%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW957+1 : TPTP v9.2.1. Released v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n018.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 May 5 05:33:28 PM UTC 2026
% Result : Theorem 1.31s 1.73s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 17
% Syntax : Number of formulae : 65 ( 37 unt; 0 def)
% Number of atoms : 97 ( 25 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 60 ( 28 ~; 24 |; 1 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 88 ( 5 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax49,axiom,
! [X10] : constr_xor(X10,constr_ZERO) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax49) ).
fof(ax50,axiom,
! [X11,X12] : constr_xor(X11,X12) = constr_xor(X12,X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax50) ).
fof(ax51,axiom,
! [X13,X14,X15] : constr_xor(X13,constr_xor(X14,X15)) = constr_xor(constr_xor(X13,X14),X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).
fof(ax48,axiom,
! [X9] : constr_xor(X9,X9) = constr_ZERO,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax48) ).
fof(ax74,axiom,
! [X40,X41] :
( pred_attacker(tuple_2(X40,X41))
=> pred_attacker(X40) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax74) ).
fof(ax45,axiom,
! [X1,X2] : constr_split(constr_concat(X1,X2)) = tuple_2(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).
fof(ax52,axiom,
! [X16,X17] :
( ( pred_attacker(X16)
& pred_attacker(X17) )
=> pred_attacker(constr_xor(X16,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).
fof(ax72,axiom,
! [X36,X37] :
( pred_attacker(tuple_B_out_1(X36,X37))
=> pred_attacker(X37) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).
fof(ax82,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/sandbox2/benchmark/theBenchmark.p',ax82) ).
fof(ax81,axiom,
! [X50] :
( pred_attacker(tuple_enc_oracle_in_1(X50))
=> pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_concat(X50,constr_C(X50)),constr_RC4(name_v,name_Kab)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).
fof(ax47,axiom,
! [X7,X8] : constr_C(constr_xor(X7,X8)) = constr_xor(constr_C(X7),constr_C(X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax47) ).
fof(ax46,axiom,
! [X3,X4,X5,X6] : constr_xor(constr_concat(X3,X5),constr_concat(X4,X6)) = constr_concat(constr_xor(X3,X4),constr_xor(X5,X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).
fof(ax54,axiom,
! [X18] :
( pred_attacker(X18)
=> pred_attacker(constr_split(X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax54) ).
fof(co0,conjecture,
pred_attacker(name_objective),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co0) ).
fof(ax58,axiom,
! [X23,X24] :
( pred_attacker(tuple_enc_oracle_out_2(X23,X24))
=> pred_attacker(X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
fof(ax59,axiom,
! [X25] :
( pred_attacker(X25)
=> pred_attacker(tuple_enc_oracle_in_1(X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax59) ).
fof(ax62,axiom,
pred_attacker(constr_ZERO),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62) ).
fof(c_0_17,plain,
! [X110] : constr_xor(X110,constr_ZERO) = X110,
inference(variable_rename,[status(thm)],[ax49]) ).
fof(c_0_18,plain,
! [X111,X112] : constr_xor(X111,X112) = constr_xor(X112,X111),
inference(variable_rename,[status(thm)],[ax50]) ).
fof(c_0_19,plain,
! [X113,X114,X115] : constr_xor(X113,constr_xor(X114,X115)) = constr_xor(constr_xor(X113,X114),X115),
inference(variable_rename,[status(thm)],[ax51]) ).
fof(c_0_20,plain,
! [X109] : constr_xor(X109,X109) = constr_ZERO,
inference(variable_rename,[status(thm)],[ax48]) ).
cnf(c_0_21,plain,
constr_xor(X1,constr_ZERO) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
constr_xor(X1,X2) = constr_xor(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_23,plain,
! [X140,X141] :
( ~ pred_attacker(tuple_2(X140,X141))
| pred_attacker(X140) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax74])]) ).
fof(c_0_24,plain,
! [X101,X102] : constr_split(constr_concat(X101,X102)) = tuple_2(X101,X102),
inference(variable_rename,[status(thm)],[ax45]) ).
fof(c_0_25,plain,
! [X116,X117] :
( ~ pred_attacker(X116)
| ~ pred_attacker(X117)
| pred_attacker(constr_xor(X116,X117)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax52])]) ).
cnf(c_0_26,plain,
constr_xor(X1,constr_xor(X2,X3)) = constr_xor(constr_xor(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
constr_xor(X1,X1) = constr_ZERO,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
constr_xor(constr_ZERO,X1) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_29,plain,
! [X136,X137] :
( ~ pred_attacker(tuple_B_out_1(X136,X137))
| pred_attacker(X137) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax72])]) ).
cnf(c_0_30,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(split_conjunct,[status(thm)],[ax82]) ).
fof(c_0_31,plain,
! [X150] :
( ~ pred_attacker(tuple_enc_oracle_in_1(X150))
| pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_concat(X150,constr_C(X150)),constr_RC4(name_v,name_Kab)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax81])]) ).
fof(c_0_32,plain,
! [X107,X108] : constr_C(constr_xor(X107,X108)) = constr_xor(constr_C(X107),constr_C(X108)),
inference(variable_rename,[status(thm)],[ax47]) ).
fof(c_0_33,plain,
! [X103,X104,X105,X106] : constr_xor(constr_concat(X103,X105),constr_concat(X104,X106)) = constr_concat(constr_xor(X103,X104),constr_xor(X105,X106)),
inference(variable_rename,[status(thm)],[ax46]) ).
cnf(c_0_34,plain,
( pred_attacker(X1)
| ~ pred_attacker(tuple_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_35,plain,
constr_split(constr_concat(X1,X2)) = tuple_2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_36,plain,
! [X118] :
( ~ pred_attacker(X118)
| pred_attacker(constr_split(X118)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax54])]) ).
cnf(c_0_37,plain,
( pred_attacker(constr_xor(X1,X2))
| ~ pred_attacker(X1)
| ~ pred_attacker(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_38,plain,
constr_xor(X1,constr_xor(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_39,plain,
( pred_attacker(X2)
| ~ pred_attacker(tuple_B_out_1(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_40,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(rw,[status(thm)],[c_0_30,c_0_22]) ).
cnf(c_0_41,plain,
( pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_concat(X1,constr_C(X1)),constr_RC4(name_v,name_Kab))))
| ~ pred_attacker(tuple_enc_oracle_in_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_42,plain,
constr_C(constr_xor(X1,X2)) = constr_xor(constr_C(X1),constr_C(X2)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_43,plain,
constr_xor(constr_concat(X1,X2),constr_concat(X3,X4)) = constr_concat(constr_xor(X1,X3),constr_xor(X2,X4)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_44,plain,
( pred_attacker(X1)
| ~ pred_attacker(constr_split(constr_concat(X1,X2))) ),
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_45,plain,
( pred_attacker(constr_split(X1))
| ~ pred_attacker(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_46,plain,
( pred_attacker(X1)
| ~ pred_attacker(constr_xor(X2,X1))
| ~ pred_attacker(X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_47,plain,
pred_attacker(constr_xor(constr_RC4(name_v,name_Kab),constr_concat(name_objective,constr_C(name_objective)))),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
fof(c_0_48,negated_conjecture,
~ pred_attacker(name_objective),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co0])]) ).
fof(c_0_49,plain,
! [X123,X124] :
( ~ pred_attacker(tuple_enc_oracle_out_2(X123,X124))
| pred_attacker(X124) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax58])]) ).
cnf(c_0_50,plain,
( pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_RC4(name_v,name_Kab),constr_concat(X1,constr_C(X1)))))
| ~ pred_attacker(tuple_enc_oracle_in_1(X1)) ),
inference(rw,[status(thm)],[c_0_41,c_0_22]) ).
cnf(c_0_51,plain,
constr_C(constr_ZERO) = constr_ZERO,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_42]),c_0_27]) ).
cnf(c_0_52,plain,
constr_concat(constr_ZERO,constr_ZERO) = constr_ZERO,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_43]),c_0_27]),c_0_27]) ).
cnf(c_0_53,plain,
( pred_attacker(X1)
| ~ pred_attacker(constr_concat(X1,X2)) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_54,plain,
( pred_attacker(constr_concat(name_objective,constr_C(name_objective)))
| ~ pred_attacker(constr_RC4(name_v,name_Kab)) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_55,negated_conjecture,
~ pred_attacker(name_objective),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_56,plain,
( pred_attacker(X2)
| ~ pred_attacker(tuple_enc_oracle_out_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_57,plain,
( pred_attacker(tuple_enc_oracle_out_2(name_v,constr_RC4(name_v,name_Kab)))
| ~ pred_attacker(tuple_enc_oracle_in_1(constr_ZERO)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_21]) ).
cnf(c_0_58,plain,
~ pred_attacker(constr_RC4(name_v,name_Kab)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
cnf(c_0_59,plain,
( pred_attacker(constr_RC4(name_v,name_Kab))
| ~ pred_attacker(tuple_enc_oracle_in_1(constr_ZERO)) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
fof(c_0_60,plain,
! [X125] :
( ~ pred_attacker(X125)
| pred_attacker(tuple_enc_oracle_in_1(X125)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax59])]) ).
cnf(c_0_61,plain,
~ pred_attacker(tuple_enc_oracle_in_1(constr_ZERO)),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_62,plain,
( pred_attacker(tuple_enc_oracle_in_1(X1))
| ~ pred_attacker(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_63,plain,
pred_attacker(constr_ZERO),
inference(split_conjunct,[status(thm)],[ax62]) ).
cnf(c_0_64,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW957+1 : TPTP v9.2.1. Released v7.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n018.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 07:36:17 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.31/1.73 % Version : CSE_E---1.7
% 1.31/1.73 % Problem : theBenchmark.p
% 1.31/1.73 % SZS status Theorem for theBenchmark.p
% 1.31/1.73 % SZS output start CNFRefutation
% See solution above
% 1.31/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------