TSTP Solution File: SWV236+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SWV236+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 : n024.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 20:11:17 EDT 2022
% Result : Theorem 0.52s 0.72s
% Output : CNFRefutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 42
% Syntax : Number of formulae : 220 ( 131 unt; 14 typ; 0 def)
% Number of atoms : 1206 ( 338 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 2803 ( 257 ~; 310 |; 38 &;2174 @)
% ( 0 <=>; 24 =>; 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 : 17 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 492 ( 0 ^ 488 !; 4 ?; 492 :)
% 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_eurk,type,
eurk: $i ).
thf(tp_exp,type,
exp: $i ).
thf(tp_id,type,
id: $i ).
thf(tp_imp,type,
imp: $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_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_9) ).
thf(3,axiom,
p @ ( crypt @ ( xor @ km @ data ) @ eurk ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_8) ).
thf(4,axiom,
p @ ( crypt @ ( xor @ km @ exp ) @ eurk ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_7) ).
thf(5,axiom,
p @ ( crypt @ ( xor @ km @ pin ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_6) ).
thf(6,axiom,
p @ pin,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_5) ).
thf(7,axiom,
p @ id,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_4) ).
thf(8,axiom,
p @ data,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_3) ).
thf(9,axiom,
p @ imp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_2) ).
thf(10,axiom,
p @ kp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_1) ).
thf(11,axiom,
! [X1: $i,X2: $i] :
( ( p @ ( crypt @ ( xor @ X1 @ data ) @ X2 ) )
=> ( p @ ( crypt @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',data_cv_is_known_to_be_zero) ).
thf(12,axiom,
! [X1: $i,X2: $i] :
( ( ( p @ X2 )
& ( p @ X1 ) )
=> ( p @ ( crypt @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',encrypt_knowledge) ).
thf(13,axiom,
! [X1: $i,X2: $i] :
( ( ( p @ ( crypt @ X1 @ X2 ) )
& ( p @ X1 ) )
=> ( p @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',decrypt_knowledge) ).
thf(14,axiom,
! [X1: $i,X2: $i] :
( ( ( p @ X1 )
& ( p @ X2 ) )
=> ( p @ ( xor @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',combine_with_XOR) ).
thf(15,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(16,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(17,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(18,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(19,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(20,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(21,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(22,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(23,axiom,
! [X1: $i] :
( ( xor @ X1 @ X1 )
= id ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_rules_2) ).
thf(24,axiom,
! [X1: $i] :
( ( xor @ X1 @ id )
= X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_rules_1) ).
thf(25,axiom,
! [X1: $i,X2: $i] :
( ( decrypt @ X1 @ ( crypt @ X1 @ X2 ) )
= X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',encryption_decryption_cancellation) ).
thf(26,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(27,axiom,
! [X1: $i,X2: $i] :
( ( xor @ X1 @ X2 )
= ( xor @ X2 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_commutative) ).
thf(28,conjecture,
? [X: $i] :
( ( p @ ( crypt @ ( xor @ km @ exp ) @ X ) )
& ( p @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',find_known_exporter) ).
thf(29,negated_conjecture,
( ( ? [X: $i] :
( ( p @ ( crypt @ ( xor @ km @ exp ) @ X ) )
& ( p @ X ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[28]) ).
thf(30,plain,
( ( ? [X: $i] :
( ( p @ ( crypt @ ( xor @ km @ exp ) @ X ) )
& ( p @ X ) ) )
= $false ),
inference(unfold_def,[status(thm)],[29]) ).
thf(31,plain,
( ( p @ a )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(32,plain,
( ( p @ exp )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(33,plain,
( ( p @ ( crypt @ ( xor @ km @ data ) @ eurk ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(34,plain,
( ( p @ ( crypt @ ( xor @ km @ exp ) @ eurk ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(35,plain,
( ( p @ ( crypt @ ( xor @ km @ pin ) @ pp ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(36,plain,
( ( p @ pin )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(37,plain,
( ( p @ id )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(38,plain,
( ( p @ data )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(39,plain,
( ( p @ imp )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(40,plain,
( ( p @ kp )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(41,plain,
( ( ! [X1: $i,X2: $i] :
( ( p @ ( crypt @ ( xor @ X1 @ data ) @ X2 ) )
=> ( p @ ( crypt @ X1 @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(42,plain,
( ( ! [X1: $i,X2: $i] :
( ( ( p @ X2 )
& ( p @ X1 ) )
=> ( p @ ( crypt @ X1 @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(43,plain,
( ( ! [X1: $i,X2: $i] :
( ( ( p @ ( crypt @ X1 @ X2 ) )
& ( p @ X1 ) )
=> ( p @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(44,plain,
( ( ! [X1: $i,X2: $i] :
( ( ( p @ X1 )
& ( p @ X2 ) )
=> ( p @ ( xor @ X1 @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(45,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)],[15]) ).
thf(46,plain,
( ( ! [X1: $i,Xk1: $i] :
( ( ( p @ X1 )
& ( p @ ( crypt @ ( xor @ km @ data ) @ Xk1 ) ) )
=> ( p @ ( decrypt @ Xk1 @ X1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(47,plain,
( ( ! [X1: $i,Xk1: $i] :
( ( ( p @ X1 )
& ( p @ ( crypt @ ( xor @ km @ data ) @ Xk1 ) ) )
=> ( p @ ( crypt @ Xk1 @ X1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(48,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)],[18]) ).
thf(49,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)],[19]) ).
thf(50,plain,
( ( ! [Xk: $i,Xtype: $i] :
( ( ( p @ Xk )
& ( p @ Xtype ) )
=> ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ Xtype ) ) @ Xk ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(51,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)],[21]) ).
thf(52,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)],[22]) ).
thf(53,plain,
( ( ! [X1: $i] :
( ( xor @ X1 @ X1 )
= id ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(54,plain,
( ( ! [X1: $i] :
( ( xor @ X1 @ id )
= X1 ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(55,plain,
( ( ! [X1: $i,X2: $i] :
( ( decrypt @ X1 @ ( crypt @ X1 @ X2 ) )
= X2 ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(56,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( xor @ X1 @ ( xor @ X2 @ X3 ) )
= ( xor @ ( xor @ X1 @ X2 ) @ X3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(57,plain,
( ( ! [X1: $i,X2: $i] :
( ( xor @ X1 @ X2 )
= ( xor @ X2 @ X1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(58,plain,
( ( ~ ? [X: $i] :
( ( p @ ( crypt @ ( xor @ km @ exp ) @ X ) )
& ( p @ X ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[30]) ).
thf(59,plain,
( ( ! [X: $i] :
( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ X ) )
| ~ ( p @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[58]) ).
thf(60,plain,
( ( ! [X1: $i,X2: $i] :
( ~ ( p @ ( crypt @ ( xor @ X1 @ data ) @ X2 ) )
| ( p @ ( crypt @ X1 @ X2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(61,plain,
( ( ! [X1: $i,X2: $i] :
( ~ ( p @ X2 )
| ~ ( p @ X1 )
| ( p @ ( crypt @ X1 @ X2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(62,plain,
( ( ! [X1: $i,X2: $i] :
( ~ ( p @ ( crypt @ X1 @ X2 ) )
| ~ ( p @ X1 )
| ( p @ X2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(63,plain,
( ( ! [X1: $i,X2: $i] :
( ~ ( p @ X1 )
| ~ ( p @ X2 )
| ( p @ ( xor @ X1 @ X2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
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)],[45]) ).
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)],[46]) ).
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)],[47]) ).
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)],[48]) ).
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)],[49]) ).
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)],[50]) ).
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)],[51]) ).
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)],[52]) ).
thf(72,plain,
( ( ! [X1: $i,X2: $i] :
( ( xor @ X1 @ X2 )
= ( xor @ X2 @ X1 ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(73,plain,
( ( ! [X1: $i,X2: $i,X3: $i] :
( ( xor @ X1 @ ( xor @ X2 @ X3 ) )
= ( xor @ ( xor @ X1 @ X2 ) @ X3 ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(74,plain,
( ( ! [X1: $i,X2: $i] :
( ( decrypt @ X1 @ ( crypt @ X1 @ X2 ) )
= X2 ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(75,plain,
( ( ! [X1: $i] :
( ( xor @ X1 @ id )
= X1 ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(76,plain,
( ( ! [X1: $i] :
( ( xor @ X1 @ X1 )
= id ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
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,
( ( ! [X1: $i,X2: $i] :
( ~ ( p @ ( crypt @ ( xor @ X1 @ data ) @ X2 ) )
| ( p @ ( crypt @ X1 @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(89,plain,
( ( p @ kp )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(90,plain,
( ( p @ imp )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(91,plain,
( ( p @ data )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(92,plain,
( ( p @ id )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(93,plain,
( ( p @ pin )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(94,plain,
( ( p @ ( crypt @ ( xor @ km @ pin ) @ pp ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(95,plain,
( ( p @ ( crypt @ ( xor @ km @ exp ) @ eurk ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(96,plain,
( ( p @ ( crypt @ ( xor @ km @ data ) @ eurk ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(97,plain,
( ( p @ exp )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(98,plain,
( ( p @ a )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(99,plain,
( ( ! [X: $i] :
( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ X ) )
| ~ ( p @ X ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(100,plain,
! [SV1: $i] :
( ( ! [SY44: $i] :
( ( xor @ SV1 @ SY44 )
= ( xor @ SY44 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(101,plain,
! [SV2: $i] :
( ( ! [SY45: $i,SY46: $i] :
( ( xor @ SV2 @ ( xor @ SY45 @ SY46 ) )
= ( xor @ ( xor @ SV2 @ SY45 ) @ SY46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(102,plain,
! [SV3: $i] :
( ( ! [SY47: $i] :
( ( decrypt @ SV3 @ ( crypt @ SV3 @ SY47 ) )
= SY47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(103,plain,
! [SV4: $i] :
( ( ( xor @ SV4 @ id )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(104,plain,
! [SV5: $i] :
( ( ( xor @ SV5 @ SV5 )
= id )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(105,plain,
! [SV6: $i] :
( ( ! [SY48: $i,SY49: $i,SY50: $i,SY51: $i] :
( ~ ( p @ ( crypt @ ( xor @ SV6 @ SY48 ) @ SY49 ) )
| ~ ( p @ SY50 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SY51 ) )
| ( p @ ( crypt @ ( xor @ km @ SY50 ) @ ( decrypt @ ( xor @ SY51 @ SY50 ) @ ( crypt @ ( xor @ SV6 @ SY48 ) @ SY49 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(106,plain,
! [SV7: $i] :
( ( ! [SY52: $i,SY53: $i] :
( ~ ( p @ ( crypt @ ( xor @ km @ SV7 ) @ SY52 ) )
| ~ ( p @ SV7 )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SY53 ) )
| ( p @ ( crypt @ ( xor @ SY53 @ SV7 ) @ SY52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(107,plain,
! [SV8: $i] :
( ( ! [SY54: $i] :
( ~ ( p @ SV8 )
| ~ ( p @ SY54 )
| ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SY54 ) ) @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(108,plain,
! [SV9: $i] :
( ( ! [SY55: $i,SY56: $i] :
( ~ ( p @ SV9 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SY55 ) ) @ SY56 ) )
| ~ ( p @ SY55 )
| ( p @ ( crypt @ ( xor @ km @ ( xor @ SY55 @ kp ) ) @ ( xor @ SV9 @ SY56 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(109,plain,
! [SV10: $i] :
( ( ! [SY57: $i,SY58: $i] :
( ~ ( p @ SV10 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ SY57 @ kp ) ) @ SY58 ) )
| ~ ( p @ SY57 )
| ( p @ ( crypt @ ( xor @ km @ SY57 ) @ ( xor @ SY58 @ SV10 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(110,plain,
! [SV11: $i] :
( ( ! [SY59: $i] :
( ~ ( p @ SV11 )
| ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SY59 ) )
| ( p @ ( crypt @ SY59 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(111,plain,
! [SV12: $i] :
( ( ! [SY60: $i] :
( ~ ( p @ SV12 )
| ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SY60 ) )
| ( p @ ( decrypt @ SY60 @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(112,plain,
! [SV13: $i] :
( ( ! [SY61: $i,SY62: $i,SY63: $i,SY64: $i] :
( ~ ( p @ ( crypt @ SV13 @ SY61 ) )
| ~ ( p @ SY62 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SY63 ) )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SY64 ) )
| ! [SY65: $i] : ( p @ ( crypt @ ( xor @ SY64 @ SY65 ) @ ( decrypt @ ( xor @ SY62 @ SY63 ) @ ( crypt @ SV13 @ SY61 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(113,plain,
! [SV14: $i] :
( ( ! [SY66: $i] :
( ~ ( p @ SV14 )
| ~ ( p @ SY66 )
| ( p @ ( xor @ SV14 @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(114,plain,
! [SV15: $i] :
( ( ! [SY67: $i] :
( ~ ( p @ ( crypt @ SV15 @ SY67 ) )
| ~ ( p @ SV15 )
| ( p @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(115,plain,
! [SV16: $i] :
( ( ! [SY68: $i] :
( ~ ( p @ SY68 )
| ~ ( p @ SV16 )
| ( p @ ( crypt @ SV16 @ SY68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(116,plain,
! [SV17: $i] :
( ( ! [SY69: $i] :
( ~ ( p @ ( crypt @ ( xor @ SV17 @ data ) @ SY69 ) )
| ( p @ ( crypt @ SV17 @ SY69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(117,plain,
! [SV18: $i] :
( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV18 ) )
| ~ ( p @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(118,plain,
! [SV19: $i,SV1: $i] :
( ( ( xor @ SV1 @ SV19 )
= ( xor @ SV19 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(119,plain,
! [SV20: $i,SV2: $i] :
( ( ! [SY70: $i] :
( ( xor @ SV2 @ ( xor @ SV20 @ SY70 ) )
= ( xor @ ( xor @ SV2 @ SV20 ) @ SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(120,plain,
! [SV21: $i,SV3: $i] :
( ( ( decrypt @ SV3 @ ( crypt @ SV3 @ SV21 ) )
= SV21 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(121,plain,
! [SV22: $i,SV6: $i] :
( ( ! [SY71: $i,SY72: $i,SY73: $i] :
( ~ ( p @ ( crypt @ ( xor @ SV6 @ SV22 ) @ SY71 ) )
| ~ ( p @ SY72 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SY73 ) )
| ( p @ ( crypt @ ( xor @ km @ SY72 ) @ ( decrypt @ ( xor @ SY73 @ SY72 ) @ ( crypt @ ( xor @ SV6 @ SV22 ) @ SY71 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(122,plain,
! [SV23: $i,SV7: $i] :
( ( ! [SY74: $i] :
( ~ ( p @ ( crypt @ ( xor @ km @ SV7 ) @ SV23 ) )
| ~ ( p @ SV7 )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SY74 ) )
| ( p @ ( crypt @ ( xor @ SY74 @ SV7 ) @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(123,plain,
! [SV24: $i,SV8: $i] :
( ( ~ ( p @ SV8 )
| ~ ( p @ SV24 )
| ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV24 ) ) @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(124,plain,
! [SV25: $i,SV9: $i] :
( ( ! [SY75: $i] :
( ~ ( p @ SV9 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV25 ) ) @ SY75 ) )
| ~ ( p @ SV25 )
| ( p @ ( crypt @ ( xor @ km @ ( xor @ SV25 @ kp ) ) @ ( xor @ SV9 @ SY75 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(125,plain,
! [SV26: $i,SV10: $i] :
( ( ! [SY76: $i] :
( ~ ( p @ SV10 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ SV26 @ kp ) ) @ SY76 ) )
| ~ ( p @ SV26 )
| ( p @ ( crypt @ ( xor @ km @ SV26 ) @ ( xor @ SY76 @ SV10 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(126,plain,
! [SV27: $i,SV11: $i] :
( ( ~ ( p @ SV11 )
| ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SV27 ) )
| ( p @ ( crypt @ SV27 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(127,plain,
! [SV28: $i,SV12: $i] :
( ( ~ ( p @ SV12 )
| ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SV28 ) )
| ( p @ ( decrypt @ SV28 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(128,plain,
! [SV29: $i,SV13: $i] :
( ( ! [SY77: $i,SY78: $i,SY79: $i] :
( ~ ( p @ ( crypt @ SV13 @ SV29 ) )
| ~ ( p @ SY77 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SY78 ) )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SY79 ) )
| ! [SY80: $i] : ( p @ ( crypt @ ( xor @ SY79 @ SY80 ) @ ( decrypt @ ( xor @ SY77 @ SY78 ) @ ( crypt @ SV13 @ SV29 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(129,plain,
! [SV30: $i,SV14: $i] :
( ( ~ ( p @ SV14 )
| ~ ( p @ SV30 )
| ( p @ ( xor @ SV14 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(130,plain,
! [SV31: $i,SV15: $i] :
( ( ~ ( p @ ( crypt @ SV15 @ SV31 ) )
| ~ ( p @ SV15 )
| ( p @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(131,plain,
! [SV16: $i,SV32: $i] :
( ( ~ ( p @ SV32 )
| ~ ( p @ SV16 )
| ( p @ ( crypt @ SV16 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(132,plain,
! [SV33: $i,SV17: $i] :
( ( ~ ( p @ ( crypt @ ( xor @ SV17 @ data ) @ SV33 ) )
| ( p @ ( crypt @ SV17 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(133,plain,
! [SV18: $i] :
( ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV18 ) ) )
= $true )
| ( ( ~ ( p @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(134,plain,
! [SV34: $i,SV20: $i,SV2: $i] :
( ( ( xor @ SV2 @ ( xor @ SV20 @ SV34 ) )
= ( xor @ ( xor @ SV2 @ SV20 ) @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(135,plain,
! [SV35: $i,SV22: $i,SV6: $i] :
( ( ! [SY81: $i,SY82: $i] :
( ~ ( p @ ( crypt @ ( xor @ SV6 @ SV22 ) @ SV35 ) )
| ~ ( p @ SY81 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SY82 ) )
| ( p @ ( crypt @ ( xor @ km @ SY81 ) @ ( decrypt @ ( xor @ SY82 @ SY81 ) @ ( crypt @ ( xor @ SV6 @ SV22 ) @ SV35 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(136,plain,
! [SV36: $i,SV23: $i,SV7: $i] :
( ( ~ ( p @ ( crypt @ ( xor @ km @ SV7 ) @ SV23 ) )
| ~ ( p @ SV7 )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV36 ) )
| ( p @ ( crypt @ ( xor @ SV36 @ SV7 ) @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(137,plain,
! [SV24: $i,SV8: $i] :
( ( ( ~ ( p @ SV8 )
| ~ ( p @ SV24 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV24 ) ) @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(138,plain,
! [SV37: $i,SV25: $i,SV9: $i] :
( ( ~ ( p @ SV9 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV25 ) ) @ SV37 ) )
| ~ ( p @ SV25 )
| ( p @ ( crypt @ ( xor @ km @ ( xor @ SV25 @ kp ) ) @ ( xor @ SV9 @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(139,plain,
! [SV38: $i,SV26: $i,SV10: $i] :
( ( ~ ( p @ SV10 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ SV26 @ kp ) ) @ SV38 ) )
| ~ ( p @ SV26 )
| ( p @ ( crypt @ ( xor @ km @ SV26 ) @ ( xor @ SV38 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(140,plain,
! [SV27: $i,SV11: $i] :
( ( ( ~ ( p @ SV11 )
| ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SV27 ) ) )
= $true )
| ( ( p @ ( crypt @ SV27 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(141,plain,
! [SV28: $i,SV12: $i] :
( ( ( ~ ( p @ SV12 )
| ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SV28 ) ) )
= $true )
| ( ( p @ ( decrypt @ SV28 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(142,plain,
! [SV39: $i,SV29: $i,SV13: $i] :
( ( ! [SY83: $i,SY84: $i] :
( ~ ( p @ ( crypt @ SV13 @ SV29 ) )
| ~ ( p @ SV39 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SY83 ) )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SY84 ) )
| ! [SY85: $i] : ( p @ ( crypt @ ( xor @ SY84 @ SY85 ) @ ( decrypt @ ( xor @ SV39 @ SY83 ) @ ( crypt @ SV13 @ SV29 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(143,plain,
! [SV30: $i,SV14: $i] :
( ( ( ~ ( p @ SV14 )
| ~ ( p @ SV30 ) )
= $true )
| ( ( p @ ( xor @ SV14 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(144,plain,
! [SV31: $i,SV15: $i] :
( ( ( ~ ( p @ ( crypt @ SV15 @ SV31 ) )
| ~ ( p @ SV15 ) )
= $true )
| ( ( p @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(145,plain,
! [SV16: $i,SV32: $i] :
( ( ( ~ ( p @ SV32 )
| ~ ( p @ SV16 ) )
= $true )
| ( ( p @ ( crypt @ SV16 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(146,plain,
! [SV33: $i,SV17: $i] :
( ( ( ~ ( p @ ( crypt @ ( xor @ SV17 @ data ) @ SV33 ) ) )
= $true )
| ( ( p @ ( crypt @ SV17 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(147,plain,
! [SV18: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ exp ) @ SV18 ) )
= $false )
| ( ( ~ ( p @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(148,plain,
! [SV40: $i,SV35: $i,SV22: $i,SV6: $i] :
( ( ! [SY86: $i] :
( ~ ( p @ ( crypt @ ( xor @ SV6 @ SV22 ) @ SV35 ) )
| ~ ( p @ SV40 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SY86 ) )
| ( p @ ( crypt @ ( xor @ km @ SV40 ) @ ( decrypt @ ( xor @ SY86 @ SV40 ) @ ( crypt @ ( xor @ SV6 @ SV22 ) @ SV35 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(149,plain,
! [SV36: $i,SV23: $i,SV7: $i] :
( ( ( ~ ( p @ ( crypt @ ( xor @ km @ SV7 ) @ SV23 ) )
| ~ ( p @ SV7 )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV36 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ SV36 @ SV7 ) @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(150,plain,
! [SV24: $i,SV8: $i] :
( ( ( ~ ( p @ SV8 ) )
= $true )
| ( ( ~ ( p @ SV24 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV24 ) ) @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(151,plain,
! [SV37: $i,SV25: $i,SV9: $i] :
( ( ( ~ ( p @ SV9 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV25 ) ) @ SV37 ) )
| ~ ( p @ SV25 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV25 @ kp ) ) @ ( xor @ SV9 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(152,plain,
! [SV38: $i,SV26: $i,SV10: $i] :
( ( ( ~ ( p @ SV10 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ SV26 @ kp ) ) @ SV38 ) )
| ~ ( p @ SV26 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV26 ) @ ( xor @ SV38 @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(153,plain,
! [SV27: $i,SV11: $i] :
( ( ( ~ ( p @ SV11 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SV27 ) ) )
= $true )
| ( ( p @ ( crypt @ SV27 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(154,plain,
! [SV28: $i,SV12: $i] :
( ( ( ~ ( p @ SV12 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SV28 ) ) )
= $true )
| ( ( p @ ( decrypt @ SV28 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(155,plain,
! [SV41: $i,SV39: $i,SV29: $i,SV13: $i] :
( ( ! [SY87: $i] :
( ~ ( p @ ( crypt @ SV13 @ SV29 ) )
| ~ ( p @ SV39 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV41 ) )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SY87 ) )
| ! [SY88: $i] : ( p @ ( crypt @ ( xor @ SY87 @ SY88 ) @ ( decrypt @ ( xor @ SV39 @ SV41 ) @ ( crypt @ SV13 @ SV29 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(156,plain,
! [SV30: $i,SV14: $i] :
( ( ( ~ ( p @ SV14 ) )
= $true )
| ( ( ~ ( p @ SV30 ) )
= $true )
| ( ( p @ ( xor @ SV14 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(157,plain,
! [SV31: $i,SV15: $i] :
( ( ( ~ ( p @ ( crypt @ SV15 @ SV31 ) ) )
= $true )
| ( ( ~ ( p @ SV15 ) )
= $true )
| ( ( p @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(158,plain,
! [SV16: $i,SV32: $i] :
( ( ( ~ ( p @ SV32 ) )
= $true )
| ( ( ~ ( p @ SV16 ) )
= $true )
| ( ( p @ ( crypt @ SV16 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(159,plain,
! [SV33: $i,SV17: $i] :
( ( ( p @ ( crypt @ ( xor @ SV17 @ data ) @ SV33 ) )
= $false )
| ( ( p @ ( crypt @ SV17 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(160,plain,
! [SV18: $i] :
( ( ( p @ SV18 )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ exp ) @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(161,plain,
! [SV42: $i,SV40: $i,SV35: $i,SV22: $i,SV6: $i] :
( ( ~ ( p @ ( crypt @ ( xor @ SV6 @ SV22 ) @ SV35 ) )
| ~ ( p @ SV40 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV42 ) )
| ( p @ ( crypt @ ( xor @ km @ SV40 ) @ ( decrypt @ ( xor @ SV42 @ SV40 ) @ ( crypt @ ( xor @ SV6 @ SV22 ) @ SV35 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(162,plain,
! [SV36: $i,SV23: $i,SV7: $i] :
( ( ( ~ ( p @ ( crypt @ ( xor @ km @ SV7 ) @ SV23 ) )
| ~ ( p @ SV7 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV36 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ SV36 @ SV7 ) @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(163,plain,
! [SV24: $i,SV8: $i] :
( ( ( p @ SV8 )
= $false )
| ( ( ~ ( p @ SV24 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV24 ) ) @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(164,plain,
! [SV37: $i,SV25: $i,SV9: $i] :
( ( ( ~ ( p @ SV9 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV25 ) ) @ SV37 ) ) )
= $true )
| ( ( ~ ( p @ SV25 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV25 @ kp ) ) @ ( xor @ SV9 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(165,plain,
! [SV38: $i,SV26: $i,SV10: $i] :
( ( ( ~ ( p @ SV10 )
| ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ SV26 @ kp ) ) @ SV38 ) ) )
= $true )
| ( ( ~ ( p @ SV26 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV26 ) @ ( xor @ SV38 @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(166,plain,
! [SV27: $i,SV11: $i] :
( ( ( p @ SV11 )
= $false )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SV27 ) ) )
= $true )
| ( ( p @ ( crypt @ SV27 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(167,plain,
! [SV28: $i,SV12: $i] :
( ( ( p @ SV12 )
= $false )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ data ) @ SV28 ) ) )
= $true )
| ( ( p @ ( decrypt @ SV28 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(168,plain,
! [SV43: $i,SV41: $i,SV39: $i,SV29: $i,SV13: $i] :
( ( ~ ( p @ ( crypt @ SV13 @ SV29 ) )
| ~ ( p @ SV39 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV41 ) )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV43 ) )
| ! [SY89: $i] : ( p @ ( crypt @ ( xor @ SV43 @ SY89 ) @ ( decrypt @ ( xor @ SV39 @ SV41 ) @ ( crypt @ SV13 @ SV29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(169,plain,
! [SV30: $i,SV14: $i] :
( ( ( p @ SV14 )
= $false )
| ( ( ~ ( p @ SV30 ) )
= $true )
| ( ( p @ ( xor @ SV14 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(170,plain,
! [SV31: $i,SV15: $i] :
( ( ( p @ ( crypt @ SV15 @ SV31 ) )
= $false )
| ( ( ~ ( p @ SV15 ) )
= $true )
| ( ( p @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(171,plain,
! [SV16: $i,SV32: $i] :
( ( ( p @ SV32 )
= $false )
| ( ( ~ ( p @ SV16 ) )
= $true )
| ( ( p @ ( crypt @ SV16 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(172,plain,
! [SV42: $i,SV40: $i,SV35: $i,SV22: $i,SV6: $i] :
( ( ( ~ ( p @ ( crypt @ ( xor @ SV6 @ SV22 ) @ SV35 ) )
| ~ ( p @ SV40 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV42 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV40 ) @ ( decrypt @ ( xor @ SV42 @ SV40 ) @ ( crypt @ ( xor @ SV6 @ SV22 ) @ SV35 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(173,plain,
! [SV36: $i,SV23: $i,SV7: $i] :
( ( ( ~ ( p @ ( crypt @ ( xor @ km @ SV7 ) @ SV23 ) ) )
= $true )
| ( ( ~ ( p @ SV7 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV36 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ SV36 @ SV7 ) @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(174,plain,
! [SV8: $i,SV24: $i] :
( ( ( p @ SV24 )
= $false )
| ( ( p @ SV8 )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV24 ) ) @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(175,plain,
! [SV37: $i,SV25: $i,SV9: $i] :
( ( ( ~ ( p @ SV9 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV25 ) ) @ SV37 ) ) )
= $true )
| ( ( ~ ( p @ SV25 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV25 @ kp ) ) @ ( xor @ SV9 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(176,plain,
! [SV38: $i,SV26: $i,SV10: $i] :
( ( ( ~ ( p @ SV10 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ SV26 @ kp ) ) @ SV38 ) ) )
= $true )
| ( ( ~ ( p @ SV26 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV26 ) @ ( xor @ SV38 @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(177,plain,
! [SV11: $i,SV27: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ data ) @ SV27 ) )
= $false )
| ( ( p @ SV11 )
= $false )
| ( ( p @ ( crypt @ SV27 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(178,plain,
! [SV12: $i,SV28: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ data ) @ SV28 ) )
= $false )
| ( ( p @ SV12 )
= $false )
| ( ( p @ ( decrypt @ SV28 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(179,plain,
! [SV43: $i,SV41: $i,SV39: $i,SV29: $i,SV13: $i] :
( ( ( ~ ( p @ ( crypt @ SV13 @ SV29 ) )
| ~ ( p @ SV39 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV41 ) )
| ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV43 ) ) )
= $true )
| ( ( ! [SY89: $i] : ( p @ ( crypt @ ( xor @ SV43 @ SY89 ) @ ( decrypt @ ( xor @ SV39 @ SV41 ) @ ( crypt @ SV13 @ SV29 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(180,plain,
! [SV14: $i,SV30: $i] :
( ( ( p @ SV30 )
= $false )
| ( ( p @ SV14 )
= $false )
| ( ( p @ ( xor @ SV14 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(181,plain,
! [SV31: $i,SV15: $i] :
( ( ( p @ SV15 )
= $false )
| ( ( p @ ( crypt @ SV15 @ SV31 ) )
= $false )
| ( ( p @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(182,plain,
! [SV32: $i,SV16: $i] :
( ( ( p @ SV16 )
= $false )
| ( ( p @ SV32 )
= $false )
| ( ( p @ ( crypt @ SV16 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(183,plain,
! [SV42: $i,SV40: $i,SV35: $i,SV22: $i,SV6: $i] :
( ( ( ~ ( p @ ( crypt @ ( xor @ SV6 @ SV22 ) @ SV35 ) )
| ~ ( p @ SV40 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV42 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV40 ) @ ( decrypt @ ( xor @ SV42 @ SV40 ) @ ( crypt @ ( xor @ SV6 @ SV22 ) @ SV35 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(184,plain,
! [SV36: $i,SV23: $i,SV7: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ SV7 ) @ SV23 ) )
= $false )
| ( ( ~ ( p @ SV7 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV36 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ SV36 @ SV7 ) @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(185,plain,
! [SV37: $i,SV25: $i,SV9: $i] :
( ( ( p @ SV9 )
= $false )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV25 ) ) @ SV37 ) ) )
= $true )
| ( ( ~ ( p @ SV25 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV25 @ kp ) ) @ ( xor @ SV9 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(186,plain,
! [SV38: $i,SV26: $i,SV10: $i] :
( ( ( p @ SV10 )
= $false )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ ( xor @ SV26 @ kp ) ) @ SV38 ) ) )
= $true )
| ( ( ~ ( p @ SV26 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV26 ) @ ( xor @ SV38 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(187,plain,
! [SV43: $i,SV41: $i,SV39: $i,SV29: $i,SV13: $i] :
( ( ( ~ ( p @ ( crypt @ SV13 @ SV29 ) )
| ~ ( p @ SV39 )
| ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV41 ) ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV43 ) ) )
= $true )
| ( ( ! [SY89: $i] : ( p @ ( crypt @ ( xor @ SV43 @ SY89 ) @ ( decrypt @ ( xor @ SV39 @ SV41 ) @ ( crypt @ SV13 @ SV29 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(188,plain,
! [SV42: $i,SV40: $i,SV35: $i,SV22: $i,SV6: $i] :
( ( ( ~ ( p @ ( crypt @ ( xor @ SV6 @ SV22 ) @ SV35 ) ) )
= $true )
| ( ( ~ ( p @ SV40 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV42 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV40 ) @ ( decrypt @ ( xor @ SV42 @ SV40 ) @ ( crypt @ ( xor @ SV6 @ SV22 ) @ SV35 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(189,plain,
! [SV36: $i,SV23: $i,SV7: $i] :
( ( ( p @ SV7 )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ SV7 ) @ SV23 ) )
= $false )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV36 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ SV36 @ SV7 ) @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(190,plain,
! [SV9: $i,SV37: $i,SV25: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV25 ) ) @ SV37 ) )
= $false )
| ( ( p @ SV9 )
= $false )
| ( ( ~ ( p @ SV25 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV25 @ kp ) ) @ ( xor @ SV9 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(191,plain,
! [SV10: $i,SV38: $i,SV26: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV26 @ kp ) ) @ SV38 ) )
= $false )
| ( ( p @ SV10 )
= $false )
| ( ( ~ ( p @ SV26 ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV26 ) @ ( xor @ SV38 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(192,plain,
! [SV43: $i,SV41: $i,SV39: $i,SV29: $i,SV13: $i] :
( ( ( ~ ( p @ ( crypt @ SV13 @ SV29 ) )
| ~ ( p @ SV39 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV41 ) ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV43 ) ) )
= $true )
| ( ( ! [SY89: $i] : ( p @ ( crypt @ ( xor @ SV43 @ SY89 ) @ ( decrypt @ ( xor @ SV39 @ SV41 ) @ ( crypt @ SV13 @ SV29 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(193,plain,
! [SV42: $i,SV40: $i,SV35: $i,SV22: $i,SV6: $i] :
( ( ( p @ ( crypt @ ( xor @ SV6 @ SV22 ) @ SV35 ) )
= $false )
| ( ( ~ ( p @ SV40 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV42 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV40 ) @ ( decrypt @ ( xor @ SV42 @ SV40 ) @ ( crypt @ ( xor @ SV6 @ SV22 ) @ SV35 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(194,plain,
! [SV23: $i,SV7: $i,SV36: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ exp ) @ SV36 ) )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ SV7 ) @ SV23 ) )
= $false )
| ( ( p @ SV7 )
= $false )
| ( ( p @ ( crypt @ ( xor @ SV36 @ SV7 ) @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(195,plain,
! [SV37: $i,SV9: $i,SV25: $i] :
( ( ( p @ SV25 )
= $false )
| ( ( p @ SV9 )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ kp @ SV25 ) ) @ SV37 ) )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV25 @ kp ) ) @ ( xor @ SV9 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(196,plain,
! [SV38: $i,SV10: $i,SV26: $i] :
( ( ( p @ SV26 )
= $false )
| ( ( p @ SV10 )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ ( xor @ SV26 @ kp ) ) @ SV38 ) )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ SV26 ) @ ( xor @ SV38 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(197,plain,
! [SV43: $i,SV41: $i,SV39: $i,SV29: $i,SV13: $i] :
( ( ( ~ ( p @ ( crypt @ SV13 @ SV29 ) ) )
= $true )
| ( ( ~ ( p @ SV39 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV41 ) ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV43 ) ) )
= $true )
| ( ( ! [SY89: $i] : ( p @ ( crypt @ ( xor @ SV43 @ SY89 ) @ ( decrypt @ ( xor @ SV39 @ SV41 ) @ ( crypt @ SV13 @ SV29 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(198,plain,
! [SV42: $i,SV35: $i,SV22: $i,SV6: $i,SV40: $i] :
( ( ( p @ SV40 )
= $false )
| ( ( p @ ( crypt @ ( xor @ SV6 @ SV22 ) @ SV35 ) )
= $false )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV42 ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ SV40 ) @ ( decrypt @ ( xor @ SV42 @ SV40 ) @ ( crypt @ ( xor @ SV6 @ SV22 ) @ SV35 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(199,plain,
! [SV43: $i,SV41: $i,SV39: $i,SV29: $i,SV13: $i] :
( ( ( p @ ( crypt @ SV13 @ SV29 ) )
= $false )
| ( ( ~ ( p @ SV39 ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV41 ) ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV43 ) ) )
= $true )
| ( ( ! [SY89: $i] : ( p @ ( crypt @ ( xor @ SV43 @ SY89 ) @ ( decrypt @ ( xor @ SV39 @ SV41 ) @ ( crypt @ SV13 @ SV29 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(200,plain,
! [SV40: $i,SV35: $i,SV22: $i,SV6: $i,SV42: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ imp ) @ SV42 ) )
= $false )
| ( ( p @ ( crypt @ ( xor @ SV6 @ SV22 ) @ SV35 ) )
= $false )
| ( ( p @ SV40 )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ SV40 ) @ ( decrypt @ ( xor @ SV42 @ SV40 ) @ ( crypt @ ( xor @ SV6 @ SV22 ) @ SV35 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(201,plain,
! [SV43: $i,SV41: $i,SV29: $i,SV13: $i,SV39: $i] :
( ( ( p @ SV39 )
= $false )
| ( ( p @ ( crypt @ SV13 @ SV29 ) )
= $false )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ imp ) @ SV41 ) ) )
= $true )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV43 ) ) )
= $true )
| ( ( ! [SY89: $i] : ( p @ ( crypt @ ( xor @ SV43 @ SY89 ) @ ( decrypt @ ( xor @ SV39 @ SV41 ) @ ( crypt @ SV13 @ SV29 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(202,plain,
! [SV43: $i,SV39: $i,SV29: $i,SV13: $i,SV41: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ imp ) @ SV41 ) )
= $false )
| ( ( p @ ( crypt @ SV13 @ SV29 ) )
= $false )
| ( ( p @ SV39 )
= $false )
| ( ( ~ ( p @ ( crypt @ ( xor @ km @ exp ) @ SV43 ) ) )
= $true )
| ( ( ! [SY89: $i] : ( p @ ( crypt @ ( xor @ SV43 @ SY89 ) @ ( decrypt @ ( xor @ SV39 @ SV41 ) @ ( crypt @ SV13 @ SV29 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(203,plain,
! [SV41: $i,SV29: $i,SV13: $i,SV39: $i,SV43: $i] :
( ( ( p @ ( crypt @ ( xor @ km @ exp ) @ SV43 ) )
= $false )
| ( ( p @ SV39 )
= $false )
| ( ( p @ ( crypt @ SV13 @ SV29 ) )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ imp ) @ SV41 ) )
= $false )
| ( ( ! [SY89: $i] : ( p @ ( crypt @ ( xor @ SV43 @ SY89 ) @ ( decrypt @ ( xor @ SV39 @ SV41 ) @ ( crypt @ SV13 @ SV29 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(204,plain,
! [SV29: $i,SV13: $i,SV41: $i,SV39: $i,SV44: $i,SV43: $i] :
( ( ( p @ ( crypt @ ( xor @ SV43 @ SV44 ) @ ( decrypt @ ( xor @ SV39 @ SV41 ) @ ( crypt @ SV13 @ SV29 ) ) ) )
= $true )
| ( ( p @ ( crypt @ ( xor @ km @ imp ) @ SV41 ) )
= $false )
| ( ( p @ ( crypt @ SV13 @ SV29 ) )
= $false )
| ( ( p @ SV39 )
= $false )
| ( ( p @ ( crypt @ ( xor @ km @ exp ) @ SV43 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(205,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[89,204,200,196,195,194,182,181,180,178,177,174,160,159,134,120,118,104,103,98,97,96,95,94,93,92,91,90]) ).
thf(206,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[205]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV236+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n024.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
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 22:20:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 27
% 0.13/0.36
% 0.13/0.36 Length.of.Defs: 0
% 0.13/0.36
% 0.13/0.36 Contains.Choice.Funs: false
% 0.13/0.38 (rf:0,axioms:27,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:29,loop_count:0,foatp_calls:0,translation:fof_full)..........
% 0.52/0.72
% 0.52/0.72 ********************************
% 0.52/0.72 * All subproblems solved! *
% 0.52/0.72 ********************************
% 0.52/0.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:27,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:205,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.52/0.73
% 0.52/0.73 %**** Beginning of derivation protocol ****
% 0.52/0.73 % SZS output start CNFRefutation
% See solution above
% 0.52/0.73
% 0.52/0.73 %**** End of derivation protocol ****
% 0.52/0.73 %**** no. of clauses in derivation: 206 ****
% 0.52/0.73 %**** clause counter: 205 ****
% 0.52/0.73
% 0.52/0.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:27,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:205,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------