111) & big_r(skolem_X1010, skolem_X1010))
% 0.19/0.56 -> [133] ~big_p(skolem_Y1111)
% 0.19/0.56 -> [134] ~big_r(skolem_X1010, skolem_X1010)
% 0.19/0.56
% 0.19/0.56 [133] CLOSURE : ~big_p(skolem_Y1111)
% 0.19/0.56
% 0.19/0.56 [134] GAMMA_NOT_EXISTS : ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17)))
% 0.19/0.56 -> [140] ~(big_p(skolem_Y1111) & big_r(skolem_X1010, skolem_Y1111))
% 0.19/0.56
% 0.19/0.56 [140] BETA_NOT_AND : ~(big_p(skolem_Y1111) & big_r(skolem_X1010, skolem_Y1111))
% 0.19/0.56 -> [141] ~big_p(skolem_Y1111)
% 0.19/0.56 -> [142] ~big_r(skolem_X1010, skolem_Y1111)
% 0.19/0.56
% 0.19/0.56 [141] CLOSURE : ~big_p(skolem_Y1111)
% 0.19/0.56
% 0.19/0.56 [142] CLOSURE : ~big_r(skolem_X1010, skolem_Y1111)
% 0.19/0.56
% 0.19/0.56 [51] DELTA_EXISTS : ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X1010, W219_19)) & big_r(W219_19, Z218_18)))
% 0.19/0.56 -> [61] ((big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010))) & big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010)))
% 0.19/0.56
% 0.19/0.56 [61] ALPHA_AND : ((big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010))) & big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010)))
% 0.19/0.56 -> [62] (big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010))), big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [62] ALPHA_AND : (big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010)))
% 0.19/0.56 -> [84] big_p(skolem_Z21818(skolem_X1010)), big_r(skolem_X1010, skolem_W21919(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [84] BETA_OR : (~big_p(a) | big_p(skolem_X1010))
% 0.19/0.56 -> [102] ~big_p(a)
% 0.19/0.56 -> [103] big_p(skolem_X1010)
% 0.19/0.56
% 0.19/0.56 [102] CLOSURE : ~big_p(a)
% 0.19/0.56
% 0.19/0.56 [103] GAMMA_NOT_EXISTS : ~? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(skolem_X1010, W13_13)) & big_r(W13_13, Z12_12)))
% 0.19/0.56 -> [120] ~((big_p(skolem_Y1111) & big_r(skolem_X1010, skolem_X1010)) & big_r(skolem_X1010, skolem_Y1111))
% 0.19/0.56
% 0.19/0.56 [120] BETA_NOT_AND : ~((big_p(skolem_Y1111) & big_r(skolem_X1010, skolem_X1010)) & big_r(skolem_X1010, skolem_Y1111))
% 0.19/0.56 -> [124] ~(big_p(skolem_Y1111) & big_r(skolem_X1010, skolem_X1010))
% 0.19/0.56 -> [125] ~big_r(skolem_X1010, skolem_Y1111)
% 0.19/0.56
% 0.19/0.56 [125] CLOSURE : ~big_r(skolem_X1010, skolem_Y1111)
% 0.19/0.56
% 0.19/0.56 [124] BETA_NOT_AND : ~(big_p(skolem_Y1111) & big_r(skolem_X1010, skolem_X1010))
% 0.19/0.56 -> [151] ~big_p(skolem_Y1111)
% 0.19/0.56 -> [152] ~big_r(skolem_X1010, skolem_X1010)
% 0.19/0.56
% 0.19/0.56 [151] CLOSURE : ~big_p(skolem_Y1111)
% 0.19/0.56
% 0.19/0.56 [152] : ! [X114_14] : ((((~big_p(a) | big_p(X114_14)) | ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(X114_14, W116_16)) & big_r(W116_16, Z115_15)))) & ((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(X114_14, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(X114_14, W219_19)) & big_r(W219_19, Z218_18))))))
% 0.19/0.56 -> [157] ! [X114_14] : ((((~big_p(a) | big_p(X114_14)) | ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(X114_14, W116_16)) & big_r(W116_16, Z115_15)))) & ((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(X114_14, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(X114_14, W219_19)) & big_r(W219_19, Z218_18))))))
% 0.19/0.56
% 0.19/0.56 [157] GAMMA_FORALL : ! [X114_14] : ((((~big_p(a) | big_p(X114_14)) | ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(X114_14, W116_16)) & big_r(W116_16, Z115_15)))) & ((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(X114_14, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(X114_14, W219_19)) & big_r(W219_19, Z218_18))))))
% 0.19/0.56 -> [158] (((~big_p(a) | big_p(skolem_X1010)) | ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(skolem_X1010, W116_16)) & big_r(W116_16, Z115_15)))) & ((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X1010, W219_19)) & big_r(W219_19, Z218_18)))))
% 0.19/0.56
% 0.19/0.56 [158] ALPHA_AND : (((~big_p(a) | big_p(skolem_X1010)) | ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(skolem_X1010, W116_16)) & big_r(W116_16, Z115_15)))) & ((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X1010, W219_19)) & big_r(W219_19, Z218_18)))))
% 0.19/0.56 -> [159] ((~big_p(a) | big_p(skolem_X1010)) | ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(skolem_X1010, W116_16)) & big_r(W116_16, Z115_15)))), ((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X1010, W219_19)) & big_r(W219_19, Z218_18))))
% 0.19/0.56
% 0.19/0.56 [159] BETA_OR : ((~big_p(a) | big_p(skolem_X1010)) | ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(skolem_X1010, W116_16)) & big_r(W116_16, Z115_15))))
% 0.19/0.56 -> [160] (~big_p(a) | big_p(skolem_X1010))
% 0.19/0.56 -> [161] ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(skolem_X1010, W116_16)) & big_r(W116_16, Z115_15)))
% 0.19/0.56
% 0.19/0.56 [161] DELTA_EXISTS : ? [Z115_15, W116_16] : (((big_p(Z115_15) & big_r(skolem_X1010, W116_16)) & big_r(W116_16, Z115_15)))
% 0.19/0.56 -> [164] ((big_p(skolem_Z11515(skolem_X1010)) & big_r(skolem_X1010, skolem_W11616(skolem_X1010))) & big_r(skolem_W11616(skolem_X1010), skolem_Z11515(skolem_X1010)))
% 0.19/0.56
% 0.19/0.56 [164] ALPHA_AND : ((big_p(skolem_Z11515(skolem_X1010)) & big_r(skolem_X1010, skolem_W11616(skolem_X1010))) & big_r(skolem_W11616(skolem_X1010), skolem_Z11515(skolem_X1010)))
% 0.19/0.56 -> [168] (big_p(skolem_Z11515(skolem_X1010)) & big_r(skolem_X1010, skolem_W11616(skolem_X1010))), big_r(skolem_W11616(skolem_X1010), skolem_Z11515(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [168] ALPHA_AND : (big_p(skolem_Z11515(skolem_X1010)) & big_r(skolem_X1010, skolem_W11616(skolem_X1010)))
% 0.19/0.56 -> [172] big_p(skolem_Z11515(skolem_X1010)), big_r(skolem_X1010, skolem_W11616(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [172] BETA_OR : ((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X1010, W219_19)) & big_r(W219_19, Z218_18))))
% 0.19/0.56 -> [177] (~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17))))
% 0.19/0.56 -> [178] ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X1010, W219_19)) & big_r(W219_19, Z218_18)))
% 0.19/0.56
% 0.19/0.56 [177] BETA_OR : (~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17))))
% 0.19/0.56 -> [181] ~big_p(a)
% 0.19/0.56 -> [182] ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17)))
% 0.19/0.56
% 0.19/0.56 [181] CLOSURE : ~big_p(a)
% 0.19/0.56
% 0.19/0.56 [182] GAMMA_NOT_EXISTS : ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17)))
% 0.19/0.56 -> [185] ~(big_p(skolem_Y1111) & big_r(skolem_X1010, skolem_Y1111))
% 0.19/0.56
% 0.19/0.56 [185] BETA_NOT_AND : ~(big_p(skolem_Y1111) & big_r(skolem_X1010, skolem_Y1111))
% 0.19/0.56 -> [186] ~big_p(skolem_Y1111)
% 0.19/0.56 -> [187] ~big_r(skolem_X1010, skolem_Y1111)
% 0.19/0.56
% 0.19/0.56 [186] CLOSURE : ~big_p(skolem_Y1111)
% 0.19/0.56
% 0.19/0.56 [187] CLOSURE : ~big_r(skolem_X1010, skolem_Y1111)
% 0.19/0.56
% 0.19/0.56 [202] BETA_NOT_AND : ~((big_p(skolem_Z11515(skolem_X1010)) & big_r(skolem_X1010, skolem_W11616(skolem_X1010))) & big_r(skolem_W11616(skolem_X1010), skolem_Z11515(skolem_X1010)))
% 0.19/0.56 -> [218] ~(big_p(skolem_Z11515(skolem_X1010)) & big_r(skolem_X1010, skolem_W11616(skolem_X1010)))
% 0.19/0.56 -> [219] ~big_r(skolem_W11616(skolem_X1010), skolem_Z11515(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [219] CLOSURE : ~big_r(skolem_W11616(skolem_X1010), skolem_Z11515(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [218] BETA_NOT_AND : ~(big_p(skolem_Z11515(skolem_X1010)) & big_r(skolem_X1010, skolem_W11616(skolem_X1010)))
% 0.19/0.56 -> [220] ~big_p(skolem_Z11515(skolem_X1010))
% 0.19/0.56 -> [221] ~big_r(skolem_X1010, skolem_W11616(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [221] CLOSURE : ~big_r(skolem_X1010, skolem_W11616(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [220] CLOSURE : ~big_p(skolem_Z11515(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [160] BETA_OR : ((~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17)))) | ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X1010, W219_19)) & big_r(W219_19, Z218_18))))
% 0.19/0.56 -> [162] (~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17))))
% 0.19/0.56 -> [163] ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X1010, W219_19)) & big_r(W219_19, Z218_18)))
% 0.19/0.56
% 0.19/0.56 [163] DELTA_EXISTS : ? [Z218_18, W219_19] : (((big_p(Z218_18) & big_r(skolem_X1010, W219_19)) & big_r(W219_19, Z218_18)))
% 0.19/0.56 -> [167] ((big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010))) & big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010)))
% 0.19/0.56
% 0.19/0.56 [167] ALPHA_AND : ((big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010))) & big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010)))
% 0.19/0.56 -> [169] (big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010))), big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [169] ALPHA_AND : (big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010)))
% 0.19/0.56 -> [173] big_p(skolem_Z21818(skolem_X1010)), big_r(skolem_X1010, skolem_W21919(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [173] BETA_OR : (~big_p(a) | big_p(skolem_X1010))
% 0.19/0.56 -> [179] ~big_p(a)
% 0.19/0.56 -> [180] big_p(skolem_X1010)
% 0.19/0.56
% 0.19/0.56 [179] CLOSURE : ~big_p(a)
% 0.19/0.56
% 0.19/0.56 [180] : ~? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(skolem_X1010, W13_13)) & big_r(W13_13, Z12_12)))
% 0.19/0.56 -> [188] ~? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(skolem_X1010, W13_13)) & big_r(W13_13, Z12_12)))
% 0.19/0.56
% 0.19/0.56 [188] GAMMA_NOT_EXISTS : ~? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(skolem_X1010, W13_13)) & big_r(W13_13, Z12_12)))
% 0.19/0.56 -> [189] ~((big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010))) & big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010)))
% 0.19/0.56
% 0.19/0.56 [189] BETA_NOT_AND : ~((big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010))) & big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010)))
% 0.19/0.56 -> [192] ~(big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010)))
% 0.19/0.56 -> [193] ~big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [193] CLOSURE : ~big_r(skolem_W21919(skolem_X1010), skolem_Z21818(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [192] BETA_NOT_AND : ~(big_p(skolem_Z21818(skolem_X1010)) & big_r(skolem_X1010, skolem_W21919(skolem_X1010)))
% 0.19/0.56 -> [207] ~big_p(skolem_Z21818(skolem_X1010))
% 0.19/0.56 -> [208] ~big_r(skolem_X1010, skolem_W21919(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [207] CLOSURE : ~big_p(skolem_Z21818(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [208] CLOSURE : ~big_r(skolem_X1010, skolem_W21919(skolem_X1010))
% 0.19/0.56
% 0.19/0.56 [162] BETA_OR : (~big_p(a) | big_p(skolem_X1010))
% 0.19/0.56 -> [165] ~big_p(a)
% 0.19/0.56 -> [166] big_p(skolem_X1010)
% 0.19/0.56
% 0.19/0.56 [165] CLOSURE : ~big_p(a)
% 0.19/0.56
% 0.19/0.56 [166] BETA_OR : (~big_p(a) | ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17))))
% 0.19/0.56 -> [170] ~big_p(a)
% 0.19/0.56 -> [171] ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17)))
% 0.19/0.56
% 0.19/0.56 [170] CLOSURE : ~big_p(a)
% 0.19/0.56
% 0.19/0.56 [171] GAMMA_NOT_EXISTS : ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17)))
% 0.19/0.56 -> [174] ~(big_p(a) & big_r(skolem_X1010, a))
% 0.19/0.56
% 0.19/0.56 [174] BETA_NOT_AND : ~(big_p(a) & big_r(skolem_X1010, a))
% 0.19/0.56 -> [175] ~big_p(a)
% 0.19/0.56 -> [176] ~big_r(skolem_X1010, a)
% 0.19/0.56
% 0.19/0.56 [175] CLOSURE : ~big_p(a)
% 0.19/0.56
% 0.19/0.56 [176] : ~? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(skolem_X1010, W13_13)) & big_r(W13_13, Z12_12)))
% 0.19/0.56 -> [191] ~? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(skolem_X1010, W13_13)) & big_r(W13_13, Z12_12)))
% 0.19/0.56
% 0.19/0.56 [191] GAMMA_NOT_EXISTS : ~? [Z12_12, W13_13] : (((big_p(Z12_12) & big_r(skolem_X1010, W13_13)) & big_r(W13_13, Z12_12)))
% 0.19/0.56 -> [194] ~((big_p(skolem_Y1111) & big_r(skolem_X1010, skolem_X1010)) & big_r(skolem_X1010, skolem_Y1111))
% 0.19/0.56
% 0.19/0.56 [194] BETA_NOT_AND : ~((big_p(skolem_Y1111) & big_r(skolem_X1010, skolem_X1010)) & big_r(skolem_X1010, skolem_Y1111))
% 0.19/0.56 -> [197] ~(big_p(skolem_Y1111) & big_r(skolem_X1010, skolem_X1010))
% 0.19/0.56 -> [198] ~big_r(skolem_X1010, skolem_Y1111)
% 0.19/0.56
% 0.19/0.56 [198] CLOSURE : ~big_r(skolem_X1010, skolem_Y1111)
% 0.19/0.56
% 0.19/0.56 [197] BETA_NOT_AND : ~(big_p(skolem_Y1111) & big_r(skolem_X1010, skolem_X1010))
% 0.19/0.56 -> [209] ~big_p(skolem_Y1111)
% 0.19/0.56 -> [210] ~big_r(skolem_X1010, skolem_X1010)
% 0.19/0.56
% 0.19/0.56 [209] CLOSURE : ~big_p(skolem_Y1111)
% 0.19/0.56
% 0.19/0.56 [210] : ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17)))
% 0.19/0.56 -> [211] ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17)))
% 0.19/0.56
% 0.19/0.56 [211] GAMMA_NOT_EXISTS : ~? [Y117_17] : ((big_p(Y117_17) & big_r(skolem_X1010, Y117_17)))
% 0.19/0.56 -> [212] ~(big_p(skolem_Y1111) & big_r(skolem_X1010, skolem_Y1111))
% 0.19/0.56
% 0.19/0.56 [212] BETA_NOT_AND : ~(big_p(skolem_Y1111) & big_r(skolem_X1010, skolem_Y1111))
% 0.19/0.56 -> [215] ~big_p(skolem_Y1111)
% 0.19/0.56 -> [216] ~big_r(skolem_X1010, skolem_Y1111)
% 0.19/0.56
% 0.19/0.56 [215] CLOSURE : ~big_p(skolem_Y1111)
% 0.19/0.56
% 0.19/0.56 [216] CLOSURE : ~big_r(skolem_X1010, skolem_Y1111)
% 0.19/0.56
% 0.19/0.56 % SZS output end Proof for theBenchmark.p
% 0.19/0.56 [0.218281s][1][Res] 1326 goroutines created
% 0.19/0.56 ==== Result ====
% 0.19/0.56 [0.218304s][1][Res] VALID
% 0.19/0.56 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------