TSTP Solution File: SWW957+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWW957+1 : TPTP v8.1.2. Released v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n002.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 Apr 30 20:50:56 EDT 2024
% Result : Theorem 7.41s 1.35s
% Output : CNFRefutation 7.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 20
% Syntax : Number of formulae : 83 ( 34 unt; 0 def)
% Number of atoms : 138 ( 22 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 100 ( 45 ~; 44 |; 1 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 85 ( 85 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f46,axiom,
! [VAR_X_14,VAR_Y_15] : constr_split(constr_concat(VAR_X_14,VAR_Y_15)) = tuple_2(VAR_X_14,VAR_Y_15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [VAR_X1_0X30,VAR_X2_0X30,VAR_Y1_0X30,VAR_Y2_0X30] : constr_xor(constr_concat(VAR_X1_0X30,VAR_Y1_0X30),constr_concat(VAR_X2_0X30,VAR_Y2_0X30)) = constr_concat(constr_xor(VAR_X1_0X30,VAR_X2_0X30),constr_xor(VAR_Y1_0X30,VAR_Y2_0X30)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [VAR_X_12,VAR_Y_13] : constr_C(constr_xor(VAR_X_12,VAR_Y_13)) = constr_xor(constr_C(VAR_X_12),constr_C(VAR_Y_13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [VAR_X_11] : constr_xor(VAR_X_11,VAR_X_11) = constr_ZERO,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [VAR_X_10X30] : constr_xor(VAR_X_10X30,constr_ZERO) = VAR_X_10X30,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [VAR_X_8,VAR_Y_9] : constr_xor(VAR_X_8,VAR_Y_9) = constr_xor(VAR_Y_9,VAR_X_8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,axiom,
! [VAR_X_0X30,VAR_Y_0X30,VAR_Z_0X30] : constr_xor(VAR_X_0X30,constr_xor(VAR_Y_0X30,VAR_Z_0X30)) = constr_xor(constr_xor(VAR_X_0X30,VAR_Y_0X30),VAR_Z_0X30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [VAR_V_31,VAR_V_32] :
( ( pred_attacker(VAR_V_31)
& pred_attacker(VAR_V_32) )
=> pred_attacker(constr_xor(VAR_V_31,VAR_V_32)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [VAR_V_34] :
( pred_attacker(VAR_V_34)
=> pred_attacker(constr_split(VAR_V_34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f59,axiom,
! [VAR_V_49,VAR_V_50X30] :
( pred_attacker(tuple_enc_oracle_out_2(VAR_V_49,VAR_V_50X30))
=> pred_attacker(VAR_V_50X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,axiom,
! [VAR_V_53] :
( pred_attacker(VAR_V_53)
=> pred_attacker(tuple_enc_oracle_in_1(VAR_V_53)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,axiom,
pred_attacker(constr_ZERO),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f73,axiom,
! [VAR_V_81,VAR_V_82] :
( pred_attacker(tuple_B_out_1(VAR_V_81,VAR_V_82))
=> pred_attacker(VAR_V_82) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f75,axiom,
! [VAR_V_98,VAR_V_99] :
( pred_attacker(tuple_2(VAR_V_98,VAR_V_99))
=> pred_attacker(VAR_V_98) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f82,axiom,
! [VAR_M_150X30] :
( pred_attacker(tuple_enc_oracle_in_1(VAR_M_150X30))
=> pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_concat(VAR_M_150X30,constr_C(VAR_M_150X30)),constr_RC4(name_v,name_Kab)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f83,axiom,
pred_attacker(tuple_B_out_1(name_v,constr_xor(constr_concat(name_objective,constr_C(name_objective)),constr_RC4(name_v,name_Kab)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f84,conjecture,
pred_attacker(name_objective),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f85,negated_conjecture,
~ pred_attacker(name_objective),
inference(negated_conjecture,[status(cth)],[f84]) ).
fof(f131,plain,
! [X0,X1] : constr_split(constr_concat(X0,X1)) = tuple_2(X0,X1),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f132,plain,
! [X0,X1,X2,X3] : constr_xor(constr_concat(X0,X1),constr_concat(X2,X3)) = constr_concat(constr_xor(X0,X2),constr_xor(X1,X3)),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f133,plain,
! [X0,X1] : constr_C(constr_xor(X0,X1)) = constr_xor(constr_C(X0),constr_C(X1)),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f134,plain,
! [X0] : constr_xor(X0,X0) = constr_ZERO,
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f135,plain,
! [X0] : constr_xor(X0,constr_ZERO) = X0,
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f136,plain,
! [X0,X1] : constr_xor(X0,X1) = constr_xor(X1,X0),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f137,plain,
! [X0,X1,X2] : constr_xor(X0,constr_xor(X1,X2)) = constr_xor(constr_xor(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f138,plain,
! [VAR_V_31,VAR_V_32] :
( ~ pred_attacker(VAR_V_31)
| ~ pred_attacker(VAR_V_32)
| pred_attacker(constr_xor(VAR_V_31,VAR_V_32)) ),
inference(pre_NNF_transformation,[status(esa)],[f53]) ).
fof(f139,plain,
! [X0,X1] :
( ~ pred_attacker(X0)
| ~ pred_attacker(X1)
| pred_attacker(constr_xor(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f138]) ).
fof(f141,plain,
! [VAR_V_34] :
( ~ pred_attacker(VAR_V_34)
| pred_attacker(constr_split(VAR_V_34)) ),
inference(pre_NNF_transformation,[status(esa)],[f55]) ).
fof(f142,plain,
! [X0] :
( ~ pred_attacker(X0)
| pred_attacker(constr_split(X0)) ),
inference(cnf_transformation,[status(esa)],[f141]) ).
fof(f149,plain,
! [VAR_V_49,VAR_V_50X30] :
( ~ pred_attacker(tuple_enc_oracle_out_2(VAR_V_49,VAR_V_50X30))
| pred_attacker(VAR_V_50X30) ),
inference(pre_NNF_transformation,[status(esa)],[f59]) ).
fof(f150,plain,
! [VAR_V_50X30] :
( ! [VAR_V_49] : ~ pred_attacker(tuple_enc_oracle_out_2(VAR_V_49,VAR_V_50X30))
| pred_attacker(VAR_V_50X30) ),
inference(miniscoping,[status(esa)],[f149]) ).
fof(f151,plain,
! [X0,X1] :
( ~ pred_attacker(tuple_enc_oracle_out_2(X0,X1))
| pred_attacker(X1) ),
inference(cnf_transformation,[status(esa)],[f150]) ).
fof(f152,plain,
! [VAR_V_53] :
( ~ pred_attacker(VAR_V_53)
| pred_attacker(tuple_enc_oracle_in_1(VAR_V_53)) ),
inference(pre_NNF_transformation,[status(esa)],[f60]) ).
fof(f153,plain,
! [X0] :
( ~ pred_attacker(X0)
| pred_attacker(tuple_enc_oracle_in_1(X0)) ),
inference(cnf_transformation,[status(esa)],[f152]) ).
fof(f158,plain,
pred_attacker(constr_ZERO),
inference(cnf_transformation,[status(esa)],[f63]) ).
fof(f173,plain,
! [VAR_V_81,VAR_V_82] :
( ~ pred_attacker(tuple_B_out_1(VAR_V_81,VAR_V_82))
| pred_attacker(VAR_V_82) ),
inference(pre_NNF_transformation,[status(esa)],[f73]) ).
fof(f174,plain,
! [VAR_V_82] :
( ! [VAR_V_81] : ~ pred_attacker(tuple_B_out_1(VAR_V_81,VAR_V_82))
| pred_attacker(VAR_V_82) ),
inference(miniscoping,[status(esa)],[f173]) ).
fof(f175,plain,
! [X0,X1] :
( ~ pred_attacker(tuple_B_out_1(X0,X1))
| pred_attacker(X1) ),
inference(cnf_transformation,[status(esa)],[f174]) ).
fof(f178,plain,
! [VAR_V_98,VAR_V_99] :
( ~ pred_attacker(tuple_2(VAR_V_98,VAR_V_99))
| pred_attacker(VAR_V_98) ),
inference(pre_NNF_transformation,[status(esa)],[f75]) ).
fof(f179,plain,
! [VAR_V_98] :
( ! [VAR_V_99] : ~ pred_attacker(tuple_2(VAR_V_98,VAR_V_99))
| pred_attacker(VAR_V_98) ),
inference(miniscoping,[status(esa)],[f178]) ).
fof(f180,plain,
! [X0,X1] :
( ~ pred_attacker(tuple_2(X0,X1))
| pred_attacker(X0) ),
inference(cnf_transformation,[status(esa)],[f179]) ).
fof(f192,plain,
! [VAR_M_150X30] :
( ~ pred_attacker(tuple_enc_oracle_in_1(VAR_M_150X30))
| pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_concat(VAR_M_150X30,constr_C(VAR_M_150X30)),constr_RC4(name_v,name_Kab)))) ),
inference(pre_NNF_transformation,[status(esa)],[f82]) ).
fof(f193,plain,
! [X0] :
( ~ pred_attacker(tuple_enc_oracle_in_1(X0))
| pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_concat(X0,constr_C(X0)),constr_RC4(name_v,name_Kab)))) ),
inference(cnf_transformation,[status(esa)],[f192]) ).
fof(f194,plain,
pred_attacker(tuple_B_out_1(name_v,constr_xor(constr_concat(name_objective,constr_C(name_objective)),constr_RC4(name_v,name_Kab)))),
inference(cnf_transformation,[status(esa)],[f83]) ).
fof(f195,plain,
~ pred_attacker(name_objective),
inference(cnf_transformation,[status(esa)],[f85]) ).
fof(f196,plain,
! [X0,X1] : constr_concat(constr_xor(X0,X0),constr_xor(X1,X1)) = constr_ZERO,
inference(paramodulation,[status(thm)],[f132,f134]) ).
fof(f197,plain,
! [X0] : constr_concat(constr_ZERO,constr_xor(X0,X0)) = constr_ZERO,
inference(forward_demodulation,[status(thm)],[f134,f196]) ).
fof(f198,plain,
constr_concat(constr_ZERO,constr_ZERO) = constr_ZERO,
inference(forward_demodulation,[status(thm)],[f134,f197]) ).
fof(f204,plain,
! [X0] : X0 = constr_xor(constr_ZERO,X0),
inference(paramodulation,[status(thm)],[f135,f136]) ).
fof(f218,plain,
! [X0,X1] :
( ~ pred_attacker(constr_concat(X0,X1))
| pred_attacker(tuple_2(X0,X1)) ),
inference(paramodulation,[status(thm)],[f131,f142]) ).
fof(f223,plain,
! [X0] : constr_C(constr_xor(X0,X0)) = constr_ZERO,
inference(paramodulation,[status(thm)],[f134,f133]) ).
fof(f224,plain,
constr_C(constr_ZERO) = constr_ZERO,
inference(forward_demodulation,[status(thm)],[f134,f223]) ).
fof(f246,plain,
! [X0,X1] : constr_xor(X0,constr_xor(X0,X1)) = constr_xor(constr_ZERO,X1),
inference(paramodulation,[status(thm)],[f134,f137]) ).
fof(f247,plain,
! [X0,X1] : constr_xor(X0,constr_xor(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f204,f246]) ).
fof(f254,plain,
( spl0_0
<=> pred_attacker(constr_ZERO) ),
introduced(split_symbol_definition) ).
fof(f256,plain,
( ~ pred_attacker(constr_ZERO)
| spl0_0 ),
inference(component_clause,[status(thm)],[f254]) ).
fof(f304,plain,
! [X0,X1] :
( ~ pred_attacker(X0)
| ~ pred_attacker(constr_xor(X0,X1))
| pred_attacker(X1) ),
inference(paramodulation,[status(thm)],[f247,f139]) ).
fof(f359,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f256,f158]) ).
fof(f360,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f359]) ).
fof(f431,plain,
! [X0] :
( ~ pred_attacker(tuple_enc_oracle_in_1(X0))
| pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_RC4(name_v,name_Kab),constr_concat(X0,constr_C(X0))))) ),
inference(forward_demodulation,[status(thm)],[f136,f193]) ).
fof(f432,plain,
! [X0] :
( pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_RC4(name_v,name_Kab),constr_concat(X0,constr_C(X0)))))
| ~ pred_attacker(X0) ),
inference(resolution,[status(thm)],[f431,f153]) ).
fof(f434,plain,
pred_attacker(tuple_B_out_1(name_v,constr_xor(constr_RC4(name_v,name_Kab),constr_concat(name_objective,constr_C(name_objective))))),
inference(forward_demodulation,[status(thm)],[f136,f194]) ).
fof(f435,plain,
pred_attacker(constr_xor(constr_RC4(name_v,name_Kab),constr_concat(name_objective,constr_C(name_objective)))),
inference(resolution,[status(thm)],[f434,f175]) ).
fof(f6861,plain,
( spl0_94
<=> pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_RC4(name_v,name_Kab),constr_concat(constr_ZERO,constr_ZERO)))) ),
introduced(split_symbol_definition) ).
fof(f6862,plain,
( pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_RC4(name_v,name_Kab),constr_concat(constr_ZERO,constr_ZERO))))
| ~ spl0_94 ),
inference(component_clause,[status(thm)],[f6861]) ).
fof(f6864,plain,
( pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_RC4(name_v,name_Kab),constr_concat(constr_ZERO,constr_ZERO))))
| ~ pred_attacker(constr_ZERO) ),
inference(paramodulation,[status(thm)],[f224,f432]) ).
fof(f6865,plain,
( spl0_94
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f6864,f6861,f254]) ).
fof(f6866,plain,
( pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_concat(constr_ZERO,constr_ZERO),constr_RC4(name_v,name_Kab))))
| ~ spl0_94 ),
inference(forward_demodulation,[status(thm)],[f136,f6862]) ).
fof(f6867,plain,
( pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_ZERO,constr_RC4(name_v,name_Kab))))
| ~ spl0_94 ),
inference(forward_demodulation,[status(thm)],[f198,f6866]) ).
fof(f6868,plain,
( pred_attacker(tuple_enc_oracle_out_2(name_v,constr_RC4(name_v,name_Kab)))
| ~ spl0_94 ),
inference(forward_demodulation,[status(thm)],[f204,f6867]) ).
fof(f7285,plain,
( pred_attacker(constr_RC4(name_v,name_Kab))
| ~ spl0_94 ),
inference(resolution,[status(thm)],[f6868,f151]) ).
fof(f8166,plain,
( spl0_103
<=> pred_attacker(constr_concat(name_objective,constr_C(name_objective))) ),
introduced(split_symbol_definition) ).
fof(f8167,plain,
( pred_attacker(constr_concat(name_objective,constr_C(name_objective)))
| ~ spl0_103 ),
inference(component_clause,[status(thm)],[f8166]) ).
fof(f8168,plain,
( ~ pred_attacker(constr_concat(name_objective,constr_C(name_objective)))
| spl0_103 ),
inference(component_clause,[status(thm)],[f8166]) ).
fof(f8972,plain,
! [X0] :
( ~ pred_attacker(X0)
| ~ pred_attacker(constr_xor(X0,constr_concat(name_objective,constr_C(name_objective))))
| spl0_103 ),
inference(resolution,[status(thm)],[f8168,f304]) ).
fof(f9057,plain,
( ~ pred_attacker(constr_RC4(name_v,name_Kab))
| spl0_103 ),
inference(resolution,[status(thm)],[f8972,f435]) ).
fof(f9058,plain,
( $false
| ~ spl0_94
| spl0_103 ),
inference(forward_subsumption_resolution,[status(thm)],[f9057,f7285]) ).
fof(f9059,plain,
( ~ spl0_94
| spl0_103 ),
inference(contradiction_clause,[status(thm)],[f9058]) ).
fof(f9061,plain,
( pred_attacker(tuple_2(name_objective,constr_C(name_objective)))
| ~ spl0_103 ),
inference(resolution,[status(thm)],[f8167,f218]) ).
fof(f9935,plain,
( pred_attacker(name_objective)
| ~ spl0_103 ),
inference(resolution,[status(thm)],[f9061,f180]) ).
fof(f9936,plain,
( $false
| ~ spl0_103 ),
inference(forward_subsumption_resolution,[status(thm)],[f9935,f195]) ).
fof(f9937,plain,
~ spl0_103,
inference(contradiction_clause,[status(thm)],[f9936]) ).
fof(f9938,plain,
$false,
inference(sat_refutation,[status(thm)],[f360,f6865,f9059,f9937]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWW957+1 : TPTP v8.1.2. Released v7.4.0.
% 0.12/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 29 23:30:54 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % Drodi V3.6.0
% 7.41/1.35 % Refutation found
% 7.41/1.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.41/1.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.90/1.39 % Elapsed time: 1.019902 seconds
% 7.90/1.39 % CPU time: 7.969564 seconds
% 7.90/1.39 % Total memory used: 168.381 MB
% 7.90/1.39 % Net memory used: 152.720 MB
%------------------------------------------------------------------------------