TSTP Solution File: SWV233+1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SWV233+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n016.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 : Wed Aug 31 18:55:53 EDT 2022
% Result : Theorem 0.22s 0.59s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 34
% Syntax : Number of formulae : 181 ( 44 unt; 0 def)
% Number of atoms : 590 ( 78 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 741 ( 332 ~; 318 |; 58 &)
% ( 20 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 23 ( 21 usr; 20 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 9 con; 0-2 aty)
% Number of variables : 215 ( 215 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f644,plain,
$false,
inference(avatar_sat_refutation,[],[f127,f140,f167,f181,f203,f205,f219,f238,f248,f331,f363,f369,f439,f471,f496,f498,f587,f614,f628,f643]) ).
fof(f643,plain,
( spl1_17
| ~ spl1_28
| ~ spl1_58 ),
inference(avatar_split_clause,[],[f642,f626,f361,f227]) ).
fof(f227,plain,
( spl1_17
<=> ! [X0] :
( ~ knows(X0)
| ~ sP0(X0)
| ~ knows(inverse(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_17])]) ).
fof(f361,plain,
( spl1_28
<=> ! [X5] :
( knows(kgen(X5))
| ~ knows(inverse(X5))
| ~ sP0(X5)
| ~ knows(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_28])]) ).
fof(f626,plain,
( spl1_58
<=> ! [X0] :
( ~ sP0(X0)
| ~ knows(inverse(X0))
| ~ knows(kgen(X0))
| ~ knows(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_58])]) ).
fof(f642,plain,
( ! [X0] :
( ~ sP0(X0)
| ~ knows(inverse(X0))
| ~ knows(X0) )
| ~ spl1_28
| ~ spl1_58 ),
inference(duplicate_literal_removal,[],[f641]) ).
fof(f641,plain,
( ! [X0] :
( ~ knows(inverse(X0))
| ~ knows(X0)
| ~ knows(inverse(X0))
| ~ sP0(X0)
| ~ knows(X0)
| ~ sP0(X0) )
| ~ spl1_28
| ~ spl1_58 ),
inference(resolution,[],[f627,f362]) ).
fof(f362,plain,
( ! [X5] :
( knows(kgen(X5))
| ~ knows(X5)
| ~ sP0(X5)
| ~ knows(inverse(X5)) )
| ~ spl1_28 ),
inference(avatar_component_clause,[],[f361]) ).
fof(f627,plain,
( ! [X0] :
( ~ knows(kgen(X0))
| ~ knows(inverse(X0))
| ~ sP0(X0)
| ~ knows(X0) )
| ~ spl1_58 ),
inference(avatar_component_clause,[],[f626]) ).
fof(f628,plain,
( spl1_4
| spl1_58
| ~ spl1_53 ),
inference(avatar_split_clause,[],[f624,f582,f626,f132]) ).
fof(f132,plain,
( spl1_4
<=> knows(secret) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).
fof(f582,plain,
( spl1_53
<=> ! [X1] :
( ~ sP0(X1)
| ~ knows(X1)
| knows(symmetric_encrypt(secret,kgen(X1)))
| ~ knows(inverse(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_53])]) ).
fof(f624,plain,
( ! [X0] :
( ~ sP0(X0)
| ~ knows(X0)
| knows(secret)
| ~ knows(kgen(X0))
| ~ knows(inverse(X0)) )
| ~ spl1_53 ),
inference(resolution,[],[f583,f77]) ).
fof(f77,plain,
! [X0,X1] :
( ~ knows(symmetric_encrypt(X1,X0))
| knows(X1)
| ~ knows(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X1] :
( ~ knows(symmetric_encrypt(X1,X0))
| ~ knows(X0)
| knows(X1) ),
inference(flattening,[],[f46]) ).
fof(f46,plain,
! [X0,X1] :
( knows(X1)
| ~ knows(symmetric_encrypt(X1,X0))
| ~ knows(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1] :
( ( knows(symmetric_encrypt(X1,X0))
& knows(X0) )
=> knows(X1) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] :
( ( knows(X1)
& knows(symmetric_encrypt(X0,X1)) )
=> knows(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_encrypt_equation) ).
fof(f583,plain,
( ! [X1] :
( knows(symmetric_encrypt(secret,kgen(X1)))
| ~ knows(X1)
| ~ sP0(X1)
| ~ knows(inverse(X1)) )
| ~ spl1_53 ),
inference(avatar_component_clause,[],[f582]) ).
fof(f614,plain,
~ spl1_54,
inference(avatar_contradiction_clause,[],[f613]) ).
fof(f613,plain,
( $false
| ~ spl1_54 ),
inference(resolution,[],[f608,f114]) ).
fof(f114,plain,
knows(n),
inference(resolution,[],[f73,f61]) ).
fof(f61,plain,
! [X0,X1] :
( ~ knows(concatenate(X1,X0))
| knows(X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1] :
( ~ knows(concatenate(X1,X0))
| ( knows(X0)
& knows(X1) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X1,X0] :
( knows(concatenate(X1,X0))
=> ( knows(X0)
& knows(X1) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1,X0] :
( knows(concatenate(X0,X1))
=> ( knows(X1)
& knows(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',construct_message_2) ).
fof(f73,plain,
knows(concatenate(n,concatenate(k_c,sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c))))),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0,X1,X2,X3,X4] :
( knows(concatenate(n,concatenate(k_c,sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c)))))
& ( ~ knows(X3)
| knows(symmetric_encrypt(secret,first(extract(decrypt(X3,inverse(k_c)),second(extract(X1,k_ca))))))
| n != second(extract(decrypt(X3,inverse(k_c)),second(extract(X1,k_ca))))
| s != first(extract(X1,k_ca))
| ~ knows(X1) )
& ( ~ knows(X0)
| second(extract(X2,X4)) != X4
| knows(concatenate(encrypt(sign(concatenate(kgen(X4),concatenate(X0,eol)),inverse(k_s)),X4),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))))
| ~ knows(X4)
| ~ knows(X2) ) ),
inference(rectify,[],[f42]) ).
fof(f42,plain,
! [X4,X1,X0,X2,X3] :
( knows(concatenate(n,concatenate(k_c,sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c)))))
& ( ~ knows(X2)
| knows(symmetric_encrypt(secret,first(extract(decrypt(X2,inverse(k_c)),second(extract(X1,k_ca))))))
| n != second(extract(decrypt(X2,inverse(k_c)),second(extract(X1,k_ca))))
| s != first(extract(X1,k_ca))
| ~ knows(X1) )
& ( ~ knows(X4)
| second(extract(X0,X3)) != X3
| knows(concatenate(encrypt(sign(concatenate(kgen(X3),concatenate(X4,eol)),inverse(k_s)),X3),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))))
| ~ knows(X3)
| ~ knows(X0) ) ),
inference(flattening,[],[f41]) ).
fof(f41,plain,
! [X0,X4,X2,X1,X3] :
( knows(concatenate(n,concatenate(k_c,sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c)))))
& ( knows(concatenate(encrypt(sign(concatenate(kgen(X3),concatenate(X4,eol)),inverse(k_s)),X3),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))))
| ~ knows(X4)
| second(extract(X0,X3)) != X3
| ~ knows(X3)
| ~ knows(X0) )
& ( knows(symmetric_encrypt(secret,first(extract(decrypt(X2,inverse(k_c)),second(extract(X1,k_ca))))))
| ~ knows(X1)
| n != second(extract(decrypt(X2,inverse(k_c)),second(extract(X1,k_ca))))
| s != first(extract(X1,k_ca))
| ~ knows(X2) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X4,X2,X1,X3] :
( knows(concatenate(n,concatenate(k_c,sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c)))))
& ( ( knows(X4)
& second(extract(X0,X3)) = X3
& knows(X3)
& knows(X0) )
=> knows(concatenate(encrypt(sign(concatenate(kgen(X3),concatenate(X4,eol)),inverse(k_s)),X3),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca)))) )
& ( ( knows(X1)
& n = second(extract(decrypt(X2,inverse(k_c)),second(extract(X1,k_ca))))
& s = first(extract(X1,k_ca))
& knows(X2) )
=> knows(symmetric_encrypt(secret,first(extract(decrypt(X2,inverse(k_c)),second(extract(X1,k_ca)))))) ) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X8,X10,X9,X7,X6] :
( ( ( first(extract(X10,k_ca)) = s
& knows(X9)
& knows(X10)
& n = second(extract(decrypt(X9,inverse(k_c)),second(extract(X10,k_ca)))) )
=> knows(symmetric_encrypt(secret,first(extract(decrypt(X9,inverse(k_c)),second(extract(X10,k_ca)))))) )
& ( ( knows(X8)
& second(extract(X8,X7)) = X7
& knows(X7)
& knows(X6) )
=> knows(concatenate(encrypt(sign(concatenate(kgen(X7),concatenate(X6,eol)),inverse(k_s)),X7),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca)))) )
& knows(concatenate(n,concatenate(k_c,sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',protocol) ).
fof(f608,plain,
( ~ knows(n)
| ~ spl1_54 ),
inference(equality_resolution,[],[f586]) ).
fof(f586,plain,
( ! [X2] :
( n != X2
| ~ knows(X2) )
| ~ spl1_54 ),
inference(avatar_component_clause,[],[f585]) ).
fof(f585,plain,
( spl1_54
<=> ! [X2] :
( n != X2
| ~ knows(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_54])]) ).
fof(f587,plain,
( spl1_53
| spl1_54
| ~ spl1_3
| ~ spl1_19 ),
inference(avatar_split_clause,[],[f580,f236,f124,f585,f582]) ).
fof(f124,plain,
( spl1_3
<=> knows(sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).
fof(f236,plain,
( spl1_19
<=> ! [X0,X1] :
( ~ knows(sign(X0,inverse(first(tail(extract(X1,k_ca))))))
| ~ knows(X1)
| s != first(extract(X1,k_ca))
| n != first(tail(X0))
| knows(symmetric_encrypt(secret,first(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_19])]) ).
fof(f580,plain,
( ! [X2,X1] :
( n != X2
| ~ sP0(X1)
| ~ knows(inverse(X1))
| ~ knows(X2)
| knows(symmetric_encrypt(secret,kgen(X1)))
| ~ knows(X1) )
| ~ spl1_3
| ~ spl1_19 ),
inference(forward_demodulation,[],[f579,f98]) ).
fof(f98,plain,
! [X0,X1] : first(concatenate(X1,X0)) = X1,
inference(definition_unfolding,[],[f74,f91]) ).
fof(f91,plain,
! [X0] : head(X0) = first(X0),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0] : head(X0) = first(X0),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X4] : first(X4) = head(X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first_axiom) ).
fof(f74,plain,
! [X0,X1] : head(concatenate(X1,X0)) = X1,
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1] : head(concatenate(X1,X0)) = X1,
inference(rectify,[],[f34]) ).
fof(f34,plain,
! [X1,X0] : head(concatenate(X0,X1)) = X0,
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X4,X5] : head(concatenate(X4,X5)) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',head_axiom) ).
fof(f579,plain,
( ! [X2,X1] :
( n != first(concatenate(X2,eol))
| ~ sP0(X1)
| ~ knows(X1)
| ~ knows(inverse(X1))
| ~ knows(X2)
| knows(symmetric_encrypt(secret,kgen(X1))) )
| ~ spl1_3
| ~ spl1_19 ),
inference(forward_demodulation,[],[f578,f98]) ).
fof(f578,plain,
( ! [X2,X1] :
( ~ knows(X1)
| knows(symmetric_encrypt(secret,first(concatenate(kgen(X1),concatenate(X2,eol)))))
| ~ sP0(X1)
| n != first(concatenate(X2,eol))
| ~ knows(inverse(X1))
| ~ knows(X2) )
| ~ spl1_3
| ~ spl1_19 ),
inference(forward_demodulation,[],[f577,f78]) ).
fof(f78,plain,
! [X0,X1] : tail(concatenate(X0,X1)) = X1,
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0,X1] : tail(concatenate(X0,X1)) = X1,
inference(rectify,[],[f25]) ).
fof(f25,plain,
! [X1,X0] : tail(concatenate(X1,X0)) = X0,
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X5,X4] : tail(concatenate(X4,X5)) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tail_axiom) ).
fof(f577,plain,
( ! [X2,X1] :
( n != first(tail(concatenate(kgen(X1),concatenate(X2,eol))))
| ~ knows(X2)
| ~ knows(X1)
| ~ knows(inverse(X1))
| knows(symmetric_encrypt(secret,first(concatenate(kgen(X1),concatenate(X2,eol)))))
| ~ sP0(X1) )
| ~ spl1_3
| ~ spl1_19 ),
inference(resolution,[],[f570,f158]) ).
fof(f158,plain,
! [X0,X1] :
( knows(sign(concatenate(kgen(X0),concatenate(X1,eol)),inverse(k_s)))
| ~ sP0(X0)
| ~ knows(X0)
| ~ knows(X1)
| ~ knows(inverse(X0)) ),
inference(resolution,[],[f116,f64]) ).
fof(f64,plain,
! [X0,X1] :
( ~ knows(encrypt(X0,X1))
| ~ knows(inverse(X1))
| knows(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1] :
( knows(X0)
| ~ knows(inverse(X1))
| ~ knows(encrypt(X0,X1)) ),
inference(rectify,[],[f44]) ).
fof(f44,plain,
! [X1,X0] :
( knows(X1)
| ~ knows(inverse(X0))
| ~ knows(encrypt(X1,X0)) ),
inference(flattening,[],[f43]) ).
fof(f43,plain,
! [X1,X0] :
( knows(X1)
| ~ knows(inverse(X0))
| ~ knows(encrypt(X1,X0)) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,plain,
! [X1,X0] :
( ( knows(inverse(X0))
& knows(encrypt(X1,X0)) )
=> knows(X1) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X1,X0] :
( ( knows(inverse(X1))
& knows(encrypt(X0,X1)) )
=> knows(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',encrypt_equation) ).
fof(f116,plain,
! [X2,X3] :
( knows(encrypt(sign(concatenate(kgen(X2),concatenate(X3,eol)),inverse(k_s)),X2))
| ~ knows(X2)
| ~ sP0(X2)
| ~ knows(X3) ),
inference(resolution,[],[f100,f61]) ).
fof(f100,plain,
! [X0,X4] :
( knows(concatenate(encrypt(sign(concatenate(kgen(X4),concatenate(X0,eol)),inverse(k_s)),X4),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))))
| ~ sP0(X4)
| ~ knows(X0)
| ~ knows(X4) ),
inference(general_splitting,[],[f97,f99_D]) ).
fof(f99,plain,
! [X2,X4] :
( first(tail(extract(X2,X4))) != X4
| sP0(X4)
| ~ knows(X2) ),
inference(cnf_transformation,[],[f99_D]) ).
fof(f99_D,plain,
! [X4] :
( ! [X2] :
( first(tail(extract(X2,X4))) != X4
| ~ knows(X2) )
<=> ~ sP0(X4) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP0])]) ).
fof(f97,plain,
! [X2,X0,X4] :
( ~ knows(X0)
| first(tail(extract(X2,X4))) != X4
| knows(concatenate(encrypt(sign(concatenate(kgen(X4),concatenate(X0,eol)),inverse(k_s)),X4),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))))
| ~ knows(X4)
| ~ knows(X2) ),
inference(definition_unfolding,[],[f71,f93]) ).
fof(f93,plain,
! [X0] : first(tail(X0)) = second(X0),
inference(definition_unfolding,[],[f79,f91]) ).
fof(f79,plain,
! [X0] : head(tail(X0)) = second(X0),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0] : head(tail(X0)) = second(X0),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X4] : second(X4) = head(tail(X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second_axiom) ).
fof(f71,plain,
! [X2,X0,X4] :
( ~ knows(X0)
| second(extract(X2,X4)) != X4
| knows(concatenate(encrypt(sign(concatenate(kgen(X4),concatenate(X0,eol)),inverse(k_s)),X4),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))))
| ~ knows(X4)
| ~ knows(X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f570,plain,
( ! [X0] :
( ~ knows(sign(X0,inverse(k_s)))
| n != first(tail(X0))
| knows(symmetric_encrypt(secret,first(X0))) )
| ~ spl1_3
| ~ spl1_19 ),
inference(forward_demodulation,[],[f569,f98]) ).
fof(f569,plain,
( ! [X0] :
( ~ knows(sign(X0,inverse(first(concatenate(k_s,eol)))))
| knows(symmetric_encrypt(secret,first(X0)))
| n != first(tail(X0)) )
| ~ spl1_3
| ~ spl1_19 ),
inference(trivial_inequality_removal,[],[f567]) ).
fof(f567,plain,
( ! [X0] :
( ~ knows(sign(X0,inverse(first(concatenate(k_s,eol)))))
| s != s
| n != first(tail(X0))
| knows(symmetric_encrypt(secret,first(X0))) )
| ~ spl1_3
| ~ spl1_19 ),
inference(resolution,[],[f513,f126]) ).
fof(f126,plain,
( knows(sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca)))
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f513,plain,
( ! [X2,X0,X1] :
( ~ knows(sign(concatenate(X0,X1),inverse(k_ca)))
| s != X0
| ~ knows(sign(X2,inverse(first(X1))))
| n != first(tail(X2))
| knows(symmetric_encrypt(secret,first(X2))) )
| ~ spl1_19 ),
inference(forward_demodulation,[],[f512,f98]) ).
fof(f512,plain,
( ! [X2,X0,X1] :
( n != first(tail(X2))
| s != first(concatenate(X0,X1))
| knows(symmetric_encrypt(secret,first(X2)))
| ~ knows(sign(X2,inverse(first(X1))))
| ~ knows(sign(concatenate(X0,X1),inverse(k_ca))) )
| ~ spl1_19 ),
inference(superposition,[],[f371,f78]) ).
fof(f371,plain,
( ! [X0,X1] :
( ~ knows(sign(X1,inverse(first(tail(X0)))))
| ~ knows(sign(X0,inverse(k_ca)))
| knows(symmetric_encrypt(secret,first(X1)))
| s != first(X0)
| n != first(tail(X1)) )
| ~ spl1_19 ),
inference(superposition,[],[f237,f90]) ).
fof(f90,plain,
! [X0,X1] : extract(sign(X1,inverse(X0)),X0) = X1,
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1] : extract(sign(X1,inverse(X0)),X0) = X1,
inference(rectify,[],[f21]) ).
fof(f21,plain,
! [X1,X0] : extract(sign(X0,inverse(X1)),X1) = X0,
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X2,X3] : extract(sign(X2,inverse(X3)),X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sign_axiom) ).
fof(f237,plain,
( ! [X0,X1] :
( ~ knows(sign(X0,inverse(first(tail(extract(X1,k_ca))))))
| s != first(extract(X1,k_ca))
| n != first(tail(X0))
| knows(symmetric_encrypt(secret,first(X0)))
| ~ knows(X1) )
| ~ spl1_19 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f498,plain,
spl1_29,
inference(avatar_contradiction_clause,[],[f497]) ).
fof(f497,plain,
( $false
| spl1_29 ),
inference(resolution,[],[f368,f67]) ).
fof(f67,plain,
knows(k_a),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
( knows(k_a)
& knows(inverse(k_a))
& knows(k_ca) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',previous_knowledge) ).
fof(f368,plain,
( ~ knows(k_a)
| spl1_29 ),
inference(avatar_component_clause,[],[f366]) ).
fof(f366,plain,
( spl1_29
<=> knows(k_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_29])]) ).
fof(f496,plain,
( ~ spl1_29
| spl1_23
| ~ spl1_43 ),
inference(avatar_split_clause,[],[f495,f469,f334,f366]) ).
fof(f334,plain,
( spl1_23
<=> sP0(k_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_23])]) ).
fof(f469,plain,
( spl1_43
<=> ! [X0] :
( sP0(X0)
| ~ knows(inverse(X0))
| ~ knows(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_43])]) ).
fof(f495,plain,
( sP0(k_a)
| ~ knows(k_a)
| ~ spl1_43 ),
inference(resolution,[],[f470,f66]) ).
fof(f66,plain,
knows(inverse(k_a)),
inference(cnf_transformation,[],[f17]) ).
fof(f470,plain,
( ! [X0] :
( ~ knows(inverse(X0))
| ~ knows(X0)
| sP0(X0) )
| ~ spl1_43 ),
inference(avatar_component_clause,[],[f469]) ).
fof(f471,plain,
( spl1_1
| spl1_43
| ~ spl1_39 ),
inference(avatar_split_clause,[],[f450,f437,f469,f118]) ).
fof(f118,plain,
( spl1_1
<=> ! [X1] : ~ knows(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).
fof(f437,plain,
( spl1_39
<=> ! [X0] :
( ~ knows(inverse(first(X0)))
| sP0(first(X0))
| ~ knows(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_39])]) ).
fof(f450,plain,
( ! [X0,X1] :
( sP0(X0)
| ~ knows(X0)
| ~ knows(X1)
| ~ knows(inverse(X0)) )
| ~ spl1_39 ),
inference(resolution,[],[f440,f86]) ).
fof(f86,plain,
! [X0,X1] :
( knows(concatenate(X1,X0))
| ~ knows(X1)
| ~ knows(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( ( knows(concatenate(X1,X0))
& knows(decrypt(X1,X0))
& knows(encrypt(X1,X0))
& knows(extract(X1,X0))
& knows(symmetric_decrypt(X1,X0))
& knows(symmetric_encrypt(X1,X0))
& knows(sign(X1,X0)) )
| ~ knows(X0)
| ~ knows(X1) ),
inference(rectify,[],[f49]) ).
fof(f49,plain,
! [X1,X0] :
( ( knows(concatenate(X0,X1))
& knows(decrypt(X0,X1))
& knows(encrypt(X0,X1))
& knows(extract(X0,X1))
& knows(symmetric_decrypt(X0,X1))
& knows(symmetric_encrypt(X0,X1))
& knows(sign(X0,X1)) )
| ~ knows(X1)
| ~ knows(X0) ),
inference(flattening,[],[f48]) ).
fof(f48,plain,
! [X1,X0] :
( ( knows(concatenate(X0,X1))
& knows(decrypt(X0,X1))
& knows(encrypt(X0,X1))
& knows(extract(X0,X1))
& knows(symmetric_decrypt(X0,X1))
& knows(symmetric_encrypt(X0,X1))
& knows(sign(X0,X1)) )
| ~ knows(X0)
| ~ knows(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] :
( ( knows(X0)
& knows(X1) )
=> ( knows(concatenate(X0,X1))
& knows(decrypt(X0,X1))
& knows(encrypt(X0,X1))
& knows(extract(X0,X1))
& knows(symmetric_decrypt(X0,X1))
& knows(symmetric_encrypt(X0,X1))
& knows(sign(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',construct_message_1) ).
fof(f440,plain,
( ! [X0,X1] :
( ~ knows(concatenate(X0,X1))
| sP0(X0)
| ~ knows(inverse(X0)) )
| ~ spl1_39 ),
inference(superposition,[],[f438,f98]) ).
fof(f438,plain,
( ! [X0] :
( ~ knows(inverse(first(X0)))
| ~ knows(X0)
| sP0(first(X0)) )
| ~ spl1_39 ),
inference(avatar_component_clause,[],[f437]) ).
fof(f439,plain,
( spl1_39
| spl1_1 ),
inference(avatar_split_clause,[],[f406,f118,f437]) ).
fof(f406,plain,
! [X0,X1] :
( ~ knows(X1)
| ~ knows(inverse(first(X0)))
| ~ knows(X0)
| sP0(first(X0)) ),
inference(resolution,[],[f260,f86]) ).
fof(f260,plain,
! [X0,X1] :
( ~ knows(concatenate(X0,X1))
| ~ knows(inverse(first(X1)))
| sP0(first(X1)) ),
inference(superposition,[],[f179,f78]) ).
fof(f179,plain,
! [X0] :
( ~ knows(inverse(first(tail(X0))))
| sP0(first(tail(X0)))
| ~ knows(X0) ),
inference(equality_resolution,[],[f153]) ).
fof(f153,plain,
! [X0,X1] :
( first(tail(X0)) != X1
| ~ knows(inverse(X1))
| sP0(X1)
| ~ knows(X0) ),
inference(resolution,[],[f112,f80]) ).
fof(f80,plain,
! [X0,X1] :
( knows(sign(X1,X0))
| ~ knows(X1)
| ~ knows(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f112,plain,
! [X0,X1] :
( ~ knows(sign(X0,inverse(X1)))
| first(tail(X0)) != X1
| sP0(X1) ),
inference(superposition,[],[f99,f90]) ).
fof(f369,plain,
( ~ spl1_23
| ~ spl1_29
| ~ spl1_17 ),
inference(avatar_split_clause,[],[f364,f227,f366,f334]) ).
fof(f364,plain,
( ~ knows(k_a)
| ~ sP0(k_a)
| ~ spl1_17 ),
inference(resolution,[],[f228,f66]) ).
fof(f228,plain,
( ! [X0] :
( ~ knows(inverse(X0))
| ~ sP0(X0)
| ~ knows(X0) )
| ~ spl1_17 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f363,plain,
( spl1_28
| spl1_1
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f350,f217,f118,f361]) ).
fof(f217,plain,
( spl1_15
<=> ! [X2,X3] :
( ~ sP0(X2)
| knows(concatenate(kgen(X2),concatenate(X3,eol)))
| ~ knows(X3)
| ~ knows(X2)
| ~ knows(inverse(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_15])]) ).
fof(f350,plain,
( ! [X6,X5] :
( ~ knows(X6)
| knows(kgen(X5))
| ~ knows(X5)
| ~ sP0(X5)
| ~ knows(inverse(X5)) )
| ~ spl1_15 ),
inference(resolution,[],[f218,f61]) ).
fof(f218,plain,
( ! [X2,X3] :
( knows(concatenate(kgen(X2),concatenate(X3,eol)))
| ~ sP0(X2)
| ~ knows(inverse(X2))
| ~ knows(X2)
| ~ knows(X3) )
| ~ spl1_15 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f331,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f309]) ).
fof(f309,plain,
( $false
| ~ spl1_1 ),
inference(resolution,[],[f119,f114]) ).
fof(f119,plain,
( ! [X1] : ~ knows(X1)
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f248,plain,
( ~ spl1_13
| spl1_14 ),
inference(avatar_contradiction_clause,[],[f247]) ).
fof(f247,plain,
( $false
| ~ spl1_13
| spl1_14 ),
inference(resolution,[],[f209,f215]) ).
fof(f215,plain,
( ~ knows(k_s)
| spl1_14 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f213,plain,
( spl1_14
<=> knows(k_s) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_14])]) ).
fof(f209,plain,
( knows(k_s)
| ~ spl1_13 ),
inference(resolution,[],[f206,f61]) ).
fof(f206,plain,
( knows(concatenate(k_s,eol))
| ~ spl1_13 ),
inference(resolution,[],[f202,f62]) ).
fof(f62,plain,
! [X0,X1] :
( ~ knows(concatenate(X1,X0))
| knows(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f202,plain,
( knows(concatenate(s,concatenate(k_s,eol)))
| ~ spl1_13 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f200,plain,
( spl1_13
<=> knows(concatenate(s,concatenate(k_s,eol))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_13])]) ).
fof(f238,plain,
( spl1_19
| ~ spl1_6 ),
inference(avatar_split_clause,[],[f233,f145,f236]) ).
fof(f145,plain,
( spl1_6
<=> knows(k_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).
fof(f233,plain,
! [X0,X1] :
( ~ knows(k_c)
| ~ knows(sign(X0,inverse(first(tail(extract(X1,k_ca))))))
| knows(symmetric_encrypt(secret,first(X0)))
| n != first(tail(X0))
| s != first(extract(X1,k_ca))
| ~ knows(X1) ),
inference(resolution,[],[f161,f84]) ).
fof(f84,plain,
! [X0,X1] :
( knows(encrypt(X1,X0))
| ~ knows(X0)
| ~ knows(X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f161,plain,
! [X0,X1] :
( ~ knows(encrypt(sign(X0,inverse(first(tail(extract(X1,k_ca))))),k_c))
| n != first(tail(X0))
| knows(symmetric_encrypt(secret,first(X0)))
| s != first(extract(X1,k_ca))
| ~ knows(X1) ),
inference(superposition,[],[f129,f90]) ).
fof(f129,plain,
! [X0,X1] :
( knows(symmetric_encrypt(secret,first(extract(X0,first(tail(extract(X1,k_ca)))))))
| ~ knows(encrypt(X0,k_c))
| n != first(tail(extract(X0,first(tail(extract(X1,k_ca))))))
| ~ knows(X1)
| s != first(extract(X1,k_ca)) ),
inference(superposition,[],[f96,f76]) ).
fof(f76,plain,
! [X0,X1] : decrypt(encrypt(X1,X0),inverse(X0)) = X1,
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] : decrypt(encrypt(X1,X0),inverse(X0)) = X1,
inference(rectify,[],[f35]) ).
fof(f35,plain,
! [X1,X0] : decrypt(encrypt(X0,X1),inverse(X1)) = X0,
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X2,X3] : decrypt(encrypt(X2,X3),inverse(X3)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',decrypt_axiom) ).
fof(f96,plain,
! [X3,X1] :
( knows(symmetric_encrypt(secret,first(extract(decrypt(X3,inverse(k_c)),first(tail(extract(X1,k_ca)))))))
| ~ knows(X3)
| ~ knows(X1)
| s != first(extract(X1,k_ca))
| n != first(tail(extract(decrypt(X3,inverse(k_c)),first(tail(extract(X1,k_ca)))))) ),
inference(definition_unfolding,[],[f72,f93,f93,f93]) ).
fof(f72,plain,
! [X3,X1] :
( ~ knows(X3)
| knows(symmetric_encrypt(secret,first(extract(decrypt(X3,inverse(k_c)),second(extract(X1,k_ca))))))
| n != second(extract(decrypt(X3,inverse(k_c)),second(extract(X1,k_ca))))
| s != first(extract(X1,k_ca))
| ~ knows(X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f219,plain,
( ~ spl1_14
| spl1_15 ),
inference(avatar_split_clause,[],[f211,f217,f213]) ).
fof(f211,plain,
! [X2,X3] :
( ~ sP0(X2)
| ~ knows(k_s)
| ~ knows(inverse(X2))
| ~ knows(X2)
| ~ knows(X3)
| knows(concatenate(kgen(X2),concatenate(X3,eol))) ),
inference(resolution,[],[f158,f60]) ).
fof(f60,plain,
! [X0,X1] :
( ~ knows(sign(X1,inverse(X0)))
| ~ knows(X0)
| knows(X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1] :
( knows(X1)
| ~ knows(X0)
| ~ knows(sign(X1,inverse(X0))) ),
inference(flattening,[],[f50]) ).
fof(f50,plain,
! [X0,X1] :
( knows(X1)
| ~ knows(X0)
| ~ knows(sign(X1,inverse(X0))) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( ( knows(X0)
& knows(sign(X1,inverse(X0))) )
=> knows(X1) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X3,X2] :
( ( knows(X3)
& knows(sign(X2,inverse(X3))) )
=> knows(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sign_equation) ).
fof(f205,plain,
spl1_12,
inference(avatar_contradiction_clause,[],[f204]) ).
fof(f204,plain,
( $false
| spl1_12 ),
inference(resolution,[],[f198,f65]) ).
fof(f65,plain,
knows(k_ca),
inference(cnf_transformation,[],[f17]) ).
fof(f198,plain,
( ~ knows(k_ca)
| spl1_12 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f196,plain,
( spl1_12
<=> knows(k_ca) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_12])]) ).
fof(f203,plain,
( ~ spl1_12
| spl1_13
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f183,f124,f200,f196]) ).
fof(f183,plain,
( knows(concatenate(s,concatenate(k_s,eol)))
| ~ knows(k_ca)
| ~ spl1_3 ),
inference(resolution,[],[f126,f60]) ).
fof(f181,plain,
( ~ spl1_6
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f180,f121,f145]) ).
fof(f121,plain,
( spl1_2
<=> ! [X0] :
( ~ sP0(X0)
| ~ knows(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).
fof(f180,plain,
( ~ knows(k_c)
| ~ spl1_2 ),
inference(resolution,[],[f157,f122]) ).
fof(f122,plain,
( ! [X0] :
( ~ sP0(X0)
| ~ knows(X0) )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f157,plain,
sP0(k_c),
inference(trivial_inequality_removal,[],[f156]) ).
fof(f156,plain,
( k_c != k_c
| sP0(k_c) ),
inference(forward_demodulation,[],[f155,f98]) ).
fof(f155,plain,
( sP0(k_c)
| k_c != first(concatenate(k_c,eol)) ),
inference(forward_demodulation,[],[f154,f78]) ).
fof(f154,plain,
( k_c != first(tail(concatenate(c,concatenate(k_c,eol))))
| sP0(k_c) ),
inference(resolution,[],[f112,f141]) ).
fof(f141,plain,
knows(sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c))),
inference(resolution,[],[f113,f62]) ).
fof(f113,plain,
knows(concatenate(k_c,sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c)))),
inference(resolution,[],[f73,f62]) ).
fof(f167,plain,
spl1_6,
inference(avatar_contradiction_clause,[],[f166]) ).
fof(f166,plain,
( $false
| spl1_6 ),
inference(resolution,[],[f147,f142]) ).
fof(f142,plain,
knows(k_c),
inference(resolution,[],[f113,f61]) ).
fof(f147,plain,
( ~ knows(k_c)
| spl1_6 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f140,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f139]) ).
fof(f139,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f134,f87]) ).
fof(f87,plain,
~ knows(secret),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
~ knows(secret),
inference(flattening,[],[f20]) ).
fof(f20,negated_conjecture,
~ knows(secret),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
knows(secret),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',attack) ).
fof(f134,plain,
( knows(secret)
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f127,plain,
( spl1_1
| spl1_2
| spl1_3 ),
inference(avatar_split_clause,[],[f115,f124,f121,f118]) ).
fof(f115,plain,
! [X0,X1] :
( knows(sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca)))
| ~ sP0(X0)
| ~ knows(X1)
| ~ knows(X0) ),
inference(resolution,[],[f100,f62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWV233+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.35 % Computer : n016.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 : Tue Aug 30 19:30:31 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.22/0.53 % (12756)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.22/0.53 TRYING [1]
% 0.22/0.53 % (12749)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.22/0.54 TRYING [2]
% 0.22/0.54 % (12764)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.22/0.55 TRYING [3]
% 0.22/0.56 TRYING [4]
% 0.22/0.57 % (12739)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.22/0.57 % (12749)First to succeed.
% 0.22/0.58 % (12754)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.22/0.58 % (12766)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.22/0.58 % (12751)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.22/0.58 % (12758)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.22/0.59 % (12749)Refutation found. Thanks to Tanya!
% 0.22/0.59 % SZS status Theorem for theBenchmark
% 0.22/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.59 % (12749)------------------------------
% 0.22/0.59 % (12749)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.22/0.59 % (12749)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.22/0.59 % (12749)Termination reason: Refutation
% 0.22/0.59
% 0.22/0.59 % (12749)Memory used [KB]: 6012
% 0.22/0.59 % (12749)Time elapsed: 0.160 s
% 0.22/0.59 % (12749)Instructions burned: 20 (million)
% 0.22/0.59 % (12749)------------------------------
% 0.22/0.59 % (12749)------------------------------
% 0.22/0.59 % (12738)Success in time 0.225 s
%------------------------------------------------------------------------------