TSTP Solution File: SWV237+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SWV237+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 : 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 : Wed Jul 20 20:11:17 EDT 2022
% Result : Theorem 0.56s 0.72s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 40
% Syntax : Number of formulae : 224 ( 110 unt; 15 typ; 0 def)
% Number of atoms : 1486 ( 415 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 2640 ( 308 ~; 401 |; 48 &;1857 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 14 con; 0-2 aty)
% Number of variables : 499 ( 0 ^ 499 !; 0 ?; 499 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_enc,type,
enc: $i > $i > $i ).
thf(tp_i,type,
i: $i > $i ).
thf(tp_k,type,
k: $i ).
thf(tp_kk,type,
kk: $i ).
thf(tp_lp,type,
lp: $i ).
thf(tp_p,type,
p: $i > $o ).
thf(tp_pp,type,
pp: $i ).
thf(tp_t1,type,
t1: $i ).
thf(tp_t2,type,
t2: $i ).
thf(tp_tc,type,
tc: $i ).
thf(tp_tmk,type,
tmk: $i ).
thf(tp_w,type,
w: $i ).
thf(tp_wk,type,
wk: $i ).
thf(tp_zcmk,type,
zcmk: $i ).
thf(1,axiom,
p @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_knows_8) ).
thf(2,axiom,
p @ ( i @ kk ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_knows_7) ).
thf(3,axiom,
p @ kk,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_knows_6) ).
thf(4,axiom,
p @ ( enc @ tc @ k ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_knows_5) ).
thf(5,axiom,
p @ ( enc @ lp @ t2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_knows_4) ).
thf(6,axiom,
p @ ( enc @ w @ t1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_knows_3) ).
thf(7,axiom,
p @ ( enc @ wk @ w ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_knows_2) ).
thf(8,axiom,
p @ ( enc @ tmk @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intruder_knows_1) ).
thf(9,axiom,
! [U: $i,V: $i,W: $i] :
( ( ( p @ U )
& ( p @ V )
& ( p @ W ) )
=> ( p @ ( enc @ U @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',attacker_can_encrypt) ).
thf(10,axiom,
! [U: $i,V: $i,W: $i] :
( ( ( p @ U )
& ( p @ V )
& ( p @ W ) )
=> ( p @ ( enc @ ( enc @ ( i @ wk ) @ V ) @ ( enc @ ( i @ lp ) @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',data_translate_PIN_from_local_storage_to_interchange_key) ).
thf(11,axiom,
! [U: $i,V: $i,W: $i] :
( ( ( p @ U )
& ( p @ V )
& ( p @ W ) )
=> ( p @ ( enc @ ( enc @ ( i @ wk ) @ W ) @ ( enc @ ( i @ ( enc @ ( i @ wk ) @ V ) ) @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',data_translate_between_interchange_keys) ).
thf(12,axiom,
! [U: $i,V: $i,W: $i] :
( ( ( p @ U )
& ( p @ V )
& ( p @ W ) )
=> ( p @ ( enc @ ( enc @ ( i @ wk ) @ W ) @ ( enc @ ( i @ ( enc @ ( i @ tmk ) @ V ) ) @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',data_translate_PIN_from_local_to_interchange_key) ).
thf(13,axiom,
! [U: $i,V: $i,W: $i] :
( ( ( p @ U )
& ( p @ V )
& ( p @ W ) )
=> ( p @ ( enc @ ( i @ ( enc @ ( i @ tc ) @ U ) ) @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',data_decrypt) ).
thf(14,axiom,
! [U: $i,V: $i,W: $i] :
( ( ( p @ U )
& ( p @ V )
& ( p @ W ) )
=> ( p @ ( enc @ ( enc @ ( i @ tc ) @ U ) @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',data_encrypt) ).
thf(15,axiom,
! [U: $i,V: $i,W: $i] :
( ( ( p @ U )
& ( p @ V )
& ( p @ W ) )
=> ( p @ ( enc @ tc @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',encrypt_clear_key_as_Tcomms_key) ).
thf(16,axiom,
! [U: $i,V: $i,W: $i] :
( ( ( p @ U )
& ( p @ V )
& ( p @ W ) )
=> ( p @ ( enc @ ( enc @ ( i @ tmk ) @ V ) @ ( enc @ ( i @ tc ) @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',encrypt_a_stored_comms_key) ).
thf(17,axiom,
! [U: $i,V: $i,W: $i] :
( ( ( p @ U )
& ( p @ V )
& ( p @ W ) )
=> ( p @ ( enc @ ( enc @ ( i @ tmk ) @ V ) @ ( enc @ ( i @ tmk ) @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',encrypt_a_PIN_derivation_key_under_a_TMK) ).
thf(18,axiom,
! [U: $i,V: $i,W: $i] :
( ( ( p @ U )
& ( p @ V )
& ( p @ W ) )
=> ( p @ ( enc @ wk @ ( enc @ ( i @ tmk ) @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',receive_working_key_from_switch) ).
thf(19,axiom,
! [U: $i,V: $i,W: $i] :
( ( ( p @ U )
& ( p @ V )
& ( p @ W ) )
=> ( p @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ V ) ) @ ( enc @ ( i @ tmk ) @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_translate_from_TMK_to_ZCMK) ).
thf(20,axiom,
! [U: $i,V: $i,W: $i] :
( ( ( p @ U )
& ( p @ V )
& ( p @ W ) )
=> ( p @ ( enc @ tmk @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ V ) ) @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_translate_from_ZCMK_to_TMK) ).
thf(21,axiom,
! [U: $i] :
( ( p @ U )
=> ( p @ ( i @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',keys_are_symmetric) ).
thf(22,axiom,
! [U: $i] :
( ( i @ ( i @ U ) )
= U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',double_inverse_cancel) ).
thf(23,axiom,
! [U: $i,V: $i] :
( ( enc @ U @ ( enc @ ( i @ U ) @ V ) )
= V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dec_enc_cancel) ).
thf(24,axiom,
! [U: $i,V: $i] :
( ( enc @ ( i @ U ) @ ( enc @ U @ V ) )
= V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',enc_dec_cancel) ).
thf(25,conjecture,
p @ ( enc @ pp @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
thf(26,negated_conjecture,
( ( p @ ( enc @ pp @ a ) )
= $false ),
inference(negate_conjecture,[status(cth)],[25]) ).
thf(27,plain,
( ( p @ ( enc @ pp @ a ) )
= $false ),
inference(unfold_def,[status(thm)],[26]) ).
thf(28,plain,
( ( p @ a )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(29,plain,
( ( p @ ( i @ kk ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(30,plain,
( ( p @ kk )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(31,plain,
( ( p @ ( enc @ tc @ k ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(32,plain,
( ( p @ ( enc @ lp @ t2 ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(33,plain,
( ( p @ ( enc @ w @ t1 ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(34,plain,
( ( p @ ( enc @ wk @ w ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(35,plain,
( ( p @ ( enc @ tmk @ pp ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(36,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( p @ U )
& ( p @ V )
& ( p @ W ) )
=> ( p @ ( enc @ U @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(37,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( p @ U )
& ( p @ V )
& ( p @ W ) )
=> ( p @ ( enc @ ( enc @ ( i @ wk ) @ V ) @ ( enc @ ( i @ lp ) @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(38,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( p @ U )
& ( p @ V )
& ( p @ W ) )
=> ( p @ ( enc @ ( enc @ ( i @ wk ) @ W ) @ ( enc @ ( i @ ( enc @ ( i @ wk ) @ V ) ) @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(39,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( p @ U )
& ( p @ V )
& ( p @ W ) )
=> ( p @ ( enc @ ( enc @ ( i @ wk ) @ W ) @ ( enc @ ( i @ ( enc @ ( i @ tmk ) @ V ) ) @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(40,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( p @ U )
& ( p @ V )
& ( p @ W ) )
=> ( p @ ( enc @ ( i @ ( enc @ ( i @ tc ) @ U ) ) @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(41,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( p @ U )
& ( p @ V )
& ( p @ W ) )
=> ( p @ ( enc @ ( enc @ ( i @ tc ) @ U ) @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(42,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( p @ U )
& ( p @ V )
& ( p @ W ) )
=> ( p @ ( enc @ tc @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(43,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( p @ U )
& ( p @ V )
& ( p @ W ) )
=> ( p @ ( enc @ ( enc @ ( i @ tmk ) @ V ) @ ( enc @ ( i @ tc ) @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(44,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( p @ U )
& ( p @ V )
& ( p @ W ) )
=> ( p @ ( enc @ ( enc @ ( i @ tmk ) @ V ) @ ( enc @ ( i @ tmk ) @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(45,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( p @ U )
& ( p @ V )
& ( p @ W ) )
=> ( p @ ( enc @ wk @ ( enc @ ( i @ tmk ) @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(46,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( p @ U )
& ( p @ V )
& ( p @ W ) )
=> ( p @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ V ) ) @ ( enc @ ( i @ tmk ) @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(47,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( p @ U )
& ( p @ V )
& ( p @ W ) )
=> ( p @ ( enc @ tmk @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ V ) ) @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(48,plain,
( ( ! [U: $i] :
( ( p @ U )
=> ( p @ ( i @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(49,plain,
( ( ! [U: $i] :
( ( i @ ( i @ U ) )
= U ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(50,plain,
( ( ! [U: $i,V: $i] :
( ( enc @ U @ ( enc @ ( i @ U ) @ V ) )
= V ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(51,plain,
( ( ! [U: $i,V: $i] :
( ( enc @ ( i @ U ) @ ( enc @ U @ V ) )
= V ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(52,plain,
( ( ~ ( p @ ( enc @ pp @ a ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[27]) ).
thf(53,plain,
( ( ! [U: $i,V: $i] :
( ~ ( p @ U )
| ~ ( p @ V )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ U @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(54,plain,
( ( ! [U: $i,V: $i] :
( ~ ( p @ U )
| ~ ( p @ V )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ ( enc @ ( i @ wk ) @ V ) @ ( enc @ ( i @ lp ) @ U ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(55,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( p @ U )
| ~ ( p @ V )
| ~ ( p @ W )
| ( p @ ( enc @ ( enc @ ( i @ wk ) @ W ) @ ( enc @ ( i @ ( enc @ ( i @ wk ) @ V ) ) @ U ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(56,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( p @ U )
| ~ ( p @ V )
| ~ ( p @ W )
| ( p @ ( enc @ ( enc @ ( i @ wk ) @ W ) @ ( enc @ ( i @ ( enc @ ( i @ tmk ) @ V ) ) @ U ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(57,plain,
( ( ! [U: $i,V: $i] :
( ~ ( p @ U )
| ~ ( p @ V )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ ( i @ ( enc @ ( i @ tc ) @ U ) ) @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(58,plain,
( ( ! [U: $i,V: $i] :
( ~ ( p @ U )
| ~ ( p @ V )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ ( enc @ ( i @ tc ) @ U ) @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(59,plain,
( ( ! [U: $i] :
( ~ ( p @ U )
| ! [V: $i] :
~ ( p @ V )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ tc @ U ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(60,plain,
( ( ! [U: $i,V: $i] :
( ~ ( p @ U )
| ~ ( p @ V )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ ( enc @ ( i @ tmk ) @ V ) @ ( enc @ ( i @ tc ) @ U ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(61,plain,
( ( ! [U: $i,V: $i] :
( ~ ( p @ U )
| ~ ( p @ V )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ ( enc @ ( i @ tmk ) @ V ) @ ( enc @ ( i @ tmk ) @ U ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(62,plain,
( ( ! [U: $i] :
( ~ ( p @ U )
| ! [V: $i] :
~ ( p @ V )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ wk @ ( enc @ ( i @ tmk ) @ U ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(63,plain,
( ( ! [U: $i,V: $i] :
( ~ ( p @ U )
| ~ ( p @ V )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ V ) ) @ ( enc @ ( i @ tmk ) @ U ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(64,plain,
( ( ! [U: $i,V: $i] :
( ~ ( p @ U )
| ~ ( p @ V )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ tmk @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ V ) ) @ U ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(65,plain,
( ( ! [U: $i] :
( ~ ( p @ U )
| ( p @ ( i @ U ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(66,plain,
( ( ! [U: $i,V: $i] :
( ( enc @ ( i @ U ) @ ( enc @ U @ V ) )
= V ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(67,plain,
( ( ! [U: $i,V: $i] :
( ( enc @ U @ ( enc @ ( i @ U ) @ V ) )
= V ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(68,plain,
( ( ! [U: $i] :
( ( i @ ( i @ U ) )
= U ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(69,plain,
( ( ! [U: $i] :
( ~ ( p @ U )
| ( p @ ( i @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(70,plain,
( ( ! [U: $i,V: $i] :
( ~ ( p @ U )
| ~ ( p @ V )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ tmk @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ V ) ) @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(71,plain,
( ( ! [U: $i,V: $i] :
( ~ ( p @ U )
| ~ ( p @ V )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ V ) ) @ ( enc @ ( i @ tmk ) @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(72,plain,
( ( ! [U: $i] :
( ~ ( p @ U )
| ! [V: $i] :
~ ( p @ V )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ wk @ ( enc @ ( i @ tmk ) @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(73,plain,
( ( ! [U: $i,V: $i] :
( ~ ( p @ U )
| ~ ( p @ V )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ ( enc @ ( i @ tmk ) @ V ) @ ( enc @ ( i @ tmk ) @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(74,plain,
( ( ! [U: $i,V: $i] :
( ~ ( p @ U )
| ~ ( p @ V )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ ( enc @ ( i @ tmk ) @ V ) @ ( enc @ ( i @ tc ) @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(75,plain,
( ( ! [U: $i] :
( ~ ( p @ U )
| ! [V: $i] :
~ ( p @ V )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ tc @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(76,plain,
( ( ! [U: $i,V: $i] :
( ~ ( p @ U )
| ~ ( p @ V )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ ( enc @ ( i @ tc ) @ U ) @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(77,plain,
( ( ! [U: $i,V: $i] :
( ~ ( p @ U )
| ~ ( p @ V )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ ( i @ ( enc @ ( i @ tc ) @ U ) ) @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(78,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( p @ U )
| ~ ( p @ V )
| ~ ( p @ W )
| ( p @ ( enc @ ( enc @ ( i @ wk ) @ W ) @ ( enc @ ( i @ ( enc @ ( i @ tmk ) @ V ) ) @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(79,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( p @ U )
| ~ ( p @ V )
| ~ ( p @ W )
| ( p @ ( enc @ ( enc @ ( i @ wk ) @ W ) @ ( enc @ ( i @ ( enc @ ( i @ wk ) @ V ) ) @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(80,plain,
( ( ! [U: $i,V: $i] :
( ~ ( p @ U )
| ~ ( p @ V )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ ( enc @ ( i @ wk ) @ V ) @ ( enc @ ( i @ lp ) @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(81,plain,
( ( ! [U: $i,V: $i] :
( ~ ( p @ U )
| ~ ( p @ V )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ U @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(82,plain,
( ( p @ ( enc @ tmk @ pp ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(83,plain,
( ( p @ ( enc @ wk @ w ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(84,plain,
( ( p @ ( enc @ w @ t1 ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(85,plain,
( ( p @ ( enc @ lp @ t2 ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(86,plain,
( ( p @ ( enc @ tc @ k ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(87,plain,
( ( p @ kk )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(88,plain,
( ( p @ ( i @ kk ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(89,plain,
( ( p @ a )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(90,plain,
( ( ~ ( p @ ( enc @ pp @ a ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(91,plain,
! [SV1: $i] :
( ( ! [SY42: $i] :
( ( enc @ ( i @ SV1 ) @ ( enc @ SV1 @ SY42 ) )
= SY42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(92,plain,
! [SV2: $i] :
( ( ! [SY43: $i] :
( ( enc @ SV2 @ ( enc @ ( i @ SV2 ) @ SY43 ) )
= SY43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(93,plain,
! [SV3: $i] :
( ( ( i @ ( i @ SV3 ) )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(94,plain,
! [SV4: $i] :
( ( ~ ( p @ SV4 )
| ( p @ ( i @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(95,plain,
! [SV5: $i] :
( ( ! [SY44: $i] :
( ~ ( p @ SV5 )
| ~ ( p @ SY44 )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ tmk @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ SY44 ) ) @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(96,plain,
! [SV6: $i] :
( ( ! [SY46: $i] :
( ~ ( p @ SV6 )
| ~ ( p @ SY46 )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ SY46 ) ) @ ( enc @ ( i @ tmk ) @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(97,plain,
! [SV7: $i] :
( ( ~ ( p @ SV7 )
| ! [V: $i] :
~ ( p @ V )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ wk @ ( enc @ ( i @ tmk ) @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(98,plain,
! [SV8: $i] :
( ( ! [SY50: $i] :
( ~ ( p @ SV8 )
| ~ ( p @ SY50 )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ ( enc @ ( i @ tmk ) @ SY50 ) @ ( enc @ ( i @ tmk ) @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(99,plain,
! [SV9: $i] :
( ( ! [SY52: $i] :
( ~ ( p @ SV9 )
| ~ ( p @ SY52 )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ ( enc @ ( i @ tmk ) @ SY52 ) @ ( enc @ ( i @ tc ) @ SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(100,plain,
! [SV10: $i] :
( ( ~ ( p @ SV10 )
| ! [V: $i] :
~ ( p @ V )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ tc @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(101,plain,
! [SV11: $i] :
( ( ! [SY56: $i] :
( ~ ( p @ SV11 )
| ~ ( p @ SY56 )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ ( enc @ ( i @ tc ) @ SV11 ) @ SY56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(102,plain,
! [SV12: $i] :
( ( ! [SY58: $i] :
( ~ ( p @ SV12 )
| ~ ( p @ SY58 )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ ( i @ ( enc @ ( i @ tc ) @ SV12 ) ) @ SY58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(103,plain,
! [SV13: $i] :
( ( ! [SY60: $i,SY61: $i] :
( ~ ( p @ SV13 )
| ~ ( p @ SY60 )
| ~ ( p @ SY61 )
| ( p @ ( enc @ ( enc @ ( i @ wk ) @ SY61 ) @ ( enc @ ( i @ ( enc @ ( i @ tmk ) @ SY60 ) ) @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(104,plain,
! [SV14: $i] :
( ( ! [SY62: $i,SY63: $i] :
( ~ ( p @ SV14 )
| ~ ( p @ SY62 )
| ~ ( p @ SY63 )
| ( p @ ( enc @ ( enc @ ( i @ wk ) @ SY63 ) @ ( enc @ ( i @ ( enc @ ( i @ wk ) @ SY62 ) ) @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(105,plain,
! [SV15: $i] :
( ( ! [SY64: $i] :
( ~ ( p @ SV15 )
| ~ ( p @ SY64 )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ ( enc @ ( i @ wk ) @ SY64 ) @ ( enc @ ( i @ lp ) @ SV15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(106,plain,
! [SV16: $i] :
( ( ! [SY66: $i] :
( ~ ( p @ SV16 )
| ~ ( p @ SY66 )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ SV16 @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(107,plain,
( ( p @ ( enc @ pp @ a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(108,plain,
! [SV17: $i,SV1: $i] :
( ( ( enc @ ( i @ SV1 ) @ ( enc @ SV1 @ SV17 ) )
= SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(109,plain,
! [SV18: $i,SV2: $i] :
( ( ( enc @ SV2 @ ( enc @ ( i @ SV2 ) @ SV18 ) )
= SV18 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(110,plain,
! [SV4: $i] :
( ( ( ~ ( p @ SV4 ) )
= $true )
| ( ( p @ ( i @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(111,plain,
! [SV19: $i,SV5: $i] :
( ( ~ ( p @ SV5 )
| ~ ( p @ SV19 )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ tmk @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ SV19 ) ) @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(112,plain,
! [SV20: $i,SV6: $i] :
( ( ~ ( p @ SV6 )
| ~ ( p @ SV20 )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ SV20 ) ) @ ( enc @ ( i @ tmk ) @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(113,plain,
! [SV7: $i] :
( ( ( ~ ( p @ SV7 )
| ! [V: $i] :
~ ( p @ V )
| ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ wk @ ( enc @ ( i @ tmk ) @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(114,plain,
! [SV21: $i,SV8: $i] :
( ( ~ ( p @ SV8 )
| ~ ( p @ SV21 )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ ( enc @ ( i @ tmk ) @ SV21 ) @ ( enc @ ( i @ tmk ) @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(115,plain,
! [SV22: $i,SV9: $i] :
( ( ~ ( p @ SV9 )
| ~ ( p @ SV22 )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ ( enc @ ( i @ tmk ) @ SV22 ) @ ( enc @ ( i @ tc ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(116,plain,
! [SV10: $i] :
( ( ( ~ ( p @ SV10 )
| ! [V: $i] :
~ ( p @ V )
| ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ tc @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(117,plain,
! [SV23: $i,SV11: $i] :
( ( ~ ( p @ SV11 )
| ~ ( p @ SV23 )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ ( enc @ ( i @ tc ) @ SV11 ) @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(118,plain,
! [SV24: $i,SV12: $i] :
( ( ~ ( p @ SV12 )
| ~ ( p @ SV24 )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ ( i @ ( enc @ ( i @ tc ) @ SV12 ) ) @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(119,plain,
! [SV25: $i,SV13: $i] :
( ( ! [SY74: $i] :
( ~ ( p @ SV13 )
| ~ ( p @ SV25 )
| ~ ( p @ SY74 )
| ( p @ ( enc @ ( enc @ ( i @ wk ) @ SY74 ) @ ( enc @ ( i @ ( enc @ ( i @ tmk ) @ SV25 ) ) @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(120,plain,
! [SV26: $i,SV14: $i] :
( ( ! [SY75: $i] :
( ~ ( p @ SV14 )
| ~ ( p @ SV26 )
| ~ ( p @ SY75 )
| ( p @ ( enc @ ( enc @ ( i @ wk ) @ SY75 ) @ ( enc @ ( i @ ( enc @ ( i @ wk ) @ SV26 ) ) @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(121,plain,
! [SV27: $i,SV15: $i] :
( ( ~ ( p @ SV15 )
| ~ ( p @ SV27 )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ ( enc @ ( i @ wk ) @ SV27 ) @ ( enc @ ( i @ lp ) @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(122,plain,
! [SV28: $i,SV16: $i] :
( ( ~ ( p @ SV16 )
| ~ ( p @ SV28 )
| ! [W: $i] :
~ ( p @ W )
| ( p @ ( enc @ SV16 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(123,plain,
! [SV4: $i] :
( ( ( p @ SV4 )
= $false )
| ( ( p @ ( i @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(124,plain,
! [SV19: $i,SV5: $i] :
( ( ( ~ ( p @ SV5 )
| ~ ( p @ SV19 )
| ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ tmk @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ SV19 ) ) @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(125,plain,
! [SV20: $i,SV6: $i] :
( ( ( ~ ( p @ SV6 )
| ~ ( p @ SV20 )
| ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ SV20 ) ) @ ( enc @ ( i @ tmk ) @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(126,plain,
! [SV7: $i] :
( ( ( ~ ( p @ SV7 )
| ! [V: $i] :
~ ( p @ V ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ wk @ ( enc @ ( i @ tmk ) @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(127,plain,
! [SV21: $i,SV8: $i] :
( ( ( ~ ( p @ SV8 )
| ~ ( p @ SV21 )
| ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ tmk ) @ SV21 ) @ ( enc @ ( i @ tmk ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(128,plain,
! [SV22: $i,SV9: $i] :
( ( ( ~ ( p @ SV9 )
| ~ ( p @ SV22 )
| ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ tmk ) @ SV22 ) @ ( enc @ ( i @ tc ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(129,plain,
! [SV10: $i] :
( ( ( ~ ( p @ SV10 )
| ! [V: $i] :
~ ( p @ V ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ tc @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(130,plain,
! [SV23: $i,SV11: $i] :
( ( ( ~ ( p @ SV11 )
| ~ ( p @ SV23 )
| ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ tc ) @ SV11 ) @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(131,plain,
! [SV24: $i,SV12: $i] :
( ( ( ~ ( p @ SV12 )
| ~ ( p @ SV24 )
| ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( i @ ( enc @ ( i @ tc ) @ SV12 ) ) @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(132,plain,
! [SV29: $i,SV25: $i,SV13: $i] :
( ( ~ ( p @ SV13 )
| ~ ( p @ SV25 )
| ~ ( p @ SV29 )
| ( p @ ( enc @ ( enc @ ( i @ wk ) @ SV29 ) @ ( enc @ ( i @ ( enc @ ( i @ tmk ) @ SV25 ) ) @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(133,plain,
! [SV30: $i,SV26: $i,SV14: $i] :
( ( ~ ( p @ SV14 )
| ~ ( p @ SV26 )
| ~ ( p @ SV30 )
| ( p @ ( enc @ ( enc @ ( i @ wk ) @ SV30 ) @ ( enc @ ( i @ ( enc @ ( i @ wk ) @ SV26 ) ) @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(134,plain,
! [SV27: $i,SV15: $i] :
( ( ( ~ ( p @ SV15 )
| ~ ( p @ SV27 )
| ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ wk ) @ SV27 ) @ ( enc @ ( i @ lp ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(135,plain,
! [SV28: $i,SV16: $i] :
( ( ( ~ ( p @ SV16 )
| ~ ( p @ SV28 )
| ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ SV16 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(136,plain,
! [SV19: $i,SV5: $i] :
( ( ( ~ ( p @ SV5 )
| ~ ( p @ SV19 ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ tmk @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ SV19 ) ) @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(137,plain,
! [SV20: $i,SV6: $i] :
( ( ( ~ ( p @ SV6 )
| ~ ( p @ SV20 ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ SV20 ) ) @ ( enc @ ( i @ tmk ) @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(138,plain,
! [SV7: $i] :
( ( ( ~ ( p @ SV7 ) )
= $true )
| ( ( ! [V: $i] :
~ ( p @ V ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ wk @ ( enc @ ( i @ tmk ) @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(139,plain,
! [SV21: $i,SV8: $i] :
( ( ( ~ ( p @ SV8 )
| ~ ( p @ SV21 ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ tmk ) @ SV21 ) @ ( enc @ ( i @ tmk ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(140,plain,
! [SV22: $i,SV9: $i] :
( ( ( ~ ( p @ SV9 )
| ~ ( p @ SV22 ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ tmk ) @ SV22 ) @ ( enc @ ( i @ tc ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(141,plain,
! [SV10: $i] :
( ( ( ~ ( p @ SV10 ) )
= $true )
| ( ( ! [V: $i] :
~ ( p @ V ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ tc @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(142,plain,
! [SV23: $i,SV11: $i] :
( ( ( ~ ( p @ SV11 )
| ~ ( p @ SV23 ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ tc ) @ SV11 ) @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(143,plain,
! [SV24: $i,SV12: $i] :
( ( ( ~ ( p @ SV12 )
| ~ ( p @ SV24 ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( i @ ( enc @ ( i @ tc ) @ SV12 ) ) @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(144,plain,
! [SV29: $i,SV25: $i,SV13: $i] :
( ( ( ~ ( p @ SV13 )
| ~ ( p @ SV25 )
| ~ ( p @ SV29 ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ wk ) @ SV29 ) @ ( enc @ ( i @ ( enc @ ( i @ tmk ) @ SV25 ) ) @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(145,plain,
! [SV30: $i,SV26: $i,SV14: $i] :
( ( ( ~ ( p @ SV14 )
| ~ ( p @ SV26 )
| ~ ( p @ SV30 ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ wk ) @ SV30 ) @ ( enc @ ( i @ ( enc @ ( i @ wk ) @ SV26 ) ) @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(146,plain,
! [SV27: $i,SV15: $i] :
( ( ( ~ ( p @ SV15 )
| ~ ( p @ SV27 ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ wk ) @ SV27 ) @ ( enc @ ( i @ lp ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(147,plain,
! [SV28: $i,SV16: $i] :
( ( ( ~ ( p @ SV16 )
| ~ ( p @ SV28 ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ SV16 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(148,plain,
! [SV19: $i,SV5: $i] :
( ( ( ~ ( p @ SV5 ) )
= $true )
| ( ( ~ ( p @ SV19 ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ tmk @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ SV19 ) ) @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(149,plain,
! [SV20: $i,SV6: $i] :
( ( ( ~ ( p @ SV6 ) )
= $true )
| ( ( ~ ( p @ SV20 ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ SV20 ) ) @ ( enc @ ( i @ tmk ) @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(150,plain,
! [SV7: $i] :
( ( ( p @ SV7 )
= $false )
| ( ( ! [V: $i] :
~ ( p @ V ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ wk @ ( enc @ ( i @ tmk ) @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(151,plain,
! [SV21: $i,SV8: $i] :
( ( ( ~ ( p @ SV8 ) )
= $true )
| ( ( ~ ( p @ SV21 ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ tmk ) @ SV21 ) @ ( enc @ ( i @ tmk ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(152,plain,
! [SV22: $i,SV9: $i] :
( ( ( ~ ( p @ SV9 ) )
= $true )
| ( ( ~ ( p @ SV22 ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ tmk ) @ SV22 ) @ ( enc @ ( i @ tc ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(153,plain,
! [SV10: $i] :
( ( ( p @ SV10 )
= $false )
| ( ( ! [V: $i] :
~ ( p @ V ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ tc @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(154,plain,
! [SV23: $i,SV11: $i] :
( ( ( ~ ( p @ SV11 ) )
= $true )
| ( ( ~ ( p @ SV23 ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ tc ) @ SV11 ) @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(155,plain,
! [SV24: $i,SV12: $i] :
( ( ( ~ ( p @ SV12 ) )
= $true )
| ( ( ~ ( p @ SV24 ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( i @ ( enc @ ( i @ tc ) @ SV12 ) ) @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(156,plain,
! [SV29: $i,SV25: $i,SV13: $i] :
( ( ( ~ ( p @ SV13 )
| ~ ( p @ SV25 ) )
= $true )
| ( ( ~ ( p @ SV29 ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ wk ) @ SV29 ) @ ( enc @ ( i @ ( enc @ ( i @ tmk ) @ SV25 ) ) @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(157,plain,
! [SV30: $i,SV26: $i,SV14: $i] :
( ( ( ~ ( p @ SV14 )
| ~ ( p @ SV26 ) )
= $true )
| ( ( ~ ( p @ SV30 ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ wk ) @ SV30 ) @ ( enc @ ( i @ ( enc @ ( i @ wk ) @ SV26 ) ) @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(158,plain,
! [SV27: $i,SV15: $i] :
( ( ( ~ ( p @ SV15 ) )
= $true )
| ( ( ~ ( p @ SV27 ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ wk ) @ SV27 ) @ ( enc @ ( i @ lp ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(159,plain,
! [SV28: $i,SV16: $i] :
( ( ( ~ ( p @ SV16 ) )
= $true )
| ( ( ~ ( p @ SV28 ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ SV16 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(160,plain,
! [SV19: $i,SV5: $i] :
( ( ( p @ SV5 )
= $false )
| ( ( ~ ( p @ SV19 ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ tmk @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ SV19 ) ) @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(161,plain,
! [SV20: $i,SV6: $i] :
( ( ( p @ SV6 )
= $false )
| ( ( ~ ( p @ SV20 ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ SV20 ) ) @ ( enc @ ( i @ tmk ) @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(162,plain,
! [SV7: $i,SV31: $i] :
( ( ( ~ ( p @ SV31 ) )
= $true )
| ( ( p @ SV7 )
= $false )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ wk @ ( enc @ ( i @ tmk ) @ SV7 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(163,plain,
! [SV21: $i,SV8: $i] :
( ( ( p @ SV8 )
= $false )
| ( ( ~ ( p @ SV21 ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ tmk ) @ SV21 ) @ ( enc @ ( i @ tmk ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(164,plain,
! [SV22: $i,SV9: $i] :
( ( ( p @ SV9 )
= $false )
| ( ( ~ ( p @ SV22 ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ tmk ) @ SV22 ) @ ( enc @ ( i @ tc ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(165,plain,
! [SV10: $i,SV32: $i] :
( ( ( ~ ( p @ SV32 ) )
= $true )
| ( ( p @ SV10 )
= $false )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ tc @ SV10 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(166,plain,
! [SV23: $i,SV11: $i] :
( ( ( p @ SV11 )
= $false )
| ( ( ~ ( p @ SV23 ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ tc ) @ SV11 ) @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(167,plain,
! [SV24: $i,SV12: $i] :
( ( ( p @ SV12 )
= $false )
| ( ( ~ ( p @ SV24 ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( i @ ( enc @ ( i @ tc ) @ SV12 ) ) @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(168,plain,
! [SV29: $i,SV25: $i,SV13: $i] :
( ( ( ~ ( p @ SV13 ) )
= $true )
| ( ( ~ ( p @ SV25 ) )
= $true )
| ( ( ~ ( p @ SV29 ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ wk ) @ SV29 ) @ ( enc @ ( i @ ( enc @ ( i @ tmk ) @ SV25 ) ) @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(169,plain,
! [SV30: $i,SV26: $i,SV14: $i] :
( ( ( ~ ( p @ SV14 ) )
= $true )
| ( ( ~ ( p @ SV26 ) )
= $true )
| ( ( ~ ( p @ SV30 ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ wk ) @ SV30 ) @ ( enc @ ( i @ ( enc @ ( i @ wk ) @ SV26 ) ) @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(170,plain,
! [SV27: $i,SV15: $i] :
( ( ( p @ SV15 )
= $false )
| ( ( ~ ( p @ SV27 ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ wk ) @ SV27 ) @ ( enc @ ( i @ lp ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(171,plain,
! [SV28: $i,SV16: $i] :
( ( ( p @ SV16 )
= $false )
| ( ( ~ ( p @ SV28 ) )
= $true )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ SV16 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(172,plain,
! [SV5: $i,SV19: $i] :
( ( ( p @ SV19 )
= $false )
| ( ( p @ SV5 )
= $false )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ tmk @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ SV19 ) ) @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(173,plain,
! [SV6: $i,SV20: $i] :
( ( ( p @ SV20 )
= $false )
| ( ( p @ SV6 )
= $false )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ SV20 ) ) @ ( enc @ ( i @ tmk ) @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(174,plain,
! [SV7: $i,SV31: $i] :
( ( ( p @ SV31 )
= $false )
| ( ( p @ SV7 )
= $false )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ wk @ ( enc @ ( i @ tmk ) @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(175,plain,
! [SV8: $i,SV21: $i] :
( ( ( p @ SV21 )
= $false )
| ( ( p @ SV8 )
= $false )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ tmk ) @ SV21 ) @ ( enc @ ( i @ tmk ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(176,plain,
! [SV9: $i,SV22: $i] :
( ( ( p @ SV22 )
= $false )
| ( ( p @ SV9 )
= $false )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ tmk ) @ SV22 ) @ ( enc @ ( i @ tc ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(177,plain,
! [SV10: $i,SV32: $i] :
( ( ( p @ SV32 )
= $false )
| ( ( p @ SV10 )
= $false )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ tc @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(178,plain,
! [SV11: $i,SV23: $i] :
( ( ( p @ SV23 )
= $false )
| ( ( p @ SV11 )
= $false )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ tc ) @ SV11 ) @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(179,plain,
! [SV12: $i,SV24: $i] :
( ( ( p @ SV24 )
= $false )
| ( ( p @ SV12 )
= $false )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( i @ ( enc @ ( i @ tc ) @ SV12 ) ) @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(180,plain,
! [SV29: $i,SV25: $i,SV13: $i] :
( ( ( p @ SV13 )
= $false )
| ( ( ~ ( p @ SV25 ) )
= $true )
| ( ( ~ ( p @ SV29 ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ wk ) @ SV29 ) @ ( enc @ ( i @ ( enc @ ( i @ tmk ) @ SV25 ) ) @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(181,plain,
! [SV30: $i,SV26: $i,SV14: $i] :
( ( ( p @ SV14 )
= $false )
| ( ( ~ ( p @ SV26 ) )
= $true )
| ( ( ~ ( p @ SV30 ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ wk ) @ SV30 ) @ ( enc @ ( i @ ( enc @ ( i @ wk ) @ SV26 ) ) @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(182,plain,
! [SV15: $i,SV27: $i] :
( ( ( p @ SV27 )
= $false )
| ( ( p @ SV15 )
= $false )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ wk ) @ SV27 ) @ ( enc @ ( i @ lp ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(183,plain,
! [SV16: $i,SV28: $i] :
( ( ( p @ SV28 )
= $false )
| ( ( p @ SV16 )
= $false )
| ( ( ! [W: $i] :
~ ( p @ W ) )
= $true )
| ( ( p @ ( enc @ SV16 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(184,plain,
! [SV19: $i,SV5: $i,SV33: $i] :
( ( ( ~ ( p @ SV33 ) )
= $true )
| ( ( p @ SV5 )
= $false )
| ( ( p @ SV19 )
= $false )
| ( ( p @ ( enc @ tmk @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ SV19 ) ) @ SV5 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(185,plain,
! [SV20: $i,SV6: $i,SV34: $i] :
( ( ( ~ ( p @ SV34 ) )
= $true )
| ( ( p @ SV6 )
= $false )
| ( ( p @ SV20 )
= $false )
| ( ( p @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ SV20 ) ) @ ( enc @ ( i @ tmk ) @ SV6 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(186,plain,
! [SV31: $i,SV7: $i,SV35: $i] :
( ( ( ~ ( p @ SV35 ) )
= $true )
| ( ( p @ SV7 )
= $false )
| ( ( p @ SV31 )
= $false )
| ( ( p @ ( enc @ wk @ ( enc @ ( i @ tmk ) @ SV7 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(187,plain,
! [SV21: $i,SV8: $i,SV36: $i] :
( ( ( ~ ( p @ SV36 ) )
= $true )
| ( ( p @ SV8 )
= $false )
| ( ( p @ SV21 )
= $false )
| ( ( p @ ( enc @ ( enc @ ( i @ tmk ) @ SV21 ) @ ( enc @ ( i @ tmk ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(188,plain,
! [SV22: $i,SV9: $i,SV37: $i] :
( ( ( ~ ( p @ SV37 ) )
= $true )
| ( ( p @ SV9 )
= $false )
| ( ( p @ SV22 )
= $false )
| ( ( p @ ( enc @ ( enc @ ( i @ tmk ) @ SV22 ) @ ( enc @ ( i @ tc ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(189,plain,
! [SV32: $i,SV10: $i,SV38: $i] :
( ( ( ~ ( p @ SV38 ) )
= $true )
| ( ( p @ SV10 )
= $false )
| ( ( p @ SV32 )
= $false )
| ( ( p @ ( enc @ tc @ SV10 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(190,plain,
! [SV23: $i,SV11: $i,SV39: $i] :
( ( ( ~ ( p @ SV39 ) )
= $true )
| ( ( p @ SV11 )
= $false )
| ( ( p @ SV23 )
= $false )
| ( ( p @ ( enc @ ( enc @ ( i @ tc ) @ SV11 ) @ SV23 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(191,plain,
! [SV24: $i,SV12: $i,SV40: $i] :
( ( ( ~ ( p @ SV40 ) )
= $true )
| ( ( p @ SV12 )
= $false )
| ( ( p @ SV24 )
= $false )
| ( ( p @ ( enc @ ( i @ ( enc @ ( i @ tc ) @ SV12 ) ) @ SV24 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(192,plain,
! [SV29: $i,SV13: $i,SV25: $i] :
( ( ( p @ SV25 )
= $false )
| ( ( p @ SV13 )
= $false )
| ( ( ~ ( p @ SV29 ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ wk ) @ SV29 ) @ ( enc @ ( i @ ( enc @ ( i @ tmk ) @ SV25 ) ) @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(193,plain,
! [SV30: $i,SV14: $i,SV26: $i] :
( ( ( p @ SV26 )
= $false )
| ( ( p @ SV14 )
= $false )
| ( ( ~ ( p @ SV30 ) )
= $true )
| ( ( p @ ( enc @ ( enc @ ( i @ wk ) @ SV30 ) @ ( enc @ ( i @ ( enc @ ( i @ wk ) @ SV26 ) ) @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(194,plain,
! [SV27: $i,SV15: $i,SV41: $i] :
( ( ( ~ ( p @ SV41 ) )
= $true )
| ( ( p @ SV15 )
= $false )
| ( ( p @ SV27 )
= $false )
| ( ( p @ ( enc @ ( enc @ ( i @ wk ) @ SV27 ) @ ( enc @ ( i @ lp ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(195,plain,
! [SV28: $i,SV16: $i,SV42: $i] :
( ( ( ~ ( p @ SV42 ) )
= $true )
| ( ( p @ SV16 )
= $false )
| ( ( p @ SV28 )
= $false )
| ( ( p @ ( enc @ SV16 @ SV28 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(196,plain,
! [SV19: $i,SV5: $i,SV33: $i] :
( ( ( p @ SV33 )
= $false )
| ( ( p @ SV5 )
= $false )
| ( ( p @ SV19 )
= $false )
| ( ( p @ ( enc @ tmk @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ SV19 ) ) @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(197,plain,
! [SV20: $i,SV6: $i,SV34: $i] :
( ( ( p @ SV34 )
= $false )
| ( ( p @ SV6 )
= $false )
| ( ( p @ SV20 )
= $false )
| ( ( p @ ( enc @ ( i @ ( enc @ ( i @ zcmk ) @ SV20 ) ) @ ( enc @ ( i @ tmk ) @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(198,plain,
! [SV31: $i,SV7: $i,SV35: $i] :
( ( ( p @ SV35 )
= $false )
| ( ( p @ SV7 )
= $false )
| ( ( p @ SV31 )
= $false )
| ( ( p @ ( enc @ wk @ ( enc @ ( i @ tmk ) @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(199,plain,
! [SV21: $i,SV8: $i,SV36: $i] :
( ( ( p @ SV36 )
= $false )
| ( ( p @ SV8 )
= $false )
| ( ( p @ SV21 )
= $false )
| ( ( p @ ( enc @ ( enc @ ( i @ tmk ) @ SV21 ) @ ( enc @ ( i @ tmk ) @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(200,plain,
! [SV22: $i,SV9: $i,SV37: $i] :
( ( ( p @ SV37 )
= $false )
| ( ( p @ SV9 )
= $false )
| ( ( p @ SV22 )
= $false )
| ( ( p @ ( enc @ ( enc @ ( i @ tmk ) @ SV22 ) @ ( enc @ ( i @ tc ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(201,plain,
! [SV32: $i,SV10: $i,SV38: $i] :
( ( ( p @ SV38 )
= $false )
| ( ( p @ SV10 )
= $false )
| ( ( p @ SV32 )
= $false )
| ( ( p @ ( enc @ tc @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(202,plain,
! [SV23: $i,SV11: $i,SV39: $i] :
( ( ( p @ SV39 )
= $false )
| ( ( p @ SV11 )
= $false )
| ( ( p @ SV23 )
= $false )
| ( ( p @ ( enc @ ( enc @ ( i @ tc ) @ SV11 ) @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(203,plain,
! [SV24: $i,SV12: $i,SV40: $i] :
( ( ( p @ SV40 )
= $false )
| ( ( p @ SV12 )
= $false )
| ( ( p @ SV24 )
= $false )
| ( ( p @ ( enc @ ( i @ ( enc @ ( i @ tc ) @ SV12 ) ) @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(204,plain,
! [SV25: $i,SV13: $i,SV29: $i] :
( ( ( p @ SV29 )
= $false )
| ( ( p @ SV13 )
= $false )
| ( ( p @ SV25 )
= $false )
| ( ( p @ ( enc @ ( enc @ ( i @ wk ) @ SV29 ) @ ( enc @ ( i @ ( enc @ ( i @ tmk ) @ SV25 ) ) @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(205,plain,
! [SV26: $i,SV14: $i,SV30: $i] :
( ( ( p @ SV30 )
= $false )
| ( ( p @ SV14 )
= $false )
| ( ( p @ SV26 )
= $false )
| ( ( p @ ( enc @ ( enc @ ( i @ wk ) @ SV30 ) @ ( enc @ ( i @ ( enc @ ( i @ wk ) @ SV26 ) ) @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(206,plain,
! [SV27: $i,SV15: $i,SV41: $i] :
( ( ( p @ SV41 )
= $false )
| ( ( p @ SV15 )
= $false )
| ( ( p @ SV27 )
= $false )
| ( ( p @ ( enc @ ( enc @ ( i @ wk ) @ SV27 ) @ ( enc @ ( i @ lp ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(207,plain,
! [SV28: $i,SV16: $i,SV42: $i] :
( ( ( p @ SV42 )
= $false )
| ( ( p @ SV16 )
= $false )
| ( ( p @ SV28 )
= $false )
| ( ( p @ ( enc @ SV16 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(208,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[82,207,206,205,204,203,202,201,200,199,198,197,196,123,109,108,107,93,89,88,87,86,85,84,83]) ).
thf(209,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWV237+1 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 16 01:07:19 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.37
% 0.13/0.37 No.of.Axioms: 24
% 0.13/0.37
% 0.13/0.37 Length.of.Defs: 0
% 0.13/0.37
% 0.13/0.37 Contains.Choice.Funs: false
% 0.13/0.39 (rf:0,axioms:24,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:26,loop_count:0,foatp_calls:0,translation:fof_full)...........
% 0.56/0.72
% 0.56/0.72 ********************************
% 0.56/0.72 * All subproblems solved! *
% 0.56/0.72 ********************************
% 0.56/0.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:24,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:208,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.56/0.73
% 0.56/0.73 %**** Beginning of derivation protocol ****
% 0.56/0.73 % SZS output start CNFRefutation
% See solution above
% 0.56/0.73
% 0.56/0.73 %**** End of derivation protocol ****
% 0.56/0.73 %**** no. of clauses in derivation: 209 ****
% 0.56/0.73 %**** clause counter: 208 ****
% 0.56/0.73
% 0.56/0.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:24,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:208,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------