TSTP Solution File: SYN982-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYN982-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n020.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 : Thu Jul 21 08:30:58 EDT 2022
% Result : Unsatisfiable 0.44s 0.66s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 64
% Syntax : Number of formulae : 324 ( 168 unt; 26 typ; 0 def)
% Number of atoms : 1656 ( 428 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 3848 ( 398 ~; 502 |; 0 &;2948 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 8 con; 0-4 aty)
% Number of variables : 890 ( 0 ^ 890 !; 0 ?; 890 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_at,type,
at: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_bt,type,
bt: $i ).
thf(tp_encr,type,
encr: $i > $i > $i ).
thf(tp_key,type,
key: $i > $i > $i ).
thf(tp_kt,type,
kt: $i > $i ).
thf(tp_na,type,
na: $i ).
thf(tp_nb,type,
nb: $i > $i ).
thf(tp_pair,type,
pair: $i > $i > $i ).
thf(tp_quadr,type,
quadr: $i > $i > $i > $i > $i ).
thf(tp_sent,type,
sent: $i > $i > $i > $i ).
thf(tp_ssAk,type,
ssAk: $i > $o ).
thf(tp_ssBf,type,
ssBf: $i > $o ).
thf(tp_ssBk,type,
ssBk: $i > $o ).
thf(tp_ssIk,type,
ssIk: $i > $o ).
thf(tp_ssIm,type,
ssIm: $i > $o ).
thf(tp_ssM,type,
ssM: $i > $o ).
thf(tp_ssNonce,type,
ssNonce: $i > $o ).
thf(tp_ssP,type,
ssP: $i > $o ).
thf(tp_ssSa,type,
ssSa: $i > $o ).
thf(tp_ssSb,type,
ssSb: $i > $o ).
thf(tp_ssTk,type,
ssTk: $i > $o ).
thf(tp_t,type,
t: $i ).
thf(tp_tb,type,
tb: $i > $i ).
thf(tp_triple,type,
triple: $i > $i > $i > $i ).
thf(1,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i,Z: $i,X1: $i] :
( ~ ( ssM @ ( sent @ U @ t @ ( triple @ U @ V @ ( encr @ ( triple @ W @ X @ Y ) @ Z ) ) ) )
| ~ ( ssTk @ ( key @ Z @ U ) )
| ~ ( ssTk @ ( key @ X1 @ W ) )
| ~ ( ssNonce @ X )
| ( ssM @ ( sent @ t @ W @ ( triple @ ( encr @ ( quadr @ U @ X @ ( kt @ X ) @ Y ) @ X1 ) @ ( encr @ ( triple @ W @ ( kt @ X ) @ Y ) @ Z ) @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause36) ).
thf(2,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i,Z: $i] :
( ~ ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ U @ V @ W @ X ) @ at ) @ Y @ Z ) ) )
| ~ ( ssSa @ ( pair @ U @ V ) )
| ( ssM @ ( sent @ a @ U @ ( pair @ Y @ ( encr @ Z @ W ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause35) ).
thf(3,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( ssM @ ( sent @ U @ b @ ( pair @ ( encr @ ( triple @ U @ V @ ( tb @ W ) ) @ bt ) @ ( encr @ ( nb @ W ) @ V ) ) ) )
| ~ ( ssSb @ ( pair @ U @ W ) )
| ( ssBk @ ( key @ V @ U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause34) ).
thf(4,axiom,
! [U: $i,V: $i] :
( ~ ( ssM @ ( sent @ U @ b @ ( pair @ U @ V ) ) )
| ~ ( ssBf @ V )
| ( ssM @ ( sent @ b @ t @ ( triple @ b @ ( nb @ V ) @ ( encr @ ( triple @ U @ V @ ( tb @ V ) ) @ bt ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause33) ).
thf(5,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i,Z: $i] :
( ~ ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ U @ V @ W @ X ) @ at ) @ Y @ Z ) ) )
| ~ ( ssSa @ ( pair @ U @ V ) )
| ( ssAk @ ( key @ W @ U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause32) ).
thf(6,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( ssIm @ U )
| ~ ( ssIm @ V )
| ~ ( ssIm @ W )
| ~ ( ssIm @ X )
| ( ssIm @ ( quadr @ U @ V @ W @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause31) ).
thf(7,axiom,
! [U: $i,V: $i] :
( ~ ( ssM @ ( sent @ U @ b @ ( pair @ U @ V ) ) )
| ~ ( ssBf @ V )
| ( ssSb @ ( pair @ U @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause30) ).
thf(8,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( ssIm @ U )
| ~ ( ssIk @ ( key @ V @ W ) )
| ~ ( ssP @ W )
| ( ssIm @ ( encr @ U @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause29) ).
thf(9,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( ssIm @ U )
| ~ ( ssIm @ V )
| ~ ( ssIm @ W )
| ( ssIm @ ( triple @ U @ V @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause28) ).
thf(10,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( ssIm @ U )
| ~ ( ssP @ V )
| ~ ( ssP @ W )
| ( ssM @ ( sent @ V @ W @ U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause27) ).
thf(11,axiom,
! [U: $i,V: $i] :
( ~ ( ssIm @ U )
| ~ ( ssIm @ V )
| ( ssIm @ ( pair @ U @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause26) ).
thf(12,axiom,
! [U: $i,V: $i] :
( ~ ( ssIm @ U )
| ~ ( ssP @ V )
| ( ssIk @ ( key @ U @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause25) ).
thf(13,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( ssIm @ ( quadr @ U @ V @ W @ X ) )
| ( ssIm @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause24) ).
thf(14,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( ssIm @ ( quadr @ U @ V @ W @ X ) )
| ( ssIm @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause23) ).
thf(15,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( ssIm @ ( quadr @ U @ V @ W @ X ) )
| ( ssIm @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause22) ).
thf(16,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( ssIm @ ( quadr @ U @ V @ W @ X ) )
| ( ssIm @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause21) ).
thf(17,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( ssM @ ( sent @ U @ V @ W ) )
| ( ssIm @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause20) ).
thf(18,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( ssIm @ ( triple @ U @ V @ W ) )
| ( ssIm @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause19) ).
thf(19,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( ssIm @ ( triple @ U @ V @ W ) )
| ( ssIm @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause18) ).
thf(20,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( ssIm @ ( triple @ U @ V @ W ) )
| ( ssIm @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause17) ).
thf(21,axiom,
ssM @ ( sent @ a @ b @ ( pair @ a @ na ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause16) ).
thf(22,axiom,
! [U: $i,V: $i] :
( ~ ( ssIm @ ( pair @ U @ V ) )
| ( ssIm @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause15) ).
thf(23,axiom,
! [U: $i,V: $i] :
( ~ ( ssIm @ ( pair @ U @ V ) )
| ( ssIm @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause14) ).
thf(24,axiom,
ssAk @ ( key @ at @ t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause13) ).
thf(25,axiom,
ssSa @ ( pair @ b @ na ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause12) ).
thf(26,axiom,
ssBk @ ( key @ bt @ t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause11) ).
thf(27,axiom,
ssTk @ ( key @ at @ a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause10) ).
thf(28,axiom,
ssTk @ ( key @ bt @ b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause9) ).
thf(29,axiom,
! [U: $i] :
~ ( ssNonce @ ( kt @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
thf(30,axiom,
! [U: $i] : ( ssNonce @ ( tb @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause7) ).
thf(31,axiom,
! [U: $i] : ( ssNonce @ ( nb @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause6) ).
thf(32,axiom,
ssP @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause5) ).
thf(33,axiom,
ssP @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause4) ).
thf(34,axiom,
ssBf @ na,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause3) ).
thf(35,axiom,
ssP @ t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause2) ).
thf(36,axiom,
ssNonce @ na,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause1) ).
thf(37,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(38,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[37]) ).
thf(39,negated_conjecture,
! [U: $i] :
( ~ ( ssIk @ ( key @ U @ b ) )
| ~ ( ssBk @ ( key @ U @ a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause37) ).
thf(40,plain,
$false = $false,
inference(unfold_def,[status(thm)],[38]) ).
thf(41,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i,Z: $i,X1: $i] :
( ~ ( ssM @ ( sent @ U @ t @ ( triple @ U @ V @ ( encr @ ( triple @ W @ X @ Y ) @ Z ) ) ) )
| ~ ( ssTk @ ( key @ Z @ U ) )
| ~ ( ssTk @ ( key @ X1 @ W ) )
| ~ ( ssNonce @ X )
| ( ssM @ ( sent @ t @ W @ ( triple @ ( encr @ ( quadr @ U @ X @ ( kt @ X ) @ Y ) @ X1 ) @ ( encr @ ( triple @ W @ ( kt @ X ) @ Y ) @ Z ) @ V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(42,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i,Z: $i] :
( ~ ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ U @ V @ W @ X ) @ at ) @ Y @ Z ) ) )
| ~ ( ssSa @ ( pair @ U @ V ) )
| ( ssM @ ( sent @ a @ U @ ( pair @ Y @ ( encr @ Z @ W ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(43,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( ssM @ ( sent @ U @ b @ ( pair @ ( encr @ ( triple @ U @ V @ ( tb @ W ) ) @ bt ) @ ( encr @ ( nb @ W ) @ V ) ) ) )
| ~ ( ssSb @ ( pair @ U @ W ) )
| ( ssBk @ ( key @ V @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(44,plain,
( ( ! [U: $i,V: $i] :
( ~ ( ssM @ ( sent @ U @ b @ ( pair @ U @ V ) ) )
| ~ ( ssBf @ V )
| ( ssM @ ( sent @ b @ t @ ( triple @ b @ ( nb @ V ) @ ( encr @ ( triple @ U @ V @ ( tb @ V ) ) @ bt ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(45,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i,Z: $i] :
( ~ ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ U @ V @ W @ X ) @ at ) @ Y @ Z ) ) )
| ~ ( ssSa @ ( pair @ U @ V ) )
| ( ssAk @ ( key @ W @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(46,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( ssIm @ U )
| ~ ( ssIm @ V )
| ~ ( ssIm @ W )
| ~ ( ssIm @ X )
| ( ssIm @ ( quadr @ U @ V @ W @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(47,plain,
( ( ! [U: $i,V: $i] :
( ~ ( ssM @ ( sent @ U @ b @ ( pair @ U @ V ) ) )
| ~ ( ssBf @ V )
| ( ssSb @ ( pair @ U @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(48,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( ssIm @ U )
| ~ ( ssIk @ ( key @ V @ W ) )
| ~ ( ssP @ W )
| ( ssIm @ ( encr @ U @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(49,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( ssIm @ U )
| ~ ( ssIm @ V )
| ~ ( ssIm @ W )
| ( ssIm @ ( triple @ U @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(50,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( ssIm @ U )
| ~ ( ssP @ V )
| ~ ( ssP @ W )
| ( ssM @ ( sent @ V @ W @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(51,plain,
( ( ! [U: $i,V: $i] :
( ~ ( ssIm @ U )
| ~ ( ssIm @ V )
| ( ssIm @ ( pair @ U @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(52,plain,
( ( ! [U: $i,V: $i] :
( ~ ( ssIm @ U )
| ~ ( ssP @ V )
| ( ssIk @ ( key @ U @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(53,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( ssIm @ ( quadr @ U @ V @ W @ X ) )
| ( ssIm @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(54,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( ssIm @ ( quadr @ U @ V @ W @ X ) )
| ( ssIm @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(55,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( ssIm @ ( quadr @ U @ V @ W @ X ) )
| ( ssIm @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(56,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( ssIm @ ( quadr @ U @ V @ W @ X ) )
| ( ssIm @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(57,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( ssM @ ( sent @ U @ V @ W ) )
| ( ssIm @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(58,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( ssIm @ ( triple @ U @ V @ W ) )
| ( ssIm @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(59,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( ssIm @ ( triple @ U @ V @ W ) )
| ( ssIm @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(60,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( ssIm @ ( triple @ U @ V @ W ) )
| ( ssIm @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(61,plain,
( ( ssM @ ( sent @ a @ b @ ( pair @ a @ na ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(62,plain,
( ( ! [U: $i,V: $i] :
( ~ ( ssIm @ ( pair @ U @ V ) )
| ( ssIm @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(63,plain,
( ( ! [U: $i,V: $i] :
( ~ ( ssIm @ ( pair @ U @ V ) )
| ( ssIm @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(64,plain,
( ( ssAk @ ( key @ at @ t ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(65,plain,
( ( ssSa @ ( pair @ b @ na ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(66,plain,
( ( ssBk @ ( key @ bt @ t ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(67,plain,
( ( ssTk @ ( key @ at @ a ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(68,plain,
( ( ssTk @ ( key @ bt @ b ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(69,plain,
( ( ! [U: $i] :
~ ( ssNonce @ ( kt @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(70,plain,
( ( ! [U: $i] : ( ssNonce @ ( tb @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(71,plain,
( ( ! [U: $i] : ( ssNonce @ ( nb @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(72,plain,
( ( ssP @ a )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(73,plain,
( ( ssP @ b )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(74,plain,
( ( ssBf @ na )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(75,plain,
( ( ssP @ t )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(76,plain,
( ( ssNonce @ na )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(77,plain,
( ( ! [U: $i] :
( ~ ( ssIk @ ( key @ U @ b ) )
| ~ ( ssBk @ ( key @ U @ a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(78,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[40]) ).
thf(79,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i,Z: $i] :
( ~ ( ssM @ ( sent @ U @ t @ ( triple @ U @ V @ ( encr @ ( triple @ W @ X @ Y ) @ Z ) ) ) )
| ~ ( ssTk @ ( key @ Z @ U ) )
| ! [X1: $i] :
( ~ ( ssTk @ ( key @ X1 @ W ) )
| ~ ( ssNonce @ X )
| ( ssM @ ( sent @ t @ W @ ( triple @ ( encr @ ( quadr @ U @ X @ ( kt @ X ) @ Y ) @ X1 ) @ ( encr @ ( triple @ W @ ( kt @ X ) @ Y ) @ Z ) @ V ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(80,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ! [Y: $i,Z: $i] :
~ ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ U @ V @ W @ X ) @ at ) @ Y @ Z ) ) )
| ~ ( ssSa @ ( pair @ U @ V ) )
| ( ssAk @ ( key @ W @ U ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(81,plain,
( ( ! [U: $i,V: $i] :
( ~ ( ssIm @ U )
| ~ ( ssIm @ V )
| ! [W: $i] :
( ~ ( ssIm @ W )
| ! [X: $i] :
( ~ ( ssIm @ X )
| ( ssIm @ ( quadr @ U @ V @ W @ X ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(82,plain,
( ( ! [U: $i] :
( ~ ( ssIm @ U )
| ! [V: $i,W: $i] :
( ~ ( ssIk @ ( key @ V @ W ) )
| ~ ( ssP @ W )
| ( ssIm @ ( encr @ U @ V ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(83,plain,
( ( ! [U: $i] :
( ~ ( ssIm @ U )
| ! [V: $i] :
( ~ ( ssIm @ V )
| ! [W: $i] :
( ~ ( ssIm @ W )
| ( ssIm @ ( triple @ U @ V @ W ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(84,plain,
( ( ! [U: $i] :
( ~ ( ssIm @ U )
| ! [V: $i] :
( ~ ( ssP @ V )
| ! [W: $i] :
( ~ ( ssP @ W )
| ( ssM @ ( sent @ V @ W @ U ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(85,plain,
( ( ! [U: $i] :
( ~ ( ssIm @ U )
| ! [V: $i] :
( ~ ( ssIm @ V )
| ( ssIm @ ( pair @ U @ V ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(86,plain,
( ( ! [U: $i] :
( ~ ( ssIm @ U )
| ! [V: $i] :
( ~ ( ssP @ V )
| ( ssIk @ ( key @ U @ V ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(87,plain,
( ( ! [U: $i,V: $i] :
( ! [W: $i,X: $i] :
~ ( ssIm @ ( quadr @ U @ V @ W @ X ) )
| ( ssIm @ U ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(88,plain,
( ( ! [U: $i,V: $i] :
( ! [W: $i,X: $i] :
~ ( ssIm @ ( quadr @ U @ V @ W @ X ) )
| ( ssIm @ V ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(89,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ! [X: $i] :
~ ( ssIm @ ( quadr @ U @ V @ W @ X ) )
| ( ssIm @ W ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(90,plain,
( ( ! [U: $i] :
( ! [V: $i,W: $i] :
~ ( ssIm @ ( triple @ U @ V @ W ) )
| ( ssIm @ U ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[58]) ).
thf(91,plain,
( ( ! [U: $i,V: $i] :
( ! [W: $i] :
~ ( ssIm @ ( triple @ U @ V @ W ) )
| ( ssIm @ V ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[59]) ).
thf(92,plain,
( ( ! [U: $i] :
( ! [V: $i] :
~ ( ssIm @ ( pair @ U @ V ) )
| ( ssIm @ U ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[62]) ).
thf(93,plain,
( ( ! [U: $i] :
( ~ ( ssIk @ ( key @ U @ b ) )
| ~ ( ssBk @ ( key @ U @ a ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(94,plain,
( ( ssNonce @ na )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(95,plain,
( ( ssP @ t )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(96,plain,
( ( ssBf @ na )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(97,plain,
( ( ssP @ b )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(98,plain,
( ( ssP @ a )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(99,plain,
( ( ! [U: $i] : ( ssNonce @ ( nb @ U ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(100,plain,
( ( ! [U: $i] : ( ssNonce @ ( tb @ U ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(101,plain,
( ( ! [U: $i] :
~ ( ssNonce @ ( kt @ U ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(102,plain,
( ( ssTk @ ( key @ bt @ b ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(103,plain,
( ( ssTk @ ( key @ at @ a ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(104,plain,
( ( ssBk @ ( key @ bt @ t ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(105,plain,
( ( ssSa @ ( pair @ b @ na ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(106,plain,
( ( ssAk @ ( key @ at @ t ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(107,plain,
( ( ! [U: $i,V: $i] :
( ~ ( ssIm @ ( pair @ U @ V ) )
| ( ssIm @ V ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(108,plain,
( ( ! [U: $i] :
( ! [V: $i] :
~ ( ssIm @ ( pair @ U @ V ) )
| ( ssIm @ U ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(109,plain,
( ( ssM @ ( sent @ a @ b @ ( pair @ a @ na ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(110,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( ssIm @ ( triple @ U @ V @ W ) )
| ( ssIm @ W ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(111,plain,
( ( ! [U: $i,V: $i] :
( ! [W: $i] :
~ ( ssIm @ ( triple @ U @ V @ W ) )
| ( ssIm @ V ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(112,plain,
( ( ! [U: $i] :
( ! [V: $i,W: $i] :
~ ( ssIm @ ( triple @ U @ V @ W ) )
| ( ssIm @ U ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(113,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( ssM @ ( sent @ U @ V @ W ) )
| ( ssIm @ W ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(114,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( ssIm @ ( quadr @ U @ V @ W @ X ) )
| ( ssIm @ X ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(115,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ! [X: $i] :
~ ( ssIm @ ( quadr @ U @ V @ W @ X ) )
| ( ssIm @ W ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(116,plain,
( ( ! [U: $i,V: $i] :
( ! [W: $i,X: $i] :
~ ( ssIm @ ( quadr @ U @ V @ W @ X ) )
| ( ssIm @ V ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(117,plain,
( ( ! [U: $i,V: $i] :
( ! [W: $i,X: $i] :
~ ( ssIm @ ( quadr @ U @ V @ W @ X ) )
| ( ssIm @ U ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(118,plain,
( ( ! [U: $i] :
( ~ ( ssIm @ U )
| ! [V: $i] :
( ~ ( ssP @ V )
| ( ssIk @ ( key @ U @ V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(119,plain,
( ( ! [U: $i] :
( ~ ( ssIm @ U )
| ! [V: $i] :
( ~ ( ssIm @ V )
| ( ssIm @ ( pair @ U @ V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(120,plain,
( ( ! [U: $i] :
( ~ ( ssIm @ U )
| ! [V: $i] :
( ~ ( ssP @ V )
| ! [W: $i] :
( ~ ( ssP @ W )
| ( ssM @ ( sent @ V @ W @ U ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(121,plain,
( ( ! [U: $i] :
( ~ ( ssIm @ U )
| ! [V: $i] :
( ~ ( ssIm @ V )
| ! [W: $i] :
( ~ ( ssIm @ W )
| ( ssIm @ ( triple @ U @ V @ W ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(122,plain,
( ( ! [U: $i] :
( ~ ( ssIm @ U )
| ! [V: $i,W: $i] :
( ~ ( ssIk @ ( key @ V @ W ) )
| ~ ( ssP @ W )
| ( ssIm @ ( encr @ U @ V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(123,plain,
( ( ! [U: $i,V: $i] :
( ~ ( ssM @ ( sent @ U @ b @ ( pair @ U @ V ) ) )
| ~ ( ssBf @ V )
| ( ssSb @ ( pair @ U @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(124,plain,
( ( ! [U: $i,V: $i] :
( ~ ( ssIm @ U )
| ~ ( ssIm @ V )
| ! [W: $i] :
( ~ ( ssIm @ W )
| ! [X: $i] :
( ~ ( ssIm @ X )
| ( ssIm @ ( quadr @ U @ V @ W @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(125,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ! [Y: $i,Z: $i] :
~ ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ U @ V @ W @ X ) @ at ) @ Y @ Z ) ) )
| ~ ( ssSa @ ( pair @ U @ V ) )
| ( ssAk @ ( key @ W @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(126,plain,
( ( ! [U: $i,V: $i] :
( ~ ( ssM @ ( sent @ U @ b @ ( pair @ U @ V ) ) )
| ~ ( ssBf @ V )
| ( ssM @ ( sent @ b @ t @ ( triple @ b @ ( nb @ V ) @ ( encr @ ( triple @ U @ V @ ( tb @ V ) ) @ bt ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(127,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( ssM @ ( sent @ U @ b @ ( pair @ ( encr @ ( triple @ U @ V @ ( tb @ W ) ) @ bt ) @ ( encr @ ( nb @ W ) @ V ) ) ) )
| ~ ( ssSb @ ( pair @ U @ W ) )
| ( ssBk @ ( key @ V @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(128,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i,Z: $i] :
( ~ ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ U @ V @ W @ X ) @ at ) @ Y @ Z ) ) )
| ~ ( ssSa @ ( pair @ U @ V ) )
| ( ssM @ ( sent @ a @ U @ ( pair @ Y @ ( encr @ Z @ W ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(129,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i,Z: $i] :
( ~ ( ssM @ ( sent @ U @ t @ ( triple @ U @ V @ ( encr @ ( triple @ W @ X @ Y ) @ Z ) ) ) )
| ~ ( ssTk @ ( key @ Z @ U ) )
| ! [X1: $i] :
( ~ ( ssTk @ ( key @ X1 @ W ) )
| ~ ( ssNonce @ X )
| ( ssM @ ( sent @ t @ W @ ( triple @ ( encr @ ( quadr @ U @ X @ ( kt @ X ) @ Y ) @ X1 ) @ ( encr @ ( triple @ W @ ( kt @ X ) @ Y ) @ Z ) @ V ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(130,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(131,plain,
! [SV1: $i] :
( ( ~ ( ssIk @ ( key @ SV1 @ b ) )
| ~ ( ssBk @ ( key @ SV1 @ a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(132,plain,
! [SV2: $i] :
( ( ssNonce @ ( nb @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(133,plain,
! [SV3: $i] :
( ( ssNonce @ ( tb @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(134,plain,
! [SV4: $i] :
( ( ~ ( ssNonce @ ( kt @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(135,plain,
! [SV5: $i] :
( ( ! [SY79: $i] :
( ~ ( ssIm @ ( pair @ SV5 @ SY79 ) )
| ( ssIm @ SY79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(136,plain,
! [SV6: $i] :
( ( ! [SY80: $i] :
~ ( ssIm @ ( pair @ SV6 @ SY80 ) )
| ( ssIm @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(137,plain,
! [SV7: $i] :
( ( ! [SY81: $i,SY82: $i] :
( ~ ( ssIm @ ( triple @ SV7 @ SY81 @ SY82 ) )
| ( ssIm @ SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(138,plain,
! [SV8: $i] :
( ( ! [SY83: $i] :
( ! [SY84: $i] :
~ ( ssIm @ ( triple @ SV8 @ SY83 @ SY84 ) )
| ( ssIm @ SY83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(139,plain,
! [SV9: $i] :
( ( ! [SY85: $i,SY86: $i] :
~ ( ssIm @ ( triple @ SV9 @ SY85 @ SY86 ) )
| ( ssIm @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(140,plain,
! [SV10: $i] :
( ( ! [SY87: $i,SY88: $i] :
( ~ ( ssM @ ( sent @ SV10 @ SY87 @ SY88 ) )
| ( ssIm @ SY88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(141,plain,
! [SV11: $i] :
( ( ! [SY89: $i,SY90: $i,SY91: $i] :
( ~ ( ssIm @ ( quadr @ SV11 @ SY89 @ SY90 @ SY91 ) )
| ( ssIm @ SY91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(142,plain,
! [SV12: $i] :
( ( ! [SY92: $i,SY93: $i] :
( ! [SY94: $i] :
~ ( ssIm @ ( quadr @ SV12 @ SY92 @ SY93 @ SY94 ) )
| ( ssIm @ SY93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(143,plain,
! [SV13: $i] :
( ( ! [SY95: $i] :
( ! [SY96: $i,SY97: $i] :
~ ( ssIm @ ( quadr @ SV13 @ SY95 @ SY96 @ SY97 ) )
| ( ssIm @ SY95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(144,plain,
! [SV14: $i] :
( ( ! [SY98: $i] :
( ! [SY99: $i,SY100: $i] :
~ ( ssIm @ ( quadr @ SV14 @ SY98 @ SY99 @ SY100 ) )
| ( ssIm @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(145,plain,
! [SV15: $i] :
( ( ~ ( ssIm @ SV15 )
| ! [SY101: $i] :
( ~ ( ssP @ SY101 )
| ( ssIk @ ( key @ SV15 @ SY101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(146,plain,
! [SV16: $i] :
( ( ~ ( ssIm @ SV16 )
| ! [SY102: $i] :
( ~ ( ssIm @ SY102 )
| ( ssIm @ ( pair @ SV16 @ SY102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(147,plain,
! [SV17: $i] :
( ( ~ ( ssIm @ SV17 )
| ! [SY103: $i] :
( ~ ( ssP @ SY103 )
| ! [SY104: $i] :
( ~ ( ssP @ SY104 )
| ( ssM @ ( sent @ SY103 @ SY104 @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(148,plain,
! [SV18: $i] :
( ( ~ ( ssIm @ SV18 )
| ! [SY105: $i] :
( ~ ( ssIm @ SY105 )
| ! [SY106: $i] :
( ~ ( ssIm @ SY106 )
| ( ssIm @ ( triple @ SV18 @ SY105 @ SY106 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(149,plain,
! [SV19: $i] :
( ( ~ ( ssIm @ SV19 )
| ! [SY107: $i,SY108: $i] :
( ~ ( ssIk @ ( key @ SY107 @ SY108 ) )
| ~ ( ssP @ SY108 )
| ( ssIm @ ( encr @ SV19 @ SY107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(150,plain,
! [SV20: $i] :
( ( ! [SY109: $i] :
( ~ ( ssM @ ( sent @ SV20 @ b @ ( pair @ SV20 @ SY109 ) ) )
| ~ ( ssBf @ SY109 )
| ( ssSb @ ( pair @ SV20 @ SY109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(151,plain,
! [SV21: $i] :
( ( ! [SY110: $i] :
( ~ ( ssIm @ SV21 )
| ~ ( ssIm @ SY110 )
| ! [SY111: $i] :
( ~ ( ssIm @ SY111 )
| ! [SY112: $i] :
( ~ ( ssIm @ SY112 )
| ( ssIm @ ( quadr @ SV21 @ SY110 @ SY111 @ SY112 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(152,plain,
! [SV22: $i] :
( ( ! [SY113: $i,SY114: $i,SY115: $i] :
( ! [SY116: $i,SY117: $i] :
~ ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ SV22 @ SY113 @ SY114 @ SY115 ) @ at ) @ SY116 @ SY117 ) ) )
| ~ ( ssSa @ ( pair @ SV22 @ SY113 ) )
| ( ssAk @ ( key @ SY114 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(153,plain,
! [SV23: $i] :
( ( ! [SY118: $i] :
( ~ ( ssM @ ( sent @ SV23 @ b @ ( pair @ SV23 @ SY118 ) ) )
| ~ ( ssBf @ SY118 )
| ( ssM @ ( sent @ b @ t @ ( triple @ b @ ( nb @ SY118 ) @ ( encr @ ( triple @ SV23 @ SY118 @ ( tb @ SY118 ) ) @ bt ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(154,plain,
! [SV24: $i] :
( ( ! [SY119: $i,SY120: $i] :
( ~ ( ssM @ ( sent @ SV24 @ b @ ( pair @ ( encr @ ( triple @ SV24 @ SY119 @ ( tb @ SY120 ) ) @ bt ) @ ( encr @ ( nb @ SY120 ) @ SY119 ) ) ) )
| ~ ( ssSb @ ( pair @ SV24 @ SY120 ) )
| ( ssBk @ ( key @ SY119 @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(155,plain,
! [SV25: $i] :
( ( ! [SY121: $i,SY122: $i,SY123: $i,SY124: $i,SY125: $i] :
( ~ ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ SV25 @ SY121 @ SY122 @ SY123 ) @ at ) @ SY124 @ SY125 ) ) )
| ~ ( ssSa @ ( pair @ SV25 @ SY121 ) )
| ( ssM @ ( sent @ a @ SV25 @ ( pair @ SY124 @ ( encr @ SY125 @ SY122 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(156,plain,
! [SV26: $i] :
( ( ! [SY126: $i,SY127: $i,SY128: $i,SY129: $i,SY130: $i] :
( ~ ( ssM @ ( sent @ SV26 @ t @ ( triple @ SV26 @ SY126 @ ( encr @ ( triple @ SY127 @ SY128 @ SY129 ) @ SY130 ) ) ) )
| ~ ( ssTk @ ( key @ SY130 @ SV26 ) )
| ! [SY131: $i] :
( ~ ( ssTk @ ( key @ SY131 @ SY127 ) )
| ~ ( ssNonce @ SY128 )
| ( ssM @ ( sent @ t @ SY127 @ ( triple @ ( encr @ ( quadr @ SV26 @ SY128 @ ( kt @ SY128 ) @ SY129 ) @ SY131 ) @ ( encr @ ( triple @ SY127 @ ( kt @ SY128 ) @ SY129 ) @ SY130 ) @ SY126 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(157,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(158,plain,
! [SV1: $i] :
( ( ( ~ ( ssIk @ ( key @ SV1 @ b ) ) )
= $true )
| ( ( ~ ( ssBk @ ( key @ SV1 @ a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(159,plain,
! [SV4: $i] :
( ( ssNonce @ ( kt @ SV4 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(160,plain,
! [SV27: $i,SV5: $i] :
( ( ~ ( ssIm @ ( pair @ SV5 @ SV27 ) )
| ( ssIm @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(161,plain,
! [SV6: $i] :
( ( ( ! [SY80: $i] :
~ ( ssIm @ ( pair @ SV6 @ SY80 ) ) )
= $true )
| ( ( ssIm @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(162,plain,
! [SV28: $i,SV7: $i] :
( ( ! [SY132: $i] :
( ~ ( ssIm @ ( triple @ SV7 @ SV28 @ SY132 ) )
| ( ssIm @ SY132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(163,plain,
! [SV29: $i,SV8: $i] :
( ( ! [SY133: $i] :
~ ( ssIm @ ( triple @ SV8 @ SV29 @ SY133 ) )
| ( ssIm @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(164,plain,
! [SV9: $i] :
( ( ( ! [SY85: $i,SY86: $i] :
~ ( ssIm @ ( triple @ SV9 @ SY85 @ SY86 ) ) )
= $true )
| ( ( ssIm @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(165,plain,
! [SV30: $i,SV10: $i] :
( ( ! [SY134: $i] :
( ~ ( ssM @ ( sent @ SV10 @ SV30 @ SY134 ) )
| ( ssIm @ SY134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(166,plain,
! [SV31: $i,SV11: $i] :
( ( ! [SY135: $i,SY136: $i] :
( ~ ( ssIm @ ( quadr @ SV11 @ SV31 @ SY135 @ SY136 ) )
| ( ssIm @ SY136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(167,plain,
! [SV32: $i,SV12: $i] :
( ( ! [SY137: $i] :
( ! [SY138: $i] :
~ ( ssIm @ ( quadr @ SV12 @ SV32 @ SY137 @ SY138 ) )
| ( ssIm @ SY137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(168,plain,
! [SV33: $i,SV13: $i] :
( ( ! [SY139: $i,SY140: $i] :
~ ( ssIm @ ( quadr @ SV13 @ SV33 @ SY139 @ SY140 ) )
| ( ssIm @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(169,plain,
! [SV34: $i,SV14: $i] :
( ( ! [SY141: $i,SY142: $i] :
~ ( ssIm @ ( quadr @ SV14 @ SV34 @ SY141 @ SY142 ) )
| ( ssIm @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(170,plain,
! [SV15: $i] :
( ( ( ~ ( ssIm @ SV15 ) )
= $true )
| ( ( ! [SY101: $i] :
( ~ ( ssP @ SY101 )
| ( ssIk @ ( key @ SV15 @ SY101 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(171,plain,
! [SV16: $i] :
( ( ( ~ ( ssIm @ SV16 ) )
= $true )
| ( ( ! [SY102: $i] :
( ~ ( ssIm @ SY102 )
| ( ssIm @ ( pair @ SV16 @ SY102 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(172,plain,
! [SV17: $i] :
( ( ( ~ ( ssIm @ SV17 ) )
= $true )
| ( ( ! [SY103: $i] :
( ~ ( ssP @ SY103 )
| ! [SY104: $i] :
( ~ ( ssP @ SY104 )
| ( ssM @ ( sent @ SY103 @ SY104 @ SV17 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(173,plain,
! [SV18: $i] :
( ( ( ~ ( ssIm @ SV18 ) )
= $true )
| ( ( ! [SY105: $i] :
( ~ ( ssIm @ SY105 )
| ! [SY106: $i] :
( ~ ( ssIm @ SY106 )
| ( ssIm @ ( triple @ SV18 @ SY105 @ SY106 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(174,plain,
! [SV19: $i] :
( ( ( ~ ( ssIm @ SV19 ) )
= $true )
| ( ( ! [SY107: $i,SY108: $i] :
( ~ ( ssIk @ ( key @ SY107 @ SY108 ) )
| ~ ( ssP @ SY108 )
| ( ssIm @ ( encr @ SV19 @ SY107 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(175,plain,
! [SV35: $i,SV20: $i] :
( ( ~ ( ssM @ ( sent @ SV20 @ b @ ( pair @ SV20 @ SV35 ) ) )
| ~ ( ssBf @ SV35 )
| ( ssSb @ ( pair @ SV20 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(176,plain,
! [SV36: $i,SV21: $i] :
( ( ~ ( ssIm @ SV21 )
| ~ ( ssIm @ SV36 )
| ! [SY143: $i] :
( ~ ( ssIm @ SY143 )
| ! [SY144: $i] :
( ~ ( ssIm @ SY144 )
| ( ssIm @ ( quadr @ SV21 @ SV36 @ SY143 @ SY144 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(177,plain,
! [SV37: $i,SV22: $i] :
( ( ! [SY145: $i,SY146: $i] :
( ! [SY147: $i,SY148: $i] :
~ ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ SV22 @ SV37 @ SY145 @ SY146 ) @ at ) @ SY147 @ SY148 ) ) )
| ~ ( ssSa @ ( pair @ SV22 @ SV37 ) )
| ( ssAk @ ( key @ SY145 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(178,plain,
! [SV38: $i,SV23: $i] :
( ( ~ ( ssM @ ( sent @ SV23 @ b @ ( pair @ SV23 @ SV38 ) ) )
| ~ ( ssBf @ SV38 )
| ( ssM @ ( sent @ b @ t @ ( triple @ b @ ( nb @ SV38 ) @ ( encr @ ( triple @ SV23 @ SV38 @ ( tb @ SV38 ) ) @ bt ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(179,plain,
! [SV39: $i,SV24: $i] :
( ( ! [SY149: $i] :
( ~ ( ssM @ ( sent @ SV24 @ b @ ( pair @ ( encr @ ( triple @ SV24 @ SV39 @ ( tb @ SY149 ) ) @ bt ) @ ( encr @ ( nb @ SY149 ) @ SV39 ) ) ) )
| ~ ( ssSb @ ( pair @ SV24 @ SY149 ) )
| ( ssBk @ ( key @ SV39 @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(180,plain,
! [SV40: $i,SV25: $i] :
( ( ! [SY150: $i,SY151: $i,SY152: $i,SY153: $i] :
( ~ ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ SV25 @ SV40 @ SY150 @ SY151 ) @ at ) @ SY152 @ SY153 ) ) )
| ~ ( ssSa @ ( pair @ SV25 @ SV40 ) )
| ( ssM @ ( sent @ a @ SV25 @ ( pair @ SY152 @ ( encr @ SY153 @ SY150 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(181,plain,
! [SV41: $i,SV26: $i] :
( ( ! [SY154: $i,SY155: $i,SY156: $i,SY157: $i] :
( ~ ( ssM @ ( sent @ SV26 @ t @ ( triple @ SV26 @ SV41 @ ( encr @ ( triple @ SY154 @ SY155 @ SY156 ) @ SY157 ) ) ) )
| ~ ( ssTk @ ( key @ SY157 @ SV26 ) )
| ! [SY158: $i] :
( ~ ( ssTk @ ( key @ SY158 @ SY154 ) )
| ~ ( ssNonce @ SY155 )
| ( ssM @ ( sent @ t @ SY154 @ ( triple @ ( encr @ ( quadr @ SV26 @ SY155 @ ( kt @ SY155 ) @ SY156 ) @ SY158 ) @ ( encr @ ( triple @ SY154 @ ( kt @ SY155 ) @ SY156 ) @ SY157 ) @ SV41 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(182,plain,
! [SV1: $i] :
( ( ( ssIk @ ( key @ SV1 @ b ) )
= $false )
| ( ( ~ ( ssBk @ ( key @ SV1 @ a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(183,plain,
! [SV27: $i,SV5: $i] :
( ( ( ~ ( ssIm @ ( pair @ SV5 @ SV27 ) ) )
= $true )
| ( ( ssIm @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(184,plain,
! [SV42: $i,SV6: $i] :
( ( ( ~ ( ssIm @ ( pair @ SV6 @ SV42 ) ) )
= $true )
| ( ( ssIm @ SV6 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(185,plain,
! [SV43: $i,SV28: $i,SV7: $i] :
( ( ~ ( ssIm @ ( triple @ SV7 @ SV28 @ SV43 ) )
| ( ssIm @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(186,plain,
! [SV29: $i,SV8: $i] :
( ( ( ! [SY133: $i] :
~ ( ssIm @ ( triple @ SV8 @ SV29 @ SY133 ) ) )
= $true )
| ( ( ssIm @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(187,plain,
! [SV44: $i,SV9: $i] :
( ( ( ! [SY159: $i] :
~ ( ssIm @ ( triple @ SV9 @ SV44 @ SY159 ) ) )
= $true )
| ( ( ssIm @ SV9 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(188,plain,
! [SV45: $i,SV30: $i,SV10: $i] :
( ( ~ ( ssM @ ( sent @ SV10 @ SV30 @ SV45 ) )
| ( ssIm @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(189,plain,
! [SV46: $i,SV31: $i,SV11: $i] :
( ( ! [SY160: $i] :
( ~ ( ssIm @ ( quadr @ SV11 @ SV31 @ SV46 @ SY160 ) )
| ( ssIm @ SY160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(190,plain,
! [SV47: $i,SV32: $i,SV12: $i] :
( ( ! [SY161: $i] :
~ ( ssIm @ ( quadr @ SV12 @ SV32 @ SV47 @ SY161 ) )
| ( ssIm @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(191,plain,
! [SV33: $i,SV13: $i] :
( ( ( ! [SY139: $i,SY140: $i] :
~ ( ssIm @ ( quadr @ SV13 @ SV33 @ SY139 @ SY140 ) ) )
= $true )
| ( ( ssIm @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(192,plain,
! [SV34: $i,SV14: $i] :
( ( ( ! [SY141: $i,SY142: $i] :
~ ( ssIm @ ( quadr @ SV14 @ SV34 @ SY141 @ SY142 ) ) )
= $true )
| ( ( ssIm @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(193,plain,
! [SV15: $i] :
( ( ( ssIm @ SV15 )
= $false )
| ( ( ! [SY101: $i] :
( ~ ( ssP @ SY101 )
| ( ssIk @ ( key @ SV15 @ SY101 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(194,plain,
! [SV16: $i] :
( ( ( ssIm @ SV16 )
= $false )
| ( ( ! [SY102: $i] :
( ~ ( ssIm @ SY102 )
| ( ssIm @ ( pair @ SV16 @ SY102 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(195,plain,
! [SV17: $i] :
( ( ( ssIm @ SV17 )
= $false )
| ( ( ! [SY103: $i] :
( ~ ( ssP @ SY103 )
| ! [SY104: $i] :
( ~ ( ssP @ SY104 )
| ( ssM @ ( sent @ SY103 @ SY104 @ SV17 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(196,plain,
! [SV18: $i] :
( ( ( ssIm @ SV18 )
= $false )
| ( ( ! [SY105: $i] :
( ~ ( ssIm @ SY105 )
| ! [SY106: $i] :
( ~ ( ssIm @ SY106 )
| ( ssIm @ ( triple @ SV18 @ SY105 @ SY106 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(197,plain,
! [SV19: $i] :
( ( ( ssIm @ SV19 )
= $false )
| ( ( ! [SY107: $i,SY108: $i] :
( ~ ( ssIk @ ( key @ SY107 @ SY108 ) )
| ~ ( ssP @ SY108 )
| ( ssIm @ ( encr @ SV19 @ SY107 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(198,plain,
! [SV35: $i,SV20: $i] :
( ( ( ~ ( ssM @ ( sent @ SV20 @ b @ ( pair @ SV20 @ SV35 ) ) ) )
= $true )
| ( ( ~ ( ssBf @ SV35 )
| ( ssSb @ ( pair @ SV20 @ SV35 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(199,plain,
! [SV36: $i,SV21: $i] :
( ( ( ~ ( ssIm @ SV21 ) )
= $true )
| ( ( ~ ( ssIm @ SV36 )
| ! [SY143: $i] :
( ~ ( ssIm @ SY143 )
| ! [SY144: $i] :
( ~ ( ssIm @ SY144 )
| ( ssIm @ ( quadr @ SV21 @ SV36 @ SY143 @ SY144 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(200,plain,
! [SV48: $i,SV37: $i,SV22: $i] :
( ( ! [SY162: $i] :
( ! [SY163: $i,SY164: $i] :
~ ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ SV22 @ SV37 @ SV48 @ SY162 ) @ at ) @ SY163 @ SY164 ) ) )
| ~ ( ssSa @ ( pair @ SV22 @ SV37 ) )
| ( ssAk @ ( key @ SV48 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(201,plain,
! [SV38: $i,SV23: $i] :
( ( ( ~ ( ssM @ ( sent @ SV23 @ b @ ( pair @ SV23 @ SV38 ) ) ) )
= $true )
| ( ( ~ ( ssBf @ SV38 )
| ( ssM @ ( sent @ b @ t @ ( triple @ b @ ( nb @ SV38 ) @ ( encr @ ( triple @ SV23 @ SV38 @ ( tb @ SV38 ) ) @ bt ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(202,plain,
! [SV49: $i,SV39: $i,SV24: $i] :
( ( ~ ( ssM @ ( sent @ SV24 @ b @ ( pair @ ( encr @ ( triple @ SV24 @ SV39 @ ( tb @ SV49 ) ) @ bt ) @ ( encr @ ( nb @ SV49 ) @ SV39 ) ) ) )
| ~ ( ssSb @ ( pair @ SV24 @ SV49 ) )
| ( ssBk @ ( key @ SV39 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(203,plain,
! [SV50: $i,SV40: $i,SV25: $i] :
( ( ! [SY165: $i,SY166: $i,SY167: $i] :
( ~ ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ SV25 @ SV40 @ SV50 @ SY165 ) @ at ) @ SY166 @ SY167 ) ) )
| ~ ( ssSa @ ( pair @ SV25 @ SV40 ) )
| ( ssM @ ( sent @ a @ SV25 @ ( pair @ SY166 @ ( encr @ SY167 @ SV50 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(204,plain,
! [SV51: $i,SV41: $i,SV26: $i] :
( ( ! [SY168: $i,SY169: $i,SY170: $i] :
( ~ ( ssM @ ( sent @ SV26 @ t @ ( triple @ SV26 @ SV41 @ ( encr @ ( triple @ SV51 @ SY168 @ SY169 ) @ SY170 ) ) ) )
| ~ ( ssTk @ ( key @ SY170 @ SV26 ) )
| ! [SY171: $i] :
( ~ ( ssTk @ ( key @ SY171 @ SV51 ) )
| ~ ( ssNonce @ SY168 )
| ( ssM @ ( sent @ t @ SV51 @ ( triple @ ( encr @ ( quadr @ SV26 @ SY168 @ ( kt @ SY168 ) @ SY169 ) @ SY171 ) @ ( encr @ ( triple @ SV51 @ ( kt @ SY168 ) @ SY169 ) @ SY170 ) @ SV41 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(205,plain,
! [SV1: $i] :
( ( ( ssBk @ ( key @ SV1 @ a ) )
= $false )
| ( ( ssIk @ ( key @ SV1 @ b ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(206,plain,
! [SV27: $i,SV5: $i] :
( ( ( ssIm @ ( pair @ SV5 @ SV27 ) )
= $false )
| ( ( ssIm @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(207,plain,
! [SV42: $i,SV6: $i] :
( ( ( ssIm @ ( pair @ SV6 @ SV42 ) )
= $false )
| ( ( ssIm @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(208,plain,
! [SV43: $i,SV28: $i,SV7: $i] :
( ( ( ~ ( ssIm @ ( triple @ SV7 @ SV28 @ SV43 ) ) )
= $true )
| ( ( ssIm @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(209,plain,
! [SV52: $i,SV29: $i,SV8: $i] :
( ( ( ~ ( ssIm @ ( triple @ SV8 @ SV29 @ SV52 ) ) )
= $true )
| ( ( ssIm @ SV29 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(210,plain,
! [SV53: $i,SV44: $i,SV9: $i] :
( ( ( ~ ( ssIm @ ( triple @ SV9 @ SV44 @ SV53 ) ) )
= $true )
| ( ( ssIm @ SV9 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(211,plain,
! [SV45: $i,SV30: $i,SV10: $i] :
( ( ( ~ ( ssM @ ( sent @ SV10 @ SV30 @ SV45 ) ) )
= $true )
| ( ( ssIm @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(212,plain,
! [SV54: $i,SV46: $i,SV31: $i,SV11: $i] :
( ( ~ ( ssIm @ ( quadr @ SV11 @ SV31 @ SV46 @ SV54 ) )
| ( ssIm @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(213,plain,
! [SV47: $i,SV32: $i,SV12: $i] :
( ( ( ! [SY161: $i] :
~ ( ssIm @ ( quadr @ SV12 @ SV32 @ SV47 @ SY161 ) ) )
= $true )
| ( ( ssIm @ SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(214,plain,
! [SV55: $i,SV33: $i,SV13: $i] :
( ( ( ! [SY172: $i] :
~ ( ssIm @ ( quadr @ SV13 @ SV33 @ SV55 @ SY172 ) ) )
= $true )
| ( ( ssIm @ SV33 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(215,plain,
! [SV56: $i,SV34: $i,SV14: $i] :
( ( ( ! [SY173: $i] :
~ ( ssIm @ ( quadr @ SV14 @ SV34 @ SV56 @ SY173 ) ) )
= $true )
| ( ( ssIm @ SV14 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(216,plain,
! [SV15: $i,SV57: $i] :
( ( ( ~ ( ssP @ SV57 )
| ( ssIk @ ( key @ SV15 @ SV57 ) ) )
= $true )
| ( ( ssIm @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(217,plain,
! [SV16: $i,SV58: $i] :
( ( ( ~ ( ssIm @ SV58 )
| ( ssIm @ ( pair @ SV16 @ SV58 ) ) )
= $true )
| ( ( ssIm @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(218,plain,
! [SV17: $i,SV59: $i] :
( ( ( ~ ( ssP @ SV59 )
| ! [SY174: $i] :
( ~ ( ssP @ SY174 )
| ( ssM @ ( sent @ SV59 @ SY174 @ SV17 ) ) ) )
= $true )
| ( ( ssIm @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(219,plain,
! [SV18: $i,SV60: $i] :
( ( ( ~ ( ssIm @ SV60 )
| ! [SY175: $i] :
( ~ ( ssIm @ SY175 )
| ( ssIm @ ( triple @ SV18 @ SV60 @ SY175 ) ) ) )
= $true )
| ( ( ssIm @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(220,plain,
! [SV19: $i,SV61: $i] :
( ( ( ! [SY176: $i] :
( ~ ( ssIk @ ( key @ SV61 @ SY176 ) )
| ~ ( ssP @ SY176 )
| ( ssIm @ ( encr @ SV19 @ SV61 ) ) ) )
= $true )
| ( ( ssIm @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(221,plain,
! [SV35: $i,SV20: $i] :
( ( ( ssM @ ( sent @ SV20 @ b @ ( pair @ SV20 @ SV35 ) ) )
= $false )
| ( ( ~ ( ssBf @ SV35 )
| ( ssSb @ ( pair @ SV20 @ SV35 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(222,plain,
! [SV36: $i,SV21: $i] :
( ( ( ssIm @ SV21 )
= $false )
| ( ( ~ ( ssIm @ SV36 )
| ! [SY143: $i] :
( ~ ( ssIm @ SY143 )
| ! [SY144: $i] :
( ~ ( ssIm @ SY144 )
| ( ssIm @ ( quadr @ SV21 @ SV36 @ SY143 @ SY144 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(223,plain,
! [SV62: $i,SV48: $i,SV37: $i,SV22: $i] :
( ( ! [SY177: $i,SY178: $i] :
~ ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ SV22 @ SV37 @ SV48 @ SV62 ) @ at ) @ SY177 @ SY178 ) ) )
| ~ ( ssSa @ ( pair @ SV22 @ SV37 ) )
| ( ssAk @ ( key @ SV48 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(224,plain,
! [SV38: $i,SV23: $i] :
( ( ( ssM @ ( sent @ SV23 @ b @ ( pair @ SV23 @ SV38 ) ) )
= $false )
| ( ( ~ ( ssBf @ SV38 )
| ( ssM @ ( sent @ b @ t @ ( triple @ b @ ( nb @ SV38 ) @ ( encr @ ( triple @ SV23 @ SV38 @ ( tb @ SV38 ) ) @ bt ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(225,plain,
! [SV49: $i,SV39: $i,SV24: $i] :
( ( ( ~ ( ssM @ ( sent @ SV24 @ b @ ( pair @ ( encr @ ( triple @ SV24 @ SV39 @ ( tb @ SV49 ) ) @ bt ) @ ( encr @ ( nb @ SV49 ) @ SV39 ) ) ) ) )
= $true )
| ( ( ~ ( ssSb @ ( pair @ SV24 @ SV49 ) )
| ( ssBk @ ( key @ SV39 @ SV24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(226,plain,
! [SV63: $i,SV50: $i,SV40: $i,SV25: $i] :
( ( ! [SY179: $i,SY180: $i] :
( ~ ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ SV25 @ SV40 @ SV50 @ SV63 ) @ at ) @ SY179 @ SY180 ) ) )
| ~ ( ssSa @ ( pair @ SV25 @ SV40 ) )
| ( ssM @ ( sent @ a @ SV25 @ ( pair @ SY179 @ ( encr @ SY180 @ SV50 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(227,plain,
! [SV64: $i,SV51: $i,SV41: $i,SV26: $i] :
( ( ! [SY181: $i,SY182: $i] :
( ~ ( ssM @ ( sent @ SV26 @ t @ ( triple @ SV26 @ SV41 @ ( encr @ ( triple @ SV51 @ SV64 @ SY181 ) @ SY182 ) ) ) )
| ~ ( ssTk @ ( key @ SY182 @ SV26 ) )
| ! [SY183: $i] :
( ~ ( ssTk @ ( key @ SY183 @ SV51 ) )
| ~ ( ssNonce @ SV64 )
| ( ssM @ ( sent @ t @ SV51 @ ( triple @ ( encr @ ( quadr @ SV26 @ SV64 @ ( kt @ SV64 ) @ SY181 ) @ SY183 ) @ ( encr @ ( triple @ SV51 @ ( kt @ SV64 ) @ SY181 ) @ SY182 ) @ SV41 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(228,plain,
! [SV43: $i,SV28: $i,SV7: $i] :
( ( ( ssIm @ ( triple @ SV7 @ SV28 @ SV43 ) )
= $false )
| ( ( ssIm @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(229,plain,
! [SV52: $i,SV29: $i,SV8: $i] :
( ( ( ssIm @ ( triple @ SV8 @ SV29 @ SV52 ) )
= $false )
| ( ( ssIm @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(230,plain,
! [SV53: $i,SV44: $i,SV9: $i] :
( ( ( ssIm @ ( triple @ SV9 @ SV44 @ SV53 ) )
= $false )
| ( ( ssIm @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(231,plain,
! [SV45: $i,SV30: $i,SV10: $i] :
( ( ( ssM @ ( sent @ SV10 @ SV30 @ SV45 ) )
= $false )
| ( ( ssIm @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(232,plain,
! [SV54: $i,SV46: $i,SV31: $i,SV11: $i] :
( ( ( ~ ( ssIm @ ( quadr @ SV11 @ SV31 @ SV46 @ SV54 ) ) )
= $true )
| ( ( ssIm @ SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(233,plain,
! [SV65: $i,SV47: $i,SV32: $i,SV12: $i] :
( ( ( ~ ( ssIm @ ( quadr @ SV12 @ SV32 @ SV47 @ SV65 ) ) )
= $true )
| ( ( ssIm @ SV47 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(234,plain,
! [SV66: $i,SV55: $i,SV33: $i,SV13: $i] :
( ( ( ~ ( ssIm @ ( quadr @ SV13 @ SV33 @ SV55 @ SV66 ) ) )
= $true )
| ( ( ssIm @ SV33 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(235,plain,
! [SV67: $i,SV56: $i,SV34: $i,SV14: $i] :
( ( ( ~ ( ssIm @ ( quadr @ SV14 @ SV34 @ SV56 @ SV67 ) ) )
= $true )
| ( ( ssIm @ SV14 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(236,plain,
! [SV15: $i,SV57: $i] :
( ( ( ~ ( ssP @ SV57 ) )
= $true )
| ( ( ssIk @ ( key @ SV15 @ SV57 ) )
= $true )
| ( ( ssIm @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(237,plain,
! [SV16: $i,SV58: $i] :
( ( ( ~ ( ssIm @ SV58 ) )
= $true )
| ( ( ssIm @ ( pair @ SV16 @ SV58 ) )
= $true )
| ( ( ssIm @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(238,plain,
! [SV17: $i,SV59: $i] :
( ( ( ~ ( ssP @ SV59 ) )
= $true )
| ( ( ! [SY174: $i] :
( ~ ( ssP @ SY174 )
| ( ssM @ ( sent @ SV59 @ SY174 @ SV17 ) ) ) )
= $true )
| ( ( ssIm @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(239,plain,
! [SV18: $i,SV60: $i] :
( ( ( ~ ( ssIm @ SV60 ) )
= $true )
| ( ( ! [SY175: $i] :
( ~ ( ssIm @ SY175 )
| ( ssIm @ ( triple @ SV18 @ SV60 @ SY175 ) ) ) )
= $true )
| ( ( ssIm @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(240,plain,
! [SV19: $i,SV68: $i,SV61: $i] :
( ( ( ~ ( ssIk @ ( key @ SV61 @ SV68 ) )
| ~ ( ssP @ SV68 )
| ( ssIm @ ( encr @ SV19 @ SV61 ) ) )
= $true )
| ( ( ssIm @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(241,plain,
! [SV20: $i,SV35: $i] :
( ( ( ~ ( ssBf @ SV35 ) )
= $true )
| ( ( ssSb @ ( pair @ SV20 @ SV35 ) )
= $true )
| ( ( ssM @ ( sent @ SV20 @ b @ ( pair @ SV20 @ SV35 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(242,plain,
! [SV21: $i,SV36: $i] :
( ( ( ~ ( ssIm @ SV36 ) )
= $true )
| ( ( ! [SY143: $i] :
( ~ ( ssIm @ SY143 )
| ! [SY144: $i] :
( ~ ( ssIm @ SY144 )
| ( ssIm @ ( quadr @ SV21 @ SV36 @ SY143 @ SY144 ) ) ) ) )
= $true )
| ( ( ssIm @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(243,plain,
! [SV62: $i,SV48: $i,SV37: $i,SV22: $i] :
( ( ( ! [SY177: $i,SY178: $i] :
~ ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ SV22 @ SV37 @ SV48 @ SV62 ) @ at ) @ SY177 @ SY178 ) ) ) )
= $true )
| ( ( ~ ( ssSa @ ( pair @ SV22 @ SV37 ) )
| ( ssAk @ ( key @ SV48 @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(244,plain,
! [SV23: $i,SV38: $i] :
( ( ( ~ ( ssBf @ SV38 ) )
= $true )
| ( ( ssM @ ( sent @ b @ t @ ( triple @ b @ ( nb @ SV38 ) @ ( encr @ ( triple @ SV23 @ SV38 @ ( tb @ SV38 ) ) @ bt ) ) ) )
= $true )
| ( ( ssM @ ( sent @ SV23 @ b @ ( pair @ SV23 @ SV38 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(245,plain,
! [SV49: $i,SV39: $i,SV24: $i] :
( ( ( ssM @ ( sent @ SV24 @ b @ ( pair @ ( encr @ ( triple @ SV24 @ SV39 @ ( tb @ SV49 ) ) @ bt ) @ ( encr @ ( nb @ SV49 ) @ SV39 ) ) ) )
= $false )
| ( ( ~ ( ssSb @ ( pair @ SV24 @ SV49 ) )
| ( ssBk @ ( key @ SV39 @ SV24 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(246,plain,
! [SV69: $i,SV63: $i,SV50: $i,SV40: $i,SV25: $i] :
( ( ! [SY184: $i] :
( ~ ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ SV25 @ SV40 @ SV50 @ SV63 ) @ at ) @ SV69 @ SY184 ) ) )
| ~ ( ssSa @ ( pair @ SV25 @ SV40 ) )
| ( ssM @ ( sent @ a @ SV25 @ ( pair @ SV69 @ ( encr @ SY184 @ SV50 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(247,plain,
! [SV70: $i,SV64: $i,SV51: $i,SV41: $i,SV26: $i] :
( ( ! [SY185: $i] :
( ~ ( ssM @ ( sent @ SV26 @ t @ ( triple @ SV26 @ SV41 @ ( encr @ ( triple @ SV51 @ SV64 @ SV70 ) @ SY185 ) ) ) )
| ~ ( ssTk @ ( key @ SY185 @ SV26 ) )
| ! [SY186: $i] :
( ~ ( ssTk @ ( key @ SY186 @ SV51 ) )
| ~ ( ssNonce @ SV64 )
| ( ssM @ ( sent @ t @ SV51 @ ( triple @ ( encr @ ( quadr @ SV26 @ SV64 @ ( kt @ SV64 ) @ SV70 ) @ SY186 ) @ ( encr @ ( triple @ SV51 @ ( kt @ SV64 ) @ SV70 ) @ SY185 ) @ SV41 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(248,plain,
! [SV54: $i,SV46: $i,SV31: $i,SV11: $i] :
( ( ( ssIm @ ( quadr @ SV11 @ SV31 @ SV46 @ SV54 ) )
= $false )
| ( ( ssIm @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(249,plain,
! [SV65: $i,SV47: $i,SV32: $i,SV12: $i] :
( ( ( ssIm @ ( quadr @ SV12 @ SV32 @ SV47 @ SV65 ) )
= $false )
| ( ( ssIm @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(250,plain,
! [SV66: $i,SV55: $i,SV33: $i,SV13: $i] :
( ( ( ssIm @ ( quadr @ SV13 @ SV33 @ SV55 @ SV66 ) )
= $false )
| ( ( ssIm @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(251,plain,
! [SV67: $i,SV56: $i,SV34: $i,SV14: $i] :
( ( ( ssIm @ ( quadr @ SV14 @ SV34 @ SV56 @ SV67 ) )
= $false )
| ( ( ssIm @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(252,plain,
! [SV15: $i,SV57: $i] :
( ( ( ssP @ SV57 )
= $false )
| ( ( ssIk @ ( key @ SV15 @ SV57 ) )
= $true )
| ( ( ssIm @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(253,plain,
! [SV16: $i,SV58: $i] :
( ( ( ssIm @ SV58 )
= $false )
| ( ( ssIm @ ( pair @ SV16 @ SV58 ) )
= $true )
| ( ( ssIm @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(254,plain,
! [SV17: $i,SV59: $i] :
( ( ( ssP @ SV59 )
= $false )
| ( ( ! [SY174: $i] :
( ~ ( ssP @ SY174 )
| ( ssM @ ( sent @ SV59 @ SY174 @ SV17 ) ) ) )
= $true )
| ( ( ssIm @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(255,plain,
! [SV18: $i,SV60: $i] :
( ( ( ssIm @ SV60 )
= $false )
| ( ( ! [SY175: $i] :
( ~ ( ssIm @ SY175 )
| ( ssIm @ ( triple @ SV18 @ SV60 @ SY175 ) ) ) )
= $true )
| ( ( ssIm @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(256,plain,
! [SV19: $i,SV68: $i,SV61: $i] :
( ( ( ~ ( ssIk @ ( key @ SV61 @ SV68 ) ) )
= $true )
| ( ( ~ ( ssP @ SV68 )
| ( ssIm @ ( encr @ SV19 @ SV61 ) ) )
= $true )
| ( ( ssIm @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(257,plain,
! [SV20: $i,SV35: $i] :
( ( ( ssBf @ SV35 )
= $false )
| ( ( ssSb @ ( pair @ SV20 @ SV35 ) )
= $true )
| ( ( ssM @ ( sent @ SV20 @ b @ ( pair @ SV20 @ SV35 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(258,plain,
! [SV21: $i,SV36: $i] :
( ( ( ssIm @ SV36 )
= $false )
| ( ( ! [SY143: $i] :
( ~ ( ssIm @ SY143 )
| ! [SY144: $i] :
( ~ ( ssIm @ SY144 )
| ( ssIm @ ( quadr @ SV21 @ SV36 @ SY143 @ SY144 ) ) ) ) )
= $true )
| ( ( ssIm @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(259,plain,
! [SV71: $i,SV62: $i,SV48: $i,SV37: $i,SV22: $i] :
( ( ( ! [SY187: $i] :
~ ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ SV22 @ SV37 @ SV48 @ SV62 ) @ at ) @ SV71 @ SY187 ) ) ) )
= $true )
| ( ( ~ ( ssSa @ ( pair @ SV22 @ SV37 ) )
| ( ssAk @ ( key @ SV48 @ SV22 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(260,plain,
! [SV23: $i,SV38: $i] :
( ( ( ssBf @ SV38 )
= $false )
| ( ( ssM @ ( sent @ b @ t @ ( triple @ b @ ( nb @ SV38 ) @ ( encr @ ( triple @ SV23 @ SV38 @ ( tb @ SV38 ) ) @ bt ) ) ) )
= $true )
| ( ( ssM @ ( sent @ SV23 @ b @ ( pair @ SV23 @ SV38 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(261,plain,
! [SV39: $i,SV49: $i,SV24: $i] :
( ( ( ~ ( ssSb @ ( pair @ SV24 @ SV49 ) ) )
= $true )
| ( ( ssBk @ ( key @ SV39 @ SV24 ) )
= $true )
| ( ( ssM @ ( sent @ SV24 @ b @ ( pair @ ( encr @ ( triple @ SV24 @ SV39 @ ( tb @ SV49 ) ) @ bt ) @ ( encr @ ( nb @ SV49 ) @ SV39 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(262,plain,
! [SV72: $i,SV69: $i,SV63: $i,SV50: $i,SV40: $i,SV25: $i] :
( ( ~ ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ SV25 @ SV40 @ SV50 @ SV63 ) @ at ) @ SV69 @ SV72 ) ) )
| ~ ( ssSa @ ( pair @ SV25 @ SV40 ) )
| ( ssM @ ( sent @ a @ SV25 @ ( pair @ SV69 @ ( encr @ SV72 @ SV50 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(263,plain,
! [SV73: $i,SV70: $i,SV64: $i,SV51: $i,SV41: $i,SV26: $i] :
( ( ~ ( ssM @ ( sent @ SV26 @ t @ ( triple @ SV26 @ SV41 @ ( encr @ ( triple @ SV51 @ SV64 @ SV70 ) @ SV73 ) ) ) )
| ~ ( ssTk @ ( key @ SV73 @ SV26 ) )
| ! [SY188: $i] :
( ~ ( ssTk @ ( key @ SY188 @ SV51 ) )
| ~ ( ssNonce @ SV64 )
| ( ssM @ ( sent @ t @ SV51 @ ( triple @ ( encr @ ( quadr @ SV26 @ SV64 @ ( kt @ SV64 ) @ SV70 ) @ SY188 ) @ ( encr @ ( triple @ SV51 @ ( kt @ SV64 ) @ SV70 ) @ SV73 ) @ SV41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(264,plain,
! [SV17: $i,SV59: $i,SV74: $i] :
( ( ( ~ ( ssP @ SV74 )
| ( ssM @ ( sent @ SV59 @ SV74 @ SV17 ) ) )
= $true )
| ( ( ssP @ SV59 )
= $false )
| ( ( ssIm @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(265,plain,
! [SV60: $i,SV18: $i,SV75: $i] :
( ( ( ~ ( ssIm @ SV75 )
| ( ssIm @ ( triple @ SV18 @ SV60 @ SV75 ) ) )
= $true )
| ( ( ssIm @ SV60 )
= $false )
| ( ( ssIm @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(266,plain,
! [SV19: $i,SV68: $i,SV61: $i] :
( ( ( ssIk @ ( key @ SV61 @ SV68 ) )
= $false )
| ( ( ~ ( ssP @ SV68 )
| ( ssIm @ ( encr @ SV19 @ SV61 ) ) )
= $true )
| ( ( ssIm @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(267,plain,
! [SV36: $i,SV21: $i,SV76: $i] :
( ( ( ~ ( ssIm @ SV76 )
| ! [SY189: $i] :
( ~ ( ssIm @ SY189 )
| ( ssIm @ ( quadr @ SV21 @ SV36 @ SV76 @ SY189 ) ) ) )
= $true )
| ( ( ssIm @ SV36 )
= $false )
| ( ( ssIm @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(268,plain,
! [SV77: $i,SV71: $i,SV62: $i,SV48: $i,SV37: $i,SV22: $i] :
( ( ( ~ ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ SV22 @ SV37 @ SV48 @ SV62 ) @ at ) @ SV71 @ SV77 ) ) ) )
= $true )
| ( ( ~ ( ssSa @ ( pair @ SV22 @ SV37 ) )
| ( ssAk @ ( key @ SV48 @ SV22 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(269,plain,
! [SV39: $i,SV49: $i,SV24: $i] :
( ( ( ssSb @ ( pair @ SV24 @ SV49 ) )
= $false )
| ( ( ssBk @ ( key @ SV39 @ SV24 ) )
= $true )
| ( ( ssM @ ( sent @ SV24 @ b @ ( pair @ ( encr @ ( triple @ SV24 @ SV39 @ ( tb @ SV49 ) ) @ bt ) @ ( encr @ ( nb @ SV49 ) @ SV39 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(270,plain,
! [SV72: $i,SV69: $i,SV63: $i,SV50: $i,SV40: $i,SV25: $i] :
( ( ( ~ ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ SV25 @ SV40 @ SV50 @ SV63 ) @ at ) @ SV69 @ SV72 ) ) ) )
= $true )
| ( ( ~ ( ssSa @ ( pair @ SV25 @ SV40 ) )
| ( ssM @ ( sent @ a @ SV25 @ ( pair @ SV69 @ ( encr @ SV72 @ SV50 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(271,plain,
! [SV73: $i,SV70: $i,SV64: $i,SV51: $i,SV41: $i,SV26: $i] :
( ( ( ~ ( ssM @ ( sent @ SV26 @ t @ ( triple @ SV26 @ SV41 @ ( encr @ ( triple @ SV51 @ SV64 @ SV70 ) @ SV73 ) ) ) ) )
= $true )
| ( ( ~ ( ssTk @ ( key @ SV73 @ SV26 ) )
| ! [SY188: $i] :
( ~ ( ssTk @ ( key @ SY188 @ SV51 ) )
| ~ ( ssNonce @ SV64 )
| ( ssM @ ( sent @ t @ SV51 @ ( triple @ ( encr @ ( quadr @ SV26 @ SV64 @ ( kt @ SV64 ) @ SV70 ) @ SY188 ) @ ( encr @ ( triple @ SV51 @ ( kt @ SV64 ) @ SV70 ) @ SV73 ) @ SV41 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[263]) ).
thf(272,plain,
! [SV17: $i,SV59: $i,SV74: $i] :
( ( ( ~ ( ssP @ SV74 ) )
= $true )
| ( ( ssM @ ( sent @ SV59 @ SV74 @ SV17 ) )
= $true )
| ( ( ssP @ SV59 )
= $false )
| ( ( ssIm @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(273,plain,
! [SV60: $i,SV18: $i,SV75: $i] :
( ( ( ~ ( ssIm @ SV75 ) )
= $true )
| ( ( ssIm @ ( triple @ SV18 @ SV60 @ SV75 ) )
= $true )
| ( ( ssIm @ SV60 )
= $false )
| ( ( ssIm @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(274,plain,
! [SV61: $i,SV19: $i,SV68: $i] :
( ( ( ~ ( ssP @ SV68 ) )
= $true )
| ( ( ssIm @ ( encr @ SV19 @ SV61 ) )
= $true )
| ( ( ssIk @ ( key @ SV61 @ SV68 ) )
= $false )
| ( ( ssIm @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(275,plain,
! [SV36: $i,SV21: $i,SV76: $i] :
( ( ( ~ ( ssIm @ SV76 ) )
= $true )
| ( ( ! [SY189: $i] :
( ~ ( ssIm @ SY189 )
| ( ssIm @ ( quadr @ SV21 @ SV36 @ SV76 @ SY189 ) ) ) )
= $true )
| ( ( ssIm @ SV36 )
= $false )
| ( ( ssIm @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[267]) ).
thf(276,plain,
! [SV77: $i,SV71: $i,SV62: $i,SV48: $i,SV37: $i,SV22: $i] :
( ( ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ SV22 @ SV37 @ SV48 @ SV62 ) @ at ) @ SV71 @ SV77 ) ) )
= $false )
| ( ( ~ ( ssSa @ ( pair @ SV22 @ SV37 ) )
| ( ssAk @ ( key @ SV48 @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(277,plain,
! [SV72: $i,SV69: $i,SV63: $i,SV50: $i,SV40: $i,SV25: $i] :
( ( ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ SV25 @ SV40 @ SV50 @ SV63 ) @ at ) @ SV69 @ SV72 ) ) )
= $false )
| ( ( ~ ( ssSa @ ( pair @ SV25 @ SV40 ) )
| ( ssM @ ( sent @ a @ SV25 @ ( pair @ SV69 @ ( encr @ SV72 @ SV50 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(278,plain,
! [SV73: $i,SV70: $i,SV64: $i,SV51: $i,SV41: $i,SV26: $i] :
( ( ( ssM @ ( sent @ SV26 @ t @ ( triple @ SV26 @ SV41 @ ( encr @ ( triple @ SV51 @ SV64 @ SV70 ) @ SV73 ) ) ) )
= $false )
| ( ( ~ ( ssTk @ ( key @ SV73 @ SV26 ) )
| ! [SY188: $i] :
( ~ ( ssTk @ ( key @ SY188 @ SV51 ) )
| ~ ( ssNonce @ SV64 )
| ( ssM @ ( sent @ t @ SV51 @ ( triple @ ( encr @ ( quadr @ SV26 @ SV64 @ ( kt @ SV64 ) @ SV70 ) @ SY188 ) @ ( encr @ ( triple @ SV51 @ ( kt @ SV64 ) @ SV70 ) @ SV73 ) @ SV41 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(279,plain,
! [SV17: $i,SV59: $i,SV74: $i] :
( ( ( ssP @ SV74 )
= $false )
| ( ( ssM @ ( sent @ SV59 @ SV74 @ SV17 ) )
= $true )
| ( ( ssP @ SV59 )
= $false )
| ( ( ssIm @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(280,plain,
! [SV60: $i,SV18: $i,SV75: $i] :
( ( ( ssIm @ SV75 )
= $false )
| ( ( ssIm @ ( triple @ SV18 @ SV60 @ SV75 ) )
= $true )
| ( ( ssIm @ SV60 )
= $false )
| ( ( ssIm @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(281,plain,
! [SV61: $i,SV19: $i,SV68: $i] :
( ( ( ssP @ SV68 )
= $false )
| ( ( ssIm @ ( encr @ SV19 @ SV61 ) )
= $true )
| ( ( ssIk @ ( key @ SV61 @ SV68 ) )
= $false )
| ( ( ssIm @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(282,plain,
! [SV36: $i,SV21: $i,SV76: $i] :
( ( ( ssIm @ SV76 )
= $false )
| ( ( ! [SY189: $i] :
( ~ ( ssIm @ SY189 )
| ( ssIm @ ( quadr @ SV21 @ SV36 @ SV76 @ SY189 ) ) ) )
= $true )
| ( ( ssIm @ SV36 )
= $false )
| ( ( ssIm @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(283,plain,
! [SV77: $i,SV71: $i,SV62: $i,SV48: $i,SV37: $i,SV22: $i] :
( ( ( ~ ( ssSa @ ( pair @ SV22 @ SV37 ) ) )
= $true )
| ( ( ssAk @ ( key @ SV48 @ SV22 ) )
= $true )
| ( ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ SV22 @ SV37 @ SV48 @ SV62 ) @ at ) @ SV71 @ SV77 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(284,plain,
! [SV63: $i,SV50: $i,SV72: $i,SV69: $i,SV40: $i,SV25: $i] :
( ( ( ~ ( ssSa @ ( pair @ SV25 @ SV40 ) ) )
= $true )
| ( ( ssM @ ( sent @ a @ SV25 @ ( pair @ SV69 @ ( encr @ SV72 @ SV50 ) ) ) )
= $true )
| ( ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ SV25 @ SV40 @ SV50 @ SV63 ) @ at ) @ SV69 @ SV72 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(285,plain,
! [SV41: $i,SV70: $i,SV64: $i,SV51: $i,SV26: $i,SV73: $i] :
( ( ( ~ ( ssTk @ ( key @ SV73 @ SV26 ) ) )
= $true )
| ( ( ! [SY188: $i] :
( ~ ( ssTk @ ( key @ SY188 @ SV51 ) )
| ~ ( ssNonce @ SV64 )
| ( ssM @ ( sent @ t @ SV51 @ ( triple @ ( encr @ ( quadr @ SV26 @ SV64 @ ( kt @ SV64 ) @ SV70 ) @ SY188 ) @ ( encr @ ( triple @ SV51 @ ( kt @ SV64 ) @ SV70 ) @ SV73 ) @ SV41 ) ) ) ) )
= $true )
| ( ( ssM @ ( sent @ SV26 @ t @ ( triple @ SV26 @ SV41 @ ( encr @ ( triple @ SV51 @ SV64 @ SV70 ) @ SV73 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(286,plain,
! [SV76: $i,SV36: $i,SV21: $i,SV78: $i] :
( ( ( ~ ( ssIm @ SV78 )
| ( ssIm @ ( quadr @ SV21 @ SV36 @ SV76 @ SV78 ) ) )
= $true )
| ( ( ssIm @ SV76 )
= $false )
| ( ( ssIm @ SV36 )
= $false )
| ( ( ssIm @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(287,plain,
! [SV77: $i,SV71: $i,SV62: $i,SV48: $i,SV37: $i,SV22: $i] :
( ( ( ssSa @ ( pair @ SV22 @ SV37 ) )
= $false )
| ( ( ssAk @ ( key @ SV48 @ SV22 ) )
= $true )
| ( ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ SV22 @ SV37 @ SV48 @ SV62 ) @ at ) @ SV71 @ SV77 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(288,plain,
! [SV63: $i,SV50: $i,SV72: $i,SV69: $i,SV40: $i,SV25: $i] :
( ( ( ssSa @ ( pair @ SV25 @ SV40 ) )
= $false )
| ( ( ssM @ ( sent @ a @ SV25 @ ( pair @ SV69 @ ( encr @ SV72 @ SV50 ) ) ) )
= $true )
| ( ( ssM @ ( sent @ t @ a @ ( triple @ ( encr @ ( quadr @ SV25 @ SV40 @ SV50 @ SV63 ) @ at ) @ SV69 @ SV72 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(289,plain,
! [SV41: $i,SV70: $i,SV64: $i,SV51: $i,SV26: $i,SV73: $i] :
( ( ( ssTk @ ( key @ SV73 @ SV26 ) )
= $false )
| ( ( ! [SY188: $i] :
( ~ ( ssTk @ ( key @ SY188 @ SV51 ) )
| ~ ( ssNonce @ SV64 )
| ( ssM @ ( sent @ t @ SV51 @ ( triple @ ( encr @ ( quadr @ SV26 @ SV64 @ ( kt @ SV64 ) @ SV70 ) @ SY188 ) @ ( encr @ ( triple @ SV51 @ ( kt @ SV64 ) @ SV70 ) @ SV73 ) @ SV41 ) ) ) ) )
= $true )
| ( ( ssM @ ( sent @ SV26 @ t @ ( triple @ SV26 @ SV41 @ ( encr @ ( triple @ SV51 @ SV64 @ SV70 ) @ SV73 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(290,plain,
! [SV76: $i,SV36: $i,SV21: $i,SV78: $i] :
( ( ( ~ ( ssIm @ SV78 ) )
= $true )
| ( ( ssIm @ ( quadr @ SV21 @ SV36 @ SV76 @ SV78 ) )
= $true )
| ( ( ssIm @ SV76 )
= $false )
| ( ( ssIm @ SV36 )
= $false )
| ( ( ssIm @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(291,plain,
! [SV41: $i,SV73: $i,SV70: $i,SV26: $i,SV64: $i,SV51: $i,SV79: $i] :
( ( ( ~ ( ssTk @ ( key @ SV79 @ SV51 ) )
| ~ ( ssNonce @ SV64 )
| ( ssM @ ( sent @ t @ SV51 @ ( triple @ ( encr @ ( quadr @ SV26 @ SV64 @ ( kt @ SV64 ) @ SV70 ) @ SV79 ) @ ( encr @ ( triple @ SV51 @ ( kt @ SV64 ) @ SV70 ) @ SV73 ) @ SV41 ) ) ) )
= $true )
| ( ( ssTk @ ( key @ SV73 @ SV26 ) )
= $false )
| ( ( ssM @ ( sent @ SV26 @ t @ ( triple @ SV26 @ SV41 @ ( encr @ ( triple @ SV51 @ SV64 @ SV70 ) @ SV73 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(292,plain,
! [SV76: $i,SV36: $i,SV21: $i,SV78: $i] :
( ( ( ssIm @ SV78 )
= $false )
| ( ( ssIm @ ( quadr @ SV21 @ SV36 @ SV76 @ SV78 ) )
= $true )
| ( ( ssIm @ SV76 )
= $false )
| ( ( ssIm @ SV36 )
= $false )
| ( ( ssIm @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(293,plain,
! [SV41: $i,SV73: $i,SV70: $i,SV26: $i,SV64: $i,SV51: $i,SV79: $i] :
( ( ( ~ ( ssTk @ ( key @ SV79 @ SV51 ) ) )
= $true )
| ( ( ~ ( ssNonce @ SV64 )
| ( ssM @ ( sent @ t @ SV51 @ ( triple @ ( encr @ ( quadr @ SV26 @ SV64 @ ( kt @ SV64 ) @ SV70 ) @ SV79 ) @ ( encr @ ( triple @ SV51 @ ( kt @ SV64 ) @ SV70 ) @ SV73 ) @ SV41 ) ) ) )
= $true )
| ( ( ssTk @ ( key @ SV73 @ SV26 ) )
= $false )
| ( ( ssM @ ( sent @ SV26 @ t @ ( triple @ SV26 @ SV41 @ ( encr @ ( triple @ SV51 @ SV64 @ SV70 ) @ SV73 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(294,plain,
! [SV41: $i,SV73: $i,SV70: $i,SV26: $i,SV64: $i,SV51: $i,SV79: $i] :
( ( ( ssTk @ ( key @ SV79 @ SV51 ) )
= $false )
| ( ( ~ ( ssNonce @ SV64 )
| ( ssM @ ( sent @ t @ SV51 @ ( triple @ ( encr @ ( quadr @ SV26 @ SV64 @ ( kt @ SV64 ) @ SV70 ) @ SV79 ) @ ( encr @ ( triple @ SV51 @ ( kt @ SV64 ) @ SV70 ) @ SV73 ) @ SV41 ) ) ) )
= $true )
| ( ( ssTk @ ( key @ SV73 @ SV26 ) )
= $false )
| ( ( ssM @ ( sent @ SV26 @ t @ ( triple @ SV26 @ SV41 @ ( encr @ ( triple @ SV51 @ SV64 @ SV70 ) @ SV73 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(295,plain,
! [SV41: $i,SV73: $i,SV79: $i,SV70: $i,SV26: $i,SV51: $i,SV64: $i] :
( ( ( ~ ( ssNonce @ SV64 ) )
= $true )
| ( ( ssM @ ( sent @ t @ SV51 @ ( triple @ ( encr @ ( quadr @ SV26 @ SV64 @ ( kt @ SV64 ) @ SV70 ) @ SV79 ) @ ( encr @ ( triple @ SV51 @ ( kt @ SV64 ) @ SV70 ) @ SV73 ) @ SV41 ) ) )
= $true )
| ( ( ssTk @ ( key @ SV79 @ SV51 ) )
= $false )
| ( ( ssTk @ ( key @ SV73 @ SV26 ) )
= $false )
| ( ( ssM @ ( sent @ SV26 @ t @ ( triple @ SV26 @ SV41 @ ( encr @ ( triple @ SV51 @ SV64 @ SV70 ) @ SV73 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(296,plain,
! [SV41: $i,SV73: $i,SV79: $i,SV70: $i,SV26: $i,SV51: $i,SV64: $i] :
( ( ( ssNonce @ SV64 )
= $false )
| ( ( ssM @ ( sent @ t @ SV51 @ ( triple @ ( encr @ ( quadr @ SV26 @ SV64 @ ( kt @ SV64 ) @ SV70 ) @ SV79 ) @ ( encr @ ( triple @ SV51 @ ( kt @ SV64 ) @ SV70 ) @ SV73 ) @ SV41 ) ) )
= $true )
| ( ( ssTk @ ( key @ SV79 @ SV51 ) )
= $false )
| ( ( ssTk @ ( key @ SV73 @ SV26 ) )
= $false )
| ( ( ssM @ ( sent @ SV26 @ t @ ( triple @ SV26 @ SV41 @ ( encr @ ( triple @ SV51 @ SV64 @ SV70 ) @ SV73 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(297,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[94,296,292,288,287,281,280,279,269,260,257,253,252,251,250,249,248,231,230,229,228,207,206,205,159,157,133,132,109,106,105,104,103,102,98,97,96,95]) ).
thf(298,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[297]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN982-1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jul 12 03:58:42 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.39
% 0.19/0.39 No.of.Axioms: 37
% 0.19/0.39
% 0.19/0.39 Length.of.Defs: 0
% 0.19/0.39
% 0.19/0.39 Contains.Choice.Funs: false
% 0.19/0.41 .
% 0.19/0.44 (rf:0,axioms:37,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:39,loop_count:0,foatp_calls:0,translation:fof_full)................
% 0.44/0.66
% 0.44/0.66 ********************************
% 0.44/0.66 * All subproblems solved! *
% 0.44/0.66 ********************************
% 0.44/0.66 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:37,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:297,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.49/0.70
% 0.49/0.70 %**** Beginning of derivation protocol ****
% 0.49/0.70 % SZS output start CNFRefutation
% See solution above
% 0.49/0.70
% 0.49/0.70 %**** End of derivation protocol ****
% 0.49/0.70 %**** no. of clauses in derivation: 298 ****
% 0.49/0.70 %**** clause counter: 297 ****
% 0.49/0.70
% 0.49/0.70 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:37,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:297,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------