%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV233+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 : Tue Sep 29 01:08:26 PM UTC 2026
% Result : Theorem 4.65s 1.61s
% Output : Refutation 5.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 23
% Syntax : Number of formulae : 148 ( 38 unt; 9 def)
% Number of atoms : 425 ( 61 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 529 ( 252 ~; 223 |; 38 &)
% ( 9 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 9 con; 0-2 aty)
% Number of variables : 161 ( 0 sgn 161 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ( knows(encrypt(X0,X1))
& knows(inverse(X1)) )
=> knows(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',encrypt_equation) ).
fof(f2,axiom,
! [X0,X1] :
( ( knows(symmetric_encrypt(X0,X1))
& knows(X1) )
=> knows(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_encrypt_equation) ).
fof(f3,axiom,
! [X0,X1] :
( ( knows(sign(X0,inverse(X1)))
& knows(X1) )
=> knows(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sign_equation) ).
fof(f4,axiom,
! [X0,X1] :
( ( knows(X0)
& knows(X1) )
=> ( knows(concatenate(X0,X1))
& knows(encrypt(X0,X1))
& knows(symmetric_encrypt(X0,X1))
& knows(decrypt(X0,X1))
& knows(symmetric_decrypt(X0,X1))
& knows(extract(X0,X1))
& knows(sign(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',construct_message_1) ).
fof(f5,axiom,
! [X0,X1] :
( knows(concatenate(X0,X1))
=> ( knows(X0)
& knows(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',construct_message_2) ).
fof(f7,axiom,
! [X0,X1] : decrypt(encrypt(X0,X1),inverse(X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',decrypt_axiom) ).
fof(f9,axiom,
! [X0,X1] : extract(sign(X0,inverse(X1)),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sign_axiom) ).
fof(f10,axiom,
! [X0,X1] : head(concatenate(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',head_axiom) ).
fof(f11,axiom,
! [X0,X1] : tail(concatenate(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tail_axiom) ).
fof(f12,axiom,
! [X0] : first(X0) = head(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',first_axiom) ).
fof(f13,axiom,
! [X0] : second(X0) = head(tail(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',second_axiom) ).
fof(f17,axiom,
( knows(k_ca)
& knows(inverse(k_a))
& knows(k_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',previous_knowledge) ).
fof(f18,axiom,
! [X0,X1,X2,X3,X4] :
( knows(concatenate(n,concatenate(k_c,sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c)))))
& ( ( knows(X3)
& knows(X4)
& first(extract(X4,k_ca)) = s
& second(extract(decrypt(X3,inverse(k_c)),second(extract(X4,k_ca)))) = n )
=> knows(symmetric_encrypt(secret,first(extract(decrypt(X3,inverse(k_c)),second(extract(X4,k_ca)))))) )
& ( ( knows(X0)
& knows(X1)
& knows(X2)
& second(extract(X2,X1)) = X1 )
=> knows(concatenate(encrypt(sign(concatenate(kgen(X1),concatenate(X0,eol)),inverse(k_s)),X1),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',protocol) ).
fof(f19,conjecture,
knows(secret),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',attack) ).
fof(f20,negated_conjecture,
~ knows(secret),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
~ knows(secret),
inference(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( knows(X0)
| ~ knows(encrypt(X0,X1))
| ~ knows(inverse(X1)) ),
inference(ennf_transformation,[],[f1]) ).
fof(f23,plain,
! [X0,X1] :
( knows(X0)
| ~ knows(encrypt(X0,X1))
| ~ knows(inverse(X1)) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( knows(X0)
| ~ knows(symmetric_encrypt(X0,X1))
| ~ knows(X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f25,plain,
! [X0,X1] :
( knows(X0)
| ~ knows(symmetric_encrypt(X0,X1))
| ~ knows(X1) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( knows(X0)
| ~ knows(sign(X0,inverse(X1)))
| ~ knows(X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f27,plain,
! [X0,X1] :
( knows(X0)
| ~ knows(sign(X0,inverse(X1)))
| ~ knows(X1) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ( knows(concatenate(X0,X1))
& knows(encrypt(X0,X1))
& knows(symmetric_encrypt(X0,X1))
& knows(decrypt(X0,X1))
& knows(symmetric_decrypt(X0,X1))
& knows(extract(X0,X1))
& knows(sign(X0,X1)) )
| ~ knows(X0)
| ~ knows(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f29,plain,
! [X0,X1] :
( ( knows(concatenate(X0,X1))
& knows(encrypt(X0,X1))
& knows(symmetric_encrypt(X0,X1))
& knows(decrypt(X0,X1))
& knows(symmetric_decrypt(X0,X1))
& knows(extract(X0,X1))
& knows(sign(X0,X1)) )
| ~ knows(X0)
| ~ knows(X1) ),
inference(flattening,[],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( ( knows(X0)
& knows(X1) )
| ~ knows(concatenate(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f34,plain,
! [X0,X1,X2,X3,X4] :
( knows(concatenate(n,concatenate(k_c,sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c)))))
& ( knows(symmetric_encrypt(secret,first(extract(decrypt(X3,inverse(k_c)),second(extract(X4,k_ca))))))
| ~ knows(X3)
| ~ knows(X4)
| first(extract(X4,k_ca)) != s
| n != second(extract(decrypt(X3,inverse(k_c)),second(extract(X4,k_ca)))) )
& ( knows(concatenate(encrypt(sign(concatenate(kgen(X1),concatenate(X0,eol)),inverse(k_s)),X1),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))))
| ~ knows(X0)
| ~ knows(X1)
| ~ knows(X2)
| second(extract(X2,X1)) != X1 ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f35,plain,
! [X0,X1,X2,X3,X4] :
( knows(concatenate(n,concatenate(k_c,sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c)))))
& ( knows(symmetric_encrypt(secret,first(extract(decrypt(X3,inverse(k_c)),second(extract(X4,k_ca))))))
| ~ knows(X3)
| ~ knows(X4)
| first(extract(X4,k_ca)) != s
| n != second(extract(decrypt(X3,inverse(k_c)),second(extract(X4,k_ca)))) )
& ( knows(concatenate(encrypt(sign(concatenate(kgen(X1),concatenate(X0,eol)),inverse(k_s)),X1),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))))
| ~ knows(X0)
| ~ knows(X1)
| ~ knows(X2)
| second(extract(X2,X1)) != X1 ) ),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ~ knows(inverse(X1))
| ~ knows(encrypt(X0,X1))
| knows(X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f37,plain,
! [X0,X1] :
( ~ knows(symmetric_encrypt(X0,X1))
| knows(X0)
| ~ knows(X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f38,plain,
! [X0,X1] :
( ~ knows(sign(X0,inverse(X1)))
| knows(X0)
| ~ knows(X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f39,plain,
! [X0,X1] :
( knows(sign(X0,X1))
| ~ knows(X0)
| ~ knows(X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f44,plain,
! [X0,X1] :
( knows(encrypt(X0,X1))
| ~ knows(X0)
| ~ knows(X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f45,plain,
! [X0,X1] :
( knows(concatenate(X0,X1))
| ~ knows(X0)
| ~ knows(X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f46,plain,
! [X0,X1] :
( ~ knows(concatenate(X0,X1))
| knows(X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f47,plain,
! [X0,X1] :
( ~ knows(concatenate(X0,X1))
| knows(X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f51,plain,
! [X0,X1] : decrypt(encrypt(X0,X1),inverse(X1)) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f53,plain,
! [X0,X1] : extract(sign(X0,inverse(X1)),X1) = X0,
inference(cnf_transformation,[],[f9]) ).
fof(f54,plain,
! [X0,X1] : head(concatenate(X0,X1)) = X0,
inference(cnf_transformation,[],[f10]) ).
fof(f55,plain,
! [X0,X1] : tail(concatenate(X0,X1)) = X1,
inference(cnf_transformation,[],[f11]) ).
fof(f56,plain,
! [X0] : head(X0) = first(X0),
inference(cnf_transformation,[],[f12]) ).
fof(f57,plain,
! [X0] : second(X0) = head(tail(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f61,plain,
knows(k_a),
inference(cnf_transformation,[],[f17]) ).
fof(f62,plain,
knows(inverse(k_a)),
inference(cnf_transformation,[],[f17]) ).
fof(f63,plain,
knows(k_ca),
inference(cnf_transformation,[],[f17]) ).
fof(f64,plain,
! [X2,X0,X1] :
( second(extract(X2,X1)) != X1
| ~ knows(X0)
| ~ knows(X1)
| ~ knows(X2)
| knows(concatenate(encrypt(sign(concatenate(kgen(X1),concatenate(X0,eol)),inverse(k_s)),X1),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca)))) ),
inference(cnf_transformation,[],[f35]) ).
fof(f65,plain,
! [X3,X4] :
( knows(symmetric_encrypt(secret,first(extract(decrypt(X3,inverse(k_c)),second(extract(X4,k_ca))))))
| ~ knows(X3)
| ~ knows(X4)
| first(extract(X4,k_ca)) != s
| n != second(extract(decrypt(X3,inverse(k_c)),second(extract(X4,k_ca)))) ),
inference(cnf_transformation,[],[f35]) ).
fof(f66,plain,
knows(concatenate(n,concatenate(k_c,sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c))))),
inference(cnf_transformation,[],[f35]) ).
fof(f67,plain,
~ knows(secret),
inference(cnf_transformation,[],[f21]) ).
fof(f70,plain,
! [X0,X1] : head(X0) = second(concatenate(X1,X0)),
inference(superposition,[],[f57,f55]) ).
fof(f79,plain,
! [X0] :
( ~ knows(encrypt(X0,k_a))
| knows(X0) ),
inference(resolution,[],[f36,f62]) ).
fof(f83,plain,
knows(n),
inference(resolution,[],[f66,f47]) ).
fof(f84,plain,
knows(concatenate(k_c,sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c)))),
inference(resolution,[],[f66,f46]) ).
fof(f85,plain,
! [X2,X0,X1] :
( knows(concatenate(encrypt(sign(concatenate(kgen(X1),concatenate(X2,eol)),inverse(k_s)),X1),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))))
| ~ knows(X2)
| ~ knows(X1)
| ~ knows(sign(X0,inverse(X1)))
| second(X0) != X1 ),
inference(superposition,[],[f64,f53]) ).
fof(f87,plain,
! [X3,X4] :
( knows(symmetric_encrypt(secret,head(extract(decrypt(X3,inverse(k_c)),second(extract(X4,k_ca))))))
| ~ knows(X3)
| ~ knows(X4)
| first(extract(X4,k_ca)) != s
| n != second(extract(decrypt(X3,inverse(k_c)),second(extract(X4,k_ca)))) ),
inference(forward_demodulation,[],[f65,f56]) ).
fof(f88,plain,
! [X3,X4] :
( s != head(extract(X4,k_ca))
| knows(symmetric_encrypt(secret,head(extract(decrypt(X3,inverse(k_c)),second(extract(X4,k_ca))))))
| ~ knows(X3)
| ~ knows(X4)
| n != second(extract(decrypt(X3,inverse(k_c)),second(extract(X4,k_ca)))) ),
inference(forward_demodulation,[],[f87,f56]) ).
fof(f89,plain,
knows(k_c),
inference(resolution,[],[f84,f47]) ).
fof(f90,plain,
knows(sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c))),
inference(resolution,[],[f84,f46]) ).
fof(f91,plain,
! [X0,X1] :
( ~ knows(sign(X0,inverse(k_ca)))
| knows(symmetric_encrypt(secret,head(extract(decrypt(X1,inverse(k_c)),second(X0)))))
| ~ knows(X1)
| head(X0) != s
| n != second(extract(decrypt(X1,inverse(k_c)),second(X0))) ),
inference(superposition,[],[f88,f53]) ).
fof(f106,plain,
! [X2,X0,X1] :
( knows(encrypt(sign(concatenate(kgen(X1),concatenate(X0,eol)),inverse(k_s)),X1))
| ~ knows(X1)
| ~ knows(sign(X2,inverse(X1)))
| second(X2) != X1
| ~ knows(X0) ),
inference(resolution,[],[f85,f47]) ).
fof(f107,plain,
! [X2,X0,X1] :
( ~ knows(X0)
| ~ knows(X1)
| ~ knows(sign(X2,inverse(X1)))
| second(X2) != X1
| knows(sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))) ),
inference(resolution,[],[f85,f46]) ).
fof(f109,definition,
( spl0_3
<=> knows(sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f111,plain,
( knows(sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca)))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f113,definition,
( spl0_4
<=> ! [X2,X1] :
( ~ knows(X1)
| second(X2) != X1
| ~ knows(sign(X2,inverse(X1))) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f114,plain,
( ! [X2,X1] :
( ~ knows(sign(X2,inverse(X1)))
| second(X2) != X1
| ~ knows(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f116,definition,
( spl0_5
<=> ! [X0] : ~ knows(X0) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f117,plain,
( ! [X0] : ~ knows(X0)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f118,plain,
( spl0_3
| spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f107,f116,f113,f109]) ).
fof(f120,plain,
( knows(concatenate(s,concatenate(k_s,eol)))
| ~ knows(k_ca)
| ~ spl0_3 ),
inference(resolution,[],[f111,f38]) ).
fof(f121,plain,
( knows(concatenate(s,concatenate(k_s,eol)))
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f120,f63]) ).
fof(f129,plain,
! [X0,X1] :
( ~ knows(k_a)
| ~ knows(sign(X0,inverse(k_a)))
| second(X0) != k_a
| ~ knows(X1)
| knows(sign(concatenate(kgen(k_a),concatenate(X1,eol)),inverse(k_s))) ),
inference(resolution,[],[f106,f79]) ).
fof(f130,plain,
! [X0,X1] :
( ~ knows(sign(X0,inverse(k_a)))
| second(X0) != k_a
| ~ knows(X1)
| knows(sign(concatenate(kgen(k_a),concatenate(X1,eol)),inverse(k_s))) ),
inference(forward_subsumption_resolution,[],[f129,f61]) ).
fof(f132,definition,
( spl0_6
<=> ! [X1] :
( ~ knows(X1)
| knows(sign(concatenate(kgen(k_a),concatenate(X1,eol)),inverse(k_s))) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f133,plain,
( ! [X1] :
( knows(sign(concatenate(kgen(k_a),concatenate(X1,eol)),inverse(k_s)))
| ~ knows(X1) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f135,definition,
( spl0_7
<=> ! [X0] :
( ~ knows(sign(X0,inverse(k_a)))
| second(X0) != k_a ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f136,plain,
( ! [X0] :
( ~ knows(sign(X0,inverse(k_a)))
| second(X0) != k_a )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f137,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f130,f135,f132]) ).
fof(f141,plain,
( knows(concatenate(k_s,eol))
| ~ spl0_3 ),
inference(resolution,[],[f121,f46]) ).
fof(f144,definition,
( spl0_8
<=> knows(k_s) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f145,plain,
( knows(k_s)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f148,definition,
( spl0_9
<=> ! [X0] :
( ~ knows(X0)
| knows(concatenate(kgen(k_a),concatenate(X0,eol))) ) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f149,plain,
( ! [X0] :
( knows(concatenate(kgen(k_a),concatenate(X0,eol)))
| ~ knows(X0) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f153,plain,
( knows(k_s)
| ~ spl0_3 ),
inference(resolution,[],[f141,f47]) ).
fof(f157,plain,
( spl0_8
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f153,f109,f144]) ).
fof(f158,plain,
( ! [X0] :
( second(X0) != k_a
| ~ knows(X0)
| ~ knows(inverse(k_a)) )
| ~ spl0_7 ),
inference(resolution,[],[f136,f39]) ).
fof(f159,plain,
( ! [X0] :
( second(X0) != k_a
| ~ knows(X0) )
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f158,f62]) ).
fof(f160,plain,
( ! [X0,X1] :
( head(X0) != k_a
| ~ knows(concatenate(X1,X0)) )
| ~ spl0_7 ),
inference(superposition,[],[f159,f70]) ).
fof(f161,plain,
( ! [X2,X0,X1] :
( k_a != X0
| ~ knows(concatenate(X2,concatenate(X0,X1))) )
| ~ spl0_7 ),
inference(superposition,[],[f160,f54]) ).
fof(f164,plain,
( ! [X0,X1] : ~ knows(concatenate(X0,concatenate(k_a,X1)))
| ~ spl0_7 ),
inference(equality_resolution,[],[f161]) ).
fof(f178,plain,
( ! [X0,X1] :
( ~ knows(X0)
| ~ knows(concatenate(k_a,X1)) )
| ~ spl0_7 ),
inference(resolution,[],[f164,f45]) ).
fof(f180,definition,
( spl0_12
<=> ! [X1] : ~ knows(concatenate(k_a,X1)) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f181,plain,
( ! [X1] : ~ knows(concatenate(k_a,X1))
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f185,plain,
( $false
| ~ spl0_5 ),
inference(resolution,[],[f117,f62]) ).
fof(f230,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[],[f185]) ).
fof(f234,plain,
( k_c != second(concatenate(c,concatenate(k_c,eol)))
| ~ knows(k_c)
| ~ spl0_4 ),
inference(resolution,[],[f114,f90]) ).
fof(f235,plain,
( k_c != second(concatenate(c,concatenate(k_c,eol)))
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f234,f89]) ).
fof(f236,plain,
( k_c != head(concatenate(k_c,eol))
| ~ spl0_4 ),
inference(forward_demodulation,[],[f235,f70]) ).
fof(f237,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f236,f54]) ).
fof(f238,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f237]) ).
fof(f240,plain,
( ! [X0] :
( knows(symmetric_encrypt(secret,head(extract(decrypt(X0,inverse(k_c)),second(concatenate(s,concatenate(k_s,eol)))))))
| ~ knows(X0)
| s != head(concatenate(s,concatenate(k_s,eol)))
| n != second(extract(decrypt(X0,inverse(k_c)),second(concatenate(s,concatenate(k_s,eol))))) )
| ~ spl0_3 ),
inference(resolution,[],[f111,f91]) ).
fof(f243,plain,
( ! [X0] :
( knows(symmetric_encrypt(secret,head(extract(decrypt(X0,inverse(k_c)),second(concatenate(s,concatenate(k_s,eol)))))))
| ~ knows(X0)
| n != second(extract(decrypt(X0,inverse(k_c)),second(concatenate(s,concatenate(k_s,eol))))) )
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f240,f54]) ).
fof(f245,plain,
( ! [X0] :
( knows(symmetric_encrypt(secret,head(extract(decrypt(X0,inverse(k_c)),head(concatenate(k_s,eol))))))
| ~ knows(X0)
| n != second(extract(decrypt(X0,inverse(k_c)),second(concatenate(s,concatenate(k_s,eol))))) )
| ~ spl0_3 ),
inference(forward_demodulation,[],[f243,f70]) ).
fof(f247,plain,
( ! [X0] :
( knows(symmetric_encrypt(secret,head(extract(decrypt(X0,inverse(k_c)),k_s))))
| ~ knows(X0)
| n != second(extract(decrypt(X0,inverse(k_c)),second(concatenate(s,concatenate(k_s,eol))))) )
| ~ spl0_3 ),
inference(forward_demodulation,[],[f245,f54]) ).
fof(f249,plain,
( ! [X0] :
( n != second(extract(decrypt(X0,inverse(k_c)),head(concatenate(k_s,eol))))
| knows(symmetric_encrypt(secret,head(extract(decrypt(X0,inverse(k_c)),k_s))))
| ~ knows(X0) )
| ~ spl0_3 ),
inference(forward_demodulation,[],[f247,f70]) ).
fof(f250,plain,
( ! [X0] :
( n != second(extract(decrypt(X0,inverse(k_c)),k_s))
| knows(symmetric_encrypt(secret,head(extract(decrypt(X0,inverse(k_c)),k_s))))
| ~ knows(X0) )
| ~ spl0_3 ),
inference(forward_demodulation,[],[f249,f54]) ).
fof(f255,plain,
( ! [X0] :
( ~ knows(X0)
| knows(concatenate(kgen(k_a),concatenate(X0,eol)))
| ~ knows(k_s) )
| ~ spl0_6 ),
inference(resolution,[],[f133,f38]) ).
fof(f256,plain,
( ! [X0] :
( ~ knows(X0)
| knows(concatenate(kgen(k_a),concatenate(X0,eol))) )
| ~ spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f255,f145]) ).
fof(f257,plain,
( spl0_9
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f256,f144,f132,f148]) ).
fof(f258,plain,
( ! [X0] :
( n != second(extract(X0,k_s))
| knows(symmetric_encrypt(secret,head(extract(X0,k_s))))
| ~ knows(encrypt(X0,k_c)) )
| ~ spl0_3 ),
inference(superposition,[],[f250,f51]) ).
fof(f259,plain,
( ! [X0] :
( ~ knows(X0)
| knows(kgen(k_a)) )
| ~ spl0_9 ),
inference(resolution,[],[f149,f47]) ).
fof(f262,definition,
( spl0_13
<=> knows(kgen(k_a)) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f264,plain,
( knows(kgen(k_a))
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f265,plain,
( spl0_13
| spl0_5
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f259,f148,f116,f262]) ).
fof(f266,plain,
( ! [X0] :
( second(X0) != n
| knows(symmetric_encrypt(secret,head(X0)))
| ~ knows(encrypt(sign(X0,inverse(k_s)),k_c)) )
| ~ spl0_3 ),
inference(superposition,[],[f258,f53]) ).
fof(f269,plain,
( ! [X0,X1] :
( head(X0) != n
| knows(symmetric_encrypt(secret,head(concatenate(X1,X0))))
| ~ knows(encrypt(sign(concatenate(X1,X0),inverse(k_s)),k_c)) )
| ~ spl0_3 ),
inference(superposition,[],[f266,f70]) ).
fof(f270,plain,
( ! [X0,X1] :
( knows(symmetric_encrypt(secret,X1))
| head(X0) != n
| ~ knows(encrypt(sign(concatenate(X1,X0),inverse(k_s)),k_c)) )
| ~ spl0_3 ),
inference(forward_demodulation,[],[f269,f54]) ).
fof(f271,plain,
( ! [X0,X1] :
( head(X0) != n
| ~ knows(encrypt(sign(concatenate(X1,X0),inverse(k_s)),k_c))
| knows(secret)
| ~ knows(X1) )
| ~ spl0_3 ),
inference(resolution,[],[f270,f37]) ).
fof(f272,plain,
( ! [X0,X1] :
( head(X0) != n
| ~ knows(encrypt(sign(concatenate(X1,X0),inverse(k_s)),k_c))
| ~ knows(X1) )
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f271,f67]) ).
fof(f273,plain,
( ! [X2,X0,X1] :
( n != X0
| ~ knows(encrypt(sign(concatenate(X2,concatenate(X0,X1)),inverse(k_s)),k_c))
| ~ knows(X2) )
| ~ spl0_3 ),
inference(superposition,[],[f272,f54]) ).
fof(f275,plain,
( ! [X0,X1] :
( ~ knows(encrypt(sign(concatenate(X0,concatenate(n,X1)),inverse(k_s)),k_c))
| ~ knows(X0) )
| ~ spl0_3 ),
inference(equality_resolution,[],[f273]) ).
fof(f279,plain,
( ! [X0,X1] :
( ~ knows(X0)
| ~ knows(sign(concatenate(X0,concatenate(n,X1)),inverse(k_s)))
| ~ knows(k_c) )
| ~ spl0_3 ),
inference(resolution,[],[f275,f44]) ).
fof(f280,plain,
( ! [X0,X1] :
( ~ knows(sign(concatenate(X0,concatenate(n,X1)),inverse(k_s)))
| ~ knows(X0) )
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f279,f89]) ).
fof(f291,plain,
( ~ knows(kgen(k_a))
| ~ knows(n)
| ~ spl0_3
| ~ spl0_6 ),
inference(resolution,[],[f280,f133]) ).
fof(f294,plain,
( ~ knows(n)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f291,f264]) ).
fof(f303,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f294,f83]) ).
fof(f304,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f303]) ).
fof(f305,plain,
( spl0_12
| spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f178,f135,f116,f180]) ).
fof(f309,plain,
( ! [X0] :
( ~ knows(k_a)
| ~ knows(X0) )
| ~ spl0_12 ),
inference(resolution,[],[f181,f45]) ).
fof(f313,plain,
( ! [X0] : ~ knows(X0)
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f309,f61]) ).
fof(f314,plain,
( spl0_5
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f313,f180,f116]) ).
cnf(s2,plain,
( spl0_3
| spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f118]) ).
cnf(s3,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f137]) ).
cnf(s6,plain,
( ~ spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f157]) ).
cnf(s25,plain,
~ spl0_5,
inference(sat_conversion,[],[f230]) ).
cnf(s27,plain,
~ spl0_4,
inference(sat_conversion,[],[f238]) ).
cnf(s30,plain,
( ~ spl0_6
| ~ spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f257]) ).
cnf(s31,plain,
( spl0_5
| ~ spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f265]) ).
cnf(s34,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_13 ),
inference(sat_conversion,[],[f304]) ).
cnf(s35,plain,
( spl0_5
| ~ spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f305]) ).
cnf(s37,plain,
( spl0_5
| ~ spl0_12 ),
inference(sat_conversion,[],[f314]) ).
cnf(s38,plain,
~ spl0_12,
inference(rat,[],[s37,s25]) ).
cnf(s39,plain,
~ spl0_7,
inference(rat,[],[s35,s38,s25]) ).
cnf(s40,plain,
spl0_6,
inference(rat,[],[s3,s39]) ).
cnf(s41,plain,
spl0_3,
inference(rat,[],[s2,s25,s27]) ).
cnf(s42,plain,
~ spl0_13,
inference(rat,[],[s34,s40,s41]) ).
cnf(s43,plain,
spl0_8,
inference(rat,[],[s6,s41]) ).
cnf(s44,plain,
~ spl0_9,
inference(rat,[],[s31,s25,s42]) ).
cnf(s45,plain,
$false,
inference(rat,[],[s30,s40,s44,s43]) ).
fof(f315,plain,
$false,
inference(avatar_sat_refutation,[],[s45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV233+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.25 % Computer : n001.cluster.edu
% 0.12/0.25 % Model : x86_64 x86_64
% 0.12/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.25 % Memory : 8046.5625MB
% 0.12/0.25 % OS : Linux 6.8.0-71-generic
% 0.12/0.26 % CPULimit : 300
% 0.12/0.26 % WCLimit : 300
% 0.12/0.26 % DateTime : Mon Sep 28 10:20:03 UTC 2026
% 0.12/0.26 % CPUTime :
% 0.12/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.31 Running first-order theorem proving
% 0.12/0.31 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.65/1.61 % (265636)Detected formulas, will run a generic FOF schedule.
% 4.65/1.61 % (265649)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=158596142:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.65/1.61 % (265653)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3064447174:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.65/1.61 % (265653)Refutation not found, incomplete strategy
% 4.65/1.61 % (265653)------------------------------
% 4.65/1.61 % (265653)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.65/1.61 % (265653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.65/1.61 % (265653)CaDiCaL version: 2.1.3
% 4.65/1.61 % (265653)Termination reason: Refutation not found, incomplete strategy
% 4.65/1.61 % (265653)Time elapsed: 0.001 s
% 4.65/1.61 % (265653)Peak memory usage: 87 MB
% 4.65/1.61 % (265651)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1453319951:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.65/1.61 % (265650)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3458526445:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.65/1.61 % (265655)dis-21_1_sil=8000:lcm=predicate:random_seed=31871712:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 4.65/1.61 % (265654)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4230798477:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.65/1.61 % (265652)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3877082674:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.65/1.61 % (265652)Refutation not found, incomplete strategy
% 4.65/1.61 % (265652)------------------------------
% 4.65/1.61 % (265652)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.65/1.61 % (265652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.65/1.61 % (265652)CaDiCaL version: 2.1.3
% 4.65/1.61 % (265652)Termination reason: Refutation not found, incomplete strategy
% 4.65/1.61 % (265652)Time elapsed: 0.001 s
% 4.65/1.61 % (265652)Peak memory usage: 87 MB
% 4.65/1.61 % (265655)Refutation not found, incomplete strategy
% 4.65/1.61 % (265655)------------------------------
% 4.65/1.61 % (265655)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.65/1.61 % (265655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.65/1.61 % (265655)CaDiCaL version: 2.1.3
% 4.65/1.61 % (265655)Termination reason: Refutation not found, incomplete strategy
% 4.65/1.61 % (265655)Time elapsed: 0.003 s
% 4.65/1.61 % (265655)Peak memory usage: 88 MB
% 4.65/1.61 % (265655)Instructions burned: 2 (million)
% 4.65/1.61 % (265654)First to succeed.
% 4.65/1.61 % (265654)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-265636"
% 4.65/1.61 % (265653)------------------------------
% 4.65/1.61 % (265653)------------------------------
% 4.65/1.61 % (265655)------------------------------
% 4.65/1.61 % (265655)------------------------------
% 4.65/1.61 % (265652)------------------------------
% 4.65/1.61 % (265652)------------------------------
% 4.65/1.61 % (265654)Refutation found. Thanks to Tanya!
% 4.65/1.61 % SZS status Theorem for theBenchmark
% 4.65/1.61 % SZS output start Proof for theBenchmark
% See solution above
% 5.67/1.84 % (265654)------------------------------
% 5.67/1.84 % (265654)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.67/1.84 % (265654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.67/1.84 % (265654)CaDiCaL version: 2.1.3
% 5.67/1.84 % (265654)Termination reason: Refutation
% 5.67/1.84 % (265654)Time elapsed: 0.021 s
% 5.67/1.84 % (265654)Peak memory usage: 90 MB
% 5.67/1.84 % (265654)Instructions burned: 17 (million)
% 5.67/1.84 % (265654)------------------------------
% 5.67/1.84 % (265654)------------------------------
% 5.67/1.84 % (265636)Success in time 0.666 s
% 5.67/1.84 % Vampire exiting
%------------------------------------------------------------------------------