%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV105+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:54:52 AM UTC 2026
% Result : Theorem 1.50s 0.50s
% Output : CNFRefutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 25
% Syntax : Number of formulae : 241 ( 139 unt; 0 typ; 0 def)
% Number of atoms : 1413 ( 567 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 2380 ( 436 ~; 358 |; 30 &;1502 @)
% ( 9 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 37 usr; 16 con; 0-4 aty)
% Number of variables : 517 ( 0 ^; 517 !; 0 ?; 517 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a_select2,type,
a_select2: $i > $i > $i ).
thf(tp_a_select3,type,
a_select3: $i > $i > $i > $i ).
thf(tp_def,type,
def: $i ).
thf(tp_dim,type,
dim: $i > $i > $i ).
thf(tp_geq,type,
geq: $i > $i > $o ).
thf(tp_gt,type,
gt: $i > $i > $o ).
thf(tp_inv,type,
inv: $i > $i ).
thf(tp_leq,type,
leq: $i > $i > $o ).
thf(tp_lt,type,
lt: $i > $i > $o ).
thf(tp_minus,type,
minus: $i > $i > $i ).
thf(tp_n0,type,
n0: $i ).
thf(tp_n1,type,
n1: $i ).
thf(tp_n2,type,
n2: $i ).
thf(tp_n3,type,
n3: $i ).
thf(tp_n4,type,
n4: $i ).
thf(tp_n5,type,
n5: $i ).
thf(tp_n6,type,
n6: $i ).
thf(tp_plus,type,
plus: $i > $i > $i ).
thf(tp_pred,type,
pred: $i > $i ).
thf(tp_pv43,type,
pv43: $i ).
thf(tp_sK1_SY73,type,
sK1_SY73: $i > $i > $i > $i > $i ).
thf(tp_sigma,type,
sigma: $i ).
thf(tp_succ,type,
succ: $i > $i ).
thf(tp_sum,type,
sum: $i > $i > $i > $i ).
thf(tp_tptp_const_array1,type,
tptp_const_array1: $i > $i > $i ).
thf(tp_tptp_const_array2,type,
tptp_const_array2: $i > $i > $i > $i ).
thf(tp_tptp_float_0_0,type,
tptp_float_0_0: $i ).
thf(tp_tptp_madd,type,
tptp_madd: $i > $i > $i ).
thf(tp_tptp_minus_1,type,
tptp_minus_1: $i ).
thf(tp_tptp_mmul,type,
tptp_mmul: $i > $i > $i ).
thf(tp_tptp_msub,type,
tptp_msub: $i > $i > $i ).
thf(tp_tptp_update2,type,
tptp_update2: $i > $i > $i > $i ).
thf(tp_tptp_update3,type,
tptp_update3: $i > $i > $i > $i > $i ).
thf(tp_trans,type,
trans: $i > $i ).
thf(tp_true,type,
true: $o ).
thf(tp_uniform_int_rnd,type,
uniform_int_rnd: $i > $i > $i ).
thf(tp_use,type,
use: $i ).
thf(3,axiom,
( ( succ @ n0 )
= n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_1) ).
thf(4,axiom,
( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) ) )
= n6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_6) ).
thf(8,axiom,
! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n2 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_2) ).
thf(9,axiom,
! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_1) ).
thf(10,axiom,
! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_0) ).
thf(23,axiom,
gt @ n6 @ n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_6_1) ).
thf(28,axiom,
gt @ n1 @ n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_1_0) ).
thf(29,axiom,
gt @ n6 @ n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_6_0) ).
thf(43,axiom,
true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ttrue) ).
thf(44,axiom,
! [I: $i,U: $i,X: $i,VAL: $i] :
( ( ! [I0: $i] :
( ( ( leq @ n0 @ I0 )
& ( leq @ I0 @ U ) )
=> ( ( a_select2 @ X @ I0 )
= VAL ) )
& ( leq @ n0 @ I )
& ( leq @ I @ U ) )
=> ( ( a_select2 @ ( tptp_update2 @ X @ U @ VAL ) @ I )
= VAL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sel2_update_3) ).
thf(45,axiom,
! [I: $i,U: $i,X: $i,VAL: $i,VAL2: $i] :
( ( ( I != U )
& ( ( a_select2 @ X @ U )
= VAL ) )
=> ( ( a_select2 @ ( tptp_update2 @ X @ I @ VAL2 ) @ U )
= VAL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sel2_update_2) ).
thf(46,axiom,
! [X: $i,U: $i,VAL: $i] :
( ( a_select2 @ ( tptp_update2 @ X @ U @ VAL ) @ U )
= VAL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sel2_update_1) ).
thf(50,axiom,
! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_minus) ).
thf(52,axiom,
! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_succ) ).
thf(55,axiom,
! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pred_minus_1) ).
thf(79,axiom,
! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniform_int_rand_ranges_lo) ).
thf(80,axiom,
! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniform_int_rand_ranges_hi) ).
thf(82,axiom,
! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ) ).
thf(85,axiom,
! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt2) ).
thf(86,axiom,
! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt1) ).
thf(87,axiom,
! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_geq) ).
thf(88,axiom,
! [X: $i,Y: $i] :
( ( lt @ X @ Y )
<=> ( gt @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lt_gt) ).
thf(89,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_leq) ).
thf(90,axiom,
! [X: $i] : ( leq @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_leq) ).
thf(94,conjecture,
( ( ( leq @ n0 @ pv43 )
& ( leq @ pv43 @ ( minus @ n6 @ n1 ) ) )
=> ( ( lt @ n0 @ ( a_select2 @ sigma @ pv43 ) )
=> true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_inuse_0017) ).
thf(95,negated_conjecture,
( ( ( ( leq @ n0 @ pv43 )
& ( leq @ pv43 @ ( minus @ n6 @ n1 ) ) )
=> ( ( lt @ n0 @ ( a_select2 @ sigma @ pv43 ) )
=> true ) )
= $false ),
inference(negate_conjecture,[status(cth)],[94]) ).
thf(96,plain,
( ( ( ( leq @ n0 @ pv43 )
& ( leq @ pv43 @ ( minus @ n6 @ n1 ) ) )
=> ( ( lt @ n0 @ ( a_select2 @ sigma @ pv43 ) )
=> true ) )
= $false ),
inference(unfold_def,[status(thm)],[95]) ).
thf(97,plain,
( ( ( succ @ n0 )
= n1 )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(98,plain,
( ( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) ) )
= n6 )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(99,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n2 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(100,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(101,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(102,plain,
( ( gt @ n6 @ n1 )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(103,plain,
( ( gt @ n1 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(104,plain,
( ( gt @ n6 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(105,plain,
true = $true,
inference(unfold_def,[status(thm)],[43]) ).
thf(106,plain,
( ( ! [I: $i,U: $i,X: $i,VAL: $i] :
( ( ! [I0: $i] :
( ( ( leq @ n0 @ I0 )
& ( leq @ I0 @ U ) )
=> ( ( a_select2 @ X @ I0 )
= VAL ) )
& ( leq @ n0 @ I )
& ( leq @ I @ U ) )
=> ( ( a_select2 @ ( tptp_update2 @ X @ U @ VAL ) @ I )
= VAL ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(107,plain,
( ( ! [I: $i,U: $i,X: $i,VAL: $i,VAL2: $i] :
( ( ( I != U )
& ( ( a_select2 @ X @ U )
= VAL ) )
=> ( ( a_select2 @ ( tptp_update2 @ X @ I @ VAL2 ) @ U )
= VAL ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(108,plain,
( ( ! [X: $i,U: $i,VAL: $i] :
( ( a_select2 @ ( tptp_update2 @ X @ U @ VAL ) @ U )
= VAL ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(109,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(110,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(111,plain,
( ( ! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(112,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(113,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(114,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(115,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(116,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(117,plain,
( ( ! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(118,plain,
( ( ! [X: $i,Y: $i] :
( ( lt @ X @ Y )
<=> ( gt @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(119,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(120,plain,
( ( ! [X: $i] : ( leq @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(121,plain,
( ( leq @ n0 @ pv43 )
= $true ),
inference(standard_cnf,[status(thm)],[96]) ).
thf(122,plain,
( ( leq @ pv43 @ ( minus @ n6 @ n1 ) )
= $true ),
inference(standard_cnf,[status(thm)],[96]) ).
thf(123,plain,
( ( lt @ n0 @ ( a_select2 @ sigma @ pv43 ) )
= $true ),
inference(standard_cnf,[status(thm)],[96]) ).
thf(124,plain,
true = $false,
inference(standard_cnf,[status(thm)],[96]) ).
thf(125,plain,
( ( ~ true ) = $true ),
inference(polarity_switch,[status(thm)],[124]) ).
thf(126,plain,
( ( ! [X: $i] : ( leq @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(127,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(128,plain,
( ( ! [X: $i,Y: $i] :
( ( lt @ X @ Y )
<=> ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(129,plain,
( ( ! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(130,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(131,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(132,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(133,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(134,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(135,plain,
( ( ! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(136,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(137,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(138,plain,
( ( ! [X: $i,U: $i,VAL: $i] :
( ( a_select2 @ ( tptp_update2 @ X @ U @ VAL ) @ U )
= VAL ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(139,plain,
( ( ! [I: $i,U: $i,X: $i,VAL: $i,VAL2: $i] :
( ( ( I != U )
& ( ( a_select2 @ X @ U )
= VAL ) )
=> ( ( a_select2 @ ( tptp_update2 @ X @ I @ VAL2 ) @ U )
= VAL ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(140,plain,
( ( ! [I: $i,U: $i,X: $i,VAL: $i] :
( ( ! [I0: $i] :
( ( ( leq @ n0 @ I0 )
& ( leq @ I0 @ U ) )
=> ( ( a_select2 @ X @ I0 )
= VAL ) )
& ( leq @ n0 @ I )
& ( leq @ I @ U ) )
=> ( ( a_select2 @ ( tptp_update2 @ X @ U @ VAL ) @ I )
= VAL ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(141,plain,
true = $true,
inference(copy,[status(thm)],[105]) ).
thf(142,plain,
( ( gt @ n6 @ n0 )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(143,plain,
( ( gt @ n1 @ n0 )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(144,plain,
( ( gt @ n6 @ n1 )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(145,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(146,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(147,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n2 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(148,plain,
( ( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) ) )
= n6 )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(149,plain,
( ( ( succ @ n0 )
= n1 )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(150,plain,
( ( lt @ n0 @ ( a_select2 @ sigma @ pv43 ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(151,plain,
( ( leq @ pv43 @ ( minus @ n6 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(152,plain,
( ( leq @ n0 @ pv43 )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(153,plain,
( ( ~ true ) = $true ),
inference(copy,[status(thm)],[125]) ).
thf(154,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n2 ) )
| ( SX0 = n0 )
| ( SX0 = n1 )
| ( SX0 = n2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(155,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ~ ( ( SX0 != SX1 ) )
| ( ( a_select2 @ SX2 @ SX1 )
!= SX3 ) )
| ( ( a_select2 @ ( tptp_update2 @ SX2 @ SX0 @ SX4 ) @ SX1 )
= SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(156,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( leq @ SX0 @ ( succ @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(157,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n1 ) )
| ( SX0 = n0 )
| ( SX0 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(158,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ n0 @ ( uniform_int_rnd @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(159,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( lt @ SX0 @ SX1 )
| ( gt @ SX1 @ SX0 ) )
| ~ ( ~ ( gt @ SX1 @ SX0 )
| ( lt @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(160,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ ( uniform_int_rnd @ SX1 @ SX0 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(161,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( gt @ SX1 @ SX0 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(162,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( geq @ SX0 @ SX1 )
| ( leq @ SX1 @ SX0 ) )
| ~ ( ~ ( leq @ SX1 @ SX0 )
| ( geq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(163,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( leq @ ( succ @ SX0 ) @ ( succ @ SX1 ) )
| ( leq @ SX0 @ SX1 ) )
| ~ ( ~ ( leq @ SX0 @ SX1 )
| ( leq @ ( succ @ SX0 ) @ ( succ @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(164,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( leq @ SX1 @ SX2 ) )
| ( leq @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(165,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ ( minus @ SX0 @ SX1 ) @ SX0 )
| ( leq @ n0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(166,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( gt @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(167,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ~ ( ~ ! [SX4: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX4 )
| ~ ( leq @ SX4 @ SX1 ) )
| ( ( a_select2 @ SX2 @ SX4 )
= SX3 ) )
| ~ ( leq @ n0 @ SX0 ) )
| ~ ( leq @ SX0 @ SX1 ) )
| ( ( a_select2 @ ( tptp_update2 @ SX2 @ SX1 @ SX3 ) @ SX0 )
= SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(168,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n0 ) )
| ( SX0 = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(169,plain,
! [SV1: $i] :
( ( leq @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(170,plain,
! [SV2: $i] :
( ( ( minus @ SV2 @ n1 )
= ( pred @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(171,plain,
! [SV3: $i] :
( ( ! [SY39: $i,SY40: $i] :
( ( a_select2 @ ( tptp_update2 @ SV3 @ SY39 @ SY40 ) @ SY39 )
= SY40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(172,plain,
true = $false,
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(173,plain,
! [SV4: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV4 )
| ~ ( leq @ SV4 @ n2 ) )
| ( SV4 = n0 )
| ( SV4 = n1 )
| ( SV4 = n2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(174,plain,
! [SV5: $i] :
( ( ! [SY41: $i,SY42: $i,SY43: $i,SY44: $i] :
( ~ ~ ( ~ ( ( SV5 != SY41 ) )
| ( ( a_select2 @ SY42 @ SY41 )
!= SY43 ) )
| ( ( a_select2 @ ( tptp_update2 @ SY42 @ SV5 @ SY44 ) @ SY41 )
= SY43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(175,plain,
! [SV6: $i] :
( ( ! [SY45: $i] :
( ~ ( leq @ SV6 @ SY45 )
| ( leq @ SV6 @ ( succ @ SY45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(176,plain,
! [SV7: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV7 )
| ~ ( leq @ SV7 @ n1 ) )
| ( SV7 = n0 )
| ( SV7 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(177,plain,
! [SV8: $i] :
( ( ! [SY46: $i] :
( ~ ( leq @ n0 @ SV8 )
| ( leq @ n0 @ ( uniform_int_rnd @ SY46 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(178,plain,
! [SV9: $i] :
( ( ! [SY47: $i] :
~ ( ~ ( ~ ( lt @ SV9 @ SY47 )
| ( gt @ SY47 @ SV9 ) )
| ~ ( ~ ( gt @ SY47 @ SV9 )
| ( lt @ SV9 @ SY47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(179,plain,
! [SV10: $i] :
( ( ! [SY48: $i] :
( ~ ( leq @ n0 @ SV10 )
| ( leq @ ( uniform_int_rnd @ SY48 @ SV10 ) @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(180,plain,
! [SV11: $i] :
( ( ! [SY49: $i] :
( ~ ( gt @ SY49 @ SV11 )
| ( leq @ SV11 @ SY49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(181,plain,
! [SV12: $i] :
( ( ! [SY50: $i] :
~ ( ~ ( ~ ( geq @ SV12 @ SY50 )
| ( leq @ SY50 @ SV12 ) )
| ~ ( ~ ( leq @ SY50 @ SV12 )
| ( geq @ SV12 @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(182,plain,
! [SV13: $i] :
( ( ! [SY51: $i] :
~ ( ~ ( ~ ( leq @ ( succ @ SV13 ) @ ( succ @ SY51 ) )
| ( leq @ SV13 @ SY51 ) )
| ~ ( ~ ( leq @ SV13 @ SY51 )
| ( leq @ ( succ @ SV13 ) @ ( succ @ SY51 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(183,plain,
! [SV14: $i] :
( ( ! [SY52: $i,SY53: $i] :
( ~ ~ ( ~ ( leq @ SV14 @ SY52 )
| ~ ( leq @ SY52 @ SY53 ) )
| ( leq @ SV14 @ SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(184,plain,
! [SV15: $i] :
( ( ! [SY54: $i] :
( ~ ( leq @ ( minus @ SV15 @ SY54 ) @ SV15 )
| ( leq @ n0 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(185,plain,
! [SV16: $i] :
( ( ! [SY55: $i] :
( ~ ~ ( ~ ( leq @ SV16 @ SY55 )
| ~ ( ( SV16 != SY55 ) ) )
| ( gt @ SY55 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(186,plain,
! [SV17: $i] :
( ( ! [SY56: $i,SY57: $i,SY58: $i] :
( ~ ~ ( ~ ~ ( ~ ! [SX4: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX4 )
| ~ ( leq @ SX4 @ SY56 ) )
| ( ( a_select2 @ SY57 @ SX4 )
= SY58 ) )
| ~ ( leq @ n0 @ SV17 ) )
| ~ ( leq @ SV17 @ SY56 ) )
| ( ( a_select2 @ ( tptp_update2 @ SY57 @ SY56 @ SY58 ) @ SV17 )
= SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(187,plain,
! [SV18: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV18 )
| ~ ( leq @ SV18 @ n0 ) )
| ( SV18 = n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(188,plain,
! [SV19: $i,SV3: $i] :
( ( ! [SY60: $i] :
( ( a_select2 @ ( tptp_update2 @ SV3 @ SV19 @ SY60 ) @ SV19 )
= SY60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(189,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV4 )
| ~ ( leq @ SV4 @ n2 ) ) )
= $true )
| ( ( ( SV4 = n0 )
| ( SV4 = n1 )
| ( SV4 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(190,plain,
! [SV20: $i,SV5: $i] :
( ( ! [SY61: $i,SY62: $i,SY63: $i] :
( ~ ~ ( ~ ( ( SV5 != SV20 ) )
| ( ( a_select2 @ SY61 @ SV20 )
!= SY62 ) )
| ( ( a_select2 @ ( tptp_update2 @ SY61 @ SV5 @ SY63 ) @ SV20 )
= SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(191,plain,
! [SV21: $i,SV6: $i] :
( ( ~ ( leq @ SV6 @ SV21 )
| ( leq @ SV6 @ ( succ @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(192,plain,
! [SV7: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV7 )
| ~ ( leq @ SV7 @ n1 ) ) )
= $true )
| ( ( ( SV7 = n0 )
| ( SV7 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(193,plain,
! [SV22: $i,SV8: $i] :
( ( ~ ( leq @ n0 @ SV8 )
| ( leq @ n0 @ ( uniform_int_rnd @ SV22 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(194,plain,
! [SV23: $i,SV9: $i] :
( ( ~ ( ~ ( ~ ( lt @ SV9 @ SV23 )
| ( gt @ SV23 @ SV9 ) )
| ~ ( ~ ( gt @ SV23 @ SV9 )
| ( lt @ SV9 @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(195,plain,
! [SV24: $i,SV10: $i] :
( ( ~ ( leq @ n0 @ SV10 )
| ( leq @ ( uniform_int_rnd @ SV24 @ SV10 ) @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(196,plain,
! [SV11: $i,SV25: $i] :
( ( ~ ( gt @ SV25 @ SV11 )
| ( leq @ SV11 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(197,plain,
! [SV26: $i,SV12: $i] :
( ( ~ ( ~ ( ~ ( geq @ SV12 @ SV26 )
| ( leq @ SV26 @ SV12 ) )
| ~ ( ~ ( leq @ SV26 @ SV12 )
| ( geq @ SV12 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(198,plain,
! [SV27: $i,SV13: $i] :
( ( ~ ( ~ ( ~ ( leq @ ( succ @ SV13 ) @ ( succ @ SV27 ) )
| ( leq @ SV13 @ SV27 ) )
| ~ ( ~ ( leq @ SV13 @ SV27 )
| ( leq @ ( succ @ SV13 ) @ ( succ @ SV27 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(199,plain,
! [SV28: $i,SV14: $i] :
( ( ! [SY64: $i] :
( ~ ~ ( ~ ( leq @ SV14 @ SV28 )
| ~ ( leq @ SV28 @ SY64 ) )
| ( leq @ SV14 @ SY64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(200,plain,
! [SV29: $i,SV15: $i] :
( ( ~ ( leq @ ( minus @ SV15 @ SV29 ) @ SV15 )
| ( leq @ n0 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(201,plain,
! [SV30: $i,SV16: $i] :
( ( ~ ~ ( ~ ( leq @ SV16 @ SV30 )
| ~ ( ( SV16 != SV30 ) ) )
| ( gt @ SV30 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(202,plain,
! [SV17: $i,SV31: $i] :
( ( ! [SY65: $i,SY66: $i] :
( ~ ~ ( ~ ~ ( ~ ! [SY67: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SY67 )
| ~ ( leq @ SY67 @ SV31 ) )
| ( ( a_select2 @ SY65 @ SY67 )
= SY66 ) )
| ~ ( leq @ n0 @ SV17 ) )
| ~ ( leq @ SV17 @ SV31 ) )
| ( ( a_select2 @ ( tptp_update2 @ SY65 @ SV31 @ SY66 ) @ SV17 )
= SY66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(203,plain,
! [SV18: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV18 )
| ~ ( leq @ SV18 @ n0 ) ) )
= $true )
| ( ( SV18 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(204,plain,
! [SV32: $i,SV19: $i,SV3: $i] :
( ( ( a_select2 @ ( tptp_update2 @ SV3 @ SV19 @ SV32 ) @ SV19 )
= SV32 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(205,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV4 )
| ~ ( leq @ SV4 @ n2 ) ) )
= $false )
| ( ( ( SV4 = n0 )
| ( SV4 = n1 )
| ( SV4 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(206,plain,
! [SV33: $i,SV20: $i,SV5: $i] :
( ( ! [SY68: $i,SY69: $i] :
( ~ ~ ( ~ ( ( SV5 != SV20 ) )
| ( ( a_select2 @ SV33 @ SV20 )
!= SY68 ) )
| ( ( a_select2 @ ( tptp_update2 @ SV33 @ SV5 @ SY69 ) @ SV20 )
= SY68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(207,plain,
! [SV21: $i,SV6: $i] :
( ( ( ~ ( leq @ SV6 @ SV21 ) )
= $true )
| ( ( leq @ SV6 @ ( succ @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(208,plain,
! [SV7: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV7 )
| ~ ( leq @ SV7 @ n1 ) ) )
= $false )
| ( ( ( SV7 = n0 )
| ( SV7 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(209,plain,
! [SV22: $i,SV8: $i] :
( ( ( ~ ( leq @ n0 @ SV8 ) )
= $true )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV22 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(210,plain,
! [SV23: $i,SV9: $i] :
( ( ~ ( ~ ( lt @ SV9 @ SV23 )
| ( gt @ SV23 @ SV9 ) )
| ~ ( ~ ( gt @ SV23 @ SV9 )
| ( lt @ SV9 @ SV23 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(211,plain,
! [SV24: $i,SV10: $i] :
( ( ( ~ ( leq @ n0 @ SV10 ) )
= $true )
| ( ( leq @ ( uniform_int_rnd @ SV24 @ SV10 ) @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(212,plain,
! [SV11: $i,SV25: $i] :
( ( ( ~ ( gt @ SV25 @ SV11 ) )
= $true )
| ( ( leq @ SV11 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(213,plain,
! [SV26: $i,SV12: $i] :
( ( ~ ( ~ ( geq @ SV12 @ SV26 )
| ( leq @ SV26 @ SV12 ) )
| ~ ( ~ ( leq @ SV26 @ SV12 )
| ( geq @ SV12 @ SV26 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(214,plain,
! [SV27: $i,SV13: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV13 ) @ ( succ @ SV27 ) )
| ( leq @ SV13 @ SV27 ) )
| ~ ( ~ ( leq @ SV13 @ SV27 )
| ( leq @ ( succ @ SV13 ) @ ( succ @ SV27 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(215,plain,
! [SV34: $i,SV28: $i,SV14: $i] :
( ( ~ ~ ( ~ ( leq @ SV14 @ SV28 )
| ~ ( leq @ SV28 @ SV34 ) )
| ( leq @ SV14 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(216,plain,
! [SV29: $i,SV15: $i] :
( ( ( ~ ( leq @ ( minus @ SV15 @ SV29 ) @ SV15 ) )
= $true )
| ( ( leq @ n0 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(217,plain,
! [SV30: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV16 @ SV30 )
| ~ ( ( SV16 != SV30 ) ) ) )
= $true )
| ( ( gt @ SV30 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(218,plain,
! [SV17: $i,SV35: $i,SV31: $i] :
( ( ! [SY70: $i] :
( ~ ~ ( ~ ~ ( ~ ! [SY71: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SY71 )
| ~ ( leq @ SY71 @ SV31 ) )
| ( ( a_select2 @ SV35 @ SY71 )
= SY70 ) )
| ~ ( leq @ n0 @ SV17 ) )
| ~ ( leq @ SV17 @ SV31 ) )
| ( ( a_select2 @ ( tptp_update2 @ SV35 @ SV31 @ SY70 ) @ SV17 )
= SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(219,plain,
! [SV18: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV18 )
| ~ ( leq @ SV18 @ n0 ) ) )
= $false )
| ( ( SV18 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(220,plain,
! [SV4: $i] :
( ( ( ~ ( leq @ n0 @ SV4 )
| ~ ( leq @ SV4 @ n2 ) )
= $true )
| ( ( ( SV4 = n0 )
| ( SV4 = n1 )
| ( SV4 = n2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(221,plain,
! [SV36: $i,SV33: $i,SV20: $i,SV5: $i] :
( ( ! [SY72: $i] :
( ~ ~ ( ~ ( ( SV5 != SV20 ) )
| ( ( a_select2 @ SV33 @ SV20 )
!= SV36 ) )
| ( ( a_select2 @ ( tptp_update2 @ SV33 @ SV5 @ SY72 ) @ SV20 )
= SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(222,plain,
! [SV21: $i,SV6: $i] :
( ( ( leq @ SV6 @ SV21 )
= $false )
| ( ( leq @ SV6 @ ( succ @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(223,plain,
! [SV7: $i] :
( ( ( ~ ( leq @ n0 @ SV7 )
| ~ ( leq @ SV7 @ n1 ) )
= $true )
| ( ( ( SV7 = n0 )
| ( SV7 = n1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(224,plain,
! [SV22: $i,SV8: $i] :
( ( ( leq @ n0 @ SV8 )
= $false )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV22 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(225,plain,
! [SV23: $i,SV9: $i] :
( ( ~ ( ~ ( lt @ SV9 @ SV23 )
| ( gt @ SV23 @ SV9 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[210]) ).
thf(226,plain,
! [SV9: $i,SV23: $i] :
( ( ~ ( ~ ( gt @ SV23 @ SV9 )
| ( lt @ SV9 @ SV23 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[210]) ).
thf(227,plain,
! [SV24: $i,SV10: $i] :
( ( ( leq @ n0 @ SV10 )
= $false )
| ( ( leq @ ( uniform_int_rnd @ SV24 @ SV10 ) @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(228,plain,
! [SV11: $i,SV25: $i] :
( ( ( gt @ SV25 @ SV11 )
= $false )
| ( ( leq @ SV11 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(229,plain,
! [SV26: $i,SV12: $i] :
( ( ~ ( ~ ( geq @ SV12 @ SV26 )
| ( leq @ SV26 @ SV12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(230,plain,
! [SV12: $i,SV26: $i] :
( ( ~ ( ~ ( leq @ SV26 @ SV12 )
| ( geq @ SV12 @ SV26 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(231,plain,
! [SV27: $i,SV13: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV13 ) @ ( succ @ SV27 ) )
| ( leq @ SV13 @ SV27 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(232,plain,
! [SV27: $i,SV13: $i] :
( ( ~ ( ~ ( leq @ SV13 @ SV27 )
| ( leq @ ( succ @ SV13 ) @ ( succ @ SV27 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(233,plain,
! [SV34: $i,SV28: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV14 @ SV28 )
| ~ ( leq @ SV28 @ SV34 ) ) )
= $true )
| ( ( leq @ SV14 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(234,plain,
! [SV29: $i,SV15: $i] :
( ( ( leq @ ( minus @ SV15 @ SV29 ) @ SV15 )
= $false )
| ( ( leq @ n0 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(235,plain,
! [SV30: $i,SV16: $i] :
( ( ( ~ ( ~ ( leq @ SV16 @ SV30 )
| ~ ( ( SV16 != SV30 ) ) ) )
= $false )
| ( ( gt @ SV30 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(236,plain,
! [SV17: $i,SV37: $i,SV35: $i,SV31: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY73: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SY73 )
| ~ ( leq @ SY73 @ SV31 ) )
| ( ( a_select2 @ SV35 @ SY73 )
= SV37 ) )
| ~ ( leq @ n0 @ SV17 ) )
| ~ ( leq @ SV17 @ SV31 ) )
| ( ( a_select2 @ ( tptp_update2 @ SV35 @ SV31 @ SV37 ) @ SV17 )
= SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(237,plain,
! [SV18: $i] :
( ( ( ~ ( leq @ n0 @ SV18 )
| ~ ( leq @ SV18 @ n0 ) )
= $true )
| ( ( SV18 = n0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(238,plain,
! [SV4: $i] :
( ( ( ~ ( leq @ n0 @ SV4 ) )
= $true )
| ( ( ~ ( leq @ SV4 @ n2 ) )
= $true )
| ( ( ( SV4 = n0 )
| ( SV4 = n1 )
| ( SV4 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(239,plain,
! [SV38: $i,SV36: $i,SV33: $i,SV20: $i,SV5: $i] :
( ( ~ ~ ( ~ ( ( SV5 != SV20 ) )
| ( ( a_select2 @ SV33 @ SV20 )
!= SV36 ) )
| ( ( a_select2 @ ( tptp_update2 @ SV33 @ SV5 @ SV38 ) @ SV20 )
= SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(240,plain,
! [SV7: $i] :
( ( ( ~ ( leq @ n0 @ SV7 ) )
= $true )
| ( ( ~ ( leq @ SV7 @ n1 ) )
= $true )
| ( ( ( SV7 = n0 )
| ( SV7 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(241,plain,
! [SV23: $i,SV9: $i] :
( ( ~ ( lt @ SV9 @ SV23 )
| ( gt @ SV23 @ SV9 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(242,plain,
! [SV9: $i,SV23: $i] :
( ( ~ ( gt @ SV23 @ SV9 )
| ( lt @ SV9 @ SV23 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(243,plain,
! [SV26: $i,SV12: $i] :
( ( ~ ( geq @ SV12 @ SV26 )
| ( leq @ SV26 @ SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(244,plain,
! [SV12: $i,SV26: $i] :
( ( ~ ( leq @ SV26 @ SV12 )
| ( geq @ SV12 @ SV26 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(245,plain,
! [SV27: $i,SV13: $i] :
( ( ~ ( leq @ ( succ @ SV13 ) @ ( succ @ SV27 ) )
| ( leq @ SV13 @ SV27 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(246,plain,
! [SV27: $i,SV13: $i] :
( ( ~ ( leq @ SV13 @ SV27 )
| ( leq @ ( succ @ SV13 ) @ ( succ @ SV27 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(247,plain,
! [SV34: $i,SV28: $i,SV14: $i] :
( ( ( ~ ( ~ ( leq @ SV14 @ SV28 )
| ~ ( leq @ SV28 @ SV34 ) ) )
= $false )
| ( ( leq @ SV14 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(248,plain,
! [SV30: $i,SV16: $i] :
( ( ( ~ ( leq @ SV16 @ SV30 )
| ~ ( ( SV16 != SV30 ) ) )
= $true )
| ( ( gt @ SV30 @ SV16 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(249,plain,
! [SV17: $i,SV37: $i,SV35: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY73: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SY73 )
| ~ ( leq @ SY73 @ SV31 ) )
| ( ( a_select2 @ SV35 @ SY73 )
= SV37 ) )
| ~ ( leq @ n0 @ SV17 ) )
| ~ ( leq @ SV17 @ SV31 ) ) )
= $true )
| ( ( ( a_select2 @ ( tptp_update2 @ SV35 @ SV31 @ SV37 ) @ SV17 )
= SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(250,plain,
! [SV18: $i] :
( ( ( ~ ( leq @ n0 @ SV18 ) )
= $true )
| ( ( ~ ( leq @ SV18 @ n0 ) )
= $true )
| ( ( SV18 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(251,plain,
! [SV4: $i] :
( ( ( leq @ n0 @ SV4 )
= $false )
| ( ( ~ ( leq @ SV4 @ n2 ) )
= $true )
| ( ( ( SV4 = n0 )
| ( SV4 = n1 )
| ( SV4 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(252,plain,
! [SV38: $i,SV36: $i,SV33: $i,SV20: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( ( SV5 != SV20 ) )
| ( ( a_select2 @ SV33 @ SV20 )
!= SV36 ) ) )
= $true )
| ( ( ( a_select2 @ ( tptp_update2 @ SV33 @ SV5 @ SV38 ) @ SV20 )
= SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(253,plain,
! [SV7: $i] :
( ( ( leq @ n0 @ SV7 )
= $false )
| ( ( ~ ( leq @ SV7 @ n1 ) )
= $true )
| ( ( ( SV7 = n0 )
| ( SV7 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(254,plain,
! [SV23: $i,SV9: $i] :
( ( ( ~ ( lt @ SV9 @ SV23 ) )
= $true )
| ( ( gt @ SV23 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(255,plain,
! [SV9: $i,SV23: $i] :
( ( ( ~ ( gt @ SV23 @ SV9 ) )
= $true )
| ( ( lt @ SV9 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(256,plain,
! [SV26: $i,SV12: $i] :
( ( ( ~ ( geq @ SV12 @ SV26 ) )
= $true )
| ( ( leq @ SV26 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(257,plain,
! [SV12: $i,SV26: $i] :
( ( ( ~ ( leq @ SV26 @ SV12 ) )
= $true )
| ( ( geq @ SV12 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(258,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( leq @ ( succ @ SV13 ) @ ( succ @ SV27 ) ) )
= $true )
| ( ( leq @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(259,plain,
! [SV27: $i,SV13: $i] :
( ( ( ~ ( leq @ SV13 @ SV27 ) )
= $true )
| ( ( leq @ ( succ @ SV13 ) @ ( succ @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(260,plain,
! [SV34: $i,SV28: $i,SV14: $i] :
( ( ( ~ ( leq @ SV14 @ SV28 )
| ~ ( leq @ SV28 @ SV34 ) )
= $true )
| ( ( leq @ SV14 @ SV34 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(261,plain,
! [SV30: $i,SV16: $i] :
( ( ( ~ ( leq @ SV16 @ SV30 ) )
= $true )
| ( ( ~ ( ( SV16 != SV30 ) ) )
= $true )
| ( ( gt @ SV30 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(262,plain,
! [SV17: $i,SV37: $i,SV35: $i,SV31: $i] :
( ( ( ~ ( ~ ~ ( ~ ! [SY73: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SY73 )
| ~ ( leq @ SY73 @ SV31 ) )
| ( ( a_select2 @ SV35 @ SY73 )
= SV37 ) )
| ~ ( leq @ n0 @ SV17 ) )
| ~ ( leq @ SV17 @ SV31 ) ) )
= $false )
| ( ( ( a_select2 @ ( tptp_update2 @ SV35 @ SV31 @ SV37 ) @ SV17 )
= SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(263,plain,
! [SV18: $i] :
( ( ( leq @ n0 @ SV18 )
= $false )
| ( ( ~ ( leq @ SV18 @ n0 ) )
= $true )
| ( ( SV18 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(264,plain,
! [SV4: $i] :
( ( ( leq @ SV4 @ n2 )
= $false )
| ( ( leq @ n0 @ SV4 )
= $false )
| ( ( ( SV4 = n0 )
| ( SV4 = n1 )
| ( SV4 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(265,plain,
! [SV38: $i,SV36: $i,SV33: $i,SV20: $i,SV5: $i] :
( ( ( ~ ( ~ ( ( SV5 != SV20 ) )
| ( ( a_select2 @ SV33 @ SV20 )
!= SV36 ) ) )
= $false )
| ( ( ( a_select2 @ ( tptp_update2 @ SV33 @ SV5 @ SV38 ) @ SV20 )
= SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(266,plain,
! [SV7: $i] :
( ( ( leq @ SV7 @ n1 )
= $false )
| ( ( leq @ n0 @ SV7 )
= $false )
| ( ( ( SV7 = n0 )
| ( SV7 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(267,plain,
! [SV23: $i,SV9: $i] :
( ( ( lt @ SV9 @ SV23 )
= $false )
| ( ( gt @ SV23 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(268,plain,
! [SV9: $i,SV23: $i] :
( ( ( gt @ SV23 @ SV9 )
= $false )
| ( ( lt @ SV9 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(269,plain,
! [SV26: $i,SV12: $i] :
( ( ( geq @ SV12 @ SV26 )
= $false )
| ( ( leq @ SV26 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(270,plain,
! [SV12: $i,SV26: $i] :
( ( ( leq @ SV26 @ SV12 )
= $false )
| ( ( geq @ SV12 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(271,plain,
! [SV27: $i,SV13: $i] :
( ( ( leq @ ( succ @ SV13 ) @ ( succ @ SV27 ) )
= $false )
| ( ( leq @ SV13 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(272,plain,
! [SV27: $i,SV13: $i] :
( ( ( leq @ SV13 @ SV27 )
= $false )
| ( ( leq @ ( succ @ SV13 ) @ ( succ @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(273,plain,
! [SV34: $i,SV28: $i,SV14: $i] :
( ( ( ~ ( leq @ SV14 @ SV28 ) )
= $true )
| ( ( ~ ( leq @ SV28 @ SV34 ) )
= $true )
| ( ( leq @ SV14 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(274,plain,
! [SV30: $i,SV16: $i] :
( ( ( leq @ SV16 @ SV30 )
= $false )
| ( ( ~ ( ( SV16 != SV30 ) ) )
= $true )
| ( ( gt @ SV30 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(275,plain,
! [SV17: $i,SV37: $i,SV35: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ! [SY73: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SY73 )
| ~ ( leq @ SY73 @ SV31 ) )
| ( ( a_select2 @ SV35 @ SY73 )
= SV37 ) )
| ~ ( leq @ n0 @ SV17 ) )
| ~ ( leq @ SV17 @ SV31 ) )
= $true )
| ( ( ( a_select2 @ ( tptp_update2 @ SV35 @ SV31 @ SV37 ) @ SV17 )
= SV37 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(276,plain,
! [SV18: $i] :
( ( ( leq @ SV18 @ n0 )
= $false )
| ( ( leq @ n0 @ SV18 )
= $false )
| ( ( SV18 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(277,plain,
! [SV4: $i] :
( ( ( ( SV4 = n0 )
| ( SV4 = n1 ) )
= $true )
| ( ( SV4 = n2 )
= $true )
| ( ( leq @ n0 @ SV4 )
= $false )
| ( ( leq @ SV4 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(278,plain,
! [SV38: $i,SV36: $i,SV33: $i,SV20: $i,SV5: $i] :
( ( ( ~ ( ( SV5 != SV20 ) )
| ( ( a_select2 @ SV33 @ SV20 )
!= SV36 ) )
= $true )
| ( ( ( a_select2 @ ( tptp_update2 @ SV33 @ SV5 @ SV38 ) @ SV20 )
= SV36 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[265]) ).
thf(279,plain,
! [SV7: $i] :
( ( ( SV7 = n0 )
= $true )
| ( ( SV7 = n1 )
= $true )
| ( ( leq @ n0 @ SV7 )
= $false )
| ( ( leq @ SV7 @ n1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(280,plain,
! [SV34: $i,SV28: $i,SV14: $i] :
( ( ( leq @ SV14 @ SV28 )
= $false )
| ( ( ~ ( leq @ SV28 @ SV34 ) )
= $true )
| ( ( leq @ SV14 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(281,plain,
! [SV30: $i,SV16: $i] :
( ( ( SV16 != SV30 )
= $false )
| ( ( leq @ SV16 @ SV30 )
= $false )
| ( ( gt @ SV30 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(282,plain,
! [SV17: $i,SV37: $i,SV35: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ! [SY73: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SY73 )
| ~ ( leq @ SY73 @ SV31 ) )
| ( ( a_select2 @ SV35 @ SY73 )
= SV37 ) )
| ~ ( leq @ n0 @ SV17 ) ) )
= $true )
| ( ( ~ ( leq @ SV17 @ SV31 ) )
= $true )
| ( ( ( a_select2 @ ( tptp_update2 @ SV35 @ SV31 @ SV37 ) @ SV17 )
= SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(283,plain,
! [SV4: $i] :
( ( ( SV4 = n0 )
= $true )
| ( ( SV4 = n1 )
= $true )
| ( ( SV4 = n2 )
= $true )
| ( ( leq @ n0 @ SV4 )
= $false )
| ( ( leq @ SV4 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(284,plain,
! [SV38: $i,SV36: $i,SV33: $i,SV20: $i,SV5: $i] :
( ( ( ~ ( ( SV5 != SV20 ) ) )
= $true )
| ( ( ( a_select2 @ SV33 @ SV20 )
!= SV36 )
= $true )
| ( ( ( a_select2 @ ( tptp_update2 @ SV33 @ SV5 @ SV38 ) @ SV20 )
= SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(285,plain,
! [SV14: $i,SV34: $i,SV28: $i] :
( ( ( leq @ SV28 @ SV34 )
= $false )
| ( ( leq @ SV14 @ SV28 )
= $false )
| ( ( leq @ SV14 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(286,plain,
! [SV30: $i,SV16: $i] :
( ( ( SV16 = SV30 )
= $true )
| ( ( leq @ SV16 @ SV30 )
= $false )
| ( ( gt @ SV30 @ SV16 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(287,plain,
! [SV17: $i,SV37: $i,SV35: $i,SV31: $i] :
( ( ( ~ ( ~ ! [SY73: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SY73 )
| ~ ( leq @ SY73 @ SV31 ) )
| ( ( a_select2 @ SV35 @ SY73 )
= SV37 ) )
| ~ ( leq @ n0 @ SV17 ) ) )
= $false )
| ( ( ~ ( leq @ SV17 @ SV31 ) )
= $true )
| ( ( ( a_select2 @ ( tptp_update2 @ SV35 @ SV31 @ SV37 ) @ SV17 )
= SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(288,plain,
! [SV38: $i,SV36: $i,SV33: $i,SV20: $i,SV5: $i] :
( ( ( SV5 != SV20 )
= $false )
| ( ( ( a_select2 @ SV33 @ SV20 )
!= SV36 )
= $true )
| ( ( ( a_select2 @ ( tptp_update2 @ SV33 @ SV5 @ SV38 ) @ SV20 )
= SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(289,plain,
! [SV17: $i,SV37: $i,SV35: $i,SV31: $i] :
( ( ( ~ ! [SY73: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SY73 )
| ~ ( leq @ SY73 @ SV31 ) )
| ( ( a_select2 @ SV35 @ SY73 )
= SV37 ) )
| ~ ( leq @ n0 @ SV17 ) )
= $true )
| ( ( ~ ( leq @ SV17 @ SV31 ) )
= $true )
| ( ( ( a_select2 @ ( tptp_update2 @ SV35 @ SV31 @ SV37 ) @ SV17 )
= SV37 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[287]) ).
thf(290,plain,
! [SV38: $i,SV36: $i,SV33: $i,SV20: $i,SV5: $i] :
( ( ( SV5 = SV20 )
= $true )
| ( ( ( a_select2 @ SV33 @ SV20 )
!= SV36 )
= $true )
| ( ( ( a_select2 @ ( tptp_update2 @ SV33 @ SV5 @ SV38 ) @ SV20 )
= SV36 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(291,plain,
! [SV17: $i,SV37: $i,SV35: $i,SV31: $i] :
( ( ( ~ ! [SY73: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SY73 )
| ~ ( leq @ SY73 @ SV31 ) )
| ( ( a_select2 @ SV35 @ SY73 )
= SV37 ) ) )
= $true )
| ( ( ~ ( leq @ n0 @ SV17 ) )
= $true )
| ( ( ~ ( leq @ SV17 @ SV31 ) )
= $true )
| ( ( ( a_select2 @ ( tptp_update2 @ SV35 @ SV31 @ SV37 ) @ SV17 )
= SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(292,plain,
! [SV38: $i,SV5: $i,SV36: $i,SV20: $i,SV33: $i] :
( ( ( ( a_select2 @ SV33 @ SV20 )
= SV36 )
= $false )
| ( ( SV5 = SV20 )
= $true )
| ( ( ( a_select2 @ ( tptp_update2 @ SV33 @ SV5 @ SV38 ) @ SV20 )
= SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(293,plain,
! [SV17: $i,SV37: $i,SV35: $i,SV31: $i] :
( ( ( ! [SY73: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SY73 )
| ~ ( leq @ SY73 @ SV31 ) )
| ( ( a_select2 @ SV35 @ SY73 )
= SV37 ) ) )
= $false )
| ( ( ~ ( leq @ n0 @ SV17 ) )
= $true )
| ( ( ~ ( leq @ SV17 @ SV31 ) )
= $true )
| ( ( ( a_select2 @ ( tptp_update2 @ SV35 @ SV31 @ SV37 ) @ SV17 )
= SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(294,plain,
! [SV31: $i,SV35: $i,SV37: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ ( sK1_SY73 @ SV17 @ SV37 @ SV35 @ SV31 ) )
| ~ ( leq @ ( sK1_SY73 @ SV17 @ SV37 @ SV35 @ SV31 ) @ SV31 ) )
| ( ( a_select2 @ SV35 @ ( sK1_SY73 @ SV17 @ SV37 @ SV35 @ SV31 ) )
= SV37 ) )
= $false )
| ( ( ~ ( leq @ n0 @ SV17 ) )
= $true )
| ( ( ~ ( leq @ SV17 @ SV31 ) )
= $true )
| ( ( ( a_select2 @ ( tptp_update2 @ SV35 @ SV31 @ SV37 ) @ SV17 )
= SV37 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[293]) ).
thf(295,plain,
! [SV31: $i,SV35: $i,SV37: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ ( sK1_SY73 @ SV17 @ SV37 @ SV35 @ SV31 ) )
| ~ ( leq @ ( sK1_SY73 @ SV17 @ SV37 @ SV35 @ SV31 ) @ SV31 ) ) )
= $false )
| ( ( ~ ( leq @ n0 @ SV17 ) )
= $true )
| ( ( ~ ( leq @ SV17 @ SV31 ) )
= $true )
| ( ( ( a_select2 @ ( tptp_update2 @ SV35 @ SV31 @ SV37 ) @ SV17 )
= SV37 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[294]) ).
thf(296,plain,
! [SV31: $i,SV37: $i,SV17: $i,SV35: $i] :
( ( ( ( a_select2 @ SV35 @ ( sK1_SY73 @ SV17 @ SV37 @ SV35 @ SV31 ) )
= SV37 )
= $false )
| ( ( ~ ( leq @ n0 @ SV17 ) )
= $true )
| ( ( ~ ( leq @ SV17 @ SV31 ) )
= $true )
| ( ( ( a_select2 @ ( tptp_update2 @ SV35 @ SV31 @ SV37 ) @ SV17 )
= SV37 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[294]) ).
thf(297,plain,
! [SV31: $i,SV35: $i,SV37: $i,SV17: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ ( sK1_SY73 @ SV17 @ SV37 @ SV35 @ SV31 ) )
| ~ ( leq @ ( sK1_SY73 @ SV17 @ SV37 @ SV35 @ SV31 ) @ SV31 ) ) )
= $true )
| ( ( ~ ( leq @ n0 @ SV17 ) )
= $true )
| ( ( ~ ( leq @ SV17 @ SV31 ) )
= $true )
| ( ( ( a_select2 @ ( tptp_update2 @ SV35 @ SV31 @ SV37 ) @ SV17 )
= SV37 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(298,plain,
! [SV31: $i,SV37: $i,SV35: $i,SV17: $i] :
( ( ( leq @ n0 @ SV17 )
= $false )
| ( ( ( a_select2 @ SV35 @ ( sK1_SY73 @ SV17 @ SV37 @ SV35 @ SV31 ) )
= SV37 )
= $false )
| ( ( ~ ( leq @ SV17 @ SV31 ) )
= $true )
| ( ( ( a_select2 @ ( tptp_update2 @ SV35 @ SV31 @ SV37 ) @ SV17 )
= SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(299,plain,
! [SV31: $i,SV35: $i,SV37: $i,SV17: $i] :
( ( ( ~ ( leq @ n0 @ ( sK1_SY73 @ SV17 @ SV37 @ SV35 @ SV31 ) )
| ~ ( leq @ ( sK1_SY73 @ SV17 @ SV37 @ SV35 @ SV31 ) @ SV31 ) )
= $false )
| ( ( ~ ( leq @ n0 @ SV17 ) )
= $true )
| ( ( ~ ( leq @ SV17 @ SV31 ) )
= $true )
| ( ( ( a_select2 @ ( tptp_update2 @ SV35 @ SV31 @ SV37 ) @ SV17 )
= SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(300,plain,
! [SV37: $i,SV35: $i,SV31: $i,SV17: $i] :
( ( ( leq @ SV17 @ SV31 )
= $false )
| ( ( ( a_select2 @ SV35 @ ( sK1_SY73 @ SV17 @ SV37 @ SV35 @ SV31 ) )
= SV37 )
= $false )
| ( ( leq @ n0 @ SV17 )
= $false )
| ( ( ( a_select2 @ ( tptp_update2 @ SV35 @ SV31 @ SV37 ) @ SV17 )
= SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(301,plain,
! [SV31: $i,SV35: $i,SV37: $i,SV17: $i] :
( ( ( ~ ( leq @ n0 @ ( sK1_SY73 @ SV17 @ SV37 @ SV35 @ SV31 ) ) )
= $false )
| ( ( ~ ( leq @ n0 @ SV17 ) )
= $true )
| ( ( ~ ( leq @ SV17 @ SV31 ) )
= $true )
| ( ( ( a_select2 @ ( tptp_update2 @ SV35 @ SV31 @ SV37 ) @ SV17 )
= SV37 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[299]) ).
thf(302,plain,
! [SV31: $i,SV35: $i,SV37: $i,SV17: $i] :
( ( ( ~ ( leq @ ( sK1_SY73 @ SV17 @ SV37 @ SV35 @ SV31 ) @ SV31 ) )
= $false )
| ( ( ~ ( leq @ n0 @ SV17 ) )
= $true )
| ( ( ~ ( leq @ SV17 @ SV31 ) )
= $true )
| ( ( ( a_select2 @ ( tptp_update2 @ SV35 @ SV31 @ SV37 ) @ SV17 )
= SV37 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[299]) ).
thf(303,plain,
! [SV31: $i,SV35: $i,SV37: $i,SV17: $i] :
( ( ( leq @ n0 @ ( sK1_SY73 @ SV17 @ SV37 @ SV35 @ SV31 ) )
= $true )
| ( ( ~ ( leq @ n0 @ SV17 ) )
= $true )
| ( ( ~ ( leq @ SV17 @ SV31 ) )
= $true )
| ( ( ( a_select2 @ ( tptp_update2 @ SV35 @ SV31 @ SV37 ) @ SV17 )
= SV37 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[301]) ).
thf(304,plain,
! [SV31: $i,SV35: $i,SV37: $i,SV17: $i] :
( ( ( leq @ ( sK1_SY73 @ SV17 @ SV37 @ SV35 @ SV31 ) @ SV31 )
= $true )
| ( ( ~ ( leq @ n0 @ SV17 ) )
= $true )
| ( ( ~ ( leq @ SV17 @ SV31 ) )
= $true )
| ( ( ( a_select2 @ ( tptp_update2 @ SV35 @ SV31 @ SV37 ) @ SV17 )
= SV37 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[302]) ).
thf(305,plain,
! [SV31: $i,SV35: $i,SV37: $i,SV17: $i] :
( ( ( leq @ n0 @ SV17 )
= $false )
| ( ( leq @ n0 @ ( sK1_SY73 @ SV17 @ SV37 @ SV35 @ SV31 ) )
= $true )
| ( ( ~ ( leq @ SV17 @ SV31 ) )
= $true )
| ( ( ( a_select2 @ ( tptp_update2 @ SV35 @ SV31 @ SV37 ) @ SV17 )
= SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(306,plain,
! [SV31: $i,SV35: $i,SV37: $i,SV17: $i] :
( ( ( leq @ n0 @ SV17 )
= $false )
| ( ( leq @ ( sK1_SY73 @ SV17 @ SV37 @ SV35 @ SV31 ) @ SV31 )
= $true )
| ( ( ~ ( leq @ SV17 @ SV31 ) )
= $true )
| ( ( ( a_select2 @ ( tptp_update2 @ SV35 @ SV31 @ SV37 ) @ SV17 )
= SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(307,plain,
! [SV35: $i,SV37: $i,SV31: $i,SV17: $i] :
( ( ( leq @ SV17 @ SV31 )
= $false )
| ( ( leq @ n0 @ ( sK1_SY73 @ SV17 @ SV37 @ SV35 @ SV31 ) )
= $true )
| ( ( leq @ n0 @ SV17 )
= $false )
| ( ( ( a_select2 @ ( tptp_update2 @ SV35 @ SV31 @ SV37 ) @ SV17 )
= SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(308,plain,
! [SV35: $i,SV37: $i,SV31: $i,SV17: $i] :
( ( ( leq @ SV17 @ SV31 )
= $false )
| ( ( leq @ ( sK1_SY73 @ SV17 @ SV37 @ SV35 @ SV31 ) @ SV31 )
= $true )
| ( ( leq @ n0 @ SV17 )
= $false )
| ( ( ( a_select2 @ ( tptp_update2 @ SV35 @ SV31 @ SV37 ) @ SV17 )
= SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(309,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[141,308,307,300,292,286,285,283,279,276,272,271,270,269,268,267,234,228,227,224,222,204,172,170,169,152,151,150,149,148,144,143,142]) ).
thf(310,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[309]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV105+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.21 % Computer : n017.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Oct 6 16:14:01 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.50/0.50
% 1.50/0.50 No.of.Axioms: 24
% 1.50/0.50
% 1.50/0.50 Length.of.Defs: 0
% 1.50/0.50
% 1.50/0.50 Contains.Choice.Funs: false
% 1.50/0.50 .......
% 1.50/0.50
% 1.50/0.50 ********************************
% 1.50/0.50 * All subproblems solved! *
% 1.50/0.50 ********************************
% 1.50/0.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:27,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:309,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.50/0.50
% 1.50/0.50 %**** Beginning of derivation protocol ****
% 1.50/0.50 % SZS output start CNFRefutation
% See solution above
% 1.50/0.50
% 1.50/0.50 %**** End of derivation protocol ****
% 1.50/0.50 %**** no. of clauses in derivation: 241 ****
% 1.50/0.50 %**** clause counter: 309 ****
% 1.50/0.50
% 1.50/0.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:27,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:309,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------