%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV233+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n029.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 05:21:08 PM UTC 2026
% Result : Theorem 1.69s 1.83s
% Output : CNFRefutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 14
% Syntax : Number of formulae : 102 ( 41 unt; 0 def)
% Number of atoms : 323 ( 48 equ)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 410 ( 189 ~; 184 |; 30 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 9 con; 0-2 aty)
% Number of variables : 177 ( 41 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(construct_message_2,axiom,
! [X1,X2] :
( knows(concatenate(X1,X2))
=> ( knows(X1)
& knows(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',construct_message_2) ).
fof(protocol,axiom,
! [X7,X8,X9,X10,X11] :
( knows(concatenate(n,concatenate(k_c,sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c)))))
& ( ( knows(X10)
& knows(X11)
& first(extract(X11,k_ca)) = s
& second(extract(decrypt(X10,inverse(k_c)),second(extract(X11,k_ca)))) = n )
=> knows(symmetric_encrypt(secret,first(extract(decrypt(X10,inverse(k_c)),second(extract(X11,k_ca)))))) )
& ( ( knows(X7)
& knows(X8)
& knows(X9)
& second(extract(X9,X8)) = X8 )
=> knows(concatenate(encrypt(sign(concatenate(kgen(X8),concatenate(X7,eol)),inverse(k_s)),X8),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',protocol) ).
fof(second_axiom,axiom,
! [X5] : second(X5) = head(tail(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',second_axiom) ).
fof(first_axiom,axiom,
! [X5] : first(X5) = head(X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',first_axiom) ).
fof(sign_axiom,axiom,
! [X3,X4] : extract(sign(X3,inverse(X4)),X4) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sign_axiom) ).
fof(sign_equation,axiom,
! [X3,X4] :
( ( knows(sign(X3,inverse(X4)))
& knows(X4) )
=> knows(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sign_equation) ).
fof(tail_axiom,axiom,
! [X5,X6] : tail(concatenate(X5,X6)) = X6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tail_axiom) ).
fof(head_axiom,axiom,
! [X5,X6] : head(concatenate(X5,X6)) = X5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',head_axiom) ).
fof(decrypt_axiom,axiom,
! [X3,X4] : decrypt(encrypt(X3,X4),inverse(X4)) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',decrypt_axiom) ).
fof(construct_message_1,axiom,
! [X1,X2] :
( ( knows(X1)
& knows(X2) )
=> ( knows(concatenate(X1,X2))
& knows(encrypt(X1,X2))
& knows(symmetric_encrypt(X1,X2))
& knows(decrypt(X1,X2))
& knows(symmetric_decrypt(X1,X2))
& knows(extract(X1,X2))
& knows(sign(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',construct_message_1) ).
fof(previous_knowledge,axiom,
( knows(k_ca)
& knows(inverse(k_a))
& knows(k_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',previous_knowledge) ).
fof(encrypt_equation,axiom,
! [X1,X2] :
( ( knows(encrypt(X1,X2))
& knows(inverse(X2)) )
=> knows(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',encrypt_equation) ).
fof(symmetric_encrypt_equation,axiom,
! [X1,X2] :
( ( knows(symmetric_encrypt(X1,X2))
& knows(X2) )
=> knows(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_encrypt_equation) ).
fof(attack,conjecture,
knows(secret),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',attack) ).
fof(c_0_14,plain,
! [X52,X53] :
( ( knows(X52)
| ~ knows(concatenate(X52,X53)) )
& ( knows(X53)
| ~ knows(concatenate(X52,X53)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[construct_message_2])])]) ).
fof(c_0_15,plain,
! [X71,X72,X73,X74,X75] :
( knows(concatenate(n,concatenate(k_c,sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c)))))
& ( ~ knows(X74)
| ~ knows(X75)
| first(extract(X75,k_ca)) != s
| second(extract(decrypt(X74,inverse(k_c)),second(extract(X75,k_ca)))) != n
| knows(symmetric_encrypt(secret,first(extract(decrypt(X74,inverse(k_c)),second(extract(X75,k_ca)))))) )
& ( ~ knows(X71)
| ~ knows(X72)
| ~ knows(X73)
| second(extract(X73,X72)) != X72
| knows(concatenate(encrypt(sign(concatenate(kgen(X72),concatenate(X71,eol)),inverse(k_s)),X72),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[protocol])]) ).
fof(c_0_16,plain,
! [X66] : second(X66) = head(tail(X66)),
inference(variable_rename,[status(thm)],[second_axiom]) ).
cnf(c_0_17,plain,
( knows(X1)
| ~ knows(concatenate(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
knows(concatenate(n,concatenate(k_c,sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c))))),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,plain,
! [X65] : first(X65) = head(X65),
inference(variable_rename,[status(thm)],[first_axiom]) ).
cnf(c_0_20,plain,
( knows(concatenate(encrypt(sign(concatenate(kgen(X2),concatenate(X1,eol)),inverse(k_s)),X2),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))))
| ~ knows(X1)
| ~ knows(X2)
| ~ knows(X3)
| second(extract(X3,X2)) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
second(X1) = head(tail(X1)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_22,plain,
! [X59,X60] : extract(sign(X59,inverse(X60)),X60) = X59,
inference(variable_rename,[status(thm)],[sign_axiom]) ).
fof(c_0_23,plain,
! [X48,X49] :
( ~ knows(sign(X48,inverse(X49)))
| ~ knows(X49)
| knows(X48) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sign_equation])]) ).
cnf(c_0_24,plain,
knows(concatenate(k_c,sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c)))),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,plain,
( knows(X1)
| ~ knows(concatenate(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_26,plain,
( knows(symmetric_encrypt(secret,first(extract(decrypt(X1,inverse(k_c)),second(extract(X2,k_ca))))))
| ~ knows(X1)
| ~ knows(X2)
| first(extract(X2,k_ca)) != s
| second(extract(decrypt(X1,inverse(k_c)),second(extract(X2,k_ca)))) != n ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_27,plain,
first(X1) = head(X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
( knows(concatenate(encrypt(sign(concatenate(kgen(X2),concatenate(X1,eol)),inverse(k_s)),X2),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))))
| head(tail(extract(X3,X2))) != X2
| ~ knows(X3)
| ~ knows(X2)
| ~ knows(X1) ),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_29,plain,
extract(sign(X1,inverse(X2)),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_30,plain,
! [X63,X64] : tail(concatenate(X63,X64)) = X64,
inference(variable_rename,[status(thm)],[tail_axiom]) ).
fof(c_0_31,plain,
! [X61,X62] : head(concatenate(X61,X62)) = X61,
inference(variable_rename,[status(thm)],[head_axiom]) ).
cnf(c_0_32,plain,
( knows(X1)
| ~ knows(sign(X1,inverse(X2)))
| ~ knows(X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,plain,
knows(sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c))),
inference(spm,[status(thm)],[c_0_17,c_0_24]) ).
cnf(c_0_34,plain,
knows(k_c),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_35,plain,
( knows(symmetric_encrypt(secret,head(extract(decrypt(X1,inverse(k_c)),head(tail(extract(X2,k_ca)))))))
| head(extract(X2,k_ca)) != s
| head(tail(extract(decrypt(X1,inverse(k_c)),head(tail(extract(X2,k_ca)))))) != n
| ~ knows(X2)
| ~ knows(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_27]),c_0_21]),c_0_21]),c_0_21]) ).
cnf(c_0_36,plain,
( knows(concatenate(encrypt(sign(concatenate(kgen(X1),concatenate(X2,eol)),inverse(k_s)),X1),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))))
| head(tail(X3)) != X1
| ~ knows(sign(X3,inverse(X1)))
| ~ knows(X1)
| ~ knows(X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_37,plain,
tail(concatenate(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_38,plain,
head(concatenate(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_39,plain,
knows(concatenate(c,concatenate(k_c,eol))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
cnf(c_0_40,plain,
( knows(symmetric_encrypt(secret,head(extract(decrypt(X1,inverse(k_c)),head(tail(X2))))))
| head(tail(extract(decrypt(X1,inverse(k_c)),head(tail(X2))))) != n
| head(X2) != s
| ~ knows(sign(X2,inverse(k_ca)))
| ~ knows(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_29]) ).
fof(c_0_41,plain,
! [X55,X56] : decrypt(encrypt(X55,X56),inverse(X56)) = X55,
inference(variable_rename,[status(thm)],[decrypt_axiom]) ).
cnf(c_0_42,plain,
( knows(concatenate(encrypt(sign(concatenate(kgen(k_c),concatenate(X1,eol)),inverse(k_s)),k_c),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))))
| ~ knows(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_33]),c_0_37]),c_0_38]),c_0_34])]) ).
cnf(c_0_43,plain,
knows(concatenate(k_c,eol)),
inference(spm,[status(thm)],[c_0_17,c_0_39]) ).
fof(c_0_44,plain,
! [X50,X51] :
( ( knows(concatenate(X50,X51))
| ~ knows(X50)
| ~ knows(X51) )
& ( knows(encrypt(X50,X51))
| ~ knows(X50)
| ~ knows(X51) )
& ( knows(symmetric_encrypt(X50,X51))
| ~ knows(X50)
| ~ knows(X51) )
& ( knows(decrypt(X50,X51))
| ~ knows(X50)
| ~ knows(X51) )
& ( knows(symmetric_decrypt(X50,X51))
| ~ knows(X50)
| ~ knows(X51) )
& ( knows(extract(X50,X51))
| ~ knows(X50)
| ~ knows(X51) )
& ( knows(sign(X50,X51))
| ~ knows(X50)
| ~ knows(X51) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[construct_message_1])])]) ).
cnf(c_0_45,plain,
( knows(symmetric_encrypt(secret,head(extract(decrypt(X1,inverse(k_c)),head(X2)))))
| head(tail(extract(decrypt(X1,inverse(k_c)),head(X2)))) != n
| X3 != s
| ~ knows(sign(concatenate(X3,X2),inverse(k_ca)))
| ~ knows(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_37]),c_0_38]) ).
cnf(c_0_46,plain,
decrypt(encrypt(X1,X2),inverse(X2)) = X1,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_47,plain,
( knows(sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca)))
| ~ knows(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_42]) ).
cnf(c_0_48,plain,
knows(eol),
inference(spm,[status(thm)],[c_0_17,c_0_43]) ).
cnf(c_0_49,plain,
( knows(sign(X1,X2))
| ~ knows(X1)
| ~ knows(X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_50,plain,
( knows(symmetric_encrypt(secret,head(extract(X1,head(X2)))))
| head(tail(extract(X1,head(X2)))) != n
| X3 != s
| ~ knows(sign(concatenate(X3,X2),inverse(k_ca)))
| ~ knows(encrypt(X1,k_c)) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,plain,
knows(sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,plain,
( knows(concatenate(encrypt(sign(concatenate(kgen(X1),concatenate(X2,eol)),inverse(k_s)),X1),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))))
| head(tail(X3)) != X1
| ~ knows(inverse(X1))
| ~ knows(X1)
| ~ knows(X2)
| ~ knows(X3) ),
inference(spm,[status(thm)],[c_0_36,c_0_49]) ).
cnf(c_0_53,plain,
knows(k_ca),
inference(split_conjunct,[status(thm)],[previous_knowledge]) ).
cnf(c_0_54,plain,
( knows(symmetric_encrypt(secret,head(extract(X1,k_s))))
| head(tail(extract(X1,k_s))) != n
| ~ knows(encrypt(X1,k_c)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_38]),c_0_38]) ).
fof(c_0_55,plain,
! [X44,X45] :
( ~ knows(encrypt(X44,X45))
| ~ knows(inverse(X45))
| knows(X44) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[encrypt_equation])]) ).
cnf(c_0_56,plain,
( knows(concatenate(encrypt(sign(concatenate(kgen(head(tail(X1))),concatenate(X2,eol)),inverse(k_s)),head(tail(X1))),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))))
| ~ knows(inverse(head(tail(X1))))
| ~ knows(head(tail(X1)))
| ~ knows(X2)
| ~ knows(X1) ),
inference(er,[status(thm)],[c_0_52]) ).
cnf(c_0_57,plain,
knows(concatenate(s,concatenate(k_s,eol))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_51]),c_0_53])]) ).
cnf(c_0_58,plain,
( knows(symmetric_encrypt(secret,head(X1)))
| head(tail(X1)) != n
| ~ knows(encrypt(sign(X1,inverse(k_s)),k_c)) ),
inference(spm,[status(thm)],[c_0_54,c_0_29]) ).
cnf(c_0_59,plain,
( knows(encrypt(X1,X2))
| ~ knows(X1)
| ~ knows(X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_60,plain,
( knows(X1)
| ~ knows(encrypt(X1,X2))
| ~ knows(inverse(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_61,plain,
( knows(encrypt(sign(concatenate(kgen(head(tail(X1))),concatenate(X2,eol)),inverse(k_s)),head(tail(X1))))
| ~ knows(inverse(head(tail(X1))))
| ~ knows(head(tail(X1)))
| ~ knows(X2)
| ~ knows(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_56]) ).
cnf(c_0_62,plain,
knows(concatenate(k_s,eol)),
inference(spm,[status(thm)],[c_0_17,c_0_57]) ).
cnf(c_0_63,plain,
( knows(symmetric_encrypt(secret,head(X1)))
| head(tail(X1)) != n
| ~ knows(sign(X1,inverse(k_s))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_34])]) ).
cnf(c_0_64,plain,
( knows(sign(concatenate(kgen(head(tail(X1))),concatenate(X2,eol)),inverse(k_s)))
| ~ knows(inverse(head(tail(X1))))
| ~ knows(head(tail(X1)))
| ~ knows(X2)
| ~ knows(X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_65,plain,
knows(k_s),
inference(spm,[status(thm)],[c_0_25,c_0_62]) ).
cnf(c_0_66,plain,
( knows(symmetric_encrypt(secret,X1))
| head(X2) != n
| ~ knows(sign(concatenate(X1,X2),inverse(k_s))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_38]),c_0_37]) ).
cnf(c_0_67,plain,
( knows(concatenate(kgen(head(tail(X1))),concatenate(X2,eol)))
| ~ knows(inverse(head(tail(X1))))
| ~ knows(head(tail(X1)))
| ~ knows(X2)
| ~ knows(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_64]),c_0_65])]) ).
cnf(c_0_68,plain,
( knows(symmetric_encrypt(secret,kgen(head(tail(X1)))))
| X2 != n
| ~ knows(inverse(head(tail(X1))))
| ~ knows(head(tail(X1)))
| ~ knows(X2)
| ~ knows(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_64]),c_0_38]) ).
cnf(c_0_69,plain,
( knows(concatenate(X1,eol))
| ~ knows(inverse(head(tail(X2))))
| ~ knows(head(tail(X2)))
| ~ knows(X1)
| ~ knows(X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_67]) ).
cnf(c_0_70,plain,
( knows(symmetric_encrypt(secret,kgen(head(X1))))
| X2 != n
| ~ knows(inverse(head(X1)))
| ~ knows(concatenate(X3,X1))
| ~ knows(head(X1))
| ~ knows(X2) ),
inference(spm,[status(thm)],[c_0_68,c_0_37]) ).
cnf(c_0_71,plain,
( knows(concatenate(X1,eol))
| ~ knows(inverse(head(X2)))
| ~ knows(concatenate(X3,X2))
| ~ knows(head(X2))
| ~ knows(X1) ),
inference(spm,[status(thm)],[c_0_69,c_0_37]) ).
cnf(c_0_72,plain,
( knows(symmetric_encrypt(secret,kgen(X1)))
| X2 != n
| ~ knows(concatenate(X3,concatenate(X1,X4)))
| ~ knows(inverse(X1))
| ~ knows(X1)
| ~ knows(X2) ),
inference(spm,[status(thm)],[c_0_70,c_0_38]) ).
cnf(c_0_73,plain,
( knows(concatenate(X1,X2))
| ~ knows(X1)
| ~ knows(X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_74,plain,
( knows(concatenate(X1,eol))
| ~ knows(concatenate(X2,concatenate(X3,X4)))
| ~ knows(inverse(X3))
| ~ knows(X3)
| ~ knows(X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_38]) ).
cnf(c_0_75,plain,
( knows(symmetric_encrypt(secret,kgen(X1)))
| X2 != n
| ~ knows(concatenate(X1,X3))
| ~ knows(inverse(X1))
| ~ knows(X2)
| ~ knows(X4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_25]) ).
cnf(c_0_76,plain,
( knows(concatenate(X1,eol))
| ~ knows(concatenate(X2,X3))
| ~ knows(inverse(X2))
| ~ knows(X1)
| ~ knows(X4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_73]),c_0_25]) ).
cnf(c_0_77,plain,
( knows(symmetric_encrypt(secret,kgen(X1)))
| X2 != n
| ~ knows(inverse(X1))
| ~ knows(X2)
| ~ knows(X3)
| ~ knows(X4)
| ~ knows(X1) ),
inference(spm,[status(thm)],[c_0_75,c_0_73]) ).
cnf(c_0_78,plain,
knows(inverse(k_a)),
inference(split_conjunct,[status(thm)],[previous_knowledge]) ).
cnf(c_0_79,plain,
knows(k_a),
inference(split_conjunct,[status(thm)],[previous_knowledge]) ).
cnf(c_0_80,plain,
( knows(concatenate(X1,eol))
| ~ knows(inverse(X2))
| ~ knows(X1)
| ~ knows(X3)
| ~ knows(X4)
| ~ knows(X2) ),
inference(spm,[status(thm)],[c_0_76,c_0_73]) ).
cnf(c_0_81,plain,
( knows(symmetric_encrypt(secret,kgen(k_a)))
| X1 != n
| ~ knows(X1)
| ~ knows(X2)
| ~ knows(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79])]) ).
cnf(c_0_82,plain,
knows(n),
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_83,plain,
( knows(kgen(head(tail(X1))))
| ~ knows(inverse(head(tail(X1))))
| ~ knows(head(tail(X1)))
| ~ knows(X2)
| ~ knows(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_67]) ).
cnf(c_0_84,plain,
( knows(concatenate(X1,eol))
| ~ knows(X1)
| ~ knows(X2)
| ~ knows(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_78]),c_0_79])]) ).
cnf(c_0_85,plain,
( knows(symmetric_encrypt(secret,kgen(k_a)))
| ~ knows(X1)
| ~ knows(X2) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_86,plain,
( knows(kgen(head(X1)))
| ~ knows(inverse(head(X1)))
| ~ knows(concatenate(X2,X1))
| ~ knows(head(X1))
| ~ knows(X3) ),
inference(spm,[status(thm)],[c_0_83,c_0_37]) ).
cnf(c_0_87,plain,
( knows(concatenate(k_a,eol))
| ~ knows(X1)
| ~ knows(X2) ),
inference(spm,[status(thm)],[c_0_84,c_0_79]) ).
fof(c_0_88,plain,
! [X46,X47] :
( ~ knows(symmetric_encrypt(X46,X47))
| ~ knows(X47)
| knows(X46) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetric_encrypt_equation])]) ).
cnf(c_0_89,plain,
( knows(symmetric_encrypt(secret,kgen(k_a)))
| ~ knows(X1) ),
inference(spm,[status(thm)],[c_0_85,c_0_65]) ).
fof(c_0_90,negated_conjecture,
~ knows(secret),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[attack])]) ).
cnf(c_0_91,plain,
( knows(kgen(X1))
| ~ knows(concatenate(X2,concatenate(X1,X3)))
| ~ knows(inverse(X1))
| ~ knows(X1)
| ~ knows(X4) ),
inference(spm,[status(thm)],[c_0_86,c_0_38]) ).
cnf(c_0_92,plain,
( knows(concatenate(k_a,eol))
| ~ knows(X1) ),
inference(spm,[status(thm)],[c_0_87,c_0_65]) ).
cnf(c_0_93,plain,
( knows(X1)
| ~ knows(symmetric_encrypt(X1,X2))
| ~ knows(X2) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_94,plain,
knows(symmetric_encrypt(secret,kgen(k_a))),
inference(spm,[status(thm)],[c_0_89,c_0_65]) ).
cnf(c_0_95,negated_conjecture,
~ knows(secret),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_96,plain,
( knows(kgen(X1))
| ~ knows(concatenate(X1,X2))
| ~ knows(inverse(X1))
| ~ knows(X3)
| ~ knows(X4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_73]),c_0_25]) ).
cnf(c_0_97,plain,
knows(concatenate(k_a,eol)),
inference(spm,[status(thm)],[c_0_92,c_0_65]) ).
cnf(c_0_98,plain,
~ knows(kgen(k_a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95]) ).
cnf(c_0_99,plain,
( ~ knows(X1)
| ~ knows(X2) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_78])]),c_0_98]) ).
cnf(c_0_100,plain,
~ knows(X1),
inference(spm,[status(thm)],[c_0_99,c_0_65]) ).
cnf(c_0_101,plain,
$false,
inference(sr,[status(thm)],[c_0_53,c_0_100]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWV233+1 : TPTP v9.2.1. Released v3.2.0.
% 0.12/0.12 % 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
% 0.16/0.33 % Computer : n029.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 04:58:44 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.69/1.83 % Version : CSE_E---1.7
% 1.69/1.83 % Problem : theBenchmark.p
% 1.69/1.83 % SZS status Theorem for theBenchmark.p
% 1.69/1.83 % SZS output start CNFRefutation
% See solution above
% 1.69/1.83 % Total time : 1.366s
%------------------------------------------------------------------------------