TSTP Solution File: SYN551+3 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : SYN551+3 : TPTP v8.1.0. Bugfixed v3.1.0.
% 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 : Thu Sep 29 22:24:02 EDT 2022
% Result : Theorem 2.66s 1.00s
% Output : Proof 2.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN551+3 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.12/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n015.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 05:50:57 EDT 2022
% 0.18/0.33 % CPUTime :
% 0.18/0.34 [DMT] DMT loaded with preskolemization
% 0.18/0.34 [EQ] equality loaded.
% 0.18/0.34 [0.000048s][1][MAIN] Problem : theBenchmark.p
% 0.18/0.34 Start search
% 0.18/0.34 nb_step : 1 - limit : 4
% 0.18/0.34 Launch Gotab with destructive = true
% 2.66/1.00 % SZS output start Proof for theBenchmark.p
% 2.66/1.00 [0] BETA_NOT_EQUIV : ~(? [X2_2] : ((=(X2_2, f(g(X2_2))) & ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(Y3_3, X2_2))))) <=> ? [X4_4] : ((=(X4_4, g(f(X4_4))) & ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(Y5_5, X4_4))))))
% 2.66/1.00 -> [1] ~? [X2_2] : ((=(X2_2, f(g(X2_2))) & ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(Y3_3, X2_2))))), ? [X4_4] : ((=(X4_4, g(f(X4_4))) & ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(Y5_5, X4_4)))))
% 2.66/1.00 -> [2] ? [X2_2] : ((=(X2_2, f(g(X2_2))) & ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(Y3_3, X2_2))))), ~? [X4_4] : ((=(X4_4, g(f(X4_4))) & ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(Y5_5, X4_4)))))
% 2.66/1.00
% 2.66/1.00 [1] DELTA_EXISTS : ? [X4_4] : ((=(X4_4, g(f(X4_4))) & ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(Y5_5, X4_4)))))
% 2.66/1.00 -> [4] (=(skolem_X44, g(f(skolem_X44))) & ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(Y5_5, skolem_X44))))
% 2.66/1.00
% 2.66/1.00 [4] ALPHA_AND : (=(skolem_X44, g(f(skolem_X44))) & ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(Y5_5, skolem_X44))))
% 2.66/1.00 -> [6] =(skolem_X44, g(f(skolem_X44))), ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(Y5_5, skolem_X44)))
% 2.66/1.00
% 2.66/1.00 [6] GAMMA_NOT_EXISTS : ~? [X2_2] : ((=(X2_2, f(g(X2_2))) & ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(Y3_3, X2_2)))))
% 2.66/1.00 -> [7] ~(=(f(skolem_X44), f(g(f(skolem_X44)))) & ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(Y3_3, f(skolem_X44)))))
% 2.66/1.00
% 2.66/1.00 [7] BETA_NOT_AND : ~(=(f(skolem_X44), f(g(f(skolem_X44)))) & ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(Y3_3, f(skolem_X44)))))
% 2.66/1.00 -> [9] ~=(f(skolem_X44), f(g(f(skolem_X44))))
% 2.66/1.00 -> [10] ~! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(Y3_3, f(skolem_X44))))
% 2.66/1.00
% 2.66/1.00 [9] CLOSURE : =
% 2.66/1.00
% 2.66/1.00 [10] DELTA_NOT_FORALL : ~! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(Y3_3, f(skolem_X44))))
% 2.66/1.00 -> [14] ~(=(skolem_Y33(f(skolem_X44)), f(g(skolem_Y33(f(skolem_X44))))) => =(skolem_Y33(f(skolem_X44)), f(skolem_X44)))
% 2.66/1.00
% 2.66/1.00 [14] ALPHA_NOT_IMPLY : ~(=(skolem_Y33(f(skolem_X44)), f(g(skolem_Y33(f(skolem_X44))))) => =(skolem_Y33(f(skolem_X44)), f(skolem_X44)))
% 2.66/1.00 -> [16] =(skolem_Y33(f(skolem_X44)), f(g(skolem_Y33(f(skolem_X44))))), ~=(skolem_Y33(f(skolem_X44)), f(skolem_X44))
% 2.66/1.00
% 2.66/1.00 [16] GAMMA_FORALL : ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(Y5_5, skolem_X44)))
% 2.66/1.00 -> [18] (=(skolem_X44, g(f(skolem_X44))) => =(skolem_X44, skolem_X44))
% 2.66/1.00
% 2.66/1.00 [18] BETA_IMPLY : (=(skolem_X44, g(f(skolem_X44))) => =(skolem_X44, skolem_X44))
% 2.66/1.00 -> [21] ~=(skolem_X44, g(f(skolem_X44)))
% 2.66/1.00 -> [22] =(skolem_X44, skolem_X44)
% 2.66/1.00
% 2.66/1.00 [21] CLOSURE : =
% 2.66/1.00
% 2.66/1.00 [22] : ~? [X2_2] : ((=(X2_2, f(g(X2_2))) & ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(Y3_3, X2_2)))))
% 2.66/1.00 -> [29] ~? [X2_2] : ((=(X2_2, f(g(X2_2))) & ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(Y3_3, X2_2)))))
% 2.66/1.00
% 2.66/1.00 [29] GAMMA_NOT_EXISTS : ~? [X2_2] : ((=(X2_2, f(g(X2_2))) & ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(Y3_3, X2_2)))))
% 2.66/1.00 -> [30] ~(=(f(skolem_X44), f(g(f(skolem_X44)))) & ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(Y3_3, f(skolem_X44)))))
% 2.66/1.00
% 2.66/1.00 [30] BETA_NOT_AND : ~(=(f(skolem_X44), f(g(f(skolem_X44)))) & ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(Y3_3, f(skolem_X44)))))
% 2.66/1.00 -> [31] ~=(f(skolem_X44), f(g(f(skolem_X44))))
% 2.66/1.00 -> [32] ~! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(Y3_3, f(skolem_X44))))
% 2.66/1.00
% 2.66/1.00 [31] CLOSURE : =
% 2.66/1.00
% 2.66/1.00 [32] DELTA_NOT_FORALL : ~! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(Y3_3, f(skolem_X44))))
% 2.66/1.00 -> [33] ~(=(skolem_Y33(f(skolem_X44)), f(g(skolem_Y33(f(skolem_X44))))) => =(skolem_Y33(f(skolem_X44)), f(skolem_X44)))
% 2.66/1.00
% 2.66/1.00 [33] ALPHA_NOT_IMPLY : ~(=(skolem_Y33(f(skolem_X44)), f(g(skolem_Y33(f(skolem_X44))))) => =(skolem_Y33(f(skolem_X44)), f(skolem_X44)))
% 2.66/1.00 -> [34] =(skolem_Y33(f(skolem_X44)), f(g(skolem_Y33(f(skolem_X44))))), ~=(skolem_Y33(f(skolem_X44)), f(skolem_X44))
% 2.66/1.00
% 2.66/1.00 [34] ALPHA_NOT_IMPLY : ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(Y5_5, skolem_X44)))
% 2.66/1.00 -> [39] ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(Y5_5, skolem_X44)))
% 2.66/1.00
% 2.66/1.00 [39] GAMMA_FORALL : ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(Y5_5, skolem_X44)))
% 2.66/1.00 -> [40] (=(g(skolem_Y33(f(skolem_X44))), g(f(g(skolem_Y33(f(skolem_X44)))))) => =(g(skolem_Y33(f(skolem_X44))), skolem_X44))
% 2.66/1.00
% 2.66/1.00 [40] BETA_IMPLY : (=(g(skolem_Y33(f(skolem_X44))), g(f(g(skolem_Y33(f(skolem_X44)))))) => =(g(skolem_Y33(f(skolem_X44))), skolem_X44))
% 2.66/1.00 -> [41] ~=(g(skolem_Y33(f(skolem_X44))), g(f(g(skolem_Y33(f(skolem_X44))))))
% 2.66/1.00 -> [42] =(g(skolem_Y33(f(skolem_X44))), skolem_X44)
% 2.66/1.00
% 2.66/1.00 [41] CLOSURE : =
% 2.66/1.00
% 2.66/1.00 [42] CLOSURE : =
% 2.66/1.00
% 2.66/1.00 [2] DELTA_EXISTS : ? [X2_2] : ((=(X2_2, f(g(X2_2))) & ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(Y3_3, X2_2)))))
% 2.66/1.00 -> [3] (=(skolem_X22, f(g(skolem_X22))) & ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(Y3_3, skolem_X22))))
% 2.66/1.00
% 2.66/1.00 [3] ALPHA_AND : (=(skolem_X22, f(g(skolem_X22))) & ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(Y3_3, skolem_X22))))
% 2.66/1.00 -> [5] =(skolem_X22, f(g(skolem_X22))), ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(Y3_3, skolem_X22)))
% 2.66/1.00
% 2.66/1.00 [5] GAMMA_NOT_EXISTS : ~? [X4_4] : ((=(X4_4, g(f(X4_4))) & ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(Y5_5, X4_4)))))
% 2.66/1.00 -> [8] ~(=(g(skolem_X22), g(f(g(skolem_X22)))) & ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(Y5_5, g(skolem_X22)))))
% 2.66/1.00
% 2.66/1.00 [8] BETA_NOT_AND : ~(=(g(skolem_X22), g(f(g(skolem_X22)))) & ! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(Y5_5, g(skolem_X22)))))
% 2.66/1.00 -> [11] ~=(g(skolem_X22), g(f(g(skolem_X22))))
% 2.66/1.00 -> [12] ~! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(Y5_5, g(skolem_X22))))
% 2.66/1.00
% 2.66/1.00 [11] CLOSURE : =
% 2.66/1.00
% 2.66/1.00 [12] DELTA_NOT_FORALL : ~! [Y5_5] : ((=(Y5_5, g(f(Y5_5))) => =(Y5_5, g(skolem_X22))))
% 2.66/1.00 -> [13] ~(=(skolem_Y55(g(skolem_X22)), g(f(skolem_Y55(g(skolem_X22))))) => =(skolem_Y55(g(skolem_X22)), g(skolem_X22)))
% 2.66/1.00
% 2.66/1.00 [13] ALPHA_NOT_IMPLY : ~(=(skolem_Y55(g(skolem_X22)), g(f(skolem_Y55(g(skolem_X22))))) => =(skolem_Y55(g(skolem_X22)), g(skolem_X22)))
% 2.66/1.00 -> [15] =(skolem_Y55(g(skolem_X22)), g(f(skolem_Y55(g(skolem_X22))))), ~=(skolem_Y55(g(skolem_X22)), g(skolem_X22))
% 2.66/1.00
% 2.66/1.00 [15] GAMMA_FORALL : ! [Y3_3] : ((=(Y3_3, f(g(Y3_3))) => =(Y3_3, skolem_X22)))
% 2.66/1.00 -> [17] (=(f(skolem_Y55(g(skolem_X22))), f(g(f(skolem_Y55(g(skolem_X22)))))) => =(f(skolem_Y55(g(skolem_X22))), skolem_X22))
% 2.66/1.00
% 2.66/1.00 [17] BETA_IMPLY : (=(f(skolem_Y55(g(skolem_X22))), f(g(f(skolem_Y55(g(skolem_X22)))))) => =(f(skolem_Y55(g(skolem_X22))), skolem_X22))
% 2.66/1.00 -> [19] ~=(f(skolem_Y55(g(skolem_X22))), f(g(f(skolem_Y55(g(skolem_X22))))))
% 2.66/1.00 -> [20] =(f(skolem_Y55(g(skolem_X22))), skolem_X22)
% 2.66/1.00
% 2.66/1.00 [19] CLOSURE : =
% 2.66/1.00
% 2.66/1.00 [20] CLOSURE : =
% 2.66/1.00
% 2.66/1.00 % SZS output end Proof for theBenchmark.p
% 2.66/1.00 [0.666571s][1][Res] 6357 goroutines created
% 2.66/1.00 ==== Result ====
% 2.66/1.00 [0.666604s][1][Res] VALID
% 2.66/1.00 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------