TSTP Solution File: SWV235+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SWV235+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 : n027.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 1.29s 1.48s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 44
% Syntax : Number of formulae : 215 ( 132 unt; 15 typ; 0 def)
% Number of atoms : 1158 ( 326 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 2714 ( 244 ~; 298 |; 34 &;2116 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 13 con; 0-2 aty)
% Number of variables : 466 ( 0 ^ 466 !; 0 ?; 466 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_crypt,type,
crypt: $i > $i > $i ).
thf(tp_data,type,
data: $i ).
thf(tp_decrypt,type,
decrypt: $i > $i > $i ).
thf(tp_exp,type,
exp: $i ).
thf(tp_id,type,
id: $i ).
thf(tp_imp,type,
imp: $i ).
thf(tp_kek,type,
kek: $i ).
thf(tp_km,type,
km: $i ).
thf(tp_kp,type,
kp: $i ).
thf(tp_p,type,
p: $i > $o ).
thf(tp_pin,type,
pin: $i ).
thf(tp_pp,type,
pp: $i ).
thf(tp_rand,type,
rand: $i ).
thf(tp_xor,type,
xor: $i > $i > $i ).
thf(1,axiom,
p @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_account_number) ).
thf(2,axiom,
p @ exp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_11) ).
thf(3,axiom,
p @ ( crypt @ ( xor @ rand @ imp ) @ kek ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_10) ).
thf(4,axiom,
p @ ( crypt @ ( xor @ km @ ( xor @ imp @ kp ) ) @ kek ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_9) ).
thf(5,axiom,
p @ ( crypt @ ( xor @ km @ imp ) @ rand ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_8) ).
thf(6,axiom,
p @ ( crypt @ ( xor @ km @ imp ) @ ( xor @ rand @ ( xor @ imp @ exp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_7) ).
thf(7,axiom,
p @ ( crypt @ ( xor @ km @ pin ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_6) ).
thf(8,axiom,
p @ pin,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_5) ).
thf(9,axiom,
p @ id,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_4) ).
thf(10,axiom,
p @ data,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_3) ).
thf(11,axiom,
p @ imp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_2) ).
thf(12,axiom,
p @ kp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_1) ).
thf(13,axiom,
! [X1: $i,X2: $i] :
( ( ( p @ X2 )
& ( p @ X1 ) )
=> ( p @ ( crypt @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',encrypt_knowledge) ).
thf(14,axiom,
! [X1: $i,X2: $i] :
( ( ( p @ ( crypt @ X1 @ X2 ) )
& ( p @ X1 ) )
=> ( p @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',decrypt_knowledge) ).
thf(15,axiom,
! [X1: $i,X2: $i] :
( ( ( p @ X1 )
& ( p @ X2 ) )
=> ( p @ ( xor @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',combine_with_XOR) ).
thf(16,axiom,
! [Xk: $i,Xk1: $i,Xtype2: $i,Xkek1: $i,Xkek2: $i,Xtype: $i] :
( ( ( p @ ( crypt @ Xk @ Xk1 ) )
& ( p @ Xtype2 )
& ( p @ ( crypt @ ( xor @ km @ imp ) @ Xkek1 ) )
& ( p @ ( crypt @ ( xor @ km @ exp ) @ Xkek2 ) ) )
=> ( p @ ( crypt @ ( xor @ Xkek2 @ Xtype ) @ ( decrypt @ ( xor @ Xtype2 @ Xkek1 ) @ ( crypt @ Xk @ Xk1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_translate) ).
thf(17,axiom,
! [X1: $i,Xk1: $i] :
( ( ( p @ X1 )
& ( p @ ( crypt @ ( xor @ km @ data ) @ Xk1 ) ) )
=> ( p @ ( decrypt @ Xk1 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',decrypt_data) ).
thf(18,axiom,
! [X1: $i,Xk1: $i] :
( ( ( p @ X1 )
& ( p @ ( crypt @ ( xor @ km @ data ) @ Xk1 ) ) )
=> ( p @ ( crypt @ Xk1 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',encrypt_data) ).
thf(19,axiom,
! [Xk1: $i,Xtype: $i,Xk2: $i] :
( ( ( p @ Xk1 )
& ( p @ ( crypt @ ( xor @ km @ ( xor @ Xtype @ kp ) ) @ Xk2 ) )
& ( p @ Xtype ) )
=> ( p @ ( crypt @ ( xor @ km @ Xtype ) @ ( xor @ Xk2 @ Xk1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_part_import___part_3) ).
thf(20,axiom,
! [Xk1: $i,Xtype: $i,Xk2: $i] :
( ( ( p @ Xk1 )
& ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ Xtype ) ) @ Xk2 ) )
& ( p @ Xtype ) )
=> ( p @ ( crypt @ ( xor @ km @ ( xor @ Xtype @ kp ) ) @ ( xor @ Xk1 @ Xk2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_part_import___part_2) ).
thf(21,axiom,
! [Xk: $i,Xtype: $i] :
( ( ( p @ Xk )
& ( p @ Xtype ) )
=> ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ Xtype ) ) @ Xk ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_part_import___part_1) ).
thf(22,axiom,
! [Xtype: $i,Xk1: $i,Xkek1: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ Xtype ) @ Xk1 ) )
& ( p @ Xtype )
& ( p @ ( crypt @ ( xor @ km @ exp ) @ Xkek1 ) ) )
=> ( p @ ( crypt @ ( xor @ Xkek1 @ Xtype ) @ Xk1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_export) ).
thf(23,axiom,
! [Xkek1: $i,Xtype1: $i,Xk1: $i,Xtype2: $i,Xkek2: $i] :
( ( ( p @ ( crypt @ ( xor @ Xkek1 @ Xtype1 ) @ Xk1 ) )
& ( p @ Xtype2 )
& ( p @ ( crypt @ ( xor @ km @ imp ) @ Xkek2 ) ) )
=> ( p @ ( crypt @ ( xor @ km @ Xtype2 ) @ ( decrypt @ ( xor @ Xkek2 @ Xtype2 ) @ ( crypt @ ( xor @ Xkek1 @ Xtype1 ) @ Xk1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_import) ).
thf(24,axiom,
! [X1: $i] :
( ( xor @ X1 @ X1 )
= id ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_rules_2) ).
thf(25,axiom,
! [X1: $i] :
( ( xor @ X1 @ id )
= X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_rules_1) ).
thf(26,axiom,
! [X1: $i,X2: $i] :
( ( decrypt @ X1 @ ( crypt @ X1 @ X2 ) )
= X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',encryption_decryption_cancellation) ).
thf(27,axiom,
! [X1: $i,X2: $i,X3: $i] :
( ( xor @ X1 @ ( xor @ X2 @ X3 ) )
= ( xor @ ( xor @ X1 @ X2 ) @ X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_associative) ).
thf(28,axiom,
! [X1: $i,X2: $i] :
( ( xor @ X1 @ X2 )
= ( xor @ X2 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_commutative) ).
thf(29,conjecture,
p @ ( crypt @ pp @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',find_pin) ).
thf(30,negated_conjecture,
( ( p @ ( crypt @ pp @ a ) )
= $false ),
inference(negate_conjecture,[status(cth)],[29]) ).
thf(31,plain,
( ( p @ ( crypt @ pp @ a ) )
= $false ),
inference(unfold_def,[status(thm)],[30]) ).
thf(32,plain,
( ( p @ a )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(33,plain,
( ( p @ exp )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(34,plain,
( ( p @ ( crypt @ ( xor @ rand @ imp ) @ kek ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(35,plain,
( ( p @ ( crypt @ ( xor @ km @ ( xor @ imp @ kp ) ) @ kek ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(36,plain,
( ( p @ ( crypt @ ( xor @ km @ imp ) @ rand ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(37,plain,
( ( p @ ( crypt @ ( xor @ km @ imp ) @ ( xor @ rand @ ( xor @ imp @ exp ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(38,plain,
( ( p @ ( crypt @ ( xor @ km @ pin ) @ pp ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(39,plain,
( ( p @ pin )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(40,plain,
( ( p @ id )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(41,plain,
( ( p @ data )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(42,plain,
( ( p @ imp )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(43,plain,
( ( p @ kp )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(44,plain,
( ( ! [X1: $i,X2: $i] :
( ( ( p @ X2 )
& ( p @ X1 ) )
=> ( p @ ( crypt @ X1 @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(45,plain,
( ( ! [X1: $i,X2: $i] :
( ( ( p @ ( crypt @ X1 @ X2 ) )
& ( p @ X1 ) )
=> ( p @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(46,plain,
( ( ! [X1: $i,X2: $i] :
( ( ( p @ X1 )
& ( p @ X2 ) )
=> ( p @ ( xor @ X1 @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(47,plain,
( ( ! [Xk: $i,Xk1: $i,Xtype2: $i,Xkek1: $i,Xkek2: $i,Xtype: $i] :
( ( ( p @ ( crypt @ Xk @ Xk1 ) )
& ( p @ Xtype2 )
& ( p @ ( crypt @ ( xor @ km @ imp ) @ Xkek1 ) )
& ( p @ ( crypt @ ( xor @ km @ exp ) @ Xkek2 ) ) )
=> ( p @ ( crypt @ ( xor @ Xkek2 @ Xtype ) @ ( decrypt @ ( xor @ Xtype2 @ Xkek1 ) @ ( crypt @ Xk @ Xk1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(48,plain,
( ( ! [X1: $i,Xk1: $i] :
( ( ( p @ X1 )
& ( p @ ( crypt @ ( xor @ km @ data ) @ Xk1 ) ) )
=> ( p @ ( decrypt @ Xk1 @ X1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(49,plain,
( ( ! [X1: $i,Xk1: $i] :
( ( ( p @ X1 )
& ( p @ ( crypt @ ( xor @ km @ data ) @ Xk1 ) ) )
=> ( p @ ( crypt @ Xk1 @ X1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(50,plain,
( ( ! [Xk1: $i,Xtype: $i,Xk2: $i] :
( ( ( p @ Xk1 )
& ( p @ ( crypt @ ( xor @ km @ ( xor @ Xtype @ kp ) ) @ Xk2 ) )
& ( p @ Xtype ) )
=> ( p @ ( crypt @ ( xor @ km @ Xtype ) @ ( xor @ Xk2 @ Xk1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(51,plain,
( ( ! [Xk1: $i,Xtype: $i,Xk2: $i] :
( ( ( p @ Xk1 )
& ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ Xtype ) ) @ Xk2 ) )
& ( p @ Xtype ) )
=> ( p @ ( crypt @ ( xor @ km @ ( xor @ Xtype @ kp ) ) @ ( xor @ Xk1 @ Xk2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(52,plain,
( ( ! [Xk: $i,Xtype: $i] :
( ( ( p @ Xk )
& ( p @ Xtype ) )
=> ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ Xtype ) ) @ Xk ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(53,plain,
( ( ! [Xtype: $i,Xk1: $i,Xkek1: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ Xtype ) @ Xk1 ) )
& ( p @ Xtype )
& ( p @ ( crypt @ ( xor @ km @ exp ) @ Xkek1 ) ) )
=> ( p @ ( crypt @ ( xor @ Xkek1 @ Xtype ) @ Xk1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(54,plain,
( ( ! [Xkek1: $i,Xtype1: $i,Xk1: $i,Xtype2: $i,Xkek2: $i] :
( ( ( p @ ( crypt @ ( xor @ Xkek1 @ Xtype1 ) @ Xk1 ) )
& ( p @ Xtype2 )
& ( p @ ( crypt @ ( xor @ km @ imp ) @ Xkek2 ) ) )
=> ( p @ ( crypt @ ( xor @ km @ Xtype2 ) @ ( decrypt @ ( xor @ Xkek2 @ Xtype2 ) @ ( crypt @ ( xor @ Xkek1 @ Xtype1 ) @ Xk1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(55,plain,
( ( ! [X1: $i] :
( ( xor @ X1 @ X1 )
= id ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(56,plain,
( ( ! [X1: $i] :
( ( xor @ X1 @ id )
= X1 ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(57,plain,
( ( ! [X1: $i,X2: $i] :
( ( decrypt @ X1 @ ( crypt @ X1 @ X2 ) )
= X2 ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(58,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( xor @ X1 @ ( xor @ X2 @ X3 ) )
= ( xor @ ( xor @ X1 @ X2 ) @ X3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(59,plain,
( ( ! [X1: $i,X2: $i] :
( ( xor @ X1 @ X2 )
= ( xor @ X2 @ X1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(60,plain,
( ( ~ ( p @ ( crypt @ pp @ a ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[31]) ).
thf(61,plain,
( ( ! [X1: $i,X2: $i] :
( ~ ( p @ X2 )
| ~ ( p @ X1 )
| ( p @ ( crypt @ X1 @ X2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(62,plain,
( ( ! [X1: $i,X2: $i] :
( ~ ( p @ ( crypt @ X1 @ X2 ) )
| ~ ( p @ X1 )
| ( p @ X2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(63,plain,
( ( ! [X1: $i,X2: $i] :
( ~ ( p @ X1 )
| ~ ( p @ X2 )
| ( p @ ( xor @ X1 @ X2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(64,plain,
( ( ! [Xk: $i,Xk1: $i,Xtype2: $i,Xkek1: $i,Xkek2: $i] :
( ~ ( p @ ( crypt @ Xk @ Xk1 ) )
| ~ ( p @ Xtype2 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ Xkek1 ) )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ Xkek2 ) )
| ! [Xtype: $i] : ( p @ ( crypt @ ( xor @ Xkek2 @ Xtype ) @ ( decrypt @ ( xor @ Xtype2 @ Xkek1 ) @ ( crypt @ Xk @ Xk1 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(65,plain,
( ( ! [X1: $i,Xk1: $i] :
( ~ ( p @ X1 )
| ~ ( p @ ( crypt @ ( xor @ km @ data ) @ Xk1 ) )
| ( p @ ( decrypt @ Xk1 @ X1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(66,plain,
( ( ! [X1: $i,Xk1: $i] :
( ~ ( p @ X1 )
| ~ ( p @ ( crypt @ ( xor @ km @ data ) @ Xk1 ) )
| ( p @ ( crypt @ Xk1 @ X1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(67,plain,
( ( ! [Xk1: $i,Xtype: $i,Xk2: $i] :
( ~ ( p @ Xk1 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ Xtype @ kp ) ) @ Xk2 ) )
| ~ ( p @ Xtype )
| ( p @ ( crypt @ ( xor @ km @ Xtype ) @ ( xor @ Xk2 @ Xk1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(68,plain,
( ( ! [Xk1: $i,Xtype: $i,Xk2: $i] :
( ~ ( p @ Xk1 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ Xtype ) ) @ Xk2 ) )
| ~ ( p @ Xtype )
| ( p @ ( crypt @ ( xor @ km @ ( xor @ Xtype @ kp ) ) @ ( xor @ Xk1 @ Xk2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(69,plain,
( ( ! [Xk: $i,Xtype: $i] :
( ~ ( p @ Xk )
| ~ ( p @ Xtype )
| ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ Xtype ) ) @ Xk ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(70,plain,
( ( ! [Xtype: $i,Xk1: $i,Xkek1: $i] :
( ~ ( p @ ( crypt @ ( xor @ km @ Xtype ) @ Xk1 ) )
| ~ ( p @ Xtype )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ Xkek1 ) )
| ( p @ ( crypt @ ( xor @ Xkek1 @ Xtype ) @ Xk1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(71,plain,
( ( ! [Xkek1: $i,Xtype1: $i,Xk1: $i,Xtype2: $i,Xkek2: $i] :
( ~ ( p @ ( crypt @ ( xor @ Xkek1 @ Xtype1 ) @ Xk1 ) )
| ~ ( p @ Xtype2 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ Xkek2 ) )
| ( p @ ( crypt @ ( xor @ km @ Xtype2 ) @ ( decrypt @ ( xor @ Xkek2 @ Xtype2 ) @ ( crypt @ ( xor @ Xkek1 @ Xtype1 ) @ Xk1 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(72,plain,
( ( ! [X1: $i,X2: $i] :
( ( xor @ X1 @ X2 )
= ( xor @ X2 @ X1 ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(73,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( xor @ X1 @ ( xor @ X2 @ X3 ) )
= ( xor @ ( xor @ X1 @ X2 ) @ X3 ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(74,plain,
( ( ! [X1: $i,X2: $i] :
( ( decrypt @ X1 @ ( crypt @ X1 @ X2 ) )
= X2 ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(75,plain,
( ( ! [X1: $i] :
( ( xor @ X1 @ id )
= X1 ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(76,plain,
( ( ! [X1: $i] :
( ( xor @ X1 @ X1 )
= id ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(77,plain,
( ( ! [Xkek1: $i,Xtype1: $i,Xk1: $i,Xtype2: $i,Xkek2: $i] :
( ~ ( p @ ( crypt @ ( xor @ Xkek1 @ Xtype1 ) @ Xk1 ) )
| ~ ( p @ Xtype2 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ Xkek2 ) )
| ( p @ ( crypt @ ( xor @ km @ Xtype2 ) @ ( decrypt @ ( xor @ Xkek2 @ Xtype2 ) @ ( crypt @ ( xor @ Xkek1 @ Xtype1 ) @ Xk1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(78,plain,
( ( ! [Xtype: $i,Xk1: $i,Xkek1: $i] :
( ~ ( p @ ( crypt @ ( xor @ km @ Xtype ) @ Xk1 ) )
| ~ ( p @ Xtype )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ Xkek1 ) )
| ( p @ ( crypt @ ( xor @ Xkek1 @ Xtype ) @ Xk1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(79,plain,
( ( ! [Xk: $i,Xtype: $i] :
( ~ ( p @ Xk )
| ~ ( p @ Xtype )
| ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ Xtype ) ) @ Xk ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(80,plain,
( ( ! [Xk1: $i,Xtype: $i,Xk2: $i] :
( ~ ( p @ Xk1 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ Xtype ) ) @ Xk2 ) )
| ~ ( p @ Xtype )
| ( p @ ( crypt @ ( xor @ km @ ( xor @ Xtype @ kp ) ) @ ( xor @ Xk1 @ Xk2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(81,plain,
( ( ! [Xk1: $i,Xtype: $i,Xk2: $i] :
( ~ ( p @ Xk1 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ Xtype @ kp ) ) @ Xk2 ) )
| ~ ( p @ Xtype )
| ( p @ ( crypt @ ( xor @ km @ Xtype ) @ ( xor @ Xk2 @ Xk1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(82,plain,
( ( ! [X1: $i,Xk1: $i] :
( ~ ( p @ X1 )
| ~ ( p @ ( crypt @ ( xor @ km @ data ) @ Xk1 ) )
| ( p @ ( crypt @ Xk1 @ X1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(83,plain,
( ( ! [X1: $i,Xk1: $i] :
( ~ ( p @ X1 )
| ~ ( p @ ( crypt @ ( xor @ km @ data ) @ Xk1 ) )
| ( p @ ( decrypt @ Xk1 @ X1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(84,plain,
( ( ! [Xk: $i,Xk1: $i,Xtype2: $i,Xkek1: $i,Xkek2: $i] :
( ~ ( p @ ( crypt @ Xk @ Xk1 ) )
| ~ ( p @ Xtype2 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ Xkek1 ) )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ Xkek2 ) )
| ! [Xtype: $i] : ( p @ ( crypt @ ( xor @ Xkek2 @ Xtype ) @ ( decrypt @ ( xor @ Xtype2 @ Xkek1 ) @ ( crypt @ Xk @ Xk1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(85,plain,
( ( ! [X1: $i,X2: $i] :
( ~ ( p @ X1 )
| ~ ( p @ X2 )
| ( p @ ( xor @ X1 @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(86,plain,
( ( ! [X1: $i,X2: $i] :
( ~ ( p @ ( crypt @ X1 @ X2 ) )
| ~ ( p @ X1 )
| ( p @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(87,plain,
( ( ! [X1: $i,X2: $i] :
( ~ ( p @ X2 )
| ~ ( p @ X1 )
| ( p @ ( crypt @ X1 @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(88,plain,
( ( p @ kp )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(89,plain,
( ( p @ imp )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(90,plain,
( ( p @ data )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(91,plain,
( ( p @ id )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(92,plain,
( ( p @ pin )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(93,plain,
( ( p @ ( crypt @ ( xor @ km @ pin ) @ pp ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(94,plain,
( ( p @ ( crypt @ ( xor @ km @ imp ) @ ( xor @ rand @ ( xor @ imp @ exp ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(95,plain,
( ( p @ ( crypt @ ( xor @ km @ imp ) @ rand ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(96,plain,
( ( p @ ( crypt @ ( xor @ km @ ( xor @ imp @ kp ) ) @ kek ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(97,plain,
( ( p @ ( crypt @ ( xor @ rand @ imp ) @ kek ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(98,plain,
( ( p @ exp )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(99,plain,
( ( p @ a )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(100,plain,
( ( ~ ( p @ ( crypt @ pp @ a ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(101,plain,
! [SV1: $i] :
( ( ! [SY41: $i] :
( ( xor @ SV1 @ SY41 )
= ( xor @ SY41 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(102,plain,
! [SV2: $i] :
( ( ! [SY42: $i,SY43: $i] :
( ( xor @ SV2 @ ( xor @ SY42 @ SY43 ) )
= ( xor @ ( xor @ SV2 @ SY42 ) @ SY43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(103,plain,
! [SV3: $i] :
( ( ! [SY44: $i] :
( ( decrypt @ SV3 @ ( crypt @ SV3 @ SY44 ) )
= SY44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(104,plain,
! [SV4: $i] :
( ( ( xor @ SV4 @ id )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(105,plain,
! [SV5: $i] :
( ( ( xor @ SV5 @ SV5 )
= id )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(106,plain,
! [SV6: $i] :
( ( ! [SY45: $i,SY46: $i,SY47: $i,SY48: $i] :
( ~ ( p @ ( crypt @ ( xor @ SV6 @ SY45 ) @ SY46 ) )
| ~ ( p @ SY47 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SY48 ) )
| ( p @ ( crypt @ ( xor @ km @ SY47 ) @ ( decrypt @ ( xor @ SY48 @ SY47 ) @ ( crypt @ ( xor @ SV6 @ SY45 ) @ SY46 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(107,plain,
! [SV7: $i] :
( ( ! [SY49: $i,SY50: $i] :
( ~ ( p @ ( crypt @ ( xor @ km @ SV7 ) @ SY49 ) )
| ~ ( p @ SV7 )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SY50 ) )
| ( p @ ( crypt @ ( xor @ SY50 @ SV7 ) @ SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(108,plain,
! [SV8: $i] :
( ( ! [SY51: $i] :
( ~ ( p @ SV8 )
| ~ ( p @ SY51 )
| ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SY51 ) ) @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(109,plain,
! [SV9: $i] :
( ( ! [SY52: $i,SY53: $i] :
( ~ ( p @ SV9 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SY52 ) ) @ SY53 ) )
| ~ ( p @ SY52 )
| ( p @ ( crypt @ ( xor @ km @ ( xor @ SY52 @ kp ) ) @ ( xor @ SV9 @ SY53 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(110,plain,
! [SV10: $i] :
( ( ! [SY54: $i,SY55: $i] :
( ~ ( p @ SV10 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ SY54 @ kp ) ) @ SY55 ) )
| ~ ( p @ SY54 )
| ( p @ ( crypt @ ( xor @ km @ SY54 ) @ ( xor @ SY55 @ SV10 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(111,plain,
! [SV11: $i] :
( ( ! [SY56: $i] :
( ~ ( p @ SV11 )
| ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SY56 ) )
| ( p @ ( crypt @ SY56 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(112,plain,
! [SV12: $i] :
( ( ! [SY57: $i] :
( ~ ( p @ SV12 )
| ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SY57 ) )
| ( p @ ( decrypt @ SY57 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(113,plain,
! [SV13: $i] :
( ( ! [SY58: $i,SY59: $i,SY60: $i,SY61: $i] :
( ~ ( p @ ( crypt @ SV13 @ SY58 ) )
| ~ ( p @ SY59 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SY60 ) )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SY61 ) )
| ! [SY62: $i] : ( p @ ( crypt @ ( xor @ SY61 @ SY62 ) @ ( decrypt @ ( xor @ SY59 @ SY60 ) @ ( crypt @ SV13 @ SY58 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(114,plain,
! [SV14: $i] :
( ( ! [SY63: $i] :
( ~ ( p @ SV14 )
| ~ ( p @ SY63 )
| ( p @ ( xor @ SV14 @ SY63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(115,plain,
! [SV15: $i] :
( ( ! [SY64: $i] :
( ~ ( p @ ( crypt @ SV15 @ SY64 ) )
| ~ ( p @ SV15 )
| ( p @ SY64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(116,plain,
! [SV16: $i] :
( ( ! [SY65: $i] :
( ~ ( p @ SY65 )
| ~ ( p @ SV16 )
| ( p @ ( crypt @ SV16 @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(117,plain,
( ( p @ ( crypt @ pp @ a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(118,plain,
! [SV17: $i,SV1: $i] :
( ( ( xor @ SV1 @ SV17 )
= ( xor @ SV17 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(119,plain,
! [SV18: $i,SV2: $i] :
( ( ! [SY66: $i] :
( ( xor @ SV2 @ ( xor @ SV18 @ SY66 ) )
= ( xor @ ( xor @ SV2 @ SV18 ) @ SY66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(120,plain,
! [SV19: $i,SV3: $i] :
( ( ( decrypt @ SV3 @ ( crypt @ SV3 @ SV19 ) )
= SV19 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(121,plain,
! [SV20: $i,SV6: $i] :
( ( ! [SY67: $i,SY68: $i,SY69: $i] :
( ~ ( p @ ( crypt @ ( xor @ SV6 @ SV20 ) @ SY67 ) )
| ~ ( p @ SY68 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SY69 ) )
| ( p @ ( crypt @ ( xor @ km @ SY68 ) @ ( decrypt @ ( xor @ SY69 @ SY68 ) @ ( crypt @ ( xor @ SV6 @ SV20 ) @ SY67 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(122,plain,
! [SV21: $i,SV7: $i] :
( ( ! [SY70: $i] :
( ~ ( p @ ( crypt @ ( xor @ km @ SV7 ) @ SV21 ) )
| ~ ( p @ SV7 )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SY70 ) )
| ( p @ ( crypt @ ( xor @ SY70 @ SV7 ) @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(123,plain,
! [SV22: $i,SV8: $i] :
( ( ~ ( p @ SV8 )
| ~ ( p @ SV22 )
| ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV22 ) ) @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(124,plain,
! [SV23: $i,SV9: $i] :
( ( ! [SY71: $i] :
( ~ ( p @ SV9 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV23 ) ) @ SY71 ) )
| ~ ( p @ SV23 )
| ( p @ ( crypt @ ( xor @ km @ ( xor @ SV23 @ kp ) ) @ ( xor @ SV9 @ SY71 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(125,plain,
! [SV24: $i,SV10: $i] :
( ( ! [SY72: $i] :
( ~ ( p @ SV10 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ SV24 @ kp ) ) @ SY72 ) )
| ~ ( p @ SV24 )
| ( p @ ( crypt @ ( xor @ km @ SV24 ) @ ( xor @ SY72 @ SV10 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(126,plain,
! [SV25: $i,SV11: $i] :
( ( ~ ( p @ SV11 )
| ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SV25 ) )
| ( p @ ( crypt @ SV25 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(127,plain,
! [SV26: $i,SV12: $i] :
( ( ~ ( p @ SV12 )
| ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SV26 ) )
| ( p @ ( decrypt @ SV26 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(128,plain,
! [SV27: $i,SV13: $i] :
( ( ! [SY73: $i,SY74: $i,SY75: $i] :
( ~ ( p @ ( crypt @ SV13 @ SV27 ) )
| ~ ( p @ SY73 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SY74 ) )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SY75 ) )
| ! [SY76: $i] : ( p @ ( crypt @ ( xor @ SY75 @ SY76 ) @ ( decrypt @ ( xor @ SY73 @ SY74 ) @ ( crypt @ SV13 @ SV27 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(129,plain,
! [SV28: $i,SV14: $i] :
( ( ~ ( p @ SV14 )
| ~ ( p @ SV28 )
| ( p @ ( xor @ SV14 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(130,plain,
! [SV29: $i,SV15: $i] :
( ( ~ ( p @ ( crypt @ SV15 @ SV29 ) )
| ~ ( p @ SV15 )
| ( p @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(131,plain,
! [SV16: $i,SV30: $i] :
( ( ~ ( p @ SV30 )
| ~ ( p @ SV16 )
| ( p @ ( crypt @ SV16 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(132,plain,
! [SV31: $i,SV18: $i,SV2: $i] :
( ( ( xor @ SV2 @ ( xor @ SV18 @ SV31 ) )
= ( xor @ ( xor @ SV2 @ SV18 ) @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(133,plain,
! [SV32: $i,SV20: $i,SV6: $i] :
( ( ! [SY77: $i,SY78: $i] :
( ~ ( p @ ( crypt @ ( xor @ SV6 @ SV20 ) @ SV32 ) )
| ~ ( p @ SY77 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SY78 ) )
| ( p @ ( crypt @ ( xor @ km @ SY77 ) @ ( decrypt @ ( xor @ SY78 @ SY77 ) @ ( crypt @ ( xor @ SV6 @ SV20 ) @ SV32 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(134,plain,
! [SV33: $i,SV21: $i,SV7: $i] :
( ( ~ ( p @ ( crypt @ ( xor @ km @ SV7 ) @ SV21 ) )
| ~ ( p @ SV7 )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV33 ) )
| ( p @ ( crypt @ ( xor @ SV33 @ SV7 ) @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(135,plain,
! [SV22: $i,SV8: $i] :
( ( ( ~ ( p @ SV8 )
| ~ ( p @ SV22 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV22 ) ) @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(136,plain,
! [SV34: $i,SV23: $i,SV9: $i] :
( ( ~ ( p @ SV9 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV23 ) ) @ SV34 ) )
| ~ ( p @ SV23 )
| ( p @ ( crypt @ ( xor @ km @ ( xor @ SV23 @ kp ) ) @ ( xor @ SV9 @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(137,plain,
! [SV35: $i,SV24: $i,SV10: $i] :
( ( ~ ( p @ SV10 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ SV24 @ kp ) ) @ SV35 ) )
| ~ ( p @ SV24 )
| ( p @ ( crypt @ ( xor @ km @ SV24 ) @ ( xor @ SV35 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(138,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ( p @ SV11 )
| ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SV25 ) ) )
= $true )
| ( ( p @ ( crypt @ SV25 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(139,plain,
! [SV26: $i,SV12: $i] :
( ( ( ~ ( p @ SV12 )
| ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SV26 ) ) )
= $true )
| ( ( p @ ( decrypt @ SV26 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(140,plain,
! [SV36: $i,SV27: $i,SV13: $i] :
( ( ! [SY79: $i,SY80: $i] :
( ~ ( p @ ( crypt @ SV13 @ SV27 ) )
| ~ ( p @ SV36 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SY79 ) )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SY80 ) )
| ! [SY81: $i] : ( p @ ( crypt @ ( xor @ SY80 @ SY81 ) @ ( decrypt @ ( xor @ SV36 @ SY79 ) @ ( crypt @ SV13 @ SV27 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(141,plain,
! [SV28: $i,SV14: $i] :
( ( ( ~ ( p @ SV14 )
| ~ ( p @ SV28 ) )
= $true )
| ( ( p @ ( xor @ SV14 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(142,plain,
! [SV29: $i,SV15: $i] :
( ( ( ~ ( p @ ( crypt @ SV15 @ SV29 ) )
| ~ ( p @ SV15 ) )
= $true )
| ( ( p @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(143,plain,
! [SV16: $i,SV30: $i] :
( ( ( ~ ( p @ SV30 )
| ~ ( p @ SV16 ) )
= $true )
| ( ( p @ ( crypt @ SV16 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(144,plain,
! [SV37: $i,SV32: $i,SV20: $i,SV6: $i] :
( ( ! [SY82: $i] :
( ~ ( p @ ( crypt @ ( xor @ SV6 @ SV20 ) @ SV32 ) )
| ~ ( p @ SV37 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SY82 ) )
| ( p @ ( crypt @ ( xor @ km @ SV37 ) @ ( decrypt @ ( xor @ SY82 @ SV37 ) @ ( crypt @ ( xor @ SV6 @ SV20 ) @ SV32 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(145,plain,
! [SV33: $i,SV21: $i,SV7: $i] :
( ( ( ~ ( p @ ( crypt @ ( xor @ km @ SV7 ) @ SV21 ) )
| ~ ( p @ SV7 )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV33 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ SV33 @ SV7 ) @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(146,plain,
! [SV22: $i,SV8: $i] :
( ( ( ~ ( p @ SV8 ) )
= $true )
| ( ( ~ ( p @ SV22 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV22 ) ) @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(147,plain,
! [SV34: $i,SV23: $i,SV9: $i] :
( ( ( ~ ( p @ SV9 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV23 ) ) @ SV34 ) )
| ~ ( p @ SV23 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV23 @ kp ) ) @ ( xor @ SV9 @ SV34 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(148,plain,
! [SV35: $i,SV24: $i,SV10: $i] :
( ( ( ~ ( p @ SV10 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ SV24 @ kp ) ) @ SV35 ) )
| ~ ( p @ SV24 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV24 ) @ ( xor @ SV35 @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(149,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ( p @ SV11 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SV25 ) ) )
= $true )
| ( ( p @ ( crypt @ SV25 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(150,plain,
! [SV26: $i,SV12: $i] :
( ( ( ~ ( p @ SV12 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SV26 ) ) )
= $true )
| ( ( p @ ( decrypt @ SV26 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(151,plain,
! [SV38: $i,SV36: $i,SV27: $i,SV13: $i] :
( ( ! [SY83: $i] :
( ~ ( p @ ( crypt @ SV13 @ SV27 ) )
| ~ ( p @ SV36 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV38 ) )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SY83 ) )
| ! [SY84: $i] : ( p @ ( crypt @ ( xor @ SY83 @ SY84 ) @ ( decrypt @ ( xor @ SV36 @ SV38 ) @ ( crypt @ SV13 @ SV27 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(152,plain,
! [SV28: $i,SV14: $i] :
( ( ( ~ ( p @ SV14 ) )
= $true )
| ( ( ~ ( p @ SV28 ) )
= $true )
| ( ( p @ ( xor @ SV14 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(153,plain,
! [SV29: $i,SV15: $i] :
( ( ( ~ ( p @ ( crypt @ SV15 @ SV29 ) ) )
= $true )
| ( ( ~ ( p @ SV15 ) )
= $true )
| ( ( p @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(154,plain,
! [SV16: $i,SV30: $i] :
( ( ( ~ ( p @ SV30 ) )
= $true )
| ( ( ~ ( p @ SV16 ) )
= $true )
| ( ( p @ ( crypt @ SV16 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(155,plain,
! [SV39: $i,SV37: $i,SV32: $i,SV20: $i,SV6: $i] :
( ( ~ ( p @ ( crypt @ ( xor @ SV6 @ SV20 ) @ SV32 ) )
| ~ ( p @ SV37 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV39 ) )
| ( p @ ( crypt @ ( xor @ km @ SV37 ) @ ( decrypt @ ( xor @ SV39 @ SV37 ) @ ( crypt @ ( xor @ SV6 @ SV20 ) @ SV32 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(156,plain,
! [SV33: $i,SV21: $i,SV7: $i] :
( ( ( ~ ( p @ ( crypt @ ( xor @ km @ SV7 ) @ SV21 ) )
| ~ ( p @ SV7 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV33 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ SV33 @ SV7 ) @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(157,plain,
! [SV22: $i,SV8: $i] :
( ( ( p @ SV8 )
= $false )
| ( ( ~ ( p @ SV22 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV22 ) ) @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(158,plain,
! [SV34: $i,SV23: $i,SV9: $i] :
( ( ( ~ ( p @ SV9 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV23 ) ) @ SV34 ) ) )
= $true )
| ( ( ~ ( p @ SV23 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV23 @ kp ) ) @ ( xor @ SV9 @ SV34 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(159,plain,
! [SV35: $i,SV24: $i,SV10: $i] :
( ( ( ~ ( p @ SV10 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ SV24 @ kp ) ) @ SV35 ) ) )
= $true )
| ( ( ~ ( p @ SV24 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV24 ) @ ( xor @ SV35 @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(160,plain,
! [SV25: $i,SV11: $i] :
( ( ( p @ SV11 )
= $false )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SV25 ) ) )
= $true )
| ( ( p @ ( crypt @ SV25 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(161,plain,
! [SV26: $i,SV12: $i] :
( ( ( p @ SV12 )
= $false )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SV26 ) ) )
= $true )
| ( ( p @ ( decrypt @ SV26 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(162,plain,
! [SV40: $i,SV38: $i,SV36: $i,SV27: $i,SV13: $i] :
( ( ~ ( p @ ( crypt @ SV13 @ SV27 ) )
| ~ ( p @ SV36 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV38 ) )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV40 ) )
| ! [SY85: $i] : ( p @ ( crypt @ ( xor @ SV40 @ SY85 ) @ ( decrypt @ ( xor @ SV36 @ SV38 ) @ ( crypt @ SV13 @ SV27 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(163,plain,
! [SV28: $i,SV14: $i] :
( ( ( p @ SV14 )
= $false )
| ( ( ~ ( p @ SV28 ) )
= $true )
| ( ( p @ ( xor @ SV14 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(164,plain,
! [SV29: $i,SV15: $i] :
( ( ( p @ ( crypt @ SV15 @ SV29 ) )
= $false )
| ( ( ~ ( p @ SV15 ) )
= $true )
| ( ( p @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(165,plain,
! [SV16: $i,SV30: $i] :
( ( ( p @ SV30 )
= $false )
| ( ( ~ ( p @ SV16 ) )
= $true )
| ( ( p @ ( crypt @ SV16 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(166,plain,
! [SV39: $i,SV37: $i,SV32: $i,SV20: $i,SV6: $i] :
( ( ( ~ ( p @ ( crypt @ ( xor @ SV6 @ SV20 ) @ SV32 ) )
| ~ ( p @ SV37 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV39 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV37 ) @ ( decrypt @ ( xor @ SV39 @ SV37 ) @ ( crypt @ ( xor @ SV6 @ SV20 ) @ SV32 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(167,plain,
! [SV33: $i,SV21: $i,SV7: $i] :
( ( ( ~ ( p @ ( crypt @ ( xor @ km @ SV7 ) @ SV21 ) ) )
= $true )
| ( ( ~ ( p @ SV7 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV33 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ SV33 @ SV7 ) @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(168,plain,
! [SV8: $i,SV22: $i] :
( ( ( p @ SV22 )
= $false )
| ( ( p @ SV8 )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV22 ) ) @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(169,plain,
! [SV34: $i,SV23: $i,SV9: $i] :
( ( ( ~ ( p @ SV9 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV23 ) ) @ SV34 ) ) )
= $true )
| ( ( ~ ( p @ SV23 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV23 @ kp ) ) @ ( xor @ SV9 @ SV34 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(170,plain,
! [SV35: $i,SV24: $i,SV10: $i] :
( ( ( ~ ( p @ SV10 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ SV24 @ kp ) ) @ SV35 ) ) )
= $true )
| ( ( ~ ( p @ SV24 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV24 ) @ ( xor @ SV35 @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(171,plain,
! [SV11: $i,SV25: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ data ) @ SV25 ) )
= $false )
| ( ( p @ SV11 )
= $false )
| ( ( p @ ( crypt @ SV25 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(172,plain,
! [SV12: $i,SV26: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ data ) @ SV26 ) )
= $false )
| ( ( p @ SV12 )
= $false )
| ( ( p @ ( decrypt @ SV26 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(173,plain,
! [SV40: $i,SV38: $i,SV36: $i,SV27: $i,SV13: $i] :
( ( ( ~ ( p @ ( crypt @ SV13 @ SV27 ) )
| ~ ( p @ SV36 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV38 ) )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV40 ) ) )
= $true )
| ( ( ! [SY85: $i] : ( p @ ( crypt @ ( xor @ SV40 @ SY85 ) @ ( decrypt @ ( xor @ SV36 @ SV38 ) @ ( crypt @ SV13 @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(174,plain,
! [SV14: $i,SV28: $i] :
( ( ( p @ SV28 )
= $false )
| ( ( p @ SV14 )
= $false )
| ( ( p @ ( xor @ SV14 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(175,plain,
! [SV29: $i,SV15: $i] :
( ( ( p @ SV15 )
= $false )
| ( ( p @ ( crypt @ SV15 @ SV29 ) )
= $false )
| ( ( p @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(176,plain,
! [SV30: $i,SV16: $i] :
( ( ( p @ SV16 )
= $false )
| ( ( p @ SV30 )
= $false )
| ( ( p @ ( crypt @ SV16 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(177,plain,
! [SV39: $i,SV37: $i,SV32: $i,SV20: $i,SV6: $i] :
( ( ( ~ ( p @ ( crypt @ ( xor @ SV6 @ SV20 ) @ SV32 ) )
| ~ ( p @ SV37 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV39 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV37 ) @ ( decrypt @ ( xor @ SV39 @ SV37 ) @ ( crypt @ ( xor @ SV6 @ SV20 ) @ SV32 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(178,plain,
! [SV33: $i,SV21: $i,SV7: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ SV7 ) @ SV21 ) )
= $false )
| ( ( ~ ( p @ SV7 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV33 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ SV33 @ SV7 ) @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(179,plain,
! [SV34: $i,SV23: $i,SV9: $i] :
( ( ( p @ SV9 )
= $false )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV23 ) ) @ SV34 ) ) )
= $true )
| ( ( ~ ( p @ SV23 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV23 @ kp ) ) @ ( xor @ SV9 @ SV34 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(180,plain,
! [SV35: $i,SV24: $i,SV10: $i] :
( ( ( p @ SV10 )
= $false )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ SV24 @ kp ) ) @ SV35 ) ) )
= $true )
| ( ( ~ ( p @ SV24 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV24 ) @ ( xor @ SV35 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(181,plain,
! [SV40: $i,SV38: $i,SV36: $i,SV27: $i,SV13: $i] :
( ( ( ~ ( p @ ( crypt @ SV13 @ SV27 ) )
| ~ ( p @ SV36 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV38 ) ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV40 ) ) )
= $true )
| ( ( ! [SY85: $i] : ( p @ ( crypt @ ( xor @ SV40 @ SY85 ) @ ( decrypt @ ( xor @ SV36 @ SV38 ) @ ( crypt @ SV13 @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(182,plain,
! [SV39: $i,SV37: $i,SV32: $i,SV20: $i,SV6: $i] :
( ( ( ~ ( p @ ( crypt @ ( xor @ SV6 @ SV20 ) @ SV32 ) ) )
= $true )
| ( ( ~ ( p @ SV37 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV39 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV37 ) @ ( decrypt @ ( xor @ SV39 @ SV37 ) @ ( crypt @ ( xor @ SV6 @ SV20 ) @ SV32 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(183,plain,
! [SV33: $i,SV21: $i,SV7: $i] :
( ( ( p @ SV7 )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ SV7 ) @ SV21 ) )
= $false )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV33 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ SV33 @ SV7 ) @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(184,plain,
! [SV9: $i,SV34: $i,SV23: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV23 ) ) @ SV34 ) )
= $false )
| ( ( p @ SV9 )
= $false )
| ( ( ~ ( p @ SV23 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV23 @ kp ) ) @ ( xor @ SV9 @ SV34 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(185,plain,
! [SV10: $i,SV35: $i,SV24: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV24 @ kp ) ) @ SV35 ) )
= $false )
| ( ( p @ SV10 )
= $false )
| ( ( ~ ( p @ SV24 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV24 ) @ ( xor @ SV35 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(186,plain,
! [SV40: $i,SV38: $i,SV36: $i,SV27: $i,SV13: $i] :
( ( ( ~ ( p @ ( crypt @ SV13 @ SV27 ) )
| ~ ( p @ SV36 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV38 ) ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV40 ) ) )
= $true )
| ( ( ! [SY85: $i] : ( p @ ( crypt @ ( xor @ SV40 @ SY85 ) @ ( decrypt @ ( xor @ SV36 @ SV38 ) @ ( crypt @ SV13 @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(187,plain,
! [SV39: $i,SV37: $i,SV32: $i,SV20: $i,SV6: $i] :
( ( ( p @ ( crypt @ ( xor @ SV6 @ SV20 ) @ SV32 ) )
= $false )
| ( ( ~ ( p @ SV37 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV39 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV37 ) @ ( decrypt @ ( xor @ SV39 @ SV37 ) @ ( crypt @ ( xor @ SV6 @ SV20 ) @ SV32 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(188,plain,
! [SV21: $i,SV7: $i,SV33: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ exp ) @ SV33 ) )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ SV7 ) @ SV21 ) )
= $false )
| ( ( p @ SV7 )
= $false )
| ( ( p @ ( crypt @ ( xor @ SV33 @ SV7 ) @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(189,plain,
! [SV34: $i,SV9: $i,SV23: $i] :
( ( ( p @ SV23 )
= $false )
| ( ( p @ SV9 )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV23 ) ) @ SV34 ) )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV23 @ kp ) ) @ ( xor @ SV9 @ SV34 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(190,plain,
! [SV35: $i,SV10: $i,SV24: $i] :
( ( ( p @ SV24 )
= $false )
| ( ( p @ SV10 )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV24 @ kp ) ) @ SV35 ) )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ SV24 ) @ ( xor @ SV35 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(191,plain,
! [SV40: $i,SV38: $i,SV36: $i,SV27: $i,SV13: $i] :
( ( ( ~ ( p @ ( crypt @ SV13 @ SV27 ) ) )
= $true )
| ( ( ~ ( p @ SV36 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV38 ) ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV40 ) ) )
= $true )
| ( ( ! [SY85: $i] : ( p @ ( crypt @ ( xor @ SV40 @ SY85 ) @ ( decrypt @ ( xor @ SV36 @ SV38 ) @ ( crypt @ SV13 @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(192,plain,
! [SV39: $i,SV32: $i,SV20: $i,SV6: $i,SV37: $i] :
( ( ( p @ SV37 )
= $false )
| ( ( p @ ( crypt @ ( xor @ SV6 @ SV20 ) @ SV32 ) )
= $false )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV39 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV37 ) @ ( decrypt @ ( xor @ SV39 @ SV37 ) @ ( crypt @ ( xor @ SV6 @ SV20 ) @ SV32 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(193,plain,
! [SV40: $i,SV38: $i,SV36: $i,SV27: $i,SV13: $i] :
( ( ( p @ ( crypt @ SV13 @ SV27 ) )
= $false )
| ( ( ~ ( p @ SV36 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV38 ) ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV40 ) ) )
= $true )
| ( ( ! [SY85: $i] : ( p @ ( crypt @ ( xor @ SV40 @ SY85 ) @ ( decrypt @ ( xor @ SV36 @ SV38 ) @ ( crypt @ SV13 @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(194,plain,
! [SV37: $i,SV32: $i,SV20: $i,SV6: $i,SV39: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ imp ) @ SV39 ) )
= $false )
| ( ( p @ ( crypt @ ( xor @ SV6 @ SV20 ) @ SV32 ) )
= $false )
| ( ( p @ SV37 )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ SV37 ) @ ( decrypt @ ( xor @ SV39 @ SV37 ) @ ( crypt @ ( xor @ SV6 @ SV20 ) @ SV32 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(195,plain,
! [SV40: $i,SV38: $i,SV27: $i,SV13: $i,SV36: $i] :
( ( ( p @ SV36 )
= $false )
| ( ( p @ ( crypt @ SV13 @ SV27 ) )
= $false )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV38 ) ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV40 ) ) )
= $true )
| ( ( ! [SY85: $i] : ( p @ ( crypt @ ( xor @ SV40 @ SY85 ) @ ( decrypt @ ( xor @ SV36 @ SV38 ) @ ( crypt @ SV13 @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(196,plain,
! [SV40: $i,SV36: $i,SV27: $i,SV13: $i,SV38: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ imp ) @ SV38 ) )
= $false )
| ( ( p @ ( crypt @ SV13 @ SV27 ) )
= $false )
| ( ( p @ SV36 )
= $false )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV40 ) ) )
= $true )
| ( ( ! [SY85: $i] : ( p @ ( crypt @ ( xor @ SV40 @ SY85 ) @ ( decrypt @ ( xor @ SV36 @ SV38 ) @ ( crypt @ SV13 @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(197,plain,
! [SV38: $i,SV27: $i,SV13: $i,SV36: $i,SV40: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ exp ) @ SV40 ) )
= $false )
| ( ( p @ SV36 )
= $false )
| ( ( p @ ( crypt @ SV13 @ SV27 ) )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ imp ) @ SV38 ) )
= $false )
| ( ( ! [SY85: $i] : ( p @ ( crypt @ ( xor @ SV40 @ SY85 ) @ ( decrypt @ ( xor @ SV36 @ SV38 ) @ ( crypt @ SV13 @ SV27 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(198,plain,
! [SV27: $i,SV13: $i,SV38: $i,SV36: $i,SV41: $i,SV40: $i] :
( ( ( p @ ( crypt @ ( xor @ SV40 @ SV41 ) @ ( decrypt @ ( xor @ SV36 @ SV38 ) @ ( crypt @ SV13 @ SV27 ) ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ imp ) @ SV38 ) )
= $false )
| ( ( p @ ( crypt @ SV13 @ SV27 ) )
= $false )
| ( ( p @ SV36 )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ exp ) @ SV40 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(199,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[88,198,194,190,189,188,176,175,174,172,171,168,132,120,118,117,105,104,99,98,97,96,95,94,93,92,91,90,89]) ).
thf(200,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[199]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV235+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 19:59:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.36
% 0.18/0.36 No.of.Axioms: 28
% 0.18/0.36
% 0.18/0.36 Length.of.Defs: 0
% 0.18/0.36
% 0.18/0.36 Contains.Choice.Funs: false
% 0.18/0.38 (rf:0,axioms:28,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:30,loop_count:0,foatp_calls:0,translation:fof_full).........
% 1.29/1.48
% 1.29/1.48 ********************************
% 1.29/1.48 * All subproblems solved! *
% 1.29/1.48 ********************************
% 1.29/1.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:28,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:199,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.29/1.49
% 1.29/1.49 %**** Beginning of derivation protocol ****
% 1.29/1.49 % SZS output start CNFRefutation
% See solution above
% 1.29/1.49
% 1.29/1.49 %**** End of derivation protocol ****
% 1.29/1.49 %**** no. of clauses in derivation: 200 ****
% 1.29/1.49 %**** clause counter: 199 ****
% 1.29/1.49
% 1.29/1.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:28,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:199,loop_count:0,foatp_calls:1,translation:fof_full)
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