TSTP Solution File: SWV233+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SWV233+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n012.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 : 600s
% DateTime : Wed Jul 20 20:11:16 EDT 2022
% Result : Theorem 33.86s 34.05s
% Output : CNFRefutation 33.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 46
% Syntax : Number of formulae : 285 ( 175 unt; 27 typ; 0 def)
% Number of atoms : 1757 ( 489 equ; 0 cnn)
% Maximal formula atoms : 11 ( 6 avg)
% Number of connectives : 4187 ( 776 ~; 647 |; 72 &;2674 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 11 con; 0-2 aty)
% Number of variables : 622 ( 0 ^ 622 !; 0 ?; 622 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c,type,
c: $i ).
thf(tp_concatenate,type,
concatenate: $i > $i > $i ).
thf(tp_decrypt,type,
decrypt: $i > $i > $i ).
thf(tp_encrypt,type,
encrypt: $i > $i > $i ).
thf(tp_eol,type,
eol: $i ).
thf(tp_extract,type,
extract: $i > $i > $i ).
thf(tp_first,type,
first: $i > $i ).
thf(tp_fourth,type,
fourth: $i > $i ).
thf(tp_hash,type,
hash: $i > $i ).
thf(tp_head,type,
head: $i > $i ).
thf(tp_inverse,type,
inverse: $i > $i ).
thf(tp_k_a,type,
k_a: $i ).
thf(tp_k_c,type,
k_c: $i ).
thf(tp_k_ca,type,
k_ca: $i ).
thf(tp_k_s,type,
k_s: $i ).
thf(tp_kgen,type,
kgen: $i > $i ).
thf(tp_knows,type,
knows: $i > $o ).
thf(tp_mac,type,
mac: $i > $i > $i ).
thf(tp_n,type,
n: $i ).
thf(tp_s,type,
s: $i ).
thf(tp_second,type,
second: $i > $i ).
thf(tp_secret,type,
secret: $i ).
thf(tp_sign,type,
sign: $i > $i > $i ).
thf(tp_symmetric_decrypt,type,
symmetric_decrypt: $i > $i > $i ).
thf(tp_symmetric_encrypt,type,
symmetric_encrypt: $i > $i > $i ).
thf(tp_tail,type,
tail: $i > $i ).
thf(tp_third,type,
third: $i > $i ).
thf(1,axiom,
! [Init_1: $i,Init_2: $i,Init_3: $i,Resp_1: $i,Resp_2: $i] :
( ( knows @ ( concatenate @ n @ ( concatenate @ k_c @ ( sign @ ( concatenate @ c @ ( concatenate @ k_c @ eol ) ) @ ( inverse @ k_c ) ) ) ) )
& ( ( ( knows @ Resp_1 )
& ( knows @ Resp_2 )
& ( ( first @ ( extract @ Resp_2 @ k_ca ) )
= s )
& ( ( second @ ( extract @ ( decrypt @ Resp_1 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ Resp_2 @ k_ca ) ) ) )
= n ) )
=> ( knows @ ( symmetric_encrypt @ secret @ ( first @ ( extract @ ( decrypt @ Resp_1 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ Resp_2 @ k_ca ) ) ) ) ) ) )
& ( ( ( knows @ Init_1 )
& ( knows @ Init_2 )
& ( knows @ Init_3 )
& ( ( second @ ( extract @ Init_3 @ Init_2 ) )
= Init_2 ) )
=> ( knows @ ( concatenate @ ( encrypt @ ( sign @ ( concatenate @ ( kgen @ Init_2 ) @ ( concatenate @ Init_1 @ eol ) ) @ ( inverse @ k_s ) ) @ Init_2 ) @ ( sign @ ( concatenate @ s @ ( concatenate @ k_s @ eol ) ) @ ( inverse @ k_ca ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',protocol) ).
thf(2,axiom,
( ( knows @ k_ca )
& ( knows @ ( inverse @ k_a ) )
& ( knows @ k_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',previous_knowledge) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ( ( knows @ X )
& ( knows @ Y ) )
=> ( knows @ ( mac @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmac_axiom) ).
thf(4,axiom,
! [X: $i] :
( ( fourth @ X )
= ( head @ ( tail @ ( tail @ ( tail @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fourth_axiom) ).
thf(5,axiom,
! [X: $i] :
( ( third @ X )
= ( head @ ( tail @ ( tail @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',third_axiom) ).
thf(6,axiom,
! [X: $i] :
( ( second @ X )
= ( head @ ( tail @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second_axiom) ).
thf(7,axiom,
! [X: $i] :
( ( first @ X )
= ( head @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first_axiom) ).
thf(8,axiom,
! [X: $i,Y: $i] :
( ( tail @ ( concatenate @ X @ Y ) )
= Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tail_axiom) ).
thf(9,axiom,
! [X: $i,Y: $i] :
( ( head @ ( concatenate @ X @ Y ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',head_axiom) ).
thf(10,axiom,
! [E: $i,K: $i] :
( ( extract @ ( sign @ E @ ( inverse @ K ) ) @ K )
= E ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sign_axiom) ).
thf(11,axiom,
! [E: $i,K: $i] :
( ( symmetric_decrypt @ ( symmetric_encrypt @ E @ K ) @ K )
= E ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_decrypt_axiom) ).
thf(12,axiom,
! [E: $i,K: $i] :
( ( decrypt @ ( encrypt @ E @ K ) @ ( inverse @ K ) )
= E ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',decrypt_axiom) ).
thf(13,axiom,
! [E: $i] :
( ( knows @ E )
=> ( ( knows @ ( head @ E ) )
& ( knows @ ( tail @ E ) )
& ( knows @ ( hash @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',construct_message_3) ).
thf(14,axiom,
! [E1: $i,E2: $i] :
( ( knows @ ( concatenate @ E1 @ E2 ) )
=> ( ( knows @ E1 )
& ( knows @ E2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',construct_message_2) ).
thf(15,axiom,
! [E1: $i,E2: $i] :
( ( ( knows @ E1 )
& ( knows @ E2 ) )
=> ( ( knows @ ( concatenate @ E1 @ E2 ) )
& ( knows @ ( encrypt @ E1 @ E2 ) )
& ( knows @ ( symmetric_encrypt @ E1 @ E2 ) )
& ( knows @ ( decrypt @ E1 @ E2 ) )
& ( knows @ ( symmetric_decrypt @ E1 @ E2 ) )
& ( knows @ ( extract @ E1 @ E2 ) )
& ( knows @ ( sign @ E1 @ E2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',construct_message_1) ).
thf(16,axiom,
! [E: $i,K: $i] :
( ( ( knows @ ( sign @ E @ ( inverse @ K ) ) )
& ( knows @ K ) )
=> ( knows @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sign_equation) ).
thf(17,axiom,
! [E1: $i,E2: $i] :
( ( ( knows @ ( symmetric_encrypt @ E1 @ E2 ) )
& ( knows @ E2 ) )
=> ( knows @ E1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_encrypt_equation) ).
thf(18,axiom,
! [E1: $i,E2: $i] :
( ( ( knows @ ( encrypt @ E1 @ E2 ) )
& ( knows @ ( inverse @ E2 ) ) )
=> ( knows @ E1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',encrypt_equation) ).
thf(19,conjecture,
knows @ secret,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',attack) ).
thf(20,negated_conjecture,
( ( knows @ secret )
= $false ),
inference(negate_conjecture,[status(cth)],[19]) ).
thf(21,plain,
( ( knows @ secret )
= $false ),
inference(unfold_def,[status(thm)],[20]) ).
thf(22,plain,
( ( ! [Init_1: $i,Init_2: $i,Init_3: $i,Resp_1: $i,Resp_2: $i] :
( ( knows @ ( concatenate @ n @ ( concatenate @ k_c @ ( sign @ ( concatenate @ c @ ( concatenate @ k_c @ eol ) ) @ ( inverse @ k_c ) ) ) ) )
& ( ( ( knows @ Resp_1 )
& ( knows @ Resp_2 )
& ( ( first @ ( extract @ Resp_2 @ k_ca ) )
= s )
& ( ( second @ ( extract @ ( decrypt @ Resp_1 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ Resp_2 @ k_ca ) ) ) )
= n ) )
=> ( knows @ ( symmetric_encrypt @ secret @ ( first @ ( extract @ ( decrypt @ Resp_1 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ Resp_2 @ k_ca ) ) ) ) ) ) )
& ( ( ( knows @ Init_1 )
& ( knows @ Init_2 )
& ( knows @ Init_3 )
& ( ( second @ ( extract @ Init_3 @ Init_2 ) )
= Init_2 ) )
=> ( knows @ ( concatenate @ ( encrypt @ ( sign @ ( concatenate @ ( kgen @ Init_2 ) @ ( concatenate @ Init_1 @ eol ) ) @ ( inverse @ k_s ) ) @ Init_2 ) @ ( sign @ ( concatenate @ s @ ( concatenate @ k_s @ eol ) ) @ ( inverse @ k_ca ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(23,plain,
( ( ( knows @ k_ca )
& ( knows @ ( inverse @ k_a ) )
& ( knows @ k_a ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(24,plain,
( ( ! [X: $i,Y: $i] :
( ( ( knows @ X )
& ( knows @ Y ) )
=> ( knows @ ( mac @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(25,plain,
( ( ! [X: $i] :
( ( fourth @ X )
= ( head @ ( tail @ ( tail @ ( tail @ X ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(26,plain,
( ( ! [X: $i] :
( ( third @ X )
= ( head @ ( tail @ ( tail @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(27,plain,
( ( ! [X: $i] :
( ( second @ X )
= ( head @ ( tail @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(28,plain,
( ( ! [X: $i] :
( ( first @ X )
= ( head @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i] :
( ( tail @ ( concatenate @ X @ Y ) )
= Y ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(30,plain,
( ( ! [X: $i,Y: $i] :
( ( head @ ( concatenate @ X @ Y ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(31,plain,
( ( ! [E: $i,K: $i] :
( ( extract @ ( sign @ E @ ( inverse @ K ) ) @ K )
= E ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(32,plain,
( ( ! [E: $i,K: $i] :
( ( symmetric_decrypt @ ( symmetric_encrypt @ E @ K ) @ K )
= E ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(33,plain,
( ( ! [E: $i,K: $i] :
( ( decrypt @ ( encrypt @ E @ K ) @ ( inverse @ K ) )
= E ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(34,plain,
( ( ! [E: $i] :
( ( knows @ E )
=> ( ( knows @ ( head @ E ) )
& ( knows @ ( tail @ E ) )
& ( knows @ ( hash @ E ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(35,plain,
( ( ! [E1: $i,E2: $i] :
( ( knows @ ( concatenate @ E1 @ E2 ) )
=> ( ( knows @ E1 )
& ( knows @ E2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(36,plain,
( ( ! [E1: $i,E2: $i] :
( ( ( knows @ E1 )
& ( knows @ E2 ) )
=> ( ( knows @ ( concatenate @ E1 @ E2 ) )
& ( knows @ ( encrypt @ E1 @ E2 ) )
& ( knows @ ( symmetric_encrypt @ E1 @ E2 ) )
& ( knows @ ( decrypt @ E1 @ E2 ) )
& ( knows @ ( symmetric_decrypt @ E1 @ E2 ) )
& ( knows @ ( extract @ E1 @ E2 ) )
& ( knows @ ( sign @ E1 @ E2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(37,plain,
( ( ! [E: $i,K: $i] :
( ( ( knows @ ( sign @ E @ ( inverse @ K ) ) )
& ( knows @ K ) )
=> ( knows @ E ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(38,plain,
( ( ! [E1: $i,E2: $i] :
( ( ( knows @ ( symmetric_encrypt @ E1 @ E2 ) )
& ( knows @ E2 ) )
=> ( knows @ E1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(39,plain,
( ( ! [E1: $i,E2: $i] :
( ( ( knows @ ( encrypt @ E1 @ E2 ) )
& ( knows @ ( inverse @ E2 ) ) )
=> ( knows @ E1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(40,plain,
( ( ~ ( knows @ secret ) )
= $true ),
inference(polarity_switch,[status(thm)],[21]) ).
thf(41,plain,
( ( ! [Init_1: $i,Init_2: $i,Init_3: $i] :
( ! [Resp_1: $i,Resp_2: $i] :
( ~ ( knows @ Resp_1 )
| ~ ( knows @ Resp_2 )
| ( ( first @ ( extract @ Resp_2 @ k_ca ) )
!= s )
| ( ( second @ ( extract @ ( decrypt @ Resp_1 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ Resp_2 @ k_ca ) ) ) )
!= n )
| ( knows @ ( symmetric_encrypt @ secret @ ( first @ ( extract @ ( decrypt @ Resp_1 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ Resp_2 @ k_ca ) ) ) ) ) ) )
& ( knows @ ( concatenate @ n @ ( concatenate @ k_c @ ( sign @ ( concatenate @ c @ ( concatenate @ k_c @ eol ) ) @ ( inverse @ k_c ) ) ) ) )
& ( ~ ( knows @ Init_1 )
| ~ ( knows @ Init_2 )
| ~ ( knows @ Init_3 )
| ( ( second @ ( extract @ Init_3 @ Init_2 ) )
!= Init_2 )
| ( knows @ ( concatenate @ ( encrypt @ ( sign @ ( concatenate @ ( kgen @ Init_2 ) @ ( concatenate @ Init_1 @ eol ) ) @ ( inverse @ k_s ) ) @ Init_2 ) @ ( sign @ ( concatenate @ s @ ( concatenate @ k_s @ eol ) ) @ ( inverse @ k_ca ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(42,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( knows @ X )
| ~ ( knows @ Y )
| ( knows @ ( mac @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(43,plain,
( ( ! [E: $i] :
( ~ ( knows @ E )
| ( knows @ ( head @ E ) ) )
& ! [E: $i] :
( ~ ( knows @ E )
| ( knows @ ( tail @ E ) ) )
& ! [E: $i] :
( ~ ( knows @ E )
| ( knows @ ( hash @ E ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(44,plain,
( ( ! [E1: $i] :
( ! [E2: $i] :
~ ( knows @ ( concatenate @ E1 @ E2 ) )
| ( knows @ E1 ) )
& ! [E1: $i,E2: $i] :
( ~ ( knows @ ( concatenate @ E1 @ E2 ) )
| ( knows @ E2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(45,plain,
( ( ! [E1: $i,E2: $i] :
( ~ ( knows @ E1 )
| ~ ( knows @ E2 )
| ( knows @ ( concatenate @ E1 @ E2 ) ) )
& ! [E1: $i,E2: $i] :
( ~ ( knows @ E1 )
| ~ ( knows @ E2 )
| ( knows @ ( encrypt @ E1 @ E2 ) ) )
& ! [E1: $i,E2: $i] :
( ~ ( knows @ E1 )
| ~ ( knows @ E2 )
| ( knows @ ( symmetric_encrypt @ E1 @ E2 ) ) )
& ! [E1: $i,E2: $i] :
( ~ ( knows @ E1 )
| ~ ( knows @ E2 )
| ( knows @ ( decrypt @ E1 @ E2 ) ) )
& ! [E1: $i,E2: $i] :
( ~ ( knows @ E1 )
| ~ ( knows @ E2 )
| ( knows @ ( symmetric_decrypt @ E1 @ E2 ) ) )
& ! [E1: $i,E2: $i] :
( ~ ( knows @ E1 )
| ~ ( knows @ E2 )
| ( knows @ ( extract @ E1 @ E2 ) ) )
& ! [E1: $i,E2: $i] :
( ~ ( knows @ E1 )
| ~ ( knows @ E2 )
| ( knows @ ( sign @ E1 @ E2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(46,plain,
( ( ! [E: $i] :
( ! [K: $i] :
( ~ ( knows @ ( sign @ E @ ( inverse @ K ) ) )
| ~ ( knows @ K ) )
| ( knows @ E ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(47,plain,
( ( ! [E1: $i] :
( ! [E2: $i] :
( ~ ( knows @ ( symmetric_encrypt @ E1 @ E2 ) )
| ~ ( knows @ E2 ) )
| ( knows @ E1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(48,plain,
( ( ! [E1: $i] :
( ! [E2: $i] :
( ~ ( knows @ ( encrypt @ E1 @ E2 ) )
| ~ ( knows @ ( inverse @ E2 ) ) )
| ( knows @ E1 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(49,plain,
( ( ! [E1: $i] :
( ! [E2: $i] :
( ~ ( knows @ ( encrypt @ E1 @ E2 ) )
| ~ ( knows @ ( inverse @ E2 ) ) )
| ( knows @ E1 ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(50,plain,
( ( ! [E1: $i] :
( ! [E2: $i] :
( ~ ( knows @ ( symmetric_encrypt @ E1 @ E2 ) )
| ~ ( knows @ E2 ) )
| ( knows @ E1 ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(51,plain,
( ( ! [E: $i] :
( ! [K: $i] :
( ~ ( knows @ ( sign @ E @ ( inverse @ K ) ) )
| ~ ( knows @ K ) )
| ( knows @ E ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(52,plain,
( ( ! [E1: $i,E2: $i] :
( ~ ( knows @ E1 )
| ~ ( knows @ E2 )
| ( knows @ ( concatenate @ E1 @ E2 ) ) )
& ! [E1: $i,E2: $i] :
( ~ ( knows @ E1 )
| ~ ( knows @ E2 )
| ( knows @ ( encrypt @ E1 @ E2 ) ) )
& ! [E1: $i,E2: $i] :
( ~ ( knows @ E1 )
| ~ ( knows @ E2 )
| ( knows @ ( symmetric_encrypt @ E1 @ E2 ) ) )
& ! [E1: $i,E2: $i] :
( ~ ( knows @ E1 )
| ~ ( knows @ E2 )
| ( knows @ ( decrypt @ E1 @ E2 ) ) )
& ! [E1: $i,E2: $i] :
( ~ ( knows @ E1 )
| ~ ( knows @ E2 )
| ( knows @ ( symmetric_decrypt @ E1 @ E2 ) ) )
& ! [E1: $i,E2: $i] :
( ~ ( knows @ E1 )
| ~ ( knows @ E2 )
| ( knows @ ( extract @ E1 @ E2 ) ) )
& ! [E1: $i,E2: $i] :
( ~ ( knows @ E1 )
| ~ ( knows @ E2 )
| ( knows @ ( sign @ E1 @ E2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(53,plain,
( ( ! [E1: $i] :
( ! [E2: $i] :
~ ( knows @ ( concatenate @ E1 @ E2 ) )
| ( knows @ E1 ) )
& ! [E1: $i,E2: $i] :
( ~ ( knows @ ( concatenate @ E1 @ E2 ) )
| ( knows @ E2 ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(54,plain,
( ( ! [E: $i] :
( ~ ( knows @ E )
| ( knows @ ( head @ E ) ) )
& ! [E: $i] :
( ~ ( knows @ E )
| ( knows @ ( tail @ E ) ) )
& ! [E: $i] :
( ~ ( knows @ E )
| ( knows @ ( hash @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(55,plain,
( ( ! [E: $i,K: $i] :
( ( decrypt @ ( encrypt @ E @ K ) @ ( inverse @ K ) )
= E ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(56,plain,
( ( ! [E: $i,K: $i] :
( ( symmetric_decrypt @ ( symmetric_encrypt @ E @ K ) @ K )
= E ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(57,plain,
( ( ! [E: $i,K: $i] :
( ( extract @ ( sign @ E @ ( inverse @ K ) ) @ K )
= E ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(58,plain,
( ( ! [X: $i,Y: $i] :
( ( head @ ( concatenate @ X @ Y ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(59,plain,
( ( ! [X: $i,Y: $i] :
( ( tail @ ( concatenate @ X @ Y ) )
= Y ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(60,plain,
( ( ! [X: $i] :
( ( first @ X )
= ( head @ X ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(61,plain,
( ( ! [X: $i] :
( ( second @ X )
= ( head @ ( tail @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(62,plain,
( ( ! [X: $i] :
( ( third @ X )
= ( head @ ( tail @ ( tail @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(63,plain,
( ( ! [X: $i] :
( ( fourth @ X )
= ( head @ ( tail @ ( tail @ ( tail @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(64,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( knows @ X )
| ~ ( knows @ Y )
| ( knows @ ( mac @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(65,plain,
( ( ( knows @ k_ca )
& ( knows @ ( inverse @ k_a ) )
& ( knows @ k_a ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(66,plain,
( ( ! [Init_1: $i,Init_2: $i,Init_3: $i] :
( ! [Resp_1: $i,Resp_2: $i] :
( ~ ( knows @ Resp_1 )
| ~ ( knows @ Resp_2 )
| ( ( first @ ( extract @ Resp_2 @ k_ca ) )
!= s )
| ( ( second @ ( extract @ ( decrypt @ Resp_1 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ Resp_2 @ k_ca ) ) ) )
!= n )
| ( knows @ ( symmetric_encrypt @ secret @ ( first @ ( extract @ ( decrypt @ Resp_1 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ Resp_2 @ k_ca ) ) ) ) ) ) )
& ( knows @ ( concatenate @ n @ ( concatenate @ k_c @ ( sign @ ( concatenate @ c @ ( concatenate @ k_c @ eol ) ) @ ( inverse @ k_c ) ) ) ) )
& ( ~ ( knows @ Init_1 )
| ~ ( knows @ Init_2 )
| ~ ( knows @ Init_3 )
| ( ( second @ ( extract @ Init_3 @ Init_2 ) )
!= Init_2 )
| ( knows @ ( concatenate @ ( encrypt @ ( sign @ ( concatenate @ ( kgen @ Init_2 ) @ ( concatenate @ Init_1 @ eol ) ) @ ( inverse @ k_s ) ) @ Init_2 ) @ ( sign @ ( concatenate @ s @ ( concatenate @ k_s @ eol ) ) @ ( inverse @ k_ca ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(67,plain,
( ( ~ ( knows @ secret ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(68,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( knows @ SX3 )
| ~ ( knows @ SX4 )
| ( ( first @ ( extract @ SX4 @ k_ca ) )
!= s )
| ( ( second @ ( extract @ ( decrypt @ SX3 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SX4 @ k_ca ) ) ) )
!= n )
| ( knows @ ( symmetric_encrypt @ secret @ ( first @ ( extract @ ( decrypt @ SX3 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SX4 @ k_ca ) ) ) ) ) ) )
| ~ ( knows @ ( concatenate @ n @ ( concatenate @ k_c @ ( sign @ ( concatenate @ c @ ( concatenate @ k_c @ eol ) ) @ ( inverse @ k_c ) ) ) ) ) )
| ~ ( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ~ ( knows @ SX2 )
| ( ( second @ ( extract @ SX2 @ SX1 ) )
!= SX1 )
| ( knows @ ( concatenate @ ( encrypt @ ( sign @ ( concatenate @ ( kgen @ SX1 ) @ ( concatenate @ SX0 @ eol ) ) @ ( inverse @ k_s ) ) @ SX1 ) @ ( sign @ ( concatenate @ s @ ( concatenate @ k_s @ eol ) ) @ ( inverse @ k_ca ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(69,plain,
( ( ~ ( ~ ~ ( ~ ( knows @ k_ca )
| ~ ( knows @ ( inverse @ k_a ) ) )
| ~ ( knows @ k_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(70,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( knows @ ( concatenate @ SX0 @ SX1 ) )
| ( knows @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ ( concatenate @ SX0 @ SX1 ) )
| ( knows @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(71,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( knows @ SX0 )
| ( knows @ ( head @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( knows @ SX0 )
| ( knows @ ( tail @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( knows @ SX0 )
| ( knows @ ( hash @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(72,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( concatenate @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( encrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( symmetric_encrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( decrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( symmetric_decrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( extract @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( sign @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(73,plain,
! [SV1: $i] :
( ( ! [SY32: $i] :
( ~ ( knows @ ( encrypt @ SV1 @ SY32 ) )
| ~ ( knows @ ( inverse @ SY32 ) ) )
| ( knows @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(74,plain,
! [SV2: $i] :
( ( ! [SY33: $i] :
( ~ ( knows @ ( symmetric_encrypt @ SV2 @ SY33 ) )
| ~ ( knows @ SY33 ) )
| ( knows @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(75,plain,
! [SV3: $i] :
( ( ! [SY34: $i] :
( ~ ( knows @ ( sign @ SV3 @ ( inverse @ SY34 ) ) )
| ~ ( knows @ SY34 ) )
| ( knows @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(76,plain,
! [SV4: $i] :
( ( ! [SY35: $i] :
( ( decrypt @ ( encrypt @ SV4 @ SY35 ) @ ( inverse @ SY35 ) )
= SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(77,plain,
! [SV5: $i] :
( ( ! [SY36: $i] :
( ( symmetric_decrypt @ ( symmetric_encrypt @ SV5 @ SY36 ) @ SY36 )
= SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(78,plain,
! [SV6: $i] :
( ( ! [SY37: $i] :
( ( extract @ ( sign @ SV6 @ ( inverse @ SY37 ) ) @ SY37 )
= SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(79,plain,
! [SV7: $i] :
( ( ! [SY38: $i] :
( ( head @ ( concatenate @ SV7 @ SY38 ) )
= SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(80,plain,
! [SV8: $i] :
( ( ! [SY39: $i] :
( ( tail @ ( concatenate @ SV8 @ SY39 ) )
= SY39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(81,plain,
! [SV9: $i] :
( ( ( first @ SV9 )
= ( head @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(82,plain,
! [SV10: $i] :
( ( ( second @ SV10 )
= ( head @ ( tail @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(83,plain,
! [SV11: $i] :
( ( ( third @ SV11 )
= ( head @ ( tail @ ( tail @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(84,plain,
! [SV12: $i] :
( ( ( fourth @ SV12 )
= ( head @ ( tail @ ( tail @ ( tail @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(85,plain,
! [SV13: $i] :
( ( ! [SY40: $i] :
( ~ ( knows @ SV13 )
| ~ ( knows @ SY40 )
| ( knows @ ( mac @ SV13 @ SY40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(86,plain,
( ( knows @ secret )
= $false ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(87,plain,
! [SV14: $i] :
( ( ! [SY41: $i,SY42: $i] :
~ ( ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( knows @ SX3 )
| ~ ( knows @ SX4 )
| ( ( first @ ( extract @ SX4 @ k_ca ) )
!= s )
| ( ( second @ ( extract @ ( decrypt @ SX3 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SX4 @ k_ca ) ) ) )
!= n )
| ( knows @ ( symmetric_encrypt @ secret @ ( first @ ( extract @ ( decrypt @ SX3 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SX4 @ k_ca ) ) ) ) ) ) )
| ~ ( knows @ ( concatenate @ n @ ( concatenate @ k_c @ ( sign @ ( concatenate @ c @ ( concatenate @ k_c @ eol ) ) @ ( inverse @ k_c ) ) ) ) ) )
| ~ ( ~ ( knows @ SV14 )
| ~ ( knows @ SY41 )
| ~ ( knows @ SY42 )
| ( ( second @ ( extract @ SY42 @ SY41 ) )
!= SY41 )
| ( knows @ ( concatenate @ ( encrypt @ ( sign @ ( concatenate @ ( kgen @ SY41 ) @ ( concatenate @ SV14 @ eol ) ) @ ( inverse @ k_s ) ) @ SY41 ) @ ( sign @ ( concatenate @ s @ ( concatenate @ k_s @ eol ) ) @ ( inverse @ k_ca ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(88,plain,
( ( ~ ~ ( ~ ( knows @ k_ca )
| ~ ( knows @ ( inverse @ k_a ) ) )
| ~ ( knows @ k_a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(89,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( knows @ ( concatenate @ SX0 @ SX1 ) )
| ( knows @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ ( concatenate @ SX0 @ SX1 ) )
| ( knows @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(90,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( knows @ SX0 )
| ( knows @ ( head @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( knows @ SX0 )
| ( knows @ ( tail @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( knows @ SX0 )
| ( knows @ ( hash @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(91,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( concatenate @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( encrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( symmetric_encrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( decrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( symmetric_decrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( extract @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( sign @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(92,plain,
! [SV1: $i] :
( ( ( ! [SY32: $i] :
( ~ ( knows @ ( encrypt @ SV1 @ SY32 ) )
| ~ ( knows @ ( inverse @ SY32 ) ) ) )
= $true )
| ( ( knows @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(93,plain,
! [SV2: $i] :
( ( ( ! [SY33: $i] :
( ~ ( knows @ ( symmetric_encrypt @ SV2 @ SY33 ) )
| ~ ( knows @ SY33 ) ) )
= $true )
| ( ( knows @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(94,plain,
! [SV3: $i] :
( ( ( ! [SY34: $i] :
( ~ ( knows @ ( sign @ SV3 @ ( inverse @ SY34 ) ) )
| ~ ( knows @ SY34 ) ) )
= $true )
| ( ( knows @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(95,plain,
! [SV15: $i,SV4: $i] :
( ( ( decrypt @ ( encrypt @ SV4 @ SV15 ) @ ( inverse @ SV15 ) )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(96,plain,
! [SV16: $i,SV5: $i] :
( ( ( symmetric_decrypt @ ( symmetric_encrypt @ SV5 @ SV16 ) @ SV16 )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(97,plain,
! [SV17: $i,SV6: $i] :
( ( ( extract @ ( sign @ SV6 @ ( inverse @ SV17 ) ) @ SV17 )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(98,plain,
! [SV18: $i,SV7: $i] :
( ( ( head @ ( concatenate @ SV7 @ SV18 ) )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(99,plain,
! [SV19: $i,SV8: $i] :
( ( ( tail @ ( concatenate @ SV8 @ SV19 ) )
= SV19 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(100,plain,
! [SV20: $i,SV13: $i] :
( ( ~ ( knows @ SV13 )
| ~ ( knows @ SV20 )
| ( knows @ ( mac @ SV13 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(101,plain,
! [SV21: $i,SV14: $i] :
( ( ! [SY45: $i] :
~ ( ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( knows @ SX3 )
| ~ ( knows @ SX4 )
| ( ( first @ ( extract @ SX4 @ k_ca ) )
!= s )
| ( ( second @ ( extract @ ( decrypt @ SX3 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SX4 @ k_ca ) ) ) )
!= n )
| ( knows @ ( symmetric_encrypt @ secret @ ( first @ ( extract @ ( decrypt @ SX3 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SX4 @ k_ca ) ) ) ) ) ) )
| ~ ( knows @ ( concatenate @ n @ ( concatenate @ k_c @ ( sign @ ( concatenate @ c @ ( concatenate @ k_c @ eol ) ) @ ( inverse @ k_c ) ) ) ) ) )
| ~ ( ~ ( knows @ SV14 )
| ~ ( knows @ SV21 )
| ~ ( knows @ SY45 )
| ( ( second @ ( extract @ SY45 @ SV21 ) )
!= SV21 )
| ( knows @ ( concatenate @ ( encrypt @ ( sign @ ( concatenate @ ( kgen @ SV21 ) @ ( concatenate @ SV14 @ eol ) ) @ ( inverse @ k_s ) ) @ SV21 ) @ ( sign @ ( concatenate @ s @ ( concatenate @ k_s @ eol ) ) @ ( inverse @ k_ca ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(102,plain,
( ( ~ ~ ( ~ ( knows @ k_ca )
| ~ ( knows @ ( inverse @ k_a ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(103,plain,
( ( ~ ( knows @ k_a ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(104,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( knows @ ( concatenate @ SX0 @ SX1 ) )
| ( knows @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(105,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ ( concatenate @ SX0 @ SX1 ) )
| ( knows @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(106,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( knows @ SX0 )
| ( knows @ ( head @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( knows @ SX0 )
| ( knows @ ( tail @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(107,plain,
( ( ~ ! [SX0: $i] :
( ~ ( knows @ SX0 )
| ( knows @ ( hash @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(108,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( concatenate @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( encrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( symmetric_encrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( decrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( symmetric_decrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( extract @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(109,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( sign @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(110,plain,
! [SV22: $i,SV1: $i] :
( ( ( ~ ( knows @ ( encrypt @ SV1 @ SV22 ) )
| ~ ( knows @ ( inverse @ SV22 ) ) )
= $true )
| ( ( knows @ SV1 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(111,plain,
! [SV23: $i,SV2: $i] :
( ( ( ~ ( knows @ ( symmetric_encrypt @ SV2 @ SV23 ) )
| ~ ( knows @ SV23 ) )
= $true )
| ( ( knows @ SV2 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(112,plain,
! [SV24: $i,SV3: $i] :
( ( ( ~ ( knows @ ( sign @ SV3 @ ( inverse @ SV24 ) ) )
| ~ ( knows @ SV24 ) )
= $true )
| ( ( knows @ SV3 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(113,plain,
! [SV20: $i,SV13: $i] :
( ( ( ~ ( knows @ SV13 )
| ~ ( knows @ SV20 ) )
= $true )
| ( ( knows @ ( mac @ SV13 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(114,plain,
! [SV25: $i,SV21: $i,SV14: $i] :
( ( ~ ( ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( knows @ SX3 )
| ~ ( knows @ SX4 )
| ( ( first @ ( extract @ SX4 @ k_ca ) )
!= s )
| ( ( second @ ( extract @ ( decrypt @ SX3 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SX4 @ k_ca ) ) ) )
!= n )
| ( knows @ ( symmetric_encrypt @ secret @ ( first @ ( extract @ ( decrypt @ SX3 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SX4 @ k_ca ) ) ) ) ) ) )
| ~ ( knows @ ( concatenate @ n @ ( concatenate @ k_c @ ( sign @ ( concatenate @ c @ ( concatenate @ k_c @ eol ) ) @ ( inverse @ k_c ) ) ) ) ) )
| ~ ( ~ ( knows @ SV14 )
| ~ ( knows @ SV21 )
| ~ ( knows @ SV25 )
| ( ( second @ ( extract @ SV25 @ SV21 ) )
!= SV21 )
| ( knows @ ( concatenate @ ( encrypt @ ( sign @ ( concatenate @ ( kgen @ SV21 ) @ ( concatenate @ SV14 @ eol ) ) @ ( inverse @ k_s ) ) @ SV21 ) @ ( sign @ ( concatenate @ s @ ( concatenate @ k_s @ eol ) ) @ ( inverse @ k_ca ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(115,plain,
( ( ~ ( ~ ( knows @ k_ca )
| ~ ( knows @ ( inverse @ k_a ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(116,plain,
( ( knows @ k_a )
= $true ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(117,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( knows @ ( concatenate @ SX0 @ SX1 ) )
| ( knows @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(118,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( knows @ ( concatenate @ SX0 @ SX1 ) )
| ( knows @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(119,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( knows @ SX0 )
| ( knows @ ( head @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( knows @ SX0 )
| ( knows @ ( tail @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(120,plain,
( ( ! [SX0: $i] :
( ~ ( knows @ SX0 )
| ( knows @ ( hash @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(121,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( concatenate @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( encrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( symmetric_encrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( decrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( symmetric_decrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( extract @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(122,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( sign @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(123,plain,
! [SV22: $i,SV1: $i] :
( ( ( ~ ( knows @ ( encrypt @ SV1 @ SV22 ) ) )
= $true )
| ( ( ~ ( knows @ ( inverse @ SV22 ) ) )
= $true )
| ( ( knows @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(124,plain,
! [SV23: $i,SV2: $i] :
( ( ( ~ ( knows @ ( symmetric_encrypt @ SV2 @ SV23 ) ) )
= $true )
| ( ( ~ ( knows @ SV23 ) )
= $true )
| ( ( knows @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(125,plain,
! [SV24: $i,SV3: $i] :
( ( ( ~ ( knows @ ( sign @ SV3 @ ( inverse @ SV24 ) ) ) )
= $true )
| ( ( ~ ( knows @ SV24 ) )
= $true )
| ( ( knows @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(126,plain,
! [SV20: $i,SV13: $i] :
( ( ( ~ ( knows @ SV13 ) )
= $true )
| ( ( ~ ( knows @ SV20 ) )
= $true )
| ( ( knows @ ( mac @ SV13 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(127,plain,
! [SV25: $i,SV21: $i,SV14: $i] :
( ( ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( knows @ SX3 )
| ~ ( knows @ SX4 )
| ( ( first @ ( extract @ SX4 @ k_ca ) )
!= s )
| ( ( second @ ( extract @ ( decrypt @ SX3 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SX4 @ k_ca ) ) ) )
!= n )
| ( knows @ ( symmetric_encrypt @ secret @ ( first @ ( extract @ ( decrypt @ SX3 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SX4 @ k_ca ) ) ) ) ) ) )
| ~ ( knows @ ( concatenate @ n @ ( concatenate @ k_c @ ( sign @ ( concatenate @ c @ ( concatenate @ k_c @ eol ) ) @ ( inverse @ k_c ) ) ) ) ) )
| ~ ( ~ ( knows @ SV14 )
| ~ ( knows @ SV21 )
| ~ ( knows @ SV25 )
| ( ( second @ ( extract @ SV25 @ SV21 ) )
!= SV21 )
| ( knows @ ( concatenate @ ( encrypt @ ( sign @ ( concatenate @ ( kgen @ SV21 ) @ ( concatenate @ SV14 @ eol ) ) @ ( inverse @ k_s ) ) @ SV21 ) @ ( sign @ ( concatenate @ s @ ( concatenate @ k_s @ eol ) ) @ ( inverse @ k_ca ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(128,plain,
( ( ~ ( knows @ k_ca )
| ~ ( knows @ ( inverse @ k_a ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(129,plain,
! [SV26: $i] :
( ( ! [SY50: $i] :
~ ( knows @ ( concatenate @ SV26 @ SY50 ) )
| ( knows @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(130,plain,
! [SV27: $i] :
( ( ! [SY51: $i] :
( ~ ( knows @ ( concatenate @ SV27 @ SY51 ) )
| ( knows @ SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(131,plain,
( ( ~ ! [SX0: $i] :
( ~ ( knows @ SX0 )
| ( knows @ ( head @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( knows @ SX0 )
| ( knows @ ( tail @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(132,plain,
! [SV28: $i] :
( ( ~ ( knows @ SV28 )
| ( knows @ ( hash @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(133,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( concatenate @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( encrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( symmetric_encrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( decrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( symmetric_decrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( extract @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(134,plain,
! [SV29: $i] :
( ( ! [SY52: $i] :
( ~ ( knows @ SV29 )
| ~ ( knows @ SY52 )
| ( knows @ ( sign @ SV29 @ SY52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(135,plain,
! [SV22: $i,SV1: $i] :
( ( ( knows @ ( encrypt @ SV1 @ SV22 ) )
= $false )
| ( ( ~ ( knows @ ( inverse @ SV22 ) ) )
= $true )
| ( ( knows @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(136,plain,
! [SV23: $i,SV2: $i] :
( ( ( knows @ ( symmetric_encrypt @ SV2 @ SV23 ) )
= $false )
| ( ( ~ ( knows @ SV23 ) )
= $true )
| ( ( knows @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(137,plain,
! [SV24: $i,SV3: $i] :
( ( ( knows @ ( sign @ SV3 @ ( inverse @ SV24 ) ) )
= $false )
| ( ( ~ ( knows @ SV24 ) )
= $true )
| ( ( knows @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(138,plain,
! [SV20: $i,SV13: $i] :
( ( ( knows @ SV13 )
= $false )
| ( ( ~ ( knows @ SV20 ) )
= $true )
| ( ( knows @ ( mac @ SV13 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(139,plain,
( ( ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( knows @ SX3 )
| ~ ( knows @ SX4 )
| ( ( first @ ( extract @ SX4 @ k_ca ) )
!= s )
| ( ( second @ ( extract @ ( decrypt @ SX3 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SX4 @ k_ca ) ) ) )
!= n )
| ( knows @ ( symmetric_encrypt @ secret @ ( first @ ( extract @ ( decrypt @ SX3 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SX4 @ k_ca ) ) ) ) ) ) )
| ~ ( knows @ ( concatenate @ n @ ( concatenate @ k_c @ ( sign @ ( concatenate @ c @ ( concatenate @ k_c @ eol ) ) @ ( inverse @ k_c ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(140,plain,
! [SV25: $i,SV21: $i,SV14: $i] :
( ( ~ ( ~ ( knows @ SV14 )
| ~ ( knows @ SV21 )
| ~ ( knows @ SV25 )
| ( ( second @ ( extract @ SV25 @ SV21 ) )
!= SV21 )
| ( knows @ ( concatenate @ ( encrypt @ ( sign @ ( concatenate @ ( kgen @ SV21 ) @ ( concatenate @ SV14 @ eol ) ) @ ( inverse @ k_s ) ) @ SV21 ) @ ( sign @ ( concatenate @ s @ ( concatenate @ k_s @ eol ) ) @ ( inverse @ k_ca ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(141,plain,
( ( ~ ( knows @ k_ca ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(142,plain,
( ( ~ ( knows @ ( inverse @ k_a ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(143,plain,
! [SV26: $i] :
( ( ( ! [SY50: $i] :
~ ( knows @ ( concatenate @ SV26 @ SY50 ) ) )
= $true )
| ( ( knows @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(144,plain,
! [SV30: $i,SV27: $i] :
( ( ~ ( knows @ ( concatenate @ SV27 @ SV30 ) )
| ( knows @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(145,plain,
( ( ~ ! [SX0: $i] :
( ~ ( knows @ SX0 )
| ( knows @ ( head @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(146,plain,
( ( ~ ! [SX0: $i] :
( ~ ( knows @ SX0 )
| ( knows @ ( tail @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(147,plain,
! [SV28: $i] :
( ( ( ~ ( knows @ SV28 ) )
= $true )
| ( ( knows @ ( hash @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(148,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( concatenate @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( encrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( symmetric_encrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( decrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( symmetric_decrypt @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(149,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( extract @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(150,plain,
! [SV31: $i,SV29: $i] :
( ( ~ ( knows @ SV29 )
| ~ ( knows @ SV31 )
| ( knows @ ( sign @ SV29 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(151,plain,
! [SV1: $i,SV22: $i] :
( ( ( knows @ ( inverse @ SV22 ) )
= $false )
| ( ( knows @ ( encrypt @ SV1 @ SV22 ) )
= $false )
| ( ( knows @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(152,plain,
! [SV2: $i,SV23: $i] :
( ( ( knows @ SV23 )
= $false )
| ( ( knows @ ( symmetric_encrypt @ SV2 @ SV23 ) )
= $false )
| ( ( knows @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(153,plain,
! [SV3: $i,SV24: $i] :
( ( ( knows @ SV24 )
= $false )
| ( ( knows @ ( sign @ SV3 @ ( inverse @ SV24 ) ) )
= $false )
| ( ( knows @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(154,plain,
! [SV13: $i,SV20: $i] :
( ( ( knows @ SV20 )
= $false )
| ( ( knows @ SV13 )
= $false )
| ( ( knows @ ( mac @ SV13 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(155,plain,
( ( ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( knows @ SX3 )
| ~ ( knows @ SX4 )
| ( ( first @ ( extract @ SX4 @ k_ca ) )
!= s )
| ( ( second @ ( extract @ ( decrypt @ SX3 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SX4 @ k_ca ) ) ) )
!= n )
| ( knows @ ( symmetric_encrypt @ secret @ ( first @ ( extract @ ( decrypt @ SX3 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SX4 @ k_ca ) ) ) ) ) ) )
| ~ ( knows @ ( concatenate @ n @ ( concatenate @ k_c @ ( sign @ ( concatenate @ c @ ( concatenate @ k_c @ eol ) ) @ ( inverse @ k_c ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(156,plain,
! [SV25: $i,SV21: $i,SV14: $i] :
( ( ~ ( knows @ SV14 )
| ~ ( knows @ SV21 )
| ~ ( knows @ SV25 )
| ( ( second @ ( extract @ SV25 @ SV21 ) )
!= SV21 )
| ( knows @ ( concatenate @ ( encrypt @ ( sign @ ( concatenate @ ( kgen @ SV21 ) @ ( concatenate @ SV14 @ eol ) ) @ ( inverse @ k_s ) ) @ SV21 ) @ ( sign @ ( concatenate @ s @ ( concatenate @ k_s @ eol ) ) @ ( inverse @ k_ca ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(157,plain,
( ( knows @ k_ca )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(158,plain,
( ( knows @ ( inverse @ k_a ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(159,plain,
! [SV32: $i,SV26: $i] :
( ( ( ~ ( knows @ ( concatenate @ SV26 @ SV32 ) ) )
= $true )
| ( ( knows @ SV26 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(160,plain,
! [SV30: $i,SV27: $i] :
( ( ( ~ ( knows @ ( concatenate @ SV27 @ SV30 ) ) )
= $true )
| ( ( knows @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(161,plain,
( ( ! [SX0: $i] :
( ~ ( knows @ SX0 )
| ( knows @ ( head @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(162,plain,
( ( ! [SX0: $i] :
( ~ ( knows @ SX0 )
| ( knows @ ( tail @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(163,plain,
! [SV28: $i] :
( ( ( knows @ SV28 )
= $false )
| ( ( knows @ ( hash @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(164,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( concatenate @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( encrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( symmetric_encrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( decrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( symmetric_decrypt @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(165,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( extract @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(166,plain,
! [SV31: $i,SV29: $i] :
( ( ( ~ ( knows @ SV29 )
| ~ ( knows @ SV31 ) )
= $true )
| ( ( knows @ ( sign @ SV29 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(167,plain,
( ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( knows @ SX3 )
| ~ ( knows @ SX4 )
| ( ( first @ ( extract @ SX4 @ k_ca ) )
!= s )
| ( ( second @ ( extract @ ( decrypt @ SX3 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SX4 @ k_ca ) ) ) )
!= n )
| ( knows @ ( symmetric_encrypt @ secret @ ( first @ ( extract @ ( decrypt @ SX3 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SX4 @ k_ca ) ) ) ) ) ) )
| ~ ( knows @ ( concatenate @ n @ ( concatenate @ k_c @ ( sign @ ( concatenate @ c @ ( concatenate @ k_c @ eol ) ) @ ( inverse @ k_c ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(168,plain,
! [SV25: $i,SV21: $i,SV14: $i] :
( ( ( ~ ( knows @ SV14 )
| ~ ( knows @ SV21 )
| ~ ( knows @ SV25 )
| ( ( second @ ( extract @ SV25 @ SV21 ) )
!= SV21 ) )
= $true )
| ( ( knows @ ( concatenate @ ( encrypt @ ( sign @ ( concatenate @ ( kgen @ SV21 ) @ ( concatenate @ SV14 @ eol ) ) @ ( inverse @ k_s ) ) @ SV21 ) @ ( sign @ ( concatenate @ s @ ( concatenate @ k_s @ eol ) ) @ ( inverse @ k_ca ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(169,plain,
! [SV32: $i,SV26: $i] :
( ( ( knows @ ( concatenate @ SV26 @ SV32 ) )
= $false )
| ( ( knows @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(170,plain,
! [SV30: $i,SV27: $i] :
( ( ( knows @ ( concatenate @ SV27 @ SV30 ) )
= $false )
| ( ( knows @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(171,plain,
! [SV33: $i] :
( ( ~ ( knows @ SV33 )
| ( knows @ ( head @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(172,plain,
! [SV34: $i] :
( ( ~ ( knows @ SV34 )
| ( knows @ ( tail @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(173,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( concatenate @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( encrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( symmetric_encrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( decrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( symmetric_decrypt @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(174,plain,
! [SV35: $i] :
( ( ! [SY53: $i] :
( ~ ( knows @ SV35 )
| ~ ( knows @ SY53 )
| ( knows @ ( extract @ SV35 @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(175,plain,
! [SV31: $i,SV29: $i] :
( ( ( ~ ( knows @ SV29 ) )
= $true )
| ( ( ~ ( knows @ SV31 ) )
= $true )
| ( ( knows @ ( sign @ SV29 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(176,plain,
( ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( knows @ SX3 )
| ~ ( knows @ SX4 )
| ( ( first @ ( extract @ SX4 @ k_ca ) )
!= s )
| ( ( second @ ( extract @ ( decrypt @ SX3 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SX4 @ k_ca ) ) ) )
!= n )
| ( knows @ ( symmetric_encrypt @ secret @ ( first @ ( extract @ ( decrypt @ SX3 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SX4 @ k_ca ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(177,plain,
( ( ~ ( knows @ ( concatenate @ n @ ( concatenate @ k_c @ ( sign @ ( concatenate @ c @ ( concatenate @ k_c @ eol ) ) @ ( inverse @ k_c ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(178,plain,
! [SV25: $i,SV21: $i,SV14: $i] :
( ( ( ~ ( knows @ SV14 )
| ~ ( knows @ SV21 )
| ~ ( knows @ SV25 ) )
= $true )
| ( ( ( ( second @ ( extract @ SV25 @ SV21 ) )
!= SV21 ) )
= $true )
| ( ( knows @ ( concatenate @ ( encrypt @ ( sign @ ( concatenate @ ( kgen @ SV21 ) @ ( concatenate @ SV14 @ eol ) ) @ ( inverse @ k_s ) ) @ SV21 ) @ ( sign @ ( concatenate @ s @ ( concatenate @ k_s @ eol ) ) @ ( inverse @ k_ca ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(179,plain,
! [SV33: $i] :
( ( ( ~ ( knows @ SV33 ) )
= $true )
| ( ( knows @ ( head @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(180,plain,
! [SV34: $i] :
( ( ( ~ ( knows @ SV34 ) )
= $true )
| ( ( knows @ ( tail @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(181,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( concatenate @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( encrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( symmetric_encrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( decrypt @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(182,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( symmetric_decrypt @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(183,plain,
! [SV36: $i,SV35: $i] :
( ( ~ ( knows @ SV35 )
| ~ ( knows @ SV36 )
| ( knows @ ( extract @ SV35 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(184,plain,
! [SV31: $i,SV29: $i] :
( ( ( knows @ SV29 )
= $false )
| ( ( ~ ( knows @ SV31 ) )
= $true )
| ( ( knows @ ( sign @ SV29 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(185,plain,
( ( ! [SX3: $i,SX4: $i] :
( ~ ( knows @ SX3 )
| ~ ( knows @ SX4 )
| ( ( first @ ( extract @ SX4 @ k_ca ) )
!= s )
| ( ( second @ ( extract @ ( decrypt @ SX3 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SX4 @ k_ca ) ) ) )
!= n )
| ( knows @ ( symmetric_encrypt @ secret @ ( first @ ( extract @ ( decrypt @ SX3 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SX4 @ k_ca ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(186,plain,
( ( knows @ ( concatenate @ n @ ( concatenate @ k_c @ ( sign @ ( concatenate @ c @ ( concatenate @ k_c @ eol ) ) @ ( inverse @ k_c ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(187,plain,
! [SV25: $i,SV21: $i,SV14: $i] :
( ( ( ~ ( knows @ SV14 )
| ~ ( knows @ SV21 ) )
= $true )
| ( ( ~ ( knows @ SV25 ) )
= $true )
| ( ( ( ( second @ ( extract @ SV25 @ SV21 ) )
!= SV21 ) )
= $true )
| ( ( knows @ ( concatenate @ ( encrypt @ ( sign @ ( concatenate @ ( kgen @ SV21 ) @ ( concatenate @ SV14 @ eol ) ) @ ( inverse @ k_s ) ) @ SV21 ) @ ( sign @ ( concatenate @ s @ ( concatenate @ k_s @ eol ) ) @ ( inverse @ k_ca ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(188,plain,
! [SV33: $i] :
( ( ( knows @ SV33 )
= $false )
| ( ( knows @ ( head @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(189,plain,
! [SV34: $i] :
( ( ( knows @ SV34 )
= $false )
| ( ( knows @ ( tail @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(190,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( concatenate @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( encrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( symmetric_encrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( decrypt @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(191,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( symmetric_decrypt @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(192,plain,
! [SV36: $i,SV35: $i] :
( ( ( ~ ( knows @ SV35 )
| ~ ( knows @ SV36 ) )
= $true )
| ( ( knows @ ( extract @ SV35 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(193,plain,
! [SV29: $i,SV31: $i] :
( ( ( knows @ SV31 )
= $false )
| ( ( knows @ SV29 )
= $false )
| ( ( knows @ ( sign @ SV29 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(194,plain,
! [SV37: $i] :
( ( ! [SY54: $i] :
( ~ ( knows @ SV37 )
| ~ ( knows @ SY54 )
| ( ( first @ ( extract @ SY54 @ k_ca ) )
!= s )
| ( ( second @ ( extract @ ( decrypt @ SV37 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SY54 @ k_ca ) ) ) )
!= n )
| ( knows @ ( symmetric_encrypt @ secret @ ( first @ ( extract @ ( decrypt @ SV37 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SY54 @ k_ca ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(195,plain,
! [SV25: $i,SV21: $i,SV14: $i] :
( ( ( ~ ( knows @ SV14 ) )
= $true )
| ( ( ~ ( knows @ SV21 ) )
= $true )
| ( ( ~ ( knows @ SV25 ) )
= $true )
| ( ( ( ( second @ ( extract @ SV25 @ SV21 ) )
!= SV21 ) )
= $true )
| ( ( knows @ ( concatenate @ ( encrypt @ ( sign @ ( concatenate @ ( kgen @ SV21 ) @ ( concatenate @ SV14 @ eol ) ) @ ( inverse @ k_s ) ) @ SV21 ) @ ( sign @ ( concatenate @ s @ ( concatenate @ k_s @ eol ) ) @ ( inverse @ k_ca ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(196,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( concatenate @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( encrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( symmetric_encrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( decrypt @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(197,plain,
! [SV38: $i] :
( ( ! [SY55: $i] :
( ~ ( knows @ SV38 )
| ~ ( knows @ SY55 )
| ( knows @ ( symmetric_decrypt @ SV38 @ SY55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(198,plain,
! [SV36: $i,SV35: $i] :
( ( ( ~ ( knows @ SV35 ) )
= $true )
| ( ( ~ ( knows @ SV36 ) )
= $true )
| ( ( knows @ ( extract @ SV35 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(199,plain,
! [SV39: $i,SV37: $i] :
( ( ~ ( knows @ SV37 )
| ~ ( knows @ SV39 )
| ( ( first @ ( extract @ SV39 @ k_ca ) )
!= s )
| ( ( second @ ( extract @ ( decrypt @ SV37 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SV39 @ k_ca ) ) ) )
!= n )
| ( knows @ ( symmetric_encrypt @ secret @ ( first @ ( extract @ ( decrypt @ SV37 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SV39 @ k_ca ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(200,plain,
! [SV25: $i,SV21: $i,SV14: $i] :
( ( ( knows @ SV14 )
= $false )
| ( ( ~ ( knows @ SV21 ) )
= $true )
| ( ( ~ ( knows @ SV25 ) )
= $true )
| ( ( ( ( second @ ( extract @ SV25 @ SV21 ) )
!= SV21 ) )
= $true )
| ( ( knows @ ( concatenate @ ( encrypt @ ( sign @ ( concatenate @ ( kgen @ SV21 ) @ ( concatenate @ SV14 @ eol ) ) @ ( inverse @ k_s ) ) @ SV21 ) @ ( sign @ ( concatenate @ s @ ( concatenate @ k_s @ eol ) ) @ ( inverse @ k_ca ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(201,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( concatenate @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( encrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( symmetric_encrypt @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(202,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( decrypt @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(203,plain,
! [SV40: $i,SV38: $i] :
( ( ~ ( knows @ SV38 )
| ~ ( knows @ SV40 )
| ( knows @ ( symmetric_decrypt @ SV38 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(204,plain,
! [SV36: $i,SV35: $i] :
( ( ( knows @ SV35 )
= $false )
| ( ( ~ ( knows @ SV36 ) )
= $true )
| ( ( knows @ ( extract @ SV35 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(205,plain,
! [SV39: $i,SV37: $i] :
( ( ( ~ ( knows @ SV37 )
| ~ ( knows @ SV39 )
| ( ( first @ ( extract @ SV39 @ k_ca ) )
!= s )
| ( ( second @ ( extract @ ( decrypt @ SV37 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SV39 @ k_ca ) ) ) )
!= n ) )
= $true )
| ( ( knows @ ( symmetric_encrypt @ secret @ ( first @ ( extract @ ( decrypt @ SV37 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SV39 @ k_ca ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(206,plain,
! [SV25: $i,SV14: $i,SV21: $i] :
( ( ( knows @ SV21 )
= $false )
| ( ( knows @ SV14 )
= $false )
| ( ( ~ ( knows @ SV25 ) )
= $true )
| ( ( ( ( second @ ( extract @ SV25 @ SV21 ) )
!= SV21 ) )
= $true )
| ( ( knows @ ( concatenate @ ( encrypt @ ( sign @ ( concatenate @ ( kgen @ SV21 ) @ ( concatenate @ SV14 @ eol ) ) @ ( inverse @ k_s ) ) @ SV21 ) @ ( sign @ ( concatenate @ s @ ( concatenate @ k_s @ eol ) ) @ ( inverse @ k_ca ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(207,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( concatenate @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( encrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( symmetric_encrypt @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(208,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( decrypt @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(209,plain,
! [SV40: $i,SV38: $i] :
( ( ( ~ ( knows @ SV38 )
| ~ ( knows @ SV40 ) )
= $true )
| ( ( knows @ ( symmetric_decrypt @ SV38 @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(210,plain,
! [SV35: $i,SV36: $i] :
( ( ( knows @ SV36 )
= $false )
| ( ( knows @ SV35 )
= $false )
| ( ( knows @ ( extract @ SV35 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(211,plain,
! [SV39: $i,SV37: $i] :
( ( ( ~ ( knows @ SV37 )
| ~ ( knows @ SV39 )
| ( ( first @ ( extract @ SV39 @ k_ca ) )
!= s ) )
= $true )
| ( ( ( ( second @ ( extract @ ( decrypt @ SV37 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SV39 @ k_ca ) ) ) )
!= n ) )
= $true )
| ( ( knows @ ( symmetric_encrypt @ secret @ ( first @ ( extract @ ( decrypt @ SV37 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SV39 @ k_ca ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(212,plain,
! [SV21: $i,SV14: $i,SV25: $i] :
( ( ( knows @ SV25 )
= $false )
| ( ( knows @ SV14 )
= $false )
| ( ( knows @ SV21 )
= $false )
| ( ( ( ( second @ ( extract @ SV25 @ SV21 ) )
!= SV21 ) )
= $true )
| ( ( knows @ ( concatenate @ ( encrypt @ ( sign @ ( concatenate @ ( kgen @ SV21 ) @ ( concatenate @ SV14 @ eol ) ) @ ( inverse @ k_s ) ) @ SV21 ) @ ( sign @ ( concatenate @ s @ ( concatenate @ k_s @ eol ) ) @ ( inverse @ k_ca ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(213,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( concatenate @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( encrypt @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( symmetric_encrypt @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(214,plain,
! [SV41: $i] :
( ( ! [SY56: $i] :
( ~ ( knows @ SV41 )
| ~ ( knows @ SY56 )
| ( knows @ ( decrypt @ SV41 @ SY56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(215,plain,
! [SV40: $i,SV38: $i] :
( ( ( ~ ( knows @ SV38 ) )
= $true )
| ( ( ~ ( knows @ SV40 ) )
= $true )
| ( ( knows @ ( symmetric_decrypt @ SV38 @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(216,plain,
! [SV39: $i,SV37: $i] :
( ( ( ~ ( knows @ SV37 )
| ~ ( knows @ SV39 ) )
= $true )
| ( ( ( ( first @ ( extract @ SV39 @ k_ca ) )
!= s ) )
= $true )
| ( ( ( ( second @ ( extract @ ( decrypt @ SV37 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SV39 @ k_ca ) ) ) )
!= n ) )
= $true )
| ( ( knows @ ( symmetric_encrypt @ secret @ ( first @ ( extract @ ( decrypt @ SV37 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SV39 @ k_ca ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(217,plain,
! [SV14: $i,SV21: $i,SV25: $i] :
( ( ( ( second @ ( extract @ SV25 @ SV21 ) )
= SV21 )
= $false )
| ( ( knows @ SV21 )
= $false )
| ( ( knows @ SV14 )
= $false )
| ( ( knows @ SV25 )
= $false )
| ( ( knows @ ( concatenate @ ( encrypt @ ( sign @ ( concatenate @ ( kgen @ SV21 ) @ ( concatenate @ SV14 @ eol ) ) @ ( inverse @ k_s ) ) @ SV21 ) @ ( sign @ ( concatenate @ s @ ( concatenate @ k_s @ eol ) ) @ ( inverse @ k_ca ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(218,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( concatenate @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( encrypt @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(219,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( symmetric_encrypt @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(220,plain,
! [SV42: $i,SV41: $i] :
( ( ~ ( knows @ SV41 )
| ~ ( knows @ SV42 )
| ( knows @ ( decrypt @ SV41 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(221,plain,
! [SV40: $i,SV38: $i] :
( ( ( knows @ SV38 )
= $false )
| ( ( ~ ( knows @ SV40 ) )
= $true )
| ( ( knows @ ( symmetric_decrypt @ SV38 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(222,plain,
! [SV39: $i,SV37: $i] :
( ( ( ~ ( knows @ SV37 ) )
= $true )
| ( ( ~ ( knows @ SV39 ) )
= $true )
| ( ( ( ( first @ ( extract @ SV39 @ k_ca ) )
!= s ) )
= $true )
| ( ( ( ( second @ ( extract @ ( decrypt @ SV37 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SV39 @ k_ca ) ) ) )
!= n ) )
= $true )
| ( ( knows @ ( symmetric_encrypt @ secret @ ( first @ ( extract @ ( decrypt @ SV37 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SV39 @ k_ca ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(223,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( concatenate @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( encrypt @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(224,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( symmetric_encrypt @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(225,plain,
! [SV42: $i,SV41: $i] :
( ( ( ~ ( knows @ SV41 )
| ~ ( knows @ SV42 ) )
= $true )
| ( ( knows @ ( decrypt @ SV41 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(226,plain,
! [SV38: $i,SV40: $i] :
( ( ( knows @ SV40 )
= $false )
| ( ( knows @ SV38 )
= $false )
| ( ( knows @ ( symmetric_decrypt @ SV38 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(227,plain,
! [SV39: $i,SV37: $i] :
( ( ( knows @ SV37 )
= $false )
| ( ( ~ ( knows @ SV39 ) )
= $true )
| ( ( ( ( first @ ( extract @ SV39 @ k_ca ) )
!= s ) )
= $true )
| ( ( ( ( second @ ( extract @ ( decrypt @ SV37 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SV39 @ k_ca ) ) ) )
!= n ) )
= $true )
| ( ( knows @ ( symmetric_encrypt @ secret @ ( first @ ( extract @ ( decrypt @ SV37 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SV39 @ k_ca ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(228,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( concatenate @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( encrypt @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(229,plain,
! [SV43: $i] :
( ( ! [SY57: $i] :
( ~ ( knows @ SV43 )
| ~ ( knows @ SY57 )
| ( knows @ ( symmetric_encrypt @ SV43 @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(230,plain,
! [SV42: $i,SV41: $i] :
( ( ( ~ ( knows @ SV41 ) )
= $true )
| ( ( ~ ( knows @ SV42 ) )
= $true )
| ( ( knows @ ( decrypt @ SV41 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(231,plain,
! [SV37: $i,SV39: $i] :
( ( ( knows @ SV39 )
= $false )
| ( ( knows @ SV37 )
= $false )
| ( ( ( ( first @ ( extract @ SV39 @ k_ca ) )
!= s ) )
= $true )
| ( ( ( ( second @ ( extract @ ( decrypt @ SV37 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SV39 @ k_ca ) ) ) )
!= n ) )
= $true )
| ( ( knows @ ( symmetric_encrypt @ secret @ ( first @ ( extract @ ( decrypt @ SV37 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SV39 @ k_ca ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(232,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( concatenate @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[228]) ).
thf(233,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( encrypt @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[228]) ).
thf(234,plain,
! [SV44: $i,SV43: $i] :
( ( ~ ( knows @ SV43 )
| ~ ( knows @ SV44 )
| ( knows @ ( symmetric_encrypt @ SV43 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(235,plain,
! [SV42: $i,SV41: $i] :
( ( ( knows @ SV41 )
= $false )
| ( ( ~ ( knows @ SV42 ) )
= $true )
| ( ( knows @ ( decrypt @ SV41 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(236,plain,
! [SV37: $i,SV39: $i] :
( ( ( ( first @ ( extract @ SV39 @ k_ca ) )
= s )
= $false )
| ( ( knows @ SV37 )
= $false )
| ( ( knows @ SV39 )
= $false )
| ( ( ( ( second @ ( extract @ ( decrypt @ SV37 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SV39 @ k_ca ) ) ) )
!= n ) )
= $true )
| ( ( knows @ ( symmetric_encrypt @ secret @ ( first @ ( extract @ ( decrypt @ SV37 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SV39 @ k_ca ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(237,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( concatenate @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(238,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( knows @ SX0 )
| ~ ( knows @ SX1 )
| ( knows @ ( encrypt @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(239,plain,
! [SV44: $i,SV43: $i] :
( ( ( ~ ( knows @ SV43 )
| ~ ( knows @ SV44 ) )
= $true )
| ( ( knows @ ( symmetric_encrypt @ SV43 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(240,plain,
! [SV41: $i,SV42: $i] :
( ( ( knows @ SV42 )
= $false )
| ( ( knows @ SV41 )
= $false )
| ( ( knows @ ( decrypt @ SV41 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(241,plain,
! [SV39: $i,SV37: $i] :
( ( ( ( second @ ( extract @ ( decrypt @ SV37 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SV39 @ k_ca ) ) ) )
= n )
= $false )
| ( ( knows @ SV39 )
= $false )
| ( ( knows @ SV37 )
= $false )
| ( ( ( first @ ( extract @ SV39 @ k_ca ) )
= s )
= $false )
| ( ( knows @ ( symmetric_encrypt @ secret @ ( first @ ( extract @ ( decrypt @ SV37 @ ( inverse @ k_c ) ) @ ( second @ ( extract @ SV39 @ k_ca ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(242,plain,
! [SV45: $i] :
( ( ! [SY58: $i] :
( ~ ( knows @ SV45 )
| ~ ( knows @ SY58 )
| ( knows @ ( concatenate @ SV45 @ SY58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(243,plain,
! [SV46: $i] :
( ( ! [SY59: $i] :
( ~ ( knows @ SV46 )
| ~ ( knows @ SY59 )
| ( knows @ ( encrypt @ SV46 @ SY59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(244,plain,
! [SV44: $i,SV43: $i] :
( ( ( ~ ( knows @ SV43 ) )
= $true )
| ( ( ~ ( knows @ SV44 ) )
= $true )
| ( ( knows @ ( symmetric_encrypt @ SV43 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(245,plain,
! [SV47: $i,SV45: $i] :
( ( ~ ( knows @ SV45 )
| ~ ( knows @ SV47 )
| ( knows @ ( concatenate @ SV45 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(246,plain,
! [SV48: $i,SV46: $i] :
( ( ~ ( knows @ SV46 )
| ~ ( knows @ SV48 )
| ( knows @ ( encrypt @ SV46 @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(247,plain,
! [SV44: $i,SV43: $i] :
( ( ( knows @ SV43 )
= $false )
| ( ( ~ ( knows @ SV44 ) )
= $true )
| ( ( knows @ ( symmetric_encrypt @ SV43 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(248,plain,
! [SV47: $i,SV45: $i] :
( ( ( ~ ( knows @ SV45 )
| ~ ( knows @ SV47 ) )
= $true )
| ( ( knows @ ( concatenate @ SV45 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(249,plain,
! [SV48: $i,SV46: $i] :
( ( ( ~ ( knows @ SV46 )
| ~ ( knows @ SV48 ) )
= $true )
| ( ( knows @ ( encrypt @ SV46 @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(250,plain,
! [SV43: $i,SV44: $i] :
( ( ( knows @ SV44 )
= $false )
| ( ( knows @ SV43 )
= $false )
| ( ( knows @ ( symmetric_encrypt @ SV43 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(251,plain,
! [SV47: $i,SV45: $i] :
( ( ( ~ ( knows @ SV45 ) )
= $true )
| ( ( ~ ( knows @ SV47 ) )
= $true )
| ( ( knows @ ( concatenate @ SV45 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(252,plain,
! [SV48: $i,SV46: $i] :
( ( ( ~ ( knows @ SV46 ) )
= $true )
| ( ( ~ ( knows @ SV48 ) )
= $true )
| ( ( knows @ ( encrypt @ SV46 @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(253,plain,
! [SV47: $i,SV45: $i] :
( ( ( knows @ SV45 )
= $false )
| ( ( ~ ( knows @ SV47 ) )
= $true )
| ( ( knows @ ( concatenate @ SV45 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(254,plain,
! [SV48: $i,SV46: $i] :
( ( ( knows @ SV46 )
= $false )
| ( ( ~ ( knows @ SV48 ) )
= $true )
| ( ( knows @ ( encrypt @ SV46 @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(255,plain,
! [SV45: $i,SV47: $i] :
( ( ( knows @ SV47 )
= $false )
| ( ( knows @ SV45 )
= $false )
| ( ( knows @ ( concatenate @ SV45 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(256,plain,
! [SV46: $i,SV48: $i] :
( ( ( knows @ SV48 )
= $false )
| ( ( knows @ SV46 )
= $false )
| ( ( knows @ ( encrypt @ SV46 @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(257,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[81,256,255,250,241,240,226,217,210,193,189,188,186,170,169,163,158,157,154,153,152,151,116,99,98,97,96,95,86,84,83,82]) ).
thf(258,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[257]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV233+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 15 10:48:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 18
% 0.13/0.36
% 0.13/0.36 Length.of.Defs: 0
% 0.13/0.36
% 0.13/0.36 Contains.Choice.Funs: false
% 0.13/0.39 (rf:0,axioms:18,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:20,loop_count:0,foatp_calls:0,translation:fof_full).................
% 33.86/34.05
% 33.86/34.05 ********************************
% 33.86/34.05 * All subproblems solved! *
% 33.86/34.05 ********************************
% 33.86/34.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:18,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:257,loop_count:0,foatp_calls:1,translation:fof_full)
% 33.86/34.08
% 33.86/34.08 %**** Beginning of derivation protocol ****
% 33.86/34.08 % SZS output start CNFRefutation
% See solution above
% 33.86/34.08
% 33.86/34.08 %**** End of derivation protocol ****
% 33.86/34.08 %**** no. of clauses in derivation: 258 ****
% 33.86/34.08 %**** clause counter: 257 ****
% 33.86/34.08
% 33.86/34.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:18,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:257,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------