TSTP Solution File: LCL686+1.001 by Goeland---1.0.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : LCL686+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n013.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 03:44:48 EDT 2022
% Result : Theorem 0.19s 0.52s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL686+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : goeland -dmt -presko -proof %s
% 0.13/0.33 % Computer : n013.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 : Fri Sep 2 00:17:02 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 : 11
% 0.13/0.34 Launch Gotab with destructive = true
% 0.19/0.52 % SZS output start Proof for theBenchmark.p
% 0.19/0.52 [0] ALPHA_AND : (! [X3_3] : (r1(X3_3, X3_3)) & ! [X4_4, Y5_5, Z6_6] : (((r1(X4_4, Y5_5) & r1(Y5_5, Z6_6)) => r1(X4_4, Z6_6))) & ~~? [X7_7] : (~(! [Y8_8] : (((~r1(X7_7, Y8_8) | ~p3(Y8_8)) | ! [X79_9] : ((~r1(Y8_8, X79_9) | ~p1(X79_9))))) | ! [Y10_10] : ((~r1(X7_7, Y10_10) | ~! [X711_11] : ((~r1(Y10_10, X711_11) | ~(((! [Y1012_12] : ((~r1(X711_11, Y1012_12) | $false)) | ~! [Y1013_13] : ((~r1(X711_11, Y1013_13) | ~((p2(Y1013_13) & ~p1(Y1013_13)) | (~p2(Y1013_13) & p1(Y1013_13)))))) | ! [Y1014_14] : ((~r1(X711_11, Y1014_14) | p3(Y1014_14)))) | ! [Y1015_15] : (((~r1(X711_11, Y1015_15) | (~p1(Y1015_15) & ~p2(Y1015_15))) | (p2(Y1015_15) & p1(Y1015_15))))))))))))
% 0.19/0.52 -> [1] ! [X3_3] : (r1(X3_3, X3_3)), ! [X4_4, Y5_5, Z6_6] : (((r1(X4_4, Y5_5) & r1(Y5_5, Z6_6)) => r1(X4_4, Z6_6))), ~~? [X7_7] : (~(! [Y8_8] : (((~r1(X7_7, Y8_8) | ~p3(Y8_8)) | ! [X79_9] : ((~r1(Y8_8, X79_9) | ~p1(X79_9))))) | ! [Y10_10] : ((~r1(X7_7, Y10_10) | ~! [X711_11] : ((~r1(Y10_10, X711_11) | ~(((! [Y1012_12] : ((~r1(X711_11, Y1012_12) | $false)) | ~! [Y1013_13] : ((~r1(X711_11, Y1013_13) | ~((p2(Y1013_13) & ~p1(Y1013_13)) | (~p2(Y1013_13) & p1(Y1013_13)))))) | ! [Y1014_14] : ((~r1(X711_11, Y1014_14) | p3(Y1014_14)))) | ! [Y1015_15] : (((~r1(X711_11, Y1015_15) | (~p1(Y1015_15) & ~p2(Y1015_15))) | (p2(Y1015_15) & p1(Y1015_15)))))))))))
% 0.19/0.52
% 0.19/0.52 [1] ALPHA_NOT_NOT : ~~? [X7_7] : (~(! [Y8_8] : (((~r1(X7_7, Y8_8) | ~p3(Y8_8)) | ! [X79_9] : ((~r1(Y8_8, X79_9) | ~p1(X79_9))))) | ! [Y10_10] : ((~r1(X7_7, Y10_10) | ~! [X711_11] : ((~r1(Y10_10, X711_11) | ~(((! [Y1012_12] : ((~r1(X711_11, Y1012_12) | $false)) | ~! [Y1013_13] : ((~r1(X711_11, Y1013_13) | ~((p2(Y1013_13) & ~p1(Y1013_13)) | (~p2(Y1013_13) & p1(Y1013_13)))))) | ! [Y1014_14] : ((~r1(X711_11, Y1014_14) | p3(Y1014_14)))) | ! [Y1015_15] : (((~r1(X711_11, Y1015_15) | (~p1(Y1015_15) & ~p2(Y1015_15))) | (p2(Y1015_15) & p1(Y1015_15)))))))))))
% 0.19/0.52 -> [2] ? [X7_7] : (~(! [Y8_8] : (((~r1(X7_7, Y8_8) | ~p3(Y8_8)) | ! [X79_9] : ((~r1(Y8_8, X79_9) | ~p1(X79_9))))) | ! [Y10_10] : ((~r1(X7_7, Y10_10) | ~! [X711_11] : ((~r1(Y10_10, X711_11) | ~(((! [Y1012_12] : ((~r1(X711_11, Y1012_12) | $false)) | ~! [Y1013_13] : ((~r1(X711_11, Y1013_13) | ~((p2(Y1013_13) & ~p1(Y1013_13)) | (~p2(Y1013_13) & p1(Y1013_13)))))) | ! [Y1014_14] : ((~r1(X711_11, Y1014_14) | p3(Y1014_14)))) | ! [Y1015_15] : (((~r1(X711_11, Y1015_15) | (~p1(Y1015_15) & ~p2(Y1015_15))) | (p2(Y1015_15) & p1(Y1015_15)))))))))))
% 0.19/0.52
% 0.19/0.52 [2] DELTA_EXISTS : ? [X7_7] : (~(! [Y8_8] : (((~r1(X7_7, Y8_8) | ~p3(Y8_8)) | ! [X79_9] : ((~r1(Y8_8, X79_9) | ~p1(X79_9))))) | ! [Y10_10] : ((~r1(X7_7, Y10_10) | ~! [X711_11] : ((~r1(Y10_10, X711_11) | ~(((! [Y1012_12] : ((~r1(X711_11, Y1012_12) | $false)) | ~! [Y1013_13] : ((~r1(X711_11, Y1013_13) | ~((p2(Y1013_13) & ~p1(Y1013_13)) | (~p2(Y1013_13) & p1(Y1013_13)))))) | ! [Y1014_14] : ((~r1(X711_11, Y1014_14) | p3(Y1014_14)))) | ! [Y1015_15] : (((~r1(X711_11, Y1015_15) | (~p1(Y1015_15) & ~p2(Y1015_15))) | (p2(Y1015_15) & p1(Y1015_15)))))))))))
% 0.19/0.52 -> [3] ~(! [Y8_8] : (((~r1(skolem_X77, Y8_8) | ~p3(Y8_8)) | ! [X79_9] : ((~r1(Y8_8, X79_9) | ~p1(X79_9))))) | ! [Y10_10] : ((~r1(skolem_X77, Y10_10) | ~! [X711_11] : ((~r1(Y10_10, X711_11) | ~(((! [Y1012_12] : ((~r1(X711_11, Y1012_12) | $false)) | ~! [Y1013_13] : ((~r1(X711_11, Y1013_13) | ~((p2(Y1013_13) & ~p1(Y1013_13)) | (~p2(Y1013_13) & p1(Y1013_13)))))) | ! [Y1014_14] : ((~r1(X711_11, Y1014_14) | p3(Y1014_14)))) | ! [Y1015_15] : (((~r1(X711_11, Y1015_15) | (~p1(Y1015_15) & ~p2(Y1015_15))) | (p2(Y1015_15) & p1(Y1015_15))))))))))
% 0.19/0.52
% 0.19/0.52 [3] ALPHA_NOT_OR : ~(! [Y8_8] : (((~r1(skolem_X77, Y8_8) | ~p3(Y8_8)) | ! [X79_9] : ((~r1(Y8_8, X79_9) | ~p1(X79_9))))) | ! [Y10_10] : ((~r1(skolem_X77, Y10_10) | ~! [X711_11] : ((~r1(Y10_10, X711_11) | ~(((! [Y1012_12] : ((~r1(X711_11, Y1012_12) | $false)) | ~! [Y1013_13] : ((~r1(X711_11, Y1013_13) | ~((p2(Y1013_13) & ~p1(Y1013_13)) | (~p2(Y1013_13) & p1(Y1013_13)))))) | ! [Y1014_14] : ((~r1(X711_11, Y1014_14) | p3(Y1014_14)))) | ! [Y1015_15] : (((~r1(X711_11, Y1015_15) | (~p1(Y1015_15) & ~p2(Y1015_15))) | (p2(Y1015_15) & p1(Y1015_15))))))))))
% 0.19/0.52 -> [4] ~! [Y8_8] : (((~r1(skolem_X77, Y8_8) | ~p3(Y8_8)) | ! [X79_9] : ((~r1(Y8_8, X79_9) | ~p1(X79_9))))), ~! [Y10_10] : ((~r1(skolem_X77, Y10_10) | ~! [X711_11] : ((~r1(Y10_10, X711_11) | ~(((! [Y1012_12] : ((~r1(X711_11, Y1012_12) | $false)) | ~! [Y1013_13] : ((~r1(X711_11, Y1013_13) | ~((p2(Y1013_13) & ~p1(Y1013_13)) | (~p2(Y1013_13) & p1(Y1013_13)))))) | ! [Y1014_14] : ((~r1(X711_11, Y1014_14) | p3(Y1014_14)))) | ! [Y1015_15] : (((~r1(X711_11, Y1015_15) | (~p1(Y1015_15) & ~p2(Y1015_15))) | (p2(Y1015_15) & p1(Y1015_15)))))))))
% 0.19/0.52
% 0.19/0.52 [4] DELTA_NOT_FORALL : ~! [Y8_8] : (((~r1(skolem_X77, Y8_8) | ~p3(Y8_8)) | ! [X79_9] : ((~r1(Y8_8, X79_9) | ~p1(X79_9)))))
% 0.19/0.52 -> [5] ~((~r1(skolem_X77, skolem_Y88) | ~p3(skolem_Y88)) | ! [X79_9] : ((~r1(skolem_Y88, X79_9) | ~p1(X79_9))))
% 0.19/0.52
% 0.19/0.52 [5] ALPHA_NOT_OR : ~((~r1(skolem_X77, skolem_Y88) | ~p3(skolem_Y88)) | ! [X79_9] : ((~r1(skolem_Y88, X79_9) | ~p1(X79_9))))
% 0.19/0.52 -> [6] ~(~r1(skolem_X77, skolem_Y88) | ~p3(skolem_Y88)), ~! [X79_9] : ((~r1(skolem_Y88, X79_9) | ~p1(X79_9)))
% 0.19/0.52
% 0.19/0.52 [6] ALPHA_NOT_OR : ~(~r1(skolem_X77, skolem_Y88) | ~p3(skolem_Y88))
% 0.19/0.52 -> [7] ~~r1(skolem_X77, skolem_Y88), ~~p3(skolem_Y88)
% 0.19/0.52
% 0.19/0.52 [7] ALPHA_NOT_NOT : ~~r1(skolem_X77, skolem_Y88)
% 0.19/0.52 -> [8] r1(skolem_X77, skolem_Y88)
% 0.19/0.52
% 0.19/0.52 [8] ALPHA_NOT_NOT : ~~p3(skolem_Y88)
% 0.19/0.52 -> [9] p3(skolem_Y88)
% 0.19/0.52
% 0.19/0.52 [9] DELTA_NOT_FORALL : ~! [Y10_10] : ((~r1(skolem_X77, Y10_10) | ~! [X711_11] : ((~r1(Y10_10, X711_11) | ~(((! [Y1012_12] : ((~r1(X711_11, Y1012_12) | $false)) | ~! [Y1013_13] : ((~r1(X711_11, Y1013_13) | ~((p2(Y1013_13) & ~p1(Y1013_13)) | (~p2(Y1013_13) & p1(Y1013_13)))))) | ! [Y1014_14] : ((~r1(X711_11, Y1014_14) | p3(Y1014_14)))) | ! [Y1015_15] : (((~r1(X711_11, Y1015_15) | (~p1(Y1015_15) & ~p2(Y1015_15))) | (p2(Y1015_15) & p1(Y1015_15)))))))))
% 0.19/0.52 -> [10] ~(~r1(skolem_X77, skolem_Y1010) | ~! [X711_11] : ((~r1(skolem_Y1010, X711_11) | ~(((! [Y1012_12] : ((~r1(X711_11, Y1012_12) | $false)) | ~! [Y1013_13] : ((~r1(X711_11, Y1013_13) | ~((p2(Y1013_13) & ~p1(Y1013_13)) | (~p2(Y1013_13) & p1(Y1013_13)))))) | ! [Y1014_14] : ((~r1(X711_11, Y1014_14) | p3(Y1014_14)))) | ! [Y1015_15] : (((~r1(X711_11, Y1015_15) | (~p1(Y1015_15) & ~p2(Y1015_15))) | (p2(Y1015_15) & p1(Y1015_15))))))))
% 0.19/0.52
% 0.19/0.52 [10] ALPHA_NOT_OR : ~(~r1(skolem_X77, skolem_Y1010) | ~! [X711_11] : ((~r1(skolem_Y1010, X711_11) | ~(((! [Y1012_12] : ((~r1(X711_11, Y1012_12) | $false)) | ~! [Y1013_13] : ((~r1(X711_11, Y1013_13) | ~((p2(Y1013_13) & ~p1(Y1013_13)) | (~p2(Y1013_13) & p1(Y1013_13)))))) | ! [Y1014_14] : ((~r1(X711_11, Y1014_14) | p3(Y1014_14)))) | ! [Y1015_15] : (((~r1(X711_11, Y1015_15) | (~p1(Y1015_15) & ~p2(Y1015_15))) | (p2(Y1015_15) & p1(Y1015_15))))))))
% 0.19/0.52 -> [11] ~~r1(skolem_X77, skolem_Y1010), ~~! [X711_11] : ((~r1(skolem_Y1010, X711_11) | ~(((! [Y1012_12] : ((~r1(X711_11, Y1012_12) | $false)) | ~! [Y1013_13] : ((~r1(X711_11, Y1013_13) | ~((p2(Y1013_13) & ~p1(Y1013_13)) | (~p2(Y1013_13) & p1(Y1013_13)))))) | ! [Y1014_14] : ((~r1(X711_11, Y1014_14) | p3(Y1014_14)))) | ! [Y1015_15] : (((~r1(X711_11, Y1015_15) | (~p1(Y1015_15) & ~p2(Y1015_15))) | (p2(Y1015_15) & p1(Y1015_15)))))))
% 0.19/0.52
% 0.19/0.52 [11] ALPHA_NOT_NOT : ~~r1(skolem_X77, skolem_Y1010)
% 0.19/0.52 -> [12] r1(skolem_X77, skolem_Y1010)
% 0.19/0.52
% 0.19/0.52 [12] ALPHA_NOT_NOT : ~~! [X711_11] : ((~r1(skolem_Y1010, X711_11) | ~(((! [Y1012_12] : ((~r1(X711_11, Y1012_12) | $false)) | ~! [Y1013_13] : ((~r1(X711_11, Y1013_13) | ~((p2(Y1013_13) & ~p1(Y1013_13)) | (~p2(Y1013_13) & p1(Y1013_13)))))) | ! [Y1014_14] : ((~r1(X711_11, Y1014_14) | p3(Y1014_14)))) | ! [Y1015_15] : (((~r1(X711_11, Y1015_15) | (~p1(Y1015_15) & ~p2(Y1015_15))) | (p2(Y1015_15) & p1(Y1015_15)))))))
% 0.19/0.52 -> [13] ! [X711_11] : ((~r1(skolem_Y1010, X711_11) | ~(((! [Y1012_12] : ((~r1(X711_11, Y1012_12) | $false)) | ~! [Y1013_13] : ((~r1(X711_11, Y1013_13) | ~((p2(Y1013_13) & ~p1(Y1013_13)) | (~p2(Y1013_13) & p1(Y1013_13)))))) | ! [Y1014_14] : ((~r1(X711_11, Y1014_14) | p3(Y1014_14)))) | ! [Y1015_15] : (((~r1(X711_11, Y1015_15) | (~p1(Y1015_15) & ~p2(Y1015_15))) | (p2(Y1015_15) & p1(Y1015_15)))))))
% 0.19/0.52
% 0.19/0.52 [13] DELTA_NOT_FORALL : ~! [X79_9] : ((~r1(skolem_Y88, X79_9) | ~p1(X79_9)))
% 0.19/0.52 -> [14] ~(~r1(skolem_Y88, skolem_X799) | ~p1(skolem_X799))
% 0.19/0.52
% 0.19/0.52 [14] ALPHA_NOT_OR : ~(~r1(skolem_Y88, skolem_X799) | ~p1(skolem_X799))
% 0.19/0.52 -> [15] ~~r1(skolem_Y88, skolem_X799), ~~p1(skolem_X799)
% 0.19/0.52
% 0.19/0.52 [15] ALPHA_NOT_NOT : ~~r1(skolem_Y88, skolem_X799)
% 0.19/0.52 -> [16] r1(skolem_Y88, skolem_X799)
% 0.19/0.52
% 0.19/0.52 [16] ALPHA_NOT_NOT : ~~p1(skolem_X799)
% 0.19/0.52 -> [17] p1(skolem_X799)
% 0.19/0.52
% 0.19/0.52 [17] GAMMA_FORALL : ! [X3_3] : (r1(X3_3, X3_3))
% 0.19/0.52 -> [18] r1(skolem_X799, skolem_X799)
% 0.19/0.52
% 0.19/0.52 [18] GAMMA_FORALL : ! [X4_4, Y5_5, Z6_6] : (((r1(X4_4, Y5_5) & r1(Y5_5, Z6_6)) => r1(X4_4, Z6_6)))
% 0.19/0.52 -> [19] ((r1(skolem_Y88, skolem_X799) & r1(skolem_X799, skolem_X799)) => r1(skolem_Y88, skolem_X799))
% 0.19/0.52
% 0.19/0.52 [19] BETA_IMPLY : ((r1(skolem_Y88, skolem_X799) & r1(skolem_X799, skolem_X799)) => r1(skolem_Y88, skolem_X799))
% 0.19/0.52 -> [20] ~(r1(skolem_Y88, skolem_X799) & r1(skolem_X799, skolem_X799))
% 0.19/0.52 -> [21] r1(skolem_Y88, skolem_X799)
% 0.19/0.52
% 0.19/0.52 [20] BETA_NOT_AND : ~(r1(skolem_Y88, skolem_X799) & r1(skolem_X799, skolem_X799))
% 0.19/0.52 -> [22] ~r1(skolem_Y88, skolem_X799)
% 0.19/0.52 -> [23] ~r1(skolem_X799, skolem_X799)
% 0.19/0.52
% 0.19/0.52 [22] CLOSURE : ~r1(skolem_Y88, skolem_X799)
% 0.19/0.52
% 0.19/0.52 [23] CLOSURE : ~r1(skolem_X799, skolem_X799)
% 0.19/0.52
% 0.19/0.52 [24] BETA_OR : (~r1(skolem_Y1010, skolem_Y1010) | ~(((! [Y1012_12] : ((~r1(skolem_Y1010, Y1012_12) | $false)) | ~! [Y1013_13] : ((~r1(skolem_Y1010, Y1013_13) | ~((p2(Y1013_13) & ~p1(Y1013_13)) | (~p2(Y1013_13) & p1(Y1013_13)))))) | ! [Y1014_14] : ((~r1(skolem_Y1010, Y1014_14) | p3(Y1014_14)))) | ! [Y1015_15] : (((~r1(skolem_Y1010, Y1015_15) | (~p1(Y1015_15) & ~p2(Y1015_15))) | (p2(Y1015_15) & p1(Y1015_15))))))
% 0.19/0.52 -> [71] ~r1(skolem_Y1010, skolem_Y1010)
% 0.19/0.52 -> [72] ~(((! [Y1012_12] : ((~r1(skolem_Y1010, Y1012_12) | $false)) | ~! [Y1013_13] : ((~r1(skolem_Y1010, Y1013_13) | ~((p2(Y1013_13) & ~p1(Y1013_13)) | (~p2(Y1013_13) & p1(Y1013_13)))))) | ! [Y1014_14] : ((~r1(skolem_Y1010, Y1014_14) | p3(Y1014_14)))) | ! [Y1015_15] : (((~r1(skolem_Y1010, Y1015_15) | (~p1(Y1015_15) & ~p2(Y1015_15))) | (p2(Y1015_15) & p1(Y1015_15)))))
% 0.19/0.52
% 0.19/0.52 [71] : ! [X3_3] : (r1(X3_3, X3_3))
% 0.19/0.52 -> [75] ! [X3_3] : (r1(X3_3, X3_3))
% 0.19/0.52
% 0.19/0.52 [75] GAMMA_FORALL : ! [X3_3] : (r1(X3_3, X3_3))
% 0.19/0.52 -> [77] r1(X3_1_0, X3_1_0)
% 0.19/0.52
% 0.19/0.52 [77] CLOSURE : r1(X3_1_0, X3_1_0)
% 0.19/0.52
% 0.19/0.52 [72] ALPHA_NOT_OR : ~(((! [Y1012_12] : ((~r1(skolem_Y1010, Y1012_12) | $false)) | ~! [Y1013_13] : ((~r1(skolem_Y1010, Y1013_13) | ~((p2(Y1013_13) & ~p1(Y1013_13)) | (~p2(Y1013_13) & p1(Y1013_13)))))) | ! [Y1014_14] : ((~r1(skolem_Y1010, Y1014_14) | p3(Y1014_14)))) | ! [Y1015_15] : (((~r1(skolem_Y1010, Y1015_15) | (~p1(Y1015_15) & ~p2(Y1015_15))) | (p2(Y1015_15) & p1(Y1015_15)))))
% 0.19/0.52 -> [73] ~((! [Y1012_12] : ((~r1(skolem_Y1010, Y1012_12) | $false)) | ~! [Y1013_13] : ((~r1(skolem_Y1010, Y1013_13) | ~((p2(Y1013_13) & ~p1(Y1013_13)) | (~p2(Y1013_13) & p1(Y1013_13)))))) | ! [Y1014_14] : ((~r1(skolem_Y1010, Y1014_14) | p3(Y1014_14)))), ~! [Y1015_15] : (((~r1(skolem_Y1010, Y1015_15) | (~p1(Y1015_15) & ~p2(Y1015_15))) | (p2(Y1015_15) & p1(Y1015_15))))
% 0.19/0.52
% 0.19/0.52 [73] ALPHA_NOT_OR : ~((! [Y1012_12] : ((~r1(skolem_Y1010, Y1012_12) | $false)) | ~! [Y1013_13] : ((~r1(skolem_Y1010, Y1013_13) | ~((p2(Y1013_13) & ~p1(Y1013_13)) | (~p2(Y1013_13) & p1(Y1013_13)))))) | ! [Y1014_14] : ((~r1(skolem_Y1010, Y1014_14) | p3(Y1014_14))))
% 0.19/0.52 -> [74] ~(! [Y1012_12] : ((~r1(skolem_Y1010, Y1012_12) | $false)) | ~! [Y1013_13] : ((~r1(skolem_Y1010, Y1013_13) | ~((p2(Y1013_13) & ~p1(Y1013_13)) | (~p2(Y1013_13) & p1(Y1013_13)))))), ~! [Y1014_14] : ((~r1(skolem_Y1010, Y1014_14) | p3(Y1014_14)))
% 0.19/0.52
% 0.19/0.52 [74] ALPHA_NOT_OR : ~(! [Y1012_12] : ((~r1(skolem_Y1010, Y1012_12) | $false)) | ~! [Y1013_13] : ((~r1(skolem_Y1010, Y1013_13) | ~((p2(Y1013_13) & ~p1(Y1013_13)) | (~p2(Y1013_13) & p1(Y1013_13))))))
% 0.19/0.52 -> [76] ~! [Y1012_12] : ((~r1(skolem_Y1010, Y1012_12) | $false)), ~~! [Y1013_13] : ((~r1(skolem_Y1010, Y1013_13) | ~((p2(Y1013_13) & ~p1(Y1013_13)) | (~p2(Y1013_13) & p1(Y1013_13)))))
% 0.19/0.52
% 0.19/0.52 [76] ALPHA_NOT_NOT : ~~! [Y1013_13] : ((~r1(skolem_Y1010, Y1013_13) | ~((p2(Y1013_13) & ~p1(Y1013_13)) | (~p2(Y1013_13) & p1(Y1013_13)))))
% 0.19/0.52 -> [78] ! [Y1013_13] : ((~r1(skolem_Y1010, Y1013_13) | ~((p2(Y1013_13) & ~p1(Y1013_13)) | (~p2(Y1013_13) & p1(Y1013_13)))))
% 0.19/0.52
% 0.19/0.52 [78] DELTA_NOT_FORALL : ~! [Y1015_15] : (((~r1(skolem_Y1010, Y1015_15) | (~p1(Y1015_15) & ~p2(Y1015_15))) | (p2(Y1015_15) & p1(Y1015_15))))
% 0.19/0.52 -> [79] ~((~r1(skolem_Y1010, skolem_Y101515(skolem_Y1010)) | (~p1(skolem_Y101515(skolem_Y1010)) & ~p2(skolem_Y101515(skolem_Y1010)))) | (p2(skolem_Y101515(skolem_Y1010)) & p1(skolem_Y101515(skolem_Y1010))))
% 0.19/0.52
% 0.19/0.52 [79] ALPHA_NOT_OR : ~((~r1(skolem_Y1010, skolem_Y101515(skolem_Y1010)) | (~p1(skolem_Y101515(skolem_Y1010)) & ~p2(skolem_Y101515(skolem_Y1010)))) | (p2(skolem_Y101515(skolem_Y1010)) & p1(skolem_Y101515(skolem_Y1010))))
% 0.19/0.52 -> [80] ~(~r1(skolem_Y1010, skolem_Y101515(skolem_Y1010)) | (~p1(skolem_Y101515(skolem_Y1010)) & ~p2(skolem_Y101515(skolem_Y1010)))), ~(p2(skolem_Y101515(skolem_Y1010)) & p1(skolem_Y101515(skolem_Y1010)))
% 0.19/0.52
% 0.19/0.52 [80] ALPHA_NOT_OR : ~(~r1(skolem_Y1010, skolem_Y101515(skolem_Y1010)) | (~p1(skolem_Y101515(skolem_Y1010)) & ~p2(skolem_Y101515(skolem_Y1010))))
% 0.19/0.52 -> [81] ~~r1(skolem_Y1010, skolem_Y101515(skolem_Y1010)), ~(~p1(skolem_Y101515(skolem_Y1010)) & ~p2(skolem_Y101515(skolem_Y1010)))
% 0.19/0.52
% 0.19/0.52 [81] ALPHA_NOT_NOT : ~~r1(skolem_Y1010, skolem_Y101515(skolem_Y1010))
% 0.19/0.52 -> [82] r1(skolem_Y1010, skolem_Y101515(skolem_Y1010))
% 0.19/0.52
% 0.19/0.52 [82] DELTA_NOT_FORALL : ~! [Y1014_14] : ((~r1(skolem_Y1010, Y1014_14) | p3(Y1014_14)))
% 0.19/0.52 -> [83] ~(~r1(skolem_Y1010, skolem_Y101414(skolem_Y1010)) | p3(skolem_Y101414(skolem_Y1010)))
% 0.19/0.52
% 0.19/0.52 [83] ALPHA_NOT_OR : ~(~r1(skolem_Y1010, skolem_Y101414(skolem_Y1010)) | p3(skolem_Y101414(skolem_Y1010)))
% 0.19/0.52 -> [84] ~~r1(skolem_Y1010, skolem_Y101414(skolem_Y1010)), ~p3(skolem_Y101414(skolem_Y1010))
% 0.19/0.52
% 0.19/0.52 [84] ALPHA_NOT_NOT : ~~r1(skolem_Y1010, skolem_Y101414(skolem_Y1010))
% 0.19/0.52 -> [85] r1(skolem_Y1010, skolem_Y101414(skolem_Y1010))
% 0.19/0.52
% 0.19/0.52 [85] DELTA_NOT_FORALL : ~! [Y1012_12] : ((~r1(skolem_Y1010, Y1012_12) | $false))
% 0.19/0.52 -> [86] ~(~r1(skolem_Y1010, skolem_Y101212(skolem_Y1010)) | $false)
% 0.19/0.52
% 0.19/0.52 [86] ALPHA_NOT_OR : ~(~r1(skolem_Y1010, skolem_Y101212(skolem_Y1010)) | $false)
% 0.19/0.52 -> [87] ~~r1(skolem_Y1010, skolem_Y101212(skolem_Y1010)), ~$false
% 0.19/0.52
% 0.19/0.52 [87] ALPHA_NOT_NOT : ~~r1(skolem_Y1010, skolem_Y101212(skolem_Y1010))
% 0.19/0.52 -> [88] r1(skolem_Y1010, skolem_Y101212(skolem_Y1010))
% 0.19/0.52
% 0.19/0.52 [88] BETA_NOT_AND : ~(p2(skolem_Y101515(skolem_Y1010)) & p1(skolem_Y101515(skolem_Y1010)))
% 0.19/0.52 -> [89] ~p2(skolem_Y101515(skolem_Y1010))
% 0.19/0.52 -> [90] ~p1(skolem_Y101515(skolem_Y1010))
% 0.19/0.52
% 0.19/0.52 [90] BETA_NOT_AND : ~(~p1(skolem_Y101515(skolem_Y1010)) & ~p2(skolem_Y101515(skolem_Y1010)))
% 0.19/0.52 -> [93] ~~p1(skolem_Y101515(skolem_Y1010))
% 0.19/0.52 -> [94] ~~p2(skolem_Y101515(skolem_Y1010))
% 0.19/0.52
% 0.19/0.52 [93] ALPHA_NOT_NOT : ~~p1(skolem_Y101515(skolem_Y1010))
% 0.19/0.52 -> [97] p1(skolem_Y101515(skolem_Y1010))
% 0.19/0.52
% 0.19/0.52 [97] CLOSURE : p1(skolem_Y101515(skolem_Y1010))
% 0.19/0.52
% 0.19/0.52 [94] ALPHA_NOT_NOT : ~~p2(skolem_Y101515(skolem_Y1010))
% 0.19/0.52 -> [98] p2(skolem_Y101515(skolem_Y1010))
% 0.19/0.52
% 0.19/0.52 [98] GAMMA_FORALL : ! [Y1013_13] : ((~r1(skolem_Y1010, Y1013_13) | ~((p2(Y1013_13) & ~p1(Y1013_13)) | (~p2(Y1013_13) & p1(Y1013_13)))))
% 0.19/0.52 -> [102] (~r1(skolem_Y1010, skolem_Y101515(skolem_Y1010)) | ~((p2(skolem_Y101515(skolem_Y1010)) & ~p1(skolem_Y101515(skolem_Y1010))) | (~p2(skolem_Y101515(skolem_Y1010)) & p1(skolem_Y101515(skolem_Y1010)))))
% 0.19/0.52
% 0.19/0.52 [102] BETA_OR : (~r1(skolem_Y1010, skolem_Y101515(skolem_Y1010)) | ~((p2(skolem_Y101515(skolem_Y1010)) & ~p1(skolem_Y101515(skolem_Y1010))) | (~p2(skolem_Y101515(skolem_Y1010)) & p1(skolem_Y101515(skolem_Y1010)))))
% 0.19/0.52 -> [103] ~r1(skolem_Y1010, skolem_Y101515(skolem_Y1010))
% 0.19/0.52 -> [104] ~((p2(skolem_Y101515(skolem_Y1010)) & ~p1(skolem_Y101515(skolem_Y1010))) | (~p2(skolem_Y101515(skolem_Y1010)) & p1(skolem_Y101515(skolem_Y1010))))
% 0.19/0.52
% 0.19/0.52 [103] CLOSURE : ~r1(skolem_Y1010, skolem_Y101515(skolem_Y1010))
% 0.19/0.52
% 0.19/0.52 [104] ALPHA_NOT_OR : ~((p2(skolem_Y101515(skolem_Y1010)) & ~p1(skolem_Y101515(skolem_Y1010))) | (~p2(skolem_Y101515(skolem_Y1010)) & p1(skolem_Y101515(skolem_Y1010))))
% 0.19/0.52 -> [108] ~(p2(skolem_Y101515(skolem_Y1010)) & ~p1(skolem_Y101515(skolem_Y1010))), ~(~p2(skolem_Y101515(skolem_Y1010)) & p1(skolem_Y101515(skolem_Y1010)))
% 0.19/0.52
% 0.19/0.52 [108] BETA_NOT_AND : ~(p2(skolem_Y101515(skolem_Y1010)) & ~p1(skolem_Y101515(skolem_Y1010)))
% 0.19/0.52 -> [109] ~p2(skolem_Y101515(skolem_Y1010))
% 0.19/0.52 -> [110] ~~p1(skolem_Y101515(skolem_Y1010))
% 0.19/0.52
% 0.19/0.52 [109] CLOSURE : ~p2(skolem_Y101515(skolem_Y1010))
% 0.19/0.52
% 0.19/0.52 [110] ALPHA_NOT_NOT : ~~p1(skolem_Y101515(skolem_Y1010))
% 0.19/0.52 -> [112] p1(skolem_Y101515(skolem_Y1010))
% 0.19/0.52
% 0.19/0.52 [112] CLOSURE : p1(skolem_Y101515(skolem_Y1010))
% 0.19/0.52
% 0.19/0.52 [89] BETA_NOT_AND : ~(~p1(skolem_Y101515(skolem_Y1010)) & ~p2(skolem_Y101515(skolem_Y1010)))
% 0.19/0.52 -> [91] ~~p1(skolem_Y101515(skolem_Y1010))
% 0.19/0.52 -> [92] ~~p2(skolem_Y101515(skolem_Y1010))
% 0.19/0.52
% 0.19/0.52 [92] ALPHA_NOT_NOT : ~~p2(skolem_Y101515(skolem_Y1010))
% 0.19/0.52 -> [96] p2(skolem_Y101515(skolem_Y1010))
% 0.19/0.52
% 0.19/0.52 [96] CLOSURE : p2(skolem_Y101515(skolem_Y1010))
% 0.19/0.52
% 0.19/0.52 [91] ALPHA_NOT_NOT : ~~p1(skolem_Y101515(skolem_Y1010))
% 0.19/0.52 -> [95] p1(skolem_Y101515(skolem_Y1010))
% 0.19/0.52
% 0.19/0.52 [95] GAMMA_FORALL : ! [Y1013_13] : ((~r1(skolem_Y1010, Y1013_13) | ~((p2(Y1013_13) & ~p1(Y1013_13)) | (~p2(Y1013_13) & p1(Y1013_13)))))
% 0.19/0.52 -> [99] (~r1(skolem_Y1010, skolem_Y101515(skolem_Y1010)) | ~((p2(skolem_Y101515(skolem_Y1010)) & ~p1(skolem_Y101515(skolem_Y1010))) | (~p2(skolem_Y101515(skolem_Y1010)) & p1(skolem_Y101515(skolem_Y1010)))))
% 0.19/0.52
% 0.19/0.52 [99] BETA_OR : (~r1(skolem_Y1010, skolem_Y101515(skolem_Y1010)) | ~((p2(skolem_Y101515(skolem_Y1010)) & ~p1(skolem_Y101515(skolem_Y1010))) | (~p2(skolem_Y101515(skolem_Y1010)) & p1(skolem_Y101515(skolem_Y1010)))))
% 0.19/0.52 -> [100] ~r1(skolem_Y1010, skolem_Y101515(skolem_Y1010))
% 0.19/0.52 -> [101] ~((p2(skolem_Y101515(skolem_Y1010)) & ~p1(skolem_Y101515(skolem_Y1010))) | (~p2(skolem_Y101515(skolem_Y1010)) & p1(skolem_Y101515(skolem_Y1010))))
% 0.19/0.52
% 0.19/0.52 [100] CLOSURE : ~r1(skolem_Y1010, skolem_Y101515(skolem_Y1010))
% 0.19/0.52
% 0.19/0.52 [101] ALPHA_NOT_OR : ~((p2(skolem_Y101515(skolem_Y1010)) & ~p1(skolem_Y101515(skolem_Y1010))) | (~p2(skolem_Y101515(skolem_Y1010)) & p1(skolem_Y101515(skolem_Y1010))))
% 0.19/0.52 -> [105] ~(p2(skolem_Y101515(skolem_Y1010)) & ~p1(skolem_Y101515(skolem_Y1010))), ~(~p2(skolem_Y101515(skolem_Y1010)) & p1(skolem_Y101515(skolem_Y1010)))
% 0.19/0.52
% 0.19/0.52 [105] BETA_NOT_AND : ~(p2(skolem_Y101515(skolem_Y1010)) & ~p1(skolem_Y101515(skolem_Y1010)))
% 0.19/0.52 -> [106] ~p2(skolem_Y101515(skolem_Y1010))
% 0.19/0.52 -> [107] ~~p1(skolem_Y101515(skolem_Y1010))
% 0.19/0.52
% 0.19/0.52 [106] BETA_NOT_AND : ~(~p2(skolem_X799) & p1(skolem_X799))
% 0.19/0.52 -> [113] ~~p2(skolem_X799)
% 0.19/0.52 -> [114] ~p1(skolem_X799)
% 0.19/0.52
% 0.19/0.52 [113] ALPHA_NOT_NOT : ~~p2(skolem_X799)
% 0.19/0.52 -> [117] p2(skolem_X799)
% 0.19/0.52
% 0.19/0.52 [117] CLOSURE : p2(skolem_X799)
% 0.19/0.52
% 0.19/0.52 [114] CLOSURE : ~p1(skolem_X799)
% 0.19/0.52
% 0.19/0.52 [107] ALPHA_NOT_NOT : ~~p1(skolem_Y101515(skolem_Y1010))
% 0.19/0.52 -> [111] p1(skolem_Y101515(skolem_Y1010))
% 0.19/0.52
% 0.19/0.52 [111] BETA_NOT_AND : ~(~p2(skolem_Y101515(skolem_Y1010)) & p1(skolem_Y101515(skolem_Y1010)))
% 0.19/0.52 -> [115] ~~p2(skolem_Y101515(skolem_Y1010))
% 0.19/0.52 -> [116] ~p1(skolem_Y101515(skolem_Y1010))
% 0.19/0.52
% 0.19/0.52 [116] CLOSURE : ~p1(skolem_Y101515(skolem_Y1010))
% 0.19/0.52
% 0.19/0.52 [115] ALPHA_NOT_NOT : ~~p2(skolem_Y101515(skolem_Y1010))
% 0.19/0.52 -> [118] p2(skolem_Y101515(skolem_Y1010))
% 0.19/0.52
% 0.19/0.52 [118] CLOSURE : p2(skolem_Y101515(skolem_Y1010))
% 0.19/0.52
% 0.19/0.52 % SZS output end Proof for theBenchmark.p
% 0.19/0.52 [0.186169s][1][Res] 470 goroutines created
% 0.19/0.52 ==== Result ====
% 0.19/0.52 [0.186205s][1][Res] VALID
% 0.19/0.52 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------