TSTP Solution File: SEU162+3 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SEU162+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n015.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 : Tue Sep 20 05:55:39 EDT 2022
% Result : Theorem 2.24s 0.83s
% Output : Proof 2.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU162+3 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : goeland -dmt -presko -proof %s
% 0.13/0.34 % Computer : n015.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 : Sat Sep 3 10:00:10 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 [DMT] DMT loaded with preskolemization
% 0.13/0.35 [EQ] equality loaded.
% 0.13/0.35 [0.000048s][1][MAIN] Problem : theBenchmark.p
% 0.13/0.35 Start search
% 0.13/0.36 nb_step : 1 - limit : 8
% 0.13/0.36 Launch Gotab with destructive = true
% 2.24/0.83 % SZS output start Proof for theBenchmark.p
% 2.24/0.83 [0] ALPHA_AND : (! [A2_2, B3_3] : ((in(A2_2, B3_3) => ~in(B3_3, A2_2))) & ! [A4_4, B5_5] : (~(disjoint(singleton(A4_4), B5_5) & in(A4_4, B5_5))) & ! [A6_6, B7_7] : ((~in(A6_6, B7_7) => disjoint(singleton(A6_6), B7_7))) & ? [A8_8] : (empty(A8_8)) & ? [A9_9] : (~empty(A9_9)) & ! [A10_10, B11_11] : ((disjoint(A10_10, B11_11) => disjoint(B11_11, A10_10))) & ! [A14_14, B15_15] : ((disjoint(A14_14, B15_15) <=> =(set_difference(A14_14, B15_15), A14_14))) & ~! [A12_12, B13_13] : ((=(set_difference(A12_12, singleton(B13_13)), A12_12) <=> ~in(B13_13, A12_12))))
% 2.24/0.83 -> [1] ! [A2_2, B3_3] : ((in(A2_2, B3_3) => ~in(B3_3, A2_2))), ! [A4_4, B5_5] : (~(disjoint(singleton(A4_4), B5_5) & in(A4_4, B5_5))), ! [A6_6, B7_7] : ((~in(A6_6, B7_7) => disjoint(singleton(A6_6), B7_7))), ? [A8_8] : (empty(A8_8)), ? [A9_9] : (~empty(A9_9)), ! [A10_10, B11_11] : ((disjoint(A10_10, B11_11) => disjoint(B11_11, A10_10))), ! [A14_14, B15_15] : ((disjoint(A14_14, B15_15) <=> =(set_difference(A14_14, B15_15), A14_14))), ~! [A12_12, B13_13] : ((=(set_difference(A12_12, singleton(B13_13)), A12_12) <=> ~in(B13_13, A12_12)))
% 2.24/0.83
% 2.24/0.83 [1] DELTA_EXISTS : ? [A8_8] : (empty(A8_8))
% 2.24/0.83 -> [2] empty(skolem_A88)
% 2.24/0.83
% 2.24/0.83 [2] DELTA_EXISTS : ? [A9_9] : (~empty(A9_9))
% 2.24/0.83 -> [3] ~empty(skolem_A99)
% 2.24/0.83
% 2.24/0.83 [3] DELTA_NOT_FORALL : ~! [A12_12, B13_13] : ((=(set_difference(A12_12, singleton(B13_13)), A12_12) <=> ~in(B13_13, A12_12)))
% 2.24/0.83 -> [4] ~(=(set_difference(skolem_A1212, singleton(skolem_B1313)), skolem_A1212) <=> ~in(skolem_B1313, skolem_A1212))
% 2.24/0.83
% 2.24/0.83 [4] BETA_NOT_EQUIV : ~(=(set_difference(skolem_A1212, singleton(skolem_B1313)), skolem_A1212) <=> ~in(skolem_B1313, skolem_A1212))
% 2.24/0.83 -> [5] ~=(set_difference(skolem_A1212, singleton(skolem_B1313)), skolem_A1212), ~in(skolem_B1313, skolem_A1212)
% 2.24/0.83 -> [6] =(set_difference(skolem_A1212, singleton(skolem_B1313)), skolem_A1212), ~~in(skolem_B1313, skolem_A1212)
% 2.24/0.83
% 2.24/0.83 [6] ALPHA_NOT_NOT : ~~in(skolem_B1313, skolem_A1212)
% 2.24/0.83 -> [44] in(skolem_B1313, skolem_A1212)
% 2.24/0.83
% 2.24/0.83 [44] GAMMA_FORALL : ! [A2_2, B3_3] : ((in(A2_2, B3_3) => ~in(B3_3, A2_2)))
% 2.24/0.83 -> [45] (in(skolem_B1313, skolem_A1212) => ~in(skolem_A1212, skolem_B1313))
% 2.24/0.83
% 2.24/0.83 [45] BETA_IMPLY : (in(skolem_B1313, skolem_A1212) => ~in(skolem_A1212, skolem_B1313))
% 2.24/0.83 -> [46] ~in(skolem_B1313, skolem_A1212)
% 2.24/0.83 -> [47] ~in(skolem_A1212, skolem_B1313)
% 2.24/0.83
% 2.24/0.83 [46] CLOSURE : =
% 2.24/0.83
% 2.24/0.83 [47] GAMMA_FORALL : ! [A4_4, B5_5] : (~(disjoint(singleton(A4_4), B5_5) & in(A4_4, B5_5)))
% 2.24/0.83 -> [52] ~(disjoint(singleton(skolem_B1313), skolem_A1212) & in(skolem_B1313, skolem_A1212))
% 2.24/0.83
% 2.24/0.83 [52] BETA_NOT_AND : ~(disjoint(singleton(skolem_B1313), skolem_A1212) & in(skolem_B1313, skolem_A1212))
% 2.24/0.83 -> [53] ~disjoint(singleton(skolem_B1313), skolem_A1212)
% 2.24/0.83 -> [54] ~in(skolem_B1313, skolem_A1212)
% 2.24/0.83
% 2.24/0.83 [54] CLOSURE : =
% 2.24/0.83
% 2.24/0.83 [63] BETA_IMPLY : (~in(skolem_B1313, skolem_A1212) => disjoint(singleton(skolem_B1313), skolem_A1212))
% 2.24/0.83 -> [77] ~~in(skolem_B1313, skolem_A1212)
% 2.24/0.83 -> [78] disjoint(singleton(skolem_B1313), skolem_A1212)
% 2.24/0.83
% 2.24/0.83 [78] CLOSURE : =
% 2.24/0.83
% 2.24/0.83 [79] GAMMA_FORALL : ! [A10_10, B11_11] : ((disjoint(A10_10, B11_11) => disjoint(B11_11, A10_10)))
% 2.24/0.83 -> [82] (disjoint(skolem_A1212, singleton(skolem_B1313)) => disjoint(singleton(skolem_B1313), skolem_A1212))
% 2.24/0.83
% 2.24/0.83 [82] BETA_IMPLY : (disjoint(skolem_A1212, singleton(skolem_B1313)) => disjoint(singleton(skolem_B1313), skolem_A1212))
% 2.24/0.83 -> [83] ~disjoint(skolem_A1212, singleton(skolem_B1313))
% 2.24/0.83 -> [84] disjoint(singleton(skolem_B1313), skolem_A1212)
% 2.24/0.83
% 2.24/0.83 [84] CLOSURE : =
% 2.24/0.83
% 2.24/0.83 [83] GAMMA_FORALL : ! [A14_14, B15_15] : ((disjoint(A14_14, B15_15) <=> =(set_difference(A14_14, B15_15), A14_14)))
% 2.24/0.83 -> [86] (disjoint(skolem_A1212, singleton(skolem_B1313)) <=> =(set_difference(skolem_A1212, singleton(skolem_B1313)), skolem_A1212))
% 2.24/0.83
% 2.24/0.83 [86] BETA_EQUIV : (disjoint(skolem_A1212, singleton(skolem_B1313)) <=> =(set_difference(skolem_A1212, singleton(skolem_B1313)), skolem_A1212))
% 2.24/0.83 -> [88] ~disjoint(skolem_A1212, singleton(skolem_B1313)), ~=(set_difference(skolem_A1212, singleton(skolem_B1313)), skolem_A1212)
% 2.24/0.83 -> [89] disjoint(skolem_A1212, singleton(skolem_B1313)), =(set_difference(skolem_A1212, singleton(skolem_B1313)), skolem_A1212)
% 2.24/0.83
% 2.24/0.83 [88] CLOSURE : =
% 2.24/0.83
% 2.24/0.83 [89] CLOSURE : =
% 2.24/0.83
% 2.24/0.83 [5] GAMMA_FORALL : ! [A2_2, B3_3] : ((in(A2_2, B3_3) => ~in(B3_3, A2_2)))
% 2.24/0.83 -> [7] (in(A2_0_0, B3_0_0) => ~in(B3_0_0, A2_0_0))
% 2.24/0.83
% 2.24/0.83 [7] BETA_IMPLY : (in(A2_0_0, B3_0_0) => ~in(B3_0_0, A2_0_0))
% 2.24/0.83 -> [8] ~in(A2_0_0, B3_0_0)
% 2.24/0.83 -> [9] ~in(B3_0_0, A2_0_0)
% 2.24/0.83
% 2.24/0.83 [8] GAMMA_FORALL : ! [A4_4, B5_5] : (~(disjoint(singleton(A4_4), B5_5) & in(A4_4, B5_5)))
% 2.24/0.83 -> [10] ~(disjoint(singleton(skolem_B1313), skolem_A1212) & in(skolem_B1313, skolem_A1212))
% 2.24/0.83
% 2.24/0.83 [10] BETA_NOT_AND : ~(disjoint(singleton(skolem_B1313), skolem_A1212) & in(skolem_B1313, skolem_A1212))
% 2.24/0.83 -> [11] ~disjoint(singleton(skolem_B1313), skolem_A1212)
% 2.24/0.83 -> [12] ~in(skolem_B1313, skolem_A1212)
% 2.24/0.83
% 2.24/0.83 [11] GAMMA_FORALL : ! [A6_6, B7_7] : ((~in(A6_6, B7_7) => disjoint(singleton(A6_6), B7_7)))
% 2.24/0.83 -> [16] (~in(skolem_B1313, skolem_A1212) => disjoint(singleton(skolem_B1313), skolem_A1212))
% 2.24/0.83
% 2.24/0.83 [16] BETA_IMPLY : (~in(skolem_B1313, skolem_A1212) => disjoint(singleton(skolem_B1313), skolem_A1212))
% 2.24/0.83 -> [18] ~~in(skolem_B1313, skolem_A1212)
% 2.24/0.83 -> [19] disjoint(singleton(skolem_B1313), skolem_A1212)
% 2.24/0.83
% 2.24/0.83 [18] ALPHA_NOT_NOT : ~~in(skolem_B1313, skolem_A1212)
% 2.24/0.83 -> [22] in(skolem_B1313, skolem_A1212)
% 2.24/0.83
% 2.24/0.83 [22] CLOSURE : in(skolem_B1313, skolem_A1212)
% 2.24/0.83
% 2.24/0.83 [19] CLOSURE : disjoint(singleton(skolem_B1313), skolem_A1212)
% 2.24/0.83
% 2.24/0.83 [12] GAMMA_FORALL : ! [A6_6, B7_7] : ((~in(A6_6, B7_7) => disjoint(singleton(A6_6), B7_7)))
% 2.24/0.83 -> [17] (~in(skolem_B1313, skolem_A1212) => disjoint(singleton(skolem_B1313), skolem_A1212))
% 2.24/0.83
% 2.24/0.83 [17] BETA_IMPLY : (~in(skolem_B1313, skolem_A1212) => disjoint(singleton(skolem_B1313), skolem_A1212))
% 2.24/0.83 -> [20] ~~in(skolem_B1313, skolem_A1212)
% 2.24/0.83 -> [21] disjoint(singleton(skolem_B1313), skolem_A1212)
% 2.24/0.83
% 2.24/0.83 [20] ALPHA_NOT_NOT : ~~in(skolem_B1313, skolem_A1212)
% 2.24/0.83 -> [30] in(skolem_B1313, skolem_A1212)
% 2.24/0.83
% 2.24/0.83 [30] CLOSURE : in(skolem_B1313, skolem_A1212)
% 2.24/0.83
% 2.24/0.83 [21] GAMMA_FORALL : ! [A10_10, B11_11] : ((disjoint(A10_10, B11_11) => disjoint(B11_11, A10_10)))
% 2.24/0.83 -> [29] (disjoint(singleton(skolem_B1313), skolem_A1212) => disjoint(skolem_A1212, singleton(skolem_B1313)))
% 2.24/0.83
% 2.24/0.83 [29] BETA_IMPLY : (disjoint(singleton(skolem_B1313), skolem_A1212) => disjoint(skolem_A1212, singleton(skolem_B1313)))
% 2.24/0.83 -> [31] ~disjoint(singleton(skolem_B1313), skolem_A1212)
% 2.24/0.83 -> [32] disjoint(skolem_A1212, singleton(skolem_B1313))
% 2.24/0.83
% 2.24/0.83 [32] GAMMA_FORALL : ! [A14_14, B15_15] : ((disjoint(A14_14, B15_15) <=> =(set_difference(A14_14, B15_15), A14_14)))
% 2.24/0.83 -> [35] (disjoint(skolem_A1212, singleton(skolem_B1313)) <=> =(set_difference(skolem_A1212, singleton(skolem_B1313)), skolem_A1212))
% 2.24/0.83
% 2.24/0.83 [35] BETA_EQUIV : (disjoint(skolem_A1212, singleton(skolem_B1313)) <=> =(set_difference(skolem_A1212, singleton(skolem_B1313)), skolem_A1212))
% 2.24/0.83 -> [36] ~disjoint(skolem_A1212, singleton(skolem_B1313)), ~=(set_difference(skolem_A1212, singleton(skolem_B1313)), skolem_A1212)
% 2.24/0.83 -> [37] disjoint(skolem_A1212, singleton(skolem_B1313)), =(set_difference(skolem_A1212, singleton(skolem_B1313)), skolem_A1212)
% 2.24/0.83
% 2.24/0.83 [37] CLOSURE : =
% 2.24/0.83
% 2.24/0.83 [36] CLOSURE : ~disjoint(skolem_A1212, singleton(skolem_B1313))
% 2.24/0.83
% 2.24/0.83 [31] CLOSURE : ~disjoint(singleton(skolem_B1313), skolem_A1212)
% 2.24/0.83
% 2.24/0.83 [9] GAMMA_FORALL : ! [A4_4, B5_5] : (~(disjoint(singleton(A4_4), B5_5) & in(A4_4, B5_5)))
% 2.24/0.83 -> [13] ~(disjoint(singleton(skolem_B1313), skolem_A1212) & in(skolem_B1313, skolem_A1212))
% 2.24/0.83
% 2.24/0.83 [13] BETA_NOT_AND : ~(disjoint(singleton(skolem_B1313), skolem_A1212) & in(skolem_B1313, skolem_A1212))
% 2.24/0.83 -> [14] ~disjoint(singleton(skolem_B1313), skolem_A1212)
% 2.24/0.83 -> [15] ~in(skolem_B1313, skolem_A1212)
% 2.24/0.83
% 2.24/0.83 [14] GAMMA_FORALL : ! [A6_6, B7_7] : ((~in(A6_6, B7_7) => disjoint(singleton(A6_6), B7_7)))
% 2.24/0.83 -> [23] (~in(skolem_B1313, skolem_A1212) => disjoint(singleton(skolem_B1313), skolem_A1212))
% 2.24/0.83
% 2.24/0.83 [23] BETA_IMPLY : (~in(skolem_B1313, skolem_A1212) => disjoint(singleton(skolem_B1313), skolem_A1212))
% 2.24/0.83 -> [25] ~~in(skolem_B1313, skolem_A1212)
% 2.24/0.83 -> [26] disjoint(singleton(skolem_B1313), skolem_A1212)
% 2.24/0.83
% 2.24/0.83 [25] ALPHA_NOT_NOT : ~~in(skolem_B1313, skolem_A1212)
% 2.24/0.83 -> [34] in(skolem_B1313, skolem_A1212)
% 2.24/0.83
% 2.24/0.83 [34] CLOSURE : in(skolem_B1313, skolem_A1212)
% 2.24/0.83
% 2.24/0.83 [26] CLOSURE : disjoint(singleton(skolem_B1313), skolem_A1212)
% 2.24/0.83
% 2.24/0.83 [15] GAMMA_FORALL : ! [A6_6, B7_7] : ((~in(A6_6, B7_7) => disjoint(singleton(A6_6), B7_7)))
% 2.24/0.83 -> [24] (~in(skolem_B1313, skolem_A1212) => disjoint(singleton(skolem_B1313), skolem_A1212))
% 2.24/0.83
% 2.24/0.83 [24] BETA_IMPLY : (~in(skolem_B1313, skolem_A1212) => disjoint(singleton(skolem_B1313), skolem_A1212))
% 2.24/0.83 -> [27] ~~in(skolem_B1313, skolem_A1212)
% 2.24/0.83 -> [28] disjoint(singleton(skolem_B1313), skolem_A1212)
% 2.24/0.83
% 2.24/0.83 [27] ALPHA_NOT_NOT : ~~in(skolem_B1313, skolem_A1212)
% 2.24/0.83 -> [33] in(skolem_B1313, skolem_A1212)
% 2.24/0.83
% 2.24/0.83 [33] CLOSURE : in(skolem_B1313, skolem_A1212)
% 2.24/0.83
% 2.24/0.83 [28] GAMMA_FORALL : ! [A10_10, B11_11] : ((disjoint(A10_10, B11_11) => disjoint(B11_11, A10_10)))
% 2.24/0.83 -> [38] (disjoint(singleton(skolem_B1313), skolem_A1212) => disjoint(skolem_A1212, singleton(skolem_B1313)))
% 2.24/0.83
% 2.24/0.83 [38] BETA_IMPLY : (disjoint(singleton(skolem_B1313), skolem_A1212) => disjoint(skolem_A1212, singleton(skolem_B1313)))
% 2.24/0.83 -> [39] ~disjoint(singleton(skolem_B1313), skolem_A1212)
% 2.24/0.83 -> [40] disjoint(skolem_A1212, singleton(skolem_B1313))
% 2.24/0.83
% 2.24/0.83 [39] CLOSURE : ~disjoint(singleton(skolem_B1313), skolem_A1212)
% 2.24/0.83
% 2.24/0.83 [41] BETA_EQUIV : (disjoint(skolem_A1212, singleton(skolem_B1313)) <=> =(set_difference(skolem_A1212, singleton(skolem_B1313)), skolem_A1212))
% 2.24/0.83 -> [80] ~disjoint(skolem_A1212, singleton(skolem_B1313)), ~=(set_difference(skolem_A1212, singleton(skolem_B1313)), skolem_A1212)
% 2.24/0.83 -> [81] disjoint(skolem_A1212, singleton(skolem_B1313)), =(set_difference(skolem_A1212, singleton(skolem_B1313)), skolem_A1212)
% 2.24/0.83
% 2.24/0.83 [80] CLOSURE : ~disjoint(skolem_A1212, singleton(skolem_B1313))
% 2.24/0.83
% 2.24/0.83 [81] CLOSURE : =
% 2.24/0.83
% 2.24/0.83 % SZS output end Proof for theBenchmark.p
% 2.24/0.83 [0.473379s][1][Res] 4126 goroutines created
% 2.24/0.83 ==== Result ====
% 2.24/0.83 [0.473401s][1][Res] VALID
% 2.24/0.83 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------