TSTP Solution File: NUM531+2 by Goeland---1.0.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : NUM531+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 10:19:24 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
% 0.11/0.12 % Problem : NUM531+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 11:53:03 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 [DMT] DMT loaded with preskolemization
% 0.13/0.35 [EQ] equality loaded.
% 0.13/0.35 [0.000037s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.35 Start search
% 0.13/0.35 nb_step : 1 - limit : 11
% 0.13/0.35 Launch Gotab with destructive = true
% 0.20/0.55 % SZS output start Proof for theBenchmark.p
% 0.20/0.55 [0] ALPHA_AND : (! [W02_2] : ((aSet0(W02_2) => $true)) & ! [W03_3] : ((aElement0(W03_3) => $true)) & ! [W04_4] : ((aSet0(W04_4) => ! [W15_5] : ((aElementOf0(W15_5, W04_4) => aElement0(W15_5))))) & ! [W06_6] : ((aSet0(W06_6) => (isFinite0(W06_6) => $true))) & ! [W07_7] : ((=(W07_7, slcrc0) <=> (aSet0(W07_7) & ~? [W18_8] : (aElementOf0(W18_8, W07_7))))) & isFinite0(slcrc0) & ! [W09_9] : ((aSet0(W09_9) => (isCountable0(W09_9) => $true))) & ! [W010_10] : (((aSet0(W010_10) & isCountable0(W010_10)) => ~isFinite0(W010_10))) & ~! [W011_11] : (((aSet0(W011_11) & isCountable0(W011_11)) => ~(~? [W112_12] : (aElementOf0(W112_12, W011_11)) & =(W011_11, slcrc0)))))
% 0.20/0.55 -> [1] ! [W02_2] : ((aSet0(W02_2) => $true)), ! [W03_3] : ((aElement0(W03_3) => $true)), ! [W04_4] : ((aSet0(W04_4) => ! [W15_5] : ((aElementOf0(W15_5, W04_4) => aElement0(W15_5))))), ! [W06_6] : ((aSet0(W06_6) => (isFinite0(W06_6) => $true))), ! [W07_7] : ((=(W07_7, slcrc0) <=> (aSet0(W07_7) & ~? [W18_8] : (aElementOf0(W18_8, W07_7))))), isFinite0(slcrc0), ! [W09_9] : ((aSet0(W09_9) => (isCountable0(W09_9) => $true))), ! [W010_10] : (((aSet0(W010_10) & isCountable0(W010_10)) => ~isFinite0(W010_10))), ~! [W011_11] : (((aSet0(W011_11) & isCountable0(W011_11)) => ~(~? [W112_12] : (aElementOf0(W112_12, W011_11)) & =(W011_11, slcrc0))))
% 0.20/0.55
% 0.20/0.55 [1] DELTA_NOT_FORALL : ~! [W011_11] : (((aSet0(W011_11) & isCountable0(W011_11)) => ~(~? [W112_12] : (aElementOf0(W112_12, W011_11)) & =(W011_11, slcrc0))))
% 0.20/0.55 -> [2] ~((aSet0(skolem_W01111) & isCountable0(skolem_W01111)) => ~(~? [W112_12] : (aElementOf0(W112_12, skolem_W01111)) & =(skolem_W01111, slcrc0)))
% 0.20/0.55
% 0.20/0.55 [2] ALPHA_NOT_IMPLY : ~((aSet0(skolem_W01111) & isCountable0(skolem_W01111)) => ~(~? [W112_12] : (aElementOf0(W112_12, skolem_W01111)) & =(skolem_W01111, slcrc0)))
% 0.20/0.55 -> [3] (aSet0(skolem_W01111) & isCountable0(skolem_W01111)), ~~(~? [W112_12] : (aElementOf0(W112_12, skolem_W01111)) & =(skolem_W01111, slcrc0))
% 0.20/0.55
% 0.20/0.55 [3] ALPHA_AND : (aSet0(skolem_W01111) & isCountable0(skolem_W01111))
% 0.20/0.55 -> [4] aSet0(skolem_W01111), isCountable0(skolem_W01111)
% 0.20/0.55
% 0.20/0.55 [4] ALPHA_NOT_NOT : ~~(~? [W112_12] : (aElementOf0(W112_12, skolem_W01111)) & =(skolem_W01111, slcrc0))
% 0.20/0.55 -> [5] (~? [W112_12] : (aElementOf0(W112_12, skolem_W01111)) & =(skolem_W01111, slcrc0))
% 0.20/0.55
% 0.20/0.55 [5] ALPHA_AND : (~? [W112_12] : (aElementOf0(W112_12, skolem_W01111)) & =(skolem_W01111, slcrc0))
% 0.20/0.55 -> [6] ~? [W112_12] : (aElementOf0(W112_12, skolem_W01111)), =(skolem_W01111, slcrc0)
% 0.20/0.55
% 0.20/0.55 [6] GAMMA_FORALL : ! [W02_2] : ((aSet0(W02_2) => $true))
% 0.20/0.55 -> [7] (aSet0(skolem_W01111) => $true)
% 0.20/0.55
% 0.20/0.55 [7] BETA_IMPLY : (aSet0(skolem_W01111) => $true)
% 0.20/0.55 -> [8] ~aSet0(skolem_W01111)
% 0.20/0.55 -> [9] $true
% 0.20/0.55
% 0.20/0.55 [8] CLOSURE : =
% 0.20/0.55
% 0.20/0.55 [9] GAMMA_FORALL : ! [W03_3] : ((aElement0(W03_3) => $true))
% 0.20/0.55 -> [10] (aElement0(W03_0_1) => $true)
% 0.20/0.55
% 0.20/0.55 [10] BETA_IMPLY : (aElement0(W03_0_1) => $true)
% 0.20/0.55 -> [11] ~aElement0(W03_0_1)
% 0.20/0.55 -> [12] $true
% 0.20/0.55
% 0.20/0.55 [12] GAMMA_FORALL : ! [W04_4] : ((aSet0(W04_4) => ! [W15_5] : ((aElementOf0(W15_5, W04_4) => aElement0(W15_5)))))
% 0.20/0.55 -> [14] (aSet0(skolem_W01111) => ! [W15_5] : ((aElementOf0(W15_5, skolem_W01111) => aElement0(W15_5))))
% 0.20/0.55
% 0.20/0.55 [14] BETA_IMPLY : (aSet0(skolem_W01111) => ! [W15_5] : ((aElementOf0(W15_5, skolem_W01111) => aElement0(W15_5))))
% 0.20/0.55 -> [17] ~aSet0(skolem_W01111)
% 0.20/0.55 -> [18] ! [W15_5] : ((aElementOf0(W15_5, skolem_W01111) => aElement0(W15_5)))
% 0.20/0.55
% 0.20/0.55 [17] CLOSURE : =
% 0.20/0.55
% 0.20/0.55 [18] GAMMA_FORALL : ! [W06_6] : ((aSet0(W06_6) => (isFinite0(W06_6) => $true)))
% 0.20/0.55 -> [20] (aSet0(slcrc0) => (isFinite0(slcrc0) => $true))
% 0.20/0.55
% 0.20/0.55 [20] BETA_IMPLY : (aSet0(slcrc0) => (isFinite0(slcrc0) => $true))
% 0.20/0.55 -> [23] ~aSet0(slcrc0)
% 0.20/0.55 -> [24] (isFinite0(slcrc0) => $true)
% 0.20/0.55
% 0.20/0.55 [23] CLOSURE : =
% 0.20/0.55
% 0.20/0.55 [24] BETA_IMPLY : (isFinite0(slcrc0) => $true)
% 0.20/0.55 -> [27] ~isFinite0(slcrc0)
% 0.20/0.55 -> [28] $true
% 0.20/0.55
% 0.20/0.55 [27] CLOSURE : =
% 0.20/0.55
% 0.20/0.55 [28] GAMMA_FORALL : ! [W07_7] : ((=(W07_7, slcrc0) <=> (aSet0(W07_7) & ~? [W18_8] : (aElementOf0(W18_8, W07_7)))))
% 0.20/0.55 -> [32] (=(slcrc0, slcrc0) <=> (aSet0(slcrc0) & ~? [W18_8] : (aElementOf0(W18_8, slcrc0))))
% 0.20/0.55
% 0.20/0.55 [32] BETA_EQUIV : (=(slcrc0, slcrc0) <=> (aSet0(slcrc0) & ~? [W18_8] : (aElementOf0(W18_8, slcrc0))))
% 0.20/0.55 -> [33] ~=(slcrc0, slcrc0), ~(aSet0(slcrc0) & ~? [W18_8] : (aElementOf0(W18_8, slcrc0)))
% 0.20/0.55 -> [34] =(slcrc0, slcrc0), (aSet0(slcrc0) & ~? [W18_8] : (aElementOf0(W18_8, slcrc0)))
% 0.20/0.55
% 0.20/0.55 [33] CLOSURE : =
% 0.20/0.55
% 0.20/0.55 [34] ALPHA_AND : (aSet0(slcrc0) & ~? [W18_8] : (aElementOf0(W18_8, slcrc0)))
% 0.20/0.55 -> [36] aSet0(slcrc0), ~? [W18_8] : (aElementOf0(W18_8, slcrc0))
% 0.20/0.55
% 0.20/0.55 [36] GAMMA_FORALL : ! [W09_9] : ((aSet0(W09_9) => (isCountable0(W09_9) => $true)))
% 0.20/0.55 -> [37] (aSet0(skolem_W01111) => (isCountable0(skolem_W01111) => $true))
% 0.20/0.55
% 0.20/0.55 [37] BETA_IMPLY : (aSet0(skolem_W01111) => (isCountable0(skolem_W01111) => $true))
% 0.20/0.55 -> [39] ~aSet0(skolem_W01111)
% 0.20/0.55 -> [40] (isCountable0(skolem_W01111) => $true)
% 0.20/0.55
% 0.20/0.55 [39] CLOSURE : =
% 0.20/0.55
% 0.20/0.55 [40] BETA_IMPLY : (isCountable0(skolem_W01111) => $true)
% 0.20/0.55 -> [43] ~isCountable0(skolem_W01111)
% 0.20/0.55 -> [44] $true
% 0.20/0.55
% 0.20/0.55 [43] CLOSURE : =
% 0.20/0.55
% 0.20/0.55 [44] GAMMA_FORALL : ! [W010_10] : (((aSet0(W010_10) & isCountable0(W010_10)) => ~isFinite0(W010_10)))
% 0.20/0.55 -> [47] ((aSet0(W010_0_6) & isCountable0(W010_0_6)) => ~isFinite0(W010_0_6))
% 0.20/0.55
% 0.20/0.55 [47] BETA_IMPLY : ((aSet0(W010_0_6) & isCountable0(W010_0_6)) => ~isFinite0(W010_0_6))
% 0.20/0.55 -> [48] ~(aSet0(W010_0_6) & isCountable0(W010_0_6))
% 0.20/0.55 -> [49] ~isFinite0(W010_0_6)
% 0.20/0.55
% 0.20/0.55 [49] CLOSURE : =
% 0.20/0.55
% 0.20/0.55 [48] BETA_NOT_AND : ~(aSet0(W010_0_6) & isCountable0(W010_0_6))
% 0.20/0.55 -> [53] ~aSet0(W010_0_6)
% 0.20/0.55 -> [54] ~isCountable0(W010_0_6)
% 0.20/0.55
% 0.20/0.55 [54] CLOSURE : =
% 0.20/0.55
% 0.20/0.55 [53] CLOSURE : =
% 0.20/0.55
% 0.20/0.55 [11] GAMMA_FORALL : ! [W04_4] : ((aSet0(W04_4) => ! [W15_5] : ((aElementOf0(W15_5, W04_4) => aElement0(W15_5)))))
% 0.20/0.55 -> [13] (aSet0(skolem_W01111) => ! [W15_5] : ((aElementOf0(W15_5, skolem_W01111) => aElement0(W15_5))))
% 0.20/0.55
% 0.20/0.55 [13] BETA_IMPLY : (aSet0(skolem_W01111) => ! [W15_5] : ((aElementOf0(W15_5, skolem_W01111) => aElement0(W15_5))))
% 0.20/0.55 -> [15] ~aSet0(skolem_W01111)
% 0.20/0.55 -> [16] ! [W15_5] : ((aElementOf0(W15_5, skolem_W01111) => aElement0(W15_5)))
% 0.20/0.55
% 0.20/0.55 [15] CLOSURE : =
% 0.20/0.55
% 0.20/0.55 [16] GAMMA_FORALL : ! [W06_6] : ((aSet0(W06_6) => (isFinite0(W06_6) => $true)))
% 0.20/0.55 -> [19] (aSet0(slcrc0) => (isFinite0(slcrc0) => $true))
% 0.20/0.55
% 0.20/0.55 [19] BETA_IMPLY : (aSet0(slcrc0) => (isFinite0(slcrc0) => $true))
% 0.20/0.55 -> [21] ~aSet0(slcrc0)
% 0.20/0.55 -> [22] (isFinite0(slcrc0) => $true)
% 0.20/0.55
% 0.20/0.55 [21] CLOSURE : =
% 0.20/0.55
% 0.20/0.55 [22] BETA_IMPLY : (isFinite0(slcrc0) => $true)
% 0.20/0.55 -> [25] ~isFinite0(slcrc0)
% 0.20/0.55 -> [26] $true
% 0.20/0.55
% 0.20/0.55 [25] CLOSURE : =
% 0.20/0.55
% 0.20/0.55 [26] GAMMA_FORALL : ! [W07_7] : ((=(W07_7, slcrc0) <=> (aSet0(W07_7) & ~? [W18_8] : (aElementOf0(W18_8, W07_7)))))
% 0.20/0.55 -> [29] (=(slcrc0, slcrc0) <=> (aSet0(slcrc0) & ~? [W18_8] : (aElementOf0(W18_8, slcrc0))))
% 0.20/0.55
% 0.20/0.55 [29] BETA_EQUIV : (=(slcrc0, slcrc0) <=> (aSet0(slcrc0) & ~? [W18_8] : (aElementOf0(W18_8, slcrc0))))
% 0.20/0.55 -> [30] ~=(slcrc0, slcrc0), ~(aSet0(slcrc0) & ~? [W18_8] : (aElementOf0(W18_8, slcrc0)))
% 0.20/0.55 -> [31] =(slcrc0, slcrc0), (aSet0(slcrc0) & ~? [W18_8] : (aElementOf0(W18_8, slcrc0)))
% 0.20/0.55
% 0.20/0.55 [30] CLOSURE : =
% 0.20/0.55
% 0.20/0.55 [31] ALPHA_AND : (aSet0(slcrc0) & ~? [W18_8] : (aElementOf0(W18_8, slcrc0)))
% 0.20/0.55 -> [35] aSet0(slcrc0), ~? [W18_8] : (aElementOf0(W18_8, slcrc0))
% 0.20/0.55
% 0.20/0.55 [35] GAMMA_FORALL : ! [W09_9] : ((aSet0(W09_9) => (isCountable0(W09_9) => $true)))
% 0.20/0.55 -> [38] (aSet0(skolem_W01111) => (isCountable0(skolem_W01111) => $true))
% 0.20/0.55
% 0.20/0.55 [38] BETA_IMPLY : (aSet0(skolem_W01111) => (isCountable0(skolem_W01111) => $true))
% 0.20/0.55 -> [41] ~aSet0(skolem_W01111)
% 0.20/0.55 -> [42] (isCountable0(skolem_W01111) => $true)
% 0.20/0.55
% 0.20/0.55 [41] CLOSURE : =
% 0.20/0.55
% 0.20/0.55 [42] BETA_IMPLY : (isCountable0(skolem_W01111) => $true)
% 0.20/0.55 -> [45] ~isCountable0(skolem_W01111)
% 0.20/0.55 -> [46] $true
% 0.20/0.55
% 0.20/0.55 [45] CLOSURE : =
% 0.20/0.55
% 0.20/0.55 [46] GAMMA_FORALL : ! [W010_10] : (((aSet0(W010_10) & isCountable0(W010_10)) => ~isFinite0(W010_10)))
% 0.20/0.55 -> [50] ((aSet0(W010_1_6) & isCountable0(W010_1_6)) => ~isFinite0(W010_1_6))
% 0.20/0.55
% 0.20/0.55 [50] BETA_IMPLY : ((aSet0(W010_1_6) & isCountable0(W010_1_6)) => ~isFinite0(W010_1_6))
% 0.20/0.55 -> [51] ~(aSet0(W010_1_6) & isCountable0(W010_1_6))
% 0.20/0.55 -> [52] ~isFinite0(W010_1_6)
% 0.20/0.55
% 0.20/0.55 [52] CLOSURE : =
% 0.20/0.55
% 0.20/0.55 [51] BETA_NOT_AND : ~(aSet0(W010_1_6) & isCountable0(W010_1_6))
% 0.20/0.55 -> [55] ~aSet0(W010_1_6)
% 0.20/0.55 -> [56] ~isCountable0(W010_1_6)
% 0.20/0.55
% 0.20/0.55 [56] CLOSURE : =
% 0.20/0.55
% 0.20/0.55 [55] CLOSURE : =
% 0.20/0.55
% 0.20/0.55 % SZS output end Proof for theBenchmark.p
% 0.20/0.55 [0.204276s][1][Res] 937 goroutines created
% 0.20/0.55 ==== Result ====
% 0.20/0.55 [0.204299s][1][Res] VALID
% 0.20/0.55 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------