TSTP Solution File: SYN417+1 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SYN417+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 22:23:26 EDT 2022
% Result : Theorem 39.72s 6.21s
% Output : Proof 39.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYN417+1 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.32 % Computer : n005.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Sep 5 03:13:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 [DMT] DMT loaded with preskolemization
% 0.12/0.33 [EQ] equality loaded.
% 0.12/0.33 [0.000037s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.33 Start search
% 0.12/0.33 nb_step : 1 - limit : 4
% 0.12/0.33 Launch Gotab with destructive = true
% 39.72/6.21 % SZS output start Proof for theBenchmark.p
% 39.72/6.21 [0] BETA_NOT_EQUIV : ~(? [X2_2] : ((=(X2_2, f(g(X2_2))) & ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(X2_2, Y3_3))))) <=> ? [X4_4] : ((=(X4_4, g(f(X4_4))) & ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(X4_4, Y5_5))))))
% 39.72/6.21 -> [1] ~? [X2_2] : ((=(X2_2, f(g(X2_2))) & ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(X2_2, Y3_3))))), ? [X4_4] : ((=(X4_4, g(f(X4_4))) & ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(X4_4, Y5_5)))))
% 39.72/6.21 -> [2] ? [X2_2] : ((=(X2_2, f(g(X2_2))) & ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(X2_2, Y3_3))))), ~? [X4_4] : ((=(X4_4, g(f(X4_4))) & ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(X4_4, Y5_5)))))
% 39.72/6.21
% 39.72/6.21 [1] DELTA_EXISTS : ? [X4_4] : ((=(X4_4, g(f(X4_4))) & ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(X4_4, Y5_5)))))
% 39.72/6.21 -> [4] (=(skolem_X44, g(f(skolem_X44))) & ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(skolem_X44, Y5_5))))
% 39.72/6.21
% 39.72/6.21 [4] ALPHA_AND : (=(skolem_X44, g(f(skolem_X44))) & ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(skolem_X44, Y5_5))))
% 39.72/6.21 -> [6] =(skolem_X44, g(f(skolem_X44))), ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(skolem_X44, Y5_5)))
% 39.72/6.21
% 39.72/6.21 [6] GAMMA_NOT_EXISTS : ~? [X2_2] : ((=(X2_2, f(g(X2_2))) & ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(X2_2, Y3_3)))))
% 39.72/6.21 -> [8] ~(=(f(skolem_X44), f(g(f(skolem_X44)))) & ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(f(skolem_X44), Y3_3))))
% 39.72/6.21
% 39.72/6.21 [8] BETA_NOT_AND : ~(=(f(skolem_X44), f(g(f(skolem_X44)))) & ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(f(skolem_X44), Y3_3))))
% 39.72/6.21 -> [11] ~=(f(skolem_X44), f(g(f(skolem_X44))))
% 39.72/6.21 -> [12] ~! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(f(skolem_X44), Y3_3)))
% 39.72/6.21
% 39.72/6.21 [11] CLOSURE : =
% 39.72/6.21
% 39.72/6.21 [17] BETA_IMPLY : (=(g(skolem_Y33(f(skolem_X44))), g(f(g(skolem_Y33(f(skolem_X44)))))) => =(skolem_X44, g(skolem_Y33(f(skolem_X44)))))
% 39.72/6.21 -> [63] ~=(g(skolem_Y33(f(skolem_X44))), g(f(g(skolem_Y33(f(skolem_X44))))))
% 39.72/6.21 -> [64] =(skolem_X44, g(skolem_Y33(f(skolem_X44))))
% 39.72/6.21
% 39.72/6.21 [64] CLOSURE : =
% 39.72/6.21
% 39.72/6.21 [63] CLOSURE : =
% 39.72/6.21
% 39.72/6.21 [2] DELTA_EXISTS : ? [X2_2] : ((=(X2_2, f(g(X2_2))) & ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(X2_2, Y3_3)))))
% 39.72/6.21 -> [3] (=(skolem_X22, f(g(skolem_X22))) & ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(skolem_X22, Y3_3))))
% 39.72/6.21
% 39.72/6.21 [3] ALPHA_AND : (=(skolem_X22, f(g(skolem_X22))) & ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(skolem_X22, Y3_3))))
% 39.72/6.21 -> [5] =(skolem_X22, f(g(skolem_X22))), ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(skolem_X22, Y3_3)))
% 39.72/6.21
% 39.72/6.21 [5] GAMMA_NOT_EXISTS : ~? [X4_4] : ((=(X4_4, g(f(X4_4))) & ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(X4_4, Y5_5)))))
% 39.72/6.21 -> [7] ~(=(g(skolem_X22), g(f(g(skolem_X22)))) & ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(g(skolem_X22), Y5_5))))
% 39.72/6.21
% 39.72/6.21 [7] BETA_NOT_AND : ~(=(g(skolem_X22), g(f(g(skolem_X22)))) & ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(g(skolem_X22), Y5_5))))
% 39.72/6.21 -> [9] ~=(g(skolem_X22), g(f(g(skolem_X22))))
% 39.72/6.21 -> [10] ~! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(g(skolem_X22), Y5_5)))
% 39.72/6.21
% 39.72/6.21 [9] CLOSURE : =
% 39.72/6.21
% 39.72/6.21 [20] BETA_IMPLY : (=(skolem_X22, f(g(skolem_X22))) => =(skolem_X22, skolem_X22))
% 39.72/6.21 -> [65] ~=(skolem_X22, f(g(skolem_X22)))
% 39.72/6.21 -> [66] =(skolem_X22, skolem_X22)
% 39.72/6.21
% 39.72/6.21 [65] CLOSURE : =
% 39.72/6.21
% 39.72/6.21 [66] : ~? [X4_4] : ((=(X4_4, g(f(X4_4))) & ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(X4_4, Y5_5)))))
% 39.72/6.21 -> [67] ~? [X4_4] : ((=(X4_4, g(f(X4_4))) & ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(X4_4, Y5_5)))))
% 39.72/6.21
% 39.72/6.21 [67] GAMMA_NOT_EXISTS : ~? [X4_4] : ((=(X4_4, g(f(X4_4))) & ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(X4_4, Y5_5)))))
% 39.72/6.21 -> [68] ~(=(skolem_Y55(g(skolem_X22)), g(f(skolem_Y55(g(skolem_X22))))) & ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(skolem_Y55(g(skolem_X22)), Y5_5))))
% 39.72/6.21
% 39.72/6.21 [68] BETA_NOT_AND : ~(=(skolem_Y55(g(skolem_X22)), g(f(skolem_Y55(g(skolem_X22))))) & ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(skolem_Y55(g(skolem_X22)), Y5_5))))
% 39.72/6.21 -> [69] ~=(skolem_Y55(g(skolem_X22)), g(f(skolem_Y55(g(skolem_X22)))))
% 39.72/6.21 -> [70] ~! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(skolem_Y55(g(skolem_X22)), Y5_5)))
% 39.72/6.21
% 39.72/6.21 [69] CLOSURE : =
% 39.72/6.21
% 39.72/6.21 [70] DELTA_NOT_FORALL : ~! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(skolem_Y55(g(skolem_X22)), Y5_5)))
% 39.72/6.21 -> [71] ~(=(skolem_Y55(skolem_Y55(g(skolem_X22))), g(f(skolem_Y55(skolem_Y55(g(skolem_X22)))))) => =(skolem_Y55(g(skolem_X22)), skolem_Y55(skolem_Y55(g(skolem_X22)))))
% 39.72/6.21
% 39.72/6.21 [71] ALPHA_NOT_IMPLY : ~(=(skolem_Y55(skolem_Y55(g(skolem_X22))), g(f(skolem_Y55(skolem_Y55(g(skolem_X22)))))) => =(skolem_Y55(g(skolem_X22)), skolem_Y55(skolem_Y55(g(skolem_X22)))))
% 39.72/6.21 -> [72] =(skolem_Y55(skolem_Y55(g(skolem_X22))), g(f(skolem_Y55(skolem_Y55(g(skolem_X22)))))), ~=(skolem_Y55(g(skolem_X22)), skolem_Y55(skolem_Y55(g(skolem_X22))))
% 39.72/6.21
% 39.72/6.21 [72] ALPHA_NOT_IMPLY : ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(skolem_X22, Y3_3)))
% 39.72/6.21 -> [73] ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(skolem_X22, Y3_3)))
% 39.72/6.21
% 39.72/6.21 [73] GAMMA_FORALL : ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(skolem_X22, Y3_3)))
% 39.72/6.21 -> [74] (=(f(skolem_Y55(g(skolem_X22))), f(g(f(skolem_Y55(g(skolem_X22)))))) => =(skolem_X22, f(skolem_Y55(g(skolem_X22)))))
% 39.72/6.21
% 39.72/6.21 [74] BETA_IMPLY : (=(f(skolem_Y55(g(skolem_X22))), f(g(f(skolem_Y55(g(skolem_X22)))))) => =(skolem_X22, f(skolem_Y55(g(skolem_X22)))))
% 39.72/6.21 -> [75] ~=(f(skolem_Y55(g(skolem_X22))), f(g(f(skolem_Y55(g(skolem_X22))))))
% 39.72/6.21 -> [76] =(skolem_X22, f(skolem_Y55(g(skolem_X22))))
% 39.72/6.21
% 39.72/6.21 [76] CLOSURE : =
% 39.72/6.21
% 39.72/6.21 [75] CLOSURE : =
% 39.72/6.21
% 39.72/6.21 % SZS output end Proof for theBenchmark.p
% 39.72/6.21 [5.875174s][1][Res] 78771 goroutines created
% 39.72/6.21 ==== Result ====
% 39.72/6.21 [5.875201s][1][Res] VALID
% 39.72/6.21 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------