%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW957+1 : TPTP v9.3.1. Released v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:08:35 PM UTC 2026
% Result : Theorem 1.03s 0.57s
% Output : CNFRefutation 1.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 21
% Syntax : Number of formulae : 82 ( 34 unt; 4 def)
% Number of atoms : 135 ( 23 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 95 ( 42 ~; 41 |; 1 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 86 ( 86 !; 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_32)
& pred_attacker(VAR_V_31) )
=> 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(thm)],[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(thm)],[f47]) ).
fof(f133,plain,
! [X0,X1] : constr_C(constr_xor(X0,X1)) = constr_xor(constr_C(X0),constr_C(X1)),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f134,plain,
! [X0] : constr_xor(X0,X0) = constr_ZERO,
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f135,plain,
! [X0] : constr_xor(X0,constr_ZERO) = X0,
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f136,plain,
! [X0,X1] : constr_xor(X0,X1) = constr_xor(X1,X0),
inference(cnf_transformation,[status(thm)],[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(thm)],[f52]) ).
fof(f138,plain,
! [VAR_V_31,VAR_V_32] :
( pred_attacker(constr_xor(VAR_V_31,VAR_V_32))
| ~ pred_attacker(VAR_V_32)
| ~ pred_attacker(VAR_V_31) ),
inference(pre_NNF_transformation,[status(thm)],[f53]) ).
fof(f139,plain,
! [X0,X1] :
( pred_attacker(constr_xor(X0,X1))
| ~ pred_attacker(X1)
| ~ pred_attacker(X0) ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f141,plain,
! [VAR_V_34] :
( pred_attacker(constr_split(VAR_V_34))
| ~ pred_attacker(VAR_V_34) ),
inference(pre_NNF_transformation,[status(thm)],[f55]) ).
fof(f142,plain,
! [X0] :
( pred_attacker(constr_split(X0))
| ~ pred_attacker(X0) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f149,plain,
! [VAR_V_49,VAR_V_50X30] :
( pred_attacker(VAR_V_50X30)
| ~ pred_attacker(tuple_enc_oracle_out_2(VAR_V_49,VAR_V_50X30)) ),
inference(pre_NNF_transformation,[status(thm)],[f59]) ).
fof(f150,plain,
! [VAR_V_50X30] :
( pred_attacker(VAR_V_50X30)
| ! [VAR_V_49] : ~ pred_attacker(tuple_enc_oracle_out_2(VAR_V_49,VAR_V_50X30)) ),
inference(miniscoping,[status(thm)],[f149]) ).
fof(f151,plain,
! [X0,X1] :
( pred_attacker(X1)
| ~ pred_attacker(tuple_enc_oracle_out_2(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f152,plain,
! [VAR_V_53] :
( pred_attacker(tuple_enc_oracle_in_1(VAR_V_53))
| ~ pred_attacker(VAR_V_53) ),
inference(pre_NNF_transformation,[status(thm)],[f60]) ).
fof(f153,plain,
! [X0] :
( pred_attacker(tuple_enc_oracle_in_1(X0))
| ~ pred_attacker(X0) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f158,plain,
pred_attacker(constr_ZERO),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f173,plain,
! [VAR_V_81,VAR_V_82] :
( pred_attacker(VAR_V_82)
| ~ pred_attacker(tuple_B_out_1(VAR_V_81,VAR_V_82)) ),
inference(pre_NNF_transformation,[status(thm)],[f73]) ).
fof(f174,plain,
! [VAR_V_82] :
( pred_attacker(VAR_V_82)
| ! [VAR_V_81] : ~ pred_attacker(tuple_B_out_1(VAR_V_81,VAR_V_82)) ),
inference(miniscoping,[status(thm)],[f173]) ).
fof(f175,plain,
! [X0,X1] :
( pred_attacker(X1)
| ~ pred_attacker(tuple_B_out_1(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f174]) ).
fof(f178,plain,
! [VAR_V_98,VAR_V_99] :
( pred_attacker(VAR_V_98)
| ~ pred_attacker(tuple_2(VAR_V_98,VAR_V_99)) ),
inference(pre_NNF_transformation,[status(thm)],[f75]) ).
fof(f179,plain,
! [VAR_V_98] :
( pred_attacker(VAR_V_98)
| ! [VAR_V_99] : ~ pred_attacker(tuple_2(VAR_V_98,VAR_V_99)) ),
inference(miniscoping,[status(thm)],[f178]) ).
fof(f180,plain,
! [X0,X1] :
( pred_attacker(X0)
| ~ pred_attacker(tuple_2(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f179]) ).
fof(f192,plain,
! [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))))
| ~ pred_attacker(tuple_enc_oracle_in_1(VAR_M_150X30)) ),
inference(pre_NNF_transformation,[status(thm)],[f82]) ).
fof(f193,plain,
! [X0] :
( pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_concat(X0,constr_C(X0)),constr_RC4(name_v,name_Kab))))
| ~ pred_attacker(tuple_enc_oracle_in_1(X0)) ),
inference(cnf_transformation,[status(thm)],[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(thm)],[f83]) ).
fof(f195,plain,
~ pred_attacker(name_objective),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f197,plain,
! [X0,X1,X2] : constr_xor(constr_concat(X0,X1),constr_concat(X2,X1)) = constr_concat(constr_xor(X0,X2),constr_ZERO),
inference(paramodulation,[status(thm)],[f134,f132]) ).
fof(f203,plain,
! [X0] : X0 = constr_xor(constr_ZERO,X0),
inference(paramodulation,[status(thm)],[f135,f136]) ).
fof(f217,plain,
! [X0] : constr_C(constr_xor(X0,X0)) = constr_ZERO,
inference(paramodulation,[status(thm)],[f134,f133]) ).
fof(f223,plain,
constr_C(constr_ZERO) = constr_ZERO,
inference(forward_demodulation,[status(thm)],[f134,f217]) ).
fof(f249,plain,
! [X0,X1] : constr_xor(X0,constr_xor(X0,X1)) = constr_xor(constr_ZERO,X1),
inference(paramodulation,[status(thm)],[f134,f137]) ).
fof(f258,plain,
! [X0,X1] : constr_xor(X0,constr_xor(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f203,f249]) ).
fof(f275,plain,
! [X0,X1] : constr_xor(X0,constr_xor(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f136,f258]) ).
fof(f315,plain,
! [X0,X1] :
( pred_attacker(X1)
| ~ pred_attacker(constr_xor(X1,X0))
| ~ pred_attacker(X0) ),
inference(paramodulation,[status(thm)],[f275,f139]) ).
fof(f349,plain,
! [X0,X1] :
( pred_attacker(tuple_2(X0,X1))
| ~ pred_attacker(constr_concat(X0,X1)) ),
inference(paramodulation,[status(thm)],[f131,f142]) ).
fof(f368,plain,
! [X0] :
( pred_attacker(constr_xor(constr_concat(X0,constr_C(X0)),constr_RC4(name_v,name_Kab)))
| ~ pred_attacker(tuple_enc_oracle_in_1(X0)) ),
inference(resolution,[status(thm)],[f193,f151]) ).
fof(f380,definition,
( sQ6_spl
<=> pred_attacker(tuple_enc_oracle_in_1(constr_ZERO)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f382,plain,
( sQ6_spl
| ~ pred_attacker(tuple_enc_oracle_in_1(constr_ZERO)) ),
inference(component_clause,[status(thm)],[f380]) ).
fof(f416,plain,
( sQ6_spl
| ~ pred_attacker(constr_ZERO) ),
inference(resolution,[status(thm)],[f153,f382]) ).
fof(f418,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f416,f158]) ).
fof(f419,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f418]) ).
fof(f425,plain,
pred_attacker(constr_xor(constr_concat(name_objective,constr_C(name_objective)),constr_RC4(name_v,name_Kab))),
inference(resolution,[status(thm)],[f175,f194]) ).
fof(f572,plain,
! [X0] : constr_ZERO = constr_concat(constr_xor(X0,X0),constr_ZERO),
inference(paramodulation,[status(thm)],[f134,f197]) ).
fof(f589,plain,
constr_ZERO = constr_concat(constr_ZERO,constr_ZERO),
inference(forward_demodulation,[status(thm)],[f134,f572]) ).
fof(f4403,plain,
( pred_attacker(constr_xor(constr_concat(constr_ZERO,constr_ZERO),constr_RC4(name_v,name_Kab)))
| ~ pred_attacker(tuple_enc_oracle_in_1(constr_ZERO)) ),
inference(paramodulation,[status(thm)],[f223,f368]) ).
fof(f4407,definition,
( sQ19_spl
<=> pred_attacker(constr_RC4(name_v,name_Kab)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f4409,plain,
( sQ19_spl
| ~ pred_attacker(constr_RC4(name_v,name_Kab)) ),
inference(component_clause,[status(thm)],[f4407]) ).
fof(f4415,definition,
( sQ21_spl
<=> pred_attacker(constr_xor(constr_concat(constr_ZERO,constr_ZERO),constr_RC4(name_v,name_Kab))) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f4416,plain,
( ~ sQ21_spl
| pred_attacker(constr_xor(constr_concat(constr_ZERO,constr_ZERO),constr_RC4(name_v,name_Kab))) ),
inference(component_clause,[status(thm)],[f4415]) ).
fof(f4418,plain,
( sQ21_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f4403,f380,f4415]) ).
fof(f4419,plain,
( ~ sQ21_spl
| pred_attacker(constr_xor(constr_ZERO,constr_RC4(name_v,name_Kab))) ),
inference(forward_demodulation,[status(thm)],[f589,f4416]) ).
fof(f4420,plain,
( ~ sQ21_spl
| pred_attacker(constr_RC4(name_v,name_Kab)) ),
inference(forward_demodulation,[status(thm)],[f203,f4419]) ).
fof(f4434,plain,
( sQ19_spl
| ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4409,f4420]) ).
fof(f4435,plain,
( sQ19_spl
| ~ sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f4434]) ).
fof(f5361,plain,
( pred_attacker(constr_concat(name_objective,constr_C(name_objective)))
| ~ pred_attacker(constr_RC4(name_v,name_Kab)) ),
inference(resolution,[status(thm)],[f425,f315]) ).
fof(f5364,definition,
( sQ24_spl
<=> pred_attacker(constr_concat(name_objective,constr_C(name_objective))) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f5365,plain,
( ~ sQ24_spl
| pred_attacker(constr_concat(name_objective,constr_C(name_objective))) ),
inference(component_clause,[status(thm)],[f5364]) ).
fof(f5368,plain,
( sQ24_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f5361,f4407,f5364]) ).
fof(f5369,plain,
( ~ sQ24_spl
| pred_attacker(tuple_2(name_objective,constr_C(name_objective))) ),
inference(resolution,[status(thm)],[f5365,f349]) ).
fof(f5370,plain,
( ~ sQ24_spl
| pred_attacker(name_objective) ),
inference(resolution,[status(thm)],[f5369,f180]) ).
fof(f5372,plain,
( ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5370,f195]) ).
fof(f5373,plain,
~ sQ24_spl,
inference(contradiction_clause,[status(thm)],[f5372]) ).
fof(f5374,plain,
$false,
inference(sat_refutation,[status(thm)],[f419,f4418,f4435,f5368,f5373]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW957+1 : TPTP v9.3.1. Released v7.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 10:20:25 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 1.03/0.57 % Refutation found
% 1.03/0.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.03/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.03/0.59 % Elapsed time: 0.225587 seconds
% 1.03/0.59 % CPU time: 1.537063 seconds
% 1.03/0.59 % Total memory used: 89.736 MB
% 1.03/0.59 % Net memory used: 88.466 MB
%------------------------------------------------------------------------------