%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV070+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 10:54:44 AM UTC 2026
% Result : Theorem 0.70s 0.37s
% Output : CNFRefutation 0.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 19
% Syntax : Number of formulae : 289 ( 172 unt; 0 typ; 0 def)
% Number of atoms : 1593 ( 589 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 2248 ( 398 ~; 388 |; 27 &;1384 @)
% ( 8 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 35 usr; 15 con; 0-4 aty)
% Number of variables : 450 ( 0 ^; 450 !; 0 ?; 450 :)
% 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_n135300,type,
n135300: $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_plus,type,
plus: $i > $i > $i ).
thf(tp_pred,type,
pred: $i > $i ).
thf(tp_pv10,type,
pv10: $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/sandbox/benchmark/theBenchmark.p',successor_1) ).
thf(7,axiom,
! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n2 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_2) ).
thf(8,axiom,
! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_1) ).
thf(9,axiom,
! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_0) ).
thf(21,axiom,
gt @ n135300 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_135300_1) ).
thf(26,axiom,
gt @ n1 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1_0) ).
thf(27,axiom,
gt @ n135300 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_135300_0) ).
thf(48,axiom,
! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_minus) ).
thf(50,axiom,
! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ_succ) ).
thf(53,axiom,
! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pred_minus_1) ).
thf(77,axiom,
! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniform_int_rand_ranges_lo) ).
thf(78,axiom,
! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniform_int_rand_ranges_hi) ).
thf(80,axiom,
! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ) ).
thf(83,axiom,
! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt2) ).
thf(84,axiom,
! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt1) ).
thf(85,axiom,
! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_geq) ).
thf(87,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_leq) ).
thf(88,axiom,
! [X: $i] : ( leq @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_leq) ).
thf(92,conjecture,
( ( ( leq @ n0 @ pv10 )
& ( leq @ pv10 @ ( minus @ n135300 @ n1 ) ) )
=> ( ( leq @ n0 @ pv10 )
& ( leq @ pv10 @ ( minus @ n135300 @ n1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_array_0011) ).
thf(93,negated_conjecture,
( ( ( ( leq @ n0 @ pv10 )
& ( leq @ pv10 @ ( minus @ n135300 @ n1 ) ) )
=> ( ( leq @ n0 @ pv10 )
& ( leq @ pv10 @ ( minus @ n135300 @ n1 ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[92]) ).
thf(94,plain,
( ( ( ( leq @ n0 @ pv10 )
& ( leq @ pv10 @ ( minus @ n135300 @ n1 ) ) )
=> ( ( leq @ n0 @ pv10 )
& ( leq @ pv10 @ ( minus @ n135300 @ n1 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[93]) ).
thf(95,plain,
( ( ( succ @ n0 )
= n1 )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(96,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n2 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(97,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(98,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(99,plain,
( ( gt @ n135300 @ n1 )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(100,plain,
( ( gt @ n1 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(101,plain,
( ( gt @ n135300 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(102,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(103,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(104,plain,
( ( ! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(105,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(106,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(107,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(108,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(109,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(110,plain,
( ( ! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(111,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(112,plain,
( ( ! [X: $i] : ( leq @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(113,plain,
( ( leq @ n0 @ pv10 )
= $true ),
inference(standard_cnf,[status(thm)],[94]) ).
thf(114,plain,
( ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
= $true ),
inference(standard_cnf,[status(thm)],[94]) ).
thf(115,plain,
( ( ( leq @ n0 @ pv10 )
& ( leq @ pv10 @ ( minus @ n135300 @ n1 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[94]) ).
thf(116,plain,
( ( leq @ n0 @ pv10 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[115]) ).
thf(117,plain,
( ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[115]) ).
thf(118,plain,
( ( ~ ( leq @ n0 @ pv10 ) )
= $true ),
inference(polarity_switch,[status(thm)],[116]) ).
thf(119,plain,
( ( ~ ( leq @ pv10 @ ( minus @ n135300 @ n1 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[117]) ).
thf(120,plain,
( ( ! [X: $i] : ( leq @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(121,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(122,plain,
( ( ! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(123,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(124,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(125,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(126,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(127,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(128,plain,
( ( ! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(129,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(130,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(131,plain,
( ( gt @ n135300 @ n0 )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(132,plain,
( ( gt @ n1 @ n0 )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(133,plain,
( ( gt @ n135300 @ n1 )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(134,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(135,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(136,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n2 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(137,plain,
( ( ( succ @ n0 )
= n1 )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(138,plain,
( ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(139,plain,
( ( leq @ n0 @ pv10 )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(140,plain,
( ( ~ ( leq @ n0 @ pv10 ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(141,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( gt @ SX1 @ SX0 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(142,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n0 ) )
| ( SX0 = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(143,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ ( minus @ SX0 @ SX1 ) @ SX0 )
| ( leq @ n0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(144,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)],[129]) ).
thf(145,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ ( uniform_int_rnd @ SX1 @ SX0 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(146,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n2 ) )
| ( SX0 = n0 )
| ( SX0 = n1 )
| ( SX0 = n2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(147,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ n0 @ ( uniform_int_rnd @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(148,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( leq @ SX0 @ ( succ @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(149,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n1 ) )
| ( SX0 = n0 )
| ( SX0 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(150,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( geq @ SX0 @ SX1 )
| ( leq @ SX1 @ SX0 ) )
| ~ ( ~ ( leq @ SX1 @ SX0 )
| ( geq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(151,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( gt @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(152,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( leq @ SX1 @ SX2 ) )
| ( leq @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(153,plain,
! [SV1: $i] :
( ( leq @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(154,plain,
! [SV2: $i] :
( ( ( minus @ SV2 @ n1 )
= ( pred @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(155,plain,
( ( leq @ n0 @ pv10 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(156,plain,
! [SV3: $i] :
( ( ! [SY24: $i] :
( ~ ( gt @ SY24 @ SV3 )
| ( leq @ SV3 @ SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(157,plain,
! [SV4: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV4 )
| ~ ( leq @ SV4 @ n0 ) )
| ( SV4 = n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(158,plain,
! [SV5: $i] :
( ( ! [SY25: $i] :
( ~ ( leq @ ( minus @ SV5 @ SY25 ) @ SV5 )
| ( leq @ n0 @ SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(159,plain,
! [SV6: $i] :
( ( ! [SY26: $i] :
~ ( ~ ( ~ ( leq @ ( succ @ SV6 ) @ ( succ @ SY26 ) )
| ( leq @ SV6 @ SY26 ) )
| ~ ( ~ ( leq @ SV6 @ SY26 )
| ( leq @ ( succ @ SV6 ) @ ( succ @ SY26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(160,plain,
! [SV7: $i] :
( ( ! [SY27: $i] :
( ~ ( leq @ n0 @ SV7 )
| ( leq @ ( uniform_int_rnd @ SY27 @ SV7 ) @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(161,plain,
! [SV8: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV8 )
| ~ ( leq @ SV8 @ n2 ) )
| ( SV8 = n0 )
| ( SV8 = n1 )
| ( SV8 = n2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(162,plain,
! [SV9: $i] :
( ( ! [SY28: $i] :
( ~ ( leq @ n0 @ SV9 )
| ( leq @ n0 @ ( uniform_int_rnd @ SY28 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(163,plain,
! [SV10: $i] :
( ( ! [SY29: $i] :
( ~ ( leq @ SV10 @ SY29 )
| ( leq @ SV10 @ ( succ @ SY29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(164,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV11 )
| ~ ( leq @ SV11 @ n1 ) )
| ( SV11 = n0 )
| ( SV11 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(165,plain,
! [SV12: $i] :
( ( ! [SY30: $i] :
~ ( ~ ( ~ ( geq @ SV12 @ SY30 )
| ( leq @ SY30 @ SV12 ) )
| ~ ( ~ ( leq @ SY30 @ SV12 )
| ( geq @ SV12 @ SY30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(166,plain,
! [SV13: $i] :
( ( ! [SY31: $i] :
( ~ ~ ( ~ ( leq @ SV13 @ SY31 )
| ~ ( ( SV13 != SY31 ) ) )
| ( gt @ SY31 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(167,plain,
! [SV14: $i] :
( ( ! [SY32: $i,SY33: $i] :
( ~ ~ ( ~ ( leq @ SV14 @ SY32 )
| ~ ( leq @ SY32 @ SY33 ) )
| ( leq @ SV14 @ SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(168,plain,
! [SV3: $i,SV15: $i] :
( ( ~ ( gt @ SV15 @ SV3 )
| ( leq @ SV3 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(169,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV4 )
| ~ ( leq @ SV4 @ n0 ) ) )
= $true )
| ( ( SV4 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(170,plain,
! [SV16: $i,SV5: $i] :
( ( ~ ( leq @ ( minus @ SV5 @ SV16 ) @ SV5 )
| ( leq @ n0 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(171,plain,
! [SV17: $i,SV6: $i] :
( ( ~ ( ~ ( ~ ( leq @ ( succ @ SV6 ) @ ( succ @ SV17 ) )
| ( leq @ SV6 @ SV17 ) )
| ~ ( ~ ( leq @ SV6 @ SV17 )
| ( leq @ ( succ @ SV6 ) @ ( succ @ SV17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(172,plain,
! [SV18: $i,SV7: $i] :
( ( ~ ( leq @ n0 @ SV7 )
| ( leq @ ( uniform_int_rnd @ SV18 @ SV7 ) @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(173,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV8 )
| ~ ( leq @ SV8 @ n2 ) ) )
= $true )
| ( ( ( SV8 = n0 )
| ( SV8 = n1 )
| ( SV8 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(174,plain,
! [SV19: $i,SV9: $i] :
( ( ~ ( leq @ n0 @ SV9 )
| ( leq @ n0 @ ( uniform_int_rnd @ SV19 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(175,plain,
! [SV20: $i,SV10: $i] :
( ( ~ ( leq @ SV10 @ SV20 )
| ( leq @ SV10 @ ( succ @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(176,plain,
! [SV11: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV11 )
| ~ ( leq @ SV11 @ n1 ) ) )
= $true )
| ( ( ( SV11 = n0 )
| ( SV11 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(177,plain,
! [SV21: $i,SV12: $i] :
( ( ~ ( ~ ( ~ ( geq @ SV12 @ SV21 )
| ( leq @ SV21 @ SV12 ) )
| ~ ( ~ ( leq @ SV21 @ SV12 )
| ( geq @ SV12 @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(178,plain,
! [SV22: $i,SV13: $i] :
( ( ~ ~ ( ~ ( leq @ SV13 @ SV22 )
| ~ ( ( SV13 != SV22 ) ) )
| ( gt @ SV22 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(179,plain,
! [SV23: $i,SV14: $i] :
( ( ! [SY34: $i] :
( ~ ~ ( ~ ( leq @ SV14 @ SV23 )
| ~ ( leq @ SV23 @ SY34 ) )
| ( leq @ SV14 @ SY34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(180,plain,
! [SV3: $i,SV15: $i] :
( ( ( ~ ( gt @ SV15 @ SV3 ) )
= $true )
| ( ( leq @ SV3 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(181,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV4 )
| ~ ( leq @ SV4 @ n0 ) ) )
= $false )
| ( ( SV4 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(182,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ( leq @ ( minus @ SV5 @ SV16 ) @ SV5 ) )
= $true )
| ( ( leq @ n0 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(183,plain,
! [SV17: $i,SV6: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV6 ) @ ( succ @ SV17 ) )
| ( leq @ SV6 @ SV17 ) )
| ~ ( ~ ( leq @ SV6 @ SV17 )
| ( leq @ ( succ @ SV6 ) @ ( succ @ SV17 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(184,plain,
! [SV18: $i,SV7: $i] :
( ( ( ~ ( leq @ n0 @ SV7 ) )
= $true )
| ( ( leq @ ( uniform_int_rnd @ SV18 @ SV7 ) @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(185,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV8 )
| ~ ( leq @ SV8 @ n2 ) ) )
= $false )
| ( ( ( SV8 = n0 )
| ( SV8 = n1 )
| ( SV8 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(186,plain,
! [SV19: $i,SV9: $i] :
( ( ( ~ ( leq @ n0 @ SV9 ) )
= $true )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV19 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(187,plain,
! [SV20: $i,SV10: $i] :
( ( ( ~ ( leq @ SV10 @ SV20 ) )
= $true )
| ( ( leq @ SV10 @ ( succ @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(188,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV11 )
| ~ ( leq @ SV11 @ n1 ) ) )
= $false )
| ( ( ( SV11 = n0 )
| ( SV11 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(189,plain,
! [SV21: $i,SV12: $i] :
( ( ~ ( ~ ( geq @ SV12 @ SV21 )
| ( leq @ SV21 @ SV12 ) )
| ~ ( ~ ( leq @ SV21 @ SV12 )
| ( geq @ SV12 @ SV21 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(190,plain,
! [SV22: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV13 @ SV22 )
| ~ ( ( SV13 != SV22 ) ) ) )
= $true )
| ( ( gt @ SV22 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(191,plain,
! [SV24: $i,SV23: $i,SV14: $i] :
( ( ~ ~ ( ~ ( leq @ SV14 @ SV23 )
| ~ ( leq @ SV23 @ SV24 ) )
| ( leq @ SV14 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(192,plain,
! [SV3: $i,SV15: $i] :
( ( ( gt @ SV15 @ SV3 )
= $false )
| ( ( leq @ SV3 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(193,plain,
! [SV4: $i] :
( ( ( ~ ( leq @ n0 @ SV4 )
| ~ ( leq @ SV4 @ n0 ) )
= $true )
| ( ( SV4 = n0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(194,plain,
! [SV16: $i,SV5: $i] :
( ( ( leq @ ( minus @ SV5 @ SV16 ) @ SV5 )
= $false )
| ( ( leq @ n0 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(195,plain,
! [SV17: $i,SV6: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV6 ) @ ( succ @ SV17 ) )
| ( leq @ SV6 @ SV17 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(196,plain,
! [SV17: $i,SV6: $i] :
( ( ~ ( ~ ( leq @ SV6 @ SV17 )
| ( leq @ ( succ @ SV6 ) @ ( succ @ SV17 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(197,plain,
! [SV18: $i,SV7: $i] :
( ( ( leq @ n0 @ SV7 )
= $false )
| ( ( leq @ ( uniform_int_rnd @ SV18 @ SV7 ) @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(198,plain,
! [SV8: $i] :
( ( ( ~ ( leq @ n0 @ SV8 )
| ~ ( leq @ SV8 @ n2 ) )
= $true )
| ( ( ( SV8 = n0 )
| ( SV8 = n1 )
| ( SV8 = n2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(199,plain,
! [SV19: $i,SV9: $i] :
( ( ( leq @ n0 @ SV9 )
= $false )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV19 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(200,plain,
! [SV20: $i,SV10: $i] :
( ( ( leq @ SV10 @ SV20 )
= $false )
| ( ( leq @ SV10 @ ( succ @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(201,plain,
! [SV11: $i] :
( ( ( ~ ( leq @ n0 @ SV11 )
| ~ ( leq @ SV11 @ n1 ) )
= $true )
| ( ( ( SV11 = n0 )
| ( SV11 = n1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(202,plain,
! [SV21: $i,SV12: $i] :
( ( ~ ( ~ ( geq @ SV12 @ SV21 )
| ( leq @ SV21 @ SV12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(203,plain,
! [SV12: $i,SV21: $i] :
( ( ~ ( ~ ( leq @ SV21 @ SV12 )
| ( geq @ SV12 @ SV21 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(204,plain,
! [SV22: $i,SV13: $i] :
( ( ( ~ ( ~ ( leq @ SV13 @ SV22 )
| ~ ( ( SV13 != SV22 ) ) ) )
= $false )
| ( ( gt @ SV22 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(205,plain,
! [SV24: $i,SV23: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV14 @ SV23 )
| ~ ( leq @ SV23 @ SV24 ) ) )
= $true )
| ( ( leq @ SV14 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(206,plain,
! [SV4: $i] :
( ( ( ~ ( leq @ n0 @ SV4 ) )
= $true )
| ( ( ~ ( leq @ SV4 @ n0 ) )
= $true )
| ( ( SV4 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(207,plain,
! [SV17: $i,SV6: $i] :
( ( ~ ( leq @ ( succ @ SV6 ) @ ( succ @ SV17 ) )
| ( leq @ SV6 @ SV17 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(208,plain,
! [SV17: $i,SV6: $i] :
( ( ~ ( leq @ SV6 @ SV17 )
| ( leq @ ( succ @ SV6 ) @ ( succ @ SV17 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(209,plain,
! [SV8: $i] :
( ( ( ~ ( leq @ n0 @ SV8 ) )
= $true )
| ( ( ~ ( leq @ SV8 @ n2 ) )
= $true )
| ( ( ( SV8 = n0 )
| ( SV8 = n1 )
| ( SV8 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(210,plain,
! [SV11: $i] :
( ( ( ~ ( leq @ n0 @ SV11 ) )
= $true )
| ( ( ~ ( leq @ SV11 @ n1 ) )
= $true )
| ( ( ( SV11 = n0 )
| ( SV11 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(211,plain,
! [SV21: $i,SV12: $i] :
( ( ~ ( geq @ SV12 @ SV21 )
| ( leq @ SV21 @ SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(212,plain,
! [SV12: $i,SV21: $i] :
( ( ~ ( leq @ SV21 @ SV12 )
| ( geq @ SV12 @ SV21 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(213,plain,
! [SV22: $i,SV13: $i] :
( ( ( ~ ( leq @ SV13 @ SV22 )
| ~ ( ( SV13 != SV22 ) ) )
= $true )
| ( ( gt @ SV22 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(214,plain,
! [SV24: $i,SV23: $i,SV14: $i] :
( ( ( ~ ( ~ ( leq @ SV14 @ SV23 )
| ~ ( leq @ SV23 @ SV24 ) ) )
= $false )
| ( ( leq @ SV14 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(215,plain,
! [SV4: $i] :
( ( ( leq @ n0 @ SV4 )
= $false )
| ( ( ~ ( leq @ SV4 @ n0 ) )
= $true )
| ( ( SV4 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(216,plain,
! [SV17: $i,SV6: $i] :
( ( ( ~ ( leq @ ( succ @ SV6 ) @ ( succ @ SV17 ) ) )
= $true )
| ( ( leq @ SV6 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(217,plain,
! [SV17: $i,SV6: $i] :
( ( ( ~ ( leq @ SV6 @ SV17 ) )
= $true )
| ( ( leq @ ( succ @ SV6 ) @ ( succ @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(218,plain,
! [SV8: $i] :
( ( ( leq @ n0 @ SV8 )
= $false )
| ( ( ~ ( leq @ SV8 @ n2 ) )
= $true )
| ( ( ( SV8 = n0 )
| ( SV8 = n1 )
| ( SV8 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(219,plain,
! [SV11: $i] :
( ( ( leq @ n0 @ SV11 )
= $false )
| ( ( ~ ( leq @ SV11 @ n1 ) )
= $true )
| ( ( ( SV11 = n0 )
| ( SV11 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(220,plain,
! [SV21: $i,SV12: $i] :
( ( ( ~ ( geq @ SV12 @ SV21 ) )
= $true )
| ( ( leq @ SV21 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(221,plain,
! [SV12: $i,SV21: $i] :
( ( ( ~ ( leq @ SV21 @ SV12 ) )
= $true )
| ( ( geq @ SV12 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(222,plain,
! [SV22: $i,SV13: $i] :
( ( ( ~ ( leq @ SV13 @ SV22 ) )
= $true )
| ( ( ~ ( ( SV13 != SV22 ) ) )
= $true )
| ( ( gt @ SV22 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(223,plain,
! [SV24: $i,SV23: $i,SV14: $i] :
( ( ( ~ ( leq @ SV14 @ SV23 )
| ~ ( leq @ SV23 @ SV24 ) )
= $true )
| ( ( leq @ SV14 @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(224,plain,
! [SV4: $i] :
( ( ( leq @ SV4 @ n0 )
= $false )
| ( ( leq @ n0 @ SV4 )
= $false )
| ( ( SV4 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(225,plain,
! [SV17: $i,SV6: $i] :
( ( ( leq @ ( succ @ SV6 ) @ ( succ @ SV17 ) )
= $false )
| ( ( leq @ SV6 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(226,plain,
! [SV17: $i,SV6: $i] :
( ( ( leq @ SV6 @ SV17 )
= $false )
| ( ( leq @ ( succ @ SV6 ) @ ( succ @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(227,plain,
! [SV8: $i] :
( ( ( leq @ SV8 @ n2 )
= $false )
| ( ( leq @ n0 @ SV8 )
= $false )
| ( ( ( SV8 = n0 )
| ( SV8 = n1 )
| ( SV8 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(228,plain,
! [SV11: $i] :
( ( ( leq @ SV11 @ n1 )
= $false )
| ( ( leq @ n0 @ SV11 )
= $false )
| ( ( ( SV11 = n0 )
| ( SV11 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(229,plain,
! [SV21: $i,SV12: $i] :
( ( ( geq @ SV12 @ SV21 )
= $false )
| ( ( leq @ SV21 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(230,plain,
! [SV12: $i,SV21: $i] :
( ( ( leq @ SV21 @ SV12 )
= $false )
| ( ( geq @ SV12 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(231,plain,
! [SV22: $i,SV13: $i] :
( ( ( leq @ SV13 @ SV22 )
= $false )
| ( ( ~ ( ( SV13 != SV22 ) ) )
= $true )
| ( ( gt @ SV22 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(232,plain,
! [SV24: $i,SV23: $i,SV14: $i] :
( ( ( ~ ( leq @ SV14 @ SV23 ) )
= $true )
| ( ( ~ ( leq @ SV23 @ SV24 ) )
= $true )
| ( ( leq @ SV14 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(233,plain,
! [SV8: $i] :
( ( ( ( SV8 = n0 )
| ( SV8 = n1 ) )
= $true )
| ( ( SV8 = n2 )
= $true )
| ( ( leq @ n0 @ SV8 )
= $false )
| ( ( leq @ SV8 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(234,plain,
! [SV11: $i] :
( ( ( SV11 = n0 )
= $true )
| ( ( SV11 = n1 )
= $true )
| ( ( leq @ n0 @ SV11 )
= $false )
| ( ( leq @ SV11 @ n1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(235,plain,
! [SV22: $i,SV13: $i] :
( ( ( SV13 != SV22 )
= $false )
| ( ( leq @ SV13 @ SV22 )
= $false )
| ( ( gt @ SV22 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(236,plain,
! [SV24: $i,SV23: $i,SV14: $i] :
( ( ( leq @ SV14 @ SV23 )
= $false )
| ( ( ~ ( leq @ SV23 @ SV24 ) )
= $true )
| ( ( leq @ SV14 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(237,plain,
! [SV8: $i] :
( ( ( SV8 = n0 )
= $true )
| ( ( SV8 = n1 )
= $true )
| ( ( SV8 = n2 )
= $true )
| ( ( leq @ n0 @ SV8 )
= $false )
| ( ( leq @ SV8 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(238,plain,
! [SV22: $i,SV13: $i] :
( ( ( SV13 = SV22 )
= $true )
| ( ( leq @ SV13 @ SV22 )
= $false )
| ( ( gt @ SV22 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(239,plain,
! [SV14: $i,SV24: $i,SV23: $i] :
( ( ( leq @ SV23 @ SV24 )
= $false )
| ( ( leq @ SV14 @ SV23 )
= $false )
| ( ( leq @ SV14 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(240,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[131,239,238,237,234,230,229,226,225,224,200,199,197,194,192,155,154,153,139,138,137,133,132]) ).
thf(241,plain,
( ( ! [X: $i] : ( leq @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(242,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(243,plain,
( ( ! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(244,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(245,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(246,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(247,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(248,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(249,plain,
( ( ! [X: $i] :
( ( minus @ X @ n1 )
= ( pred @ X ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(250,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(251,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(252,plain,
( ( gt @ n135300 @ n0 )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(253,plain,
( ( gt @ n1 @ n0 )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(254,plain,
( ( gt @ n135300 @ n1 )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(255,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(256,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(257,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n2 ) )
=> ( ( X = n0 )
| ( X = n1 )
| ( X = n2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(258,plain,
( ( ( succ @ n0 )
= n1 )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(259,plain,
( ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(260,plain,
( ( leq @ n0 @ pv10 )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(261,plain,
( ( ~ ( leq @ pv10 @ ( minus @ n135300 @ n1 ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(262,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ n0 @ ( uniform_int_rnd @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(263,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n0 ) )
| ( SX0 = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(264,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( geq @ SX0 @ SX1 )
| ( leq @ SX1 @ SX0 ) )
| ~ ( ~ ( leq @ SX1 @ SX0 )
| ( geq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(265,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( gt @ SX1 @ SX0 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(266,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n1 ) )
| ( SX0 = n0 )
| ( SX0 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(267,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n2 ) )
| ( SX0 = n0 )
| ( SX0 = n1 )
| ( SX0 = n2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(268,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( gt @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(269,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)],[250]) ).
thf(270,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ ( minus @ SX0 @ SX1 ) @ SX0 )
| ( leq @ n0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(271,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ ( uniform_int_rnd @ SX1 @ SX0 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(272,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( leq @ SX1 @ SX2 ) )
| ( leq @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(273,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( leq @ SX0 @ ( succ @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(274,plain,
! [SV25: $i] :
( ( leq @ SV25 @ SV25 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(275,plain,
! [SV26: $i] :
( ( ( minus @ SV26 @ n1 )
= ( pred @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(276,plain,
( ( leq @ pv10 @ ( minus @ n135300 @ n1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(277,plain,
! [SV27: $i] :
( ( ! [SY35: $i] :
( ~ ( leq @ n0 @ SV27 )
| ( leq @ n0 @ ( uniform_int_rnd @ SY35 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(278,plain,
! [SV28: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV28 )
| ~ ( leq @ SV28 @ n0 ) )
| ( SV28 = n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(279,plain,
! [SV29: $i] :
( ( ! [SY36: $i] :
~ ( ~ ( ~ ( geq @ SV29 @ SY36 )
| ( leq @ SY36 @ SV29 ) )
| ~ ( ~ ( leq @ SY36 @ SV29 )
| ( geq @ SV29 @ SY36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(280,plain,
! [SV30: $i] :
( ( ! [SY37: $i] :
( ~ ( gt @ SY37 @ SV30 )
| ( leq @ SV30 @ SY37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(281,plain,
! [SV31: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV31 )
| ~ ( leq @ SV31 @ n1 ) )
| ( SV31 = n0 )
| ( SV31 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(282,plain,
! [SV32: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV32 )
| ~ ( leq @ SV32 @ n2 ) )
| ( SV32 = n0 )
| ( SV32 = n1 )
| ( SV32 = n2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(283,plain,
! [SV33: $i] :
( ( ! [SY38: $i] :
( ~ ~ ( ~ ( leq @ SV33 @ SY38 )
| ~ ( ( SV33 != SY38 ) ) )
| ( gt @ SY38 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(284,plain,
! [SV34: $i] :
( ( ! [SY39: $i] :
~ ( ~ ( ~ ( leq @ ( succ @ SV34 ) @ ( succ @ SY39 ) )
| ( leq @ SV34 @ SY39 ) )
| ~ ( ~ ( leq @ SV34 @ SY39 )
| ( leq @ ( succ @ SV34 ) @ ( succ @ SY39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(285,plain,
! [SV35: $i] :
( ( ! [SY40: $i] :
( ~ ( leq @ ( minus @ SV35 @ SY40 ) @ SV35 )
| ( leq @ n0 @ SY40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(286,plain,
! [SV36: $i] :
( ( ! [SY41: $i] :
( ~ ( leq @ n0 @ SV36 )
| ( leq @ ( uniform_int_rnd @ SY41 @ SV36 ) @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(287,plain,
! [SV37: $i] :
( ( ! [SY42: $i,SY43: $i] :
( ~ ~ ( ~ ( leq @ SV37 @ SY42 )
| ~ ( leq @ SY42 @ SY43 ) )
| ( leq @ SV37 @ SY43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(288,plain,
! [SV38: $i] :
( ( ! [SY44: $i] :
( ~ ( leq @ SV38 @ SY44 )
| ( leq @ SV38 @ ( succ @ SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(289,plain,
! [SV39: $i,SV27: $i] :
( ( ~ ( leq @ n0 @ SV27 )
| ( leq @ n0 @ ( uniform_int_rnd @ SV39 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(290,plain,
! [SV28: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV28 )
| ~ ( leq @ SV28 @ n0 ) ) )
= $true )
| ( ( SV28 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(291,plain,
! [SV40: $i,SV29: $i] :
( ( ~ ( ~ ( ~ ( geq @ SV29 @ SV40 )
| ( leq @ SV40 @ SV29 ) )
| ~ ( ~ ( leq @ SV40 @ SV29 )
| ( geq @ SV29 @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(292,plain,
! [SV30: $i,SV41: $i] :
( ( ~ ( gt @ SV41 @ SV30 )
| ( leq @ SV30 @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(293,plain,
! [SV31: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV31 )
| ~ ( leq @ SV31 @ n1 ) ) )
= $true )
| ( ( ( SV31 = n0 )
| ( SV31 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(294,plain,
! [SV32: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV32 )
| ~ ( leq @ SV32 @ n2 ) ) )
= $true )
| ( ( ( SV32 = n0 )
| ( SV32 = n1 )
| ( SV32 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(295,plain,
! [SV42: $i,SV33: $i] :
( ( ~ ~ ( ~ ( leq @ SV33 @ SV42 )
| ~ ( ( SV33 != SV42 ) ) )
| ( gt @ SV42 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(296,plain,
! [SV43: $i,SV34: $i] :
( ( ~ ( ~ ( ~ ( leq @ ( succ @ SV34 ) @ ( succ @ SV43 ) )
| ( leq @ SV34 @ SV43 ) )
| ~ ( ~ ( leq @ SV34 @ SV43 )
| ( leq @ ( succ @ SV34 ) @ ( succ @ SV43 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(297,plain,
! [SV44: $i,SV35: $i] :
( ( ~ ( leq @ ( minus @ SV35 @ SV44 ) @ SV35 )
| ( leq @ n0 @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(298,plain,
! [SV45: $i,SV36: $i] :
( ( ~ ( leq @ n0 @ SV36 )
| ( leq @ ( uniform_int_rnd @ SV45 @ SV36 ) @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(299,plain,
! [SV46: $i,SV37: $i] :
( ( ! [SY45: $i] :
( ~ ~ ( ~ ( leq @ SV37 @ SV46 )
| ~ ( leq @ SV46 @ SY45 ) )
| ( leq @ SV37 @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(300,plain,
! [SV47: $i,SV38: $i] :
( ( ~ ( leq @ SV38 @ SV47 )
| ( leq @ SV38 @ ( succ @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(301,plain,
! [SV39: $i,SV27: $i] :
( ( ( ~ ( leq @ n0 @ SV27 ) )
= $true )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV39 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(302,plain,
! [SV28: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV28 )
| ~ ( leq @ SV28 @ n0 ) ) )
= $false )
| ( ( SV28 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(303,plain,
! [SV40: $i,SV29: $i] :
( ( ~ ( ~ ( geq @ SV29 @ SV40 )
| ( leq @ SV40 @ SV29 ) )
| ~ ( ~ ( leq @ SV40 @ SV29 )
| ( geq @ SV29 @ SV40 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(304,plain,
! [SV30: $i,SV41: $i] :
( ( ( ~ ( gt @ SV41 @ SV30 ) )
= $true )
| ( ( leq @ SV30 @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(305,plain,
! [SV31: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV31 )
| ~ ( leq @ SV31 @ n1 ) ) )
= $false )
| ( ( ( SV31 = n0 )
| ( SV31 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(306,plain,
! [SV32: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV32 )
| ~ ( leq @ SV32 @ n2 ) ) )
= $false )
| ( ( ( SV32 = n0 )
| ( SV32 = n1 )
| ( SV32 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(307,plain,
! [SV42: $i,SV33: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV33 @ SV42 )
| ~ ( ( SV33 != SV42 ) ) ) )
= $true )
| ( ( gt @ SV42 @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(308,plain,
! [SV43: $i,SV34: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV34 ) @ ( succ @ SV43 ) )
| ( leq @ SV34 @ SV43 ) )
| ~ ( ~ ( leq @ SV34 @ SV43 )
| ( leq @ ( succ @ SV34 ) @ ( succ @ SV43 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(309,plain,
! [SV44: $i,SV35: $i] :
( ( ( ~ ( leq @ ( minus @ SV35 @ SV44 ) @ SV35 ) )
= $true )
| ( ( leq @ n0 @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(310,plain,
! [SV45: $i,SV36: $i] :
( ( ( ~ ( leq @ n0 @ SV36 ) )
= $true )
| ( ( leq @ ( uniform_int_rnd @ SV45 @ SV36 ) @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(311,plain,
! [SV48: $i,SV46: $i,SV37: $i] :
( ( ~ ~ ( ~ ( leq @ SV37 @ SV46 )
| ~ ( leq @ SV46 @ SV48 ) )
| ( leq @ SV37 @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(312,plain,
! [SV47: $i,SV38: $i] :
( ( ( ~ ( leq @ SV38 @ SV47 ) )
= $true )
| ( ( leq @ SV38 @ ( succ @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(313,plain,
! [SV39: $i,SV27: $i] :
( ( ( leq @ n0 @ SV27 )
= $false )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV39 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(314,plain,
! [SV28: $i] :
( ( ( ~ ( leq @ n0 @ SV28 )
| ~ ( leq @ SV28 @ n0 ) )
= $true )
| ( ( SV28 = n0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[302]) ).
thf(315,plain,
! [SV40: $i,SV29: $i] :
( ( ~ ( ~ ( geq @ SV29 @ SV40 )
| ( leq @ SV40 @ SV29 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(316,plain,
! [SV29: $i,SV40: $i] :
( ( ~ ( ~ ( leq @ SV40 @ SV29 )
| ( geq @ SV29 @ SV40 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(317,plain,
! [SV30: $i,SV41: $i] :
( ( ( gt @ SV41 @ SV30 )
= $false )
| ( ( leq @ SV30 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(318,plain,
! [SV31: $i] :
( ( ( ~ ( leq @ n0 @ SV31 )
| ~ ( leq @ SV31 @ n1 ) )
= $true )
| ( ( ( SV31 = n0 )
| ( SV31 = n1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[305]) ).
thf(319,plain,
! [SV32: $i] :
( ( ( ~ ( leq @ n0 @ SV32 )
| ~ ( leq @ SV32 @ n2 ) )
= $true )
| ( ( ( SV32 = n0 )
| ( SV32 = n1 )
| ( SV32 = n2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[306]) ).
thf(320,plain,
! [SV42: $i,SV33: $i] :
( ( ( ~ ( ~ ( leq @ SV33 @ SV42 )
| ~ ( ( SV33 != SV42 ) ) ) )
= $false )
| ( ( gt @ SV42 @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(321,plain,
! [SV43: $i,SV34: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV34 ) @ ( succ @ SV43 ) )
| ( leq @ SV34 @ SV43 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[308]) ).
thf(322,plain,
! [SV43: $i,SV34: $i] :
( ( ~ ( ~ ( leq @ SV34 @ SV43 )
| ( leq @ ( succ @ SV34 ) @ ( succ @ SV43 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[308]) ).
thf(323,plain,
! [SV44: $i,SV35: $i] :
( ( ( leq @ ( minus @ SV35 @ SV44 ) @ SV35 )
= $false )
| ( ( leq @ n0 @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(324,plain,
! [SV45: $i,SV36: $i] :
( ( ( leq @ n0 @ SV36 )
= $false )
| ( ( leq @ ( uniform_int_rnd @ SV45 @ SV36 ) @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(325,plain,
! [SV48: $i,SV46: $i,SV37: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV37 @ SV46 )
| ~ ( leq @ SV46 @ SV48 ) ) )
= $true )
| ( ( leq @ SV37 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(326,plain,
! [SV47: $i,SV38: $i] :
( ( ( leq @ SV38 @ SV47 )
= $false )
| ( ( leq @ SV38 @ ( succ @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(327,plain,
! [SV28: $i] :
( ( ( ~ ( leq @ n0 @ SV28 ) )
= $true )
| ( ( ~ ( leq @ SV28 @ n0 ) )
= $true )
| ( ( SV28 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(328,plain,
! [SV40: $i,SV29: $i] :
( ( ~ ( geq @ SV29 @ SV40 )
| ( leq @ SV40 @ SV29 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(329,plain,
! [SV29: $i,SV40: $i] :
( ( ~ ( leq @ SV40 @ SV29 )
| ( geq @ SV29 @ SV40 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(330,plain,
! [SV31: $i] :
( ( ( ~ ( leq @ n0 @ SV31 ) )
= $true )
| ( ( ~ ( leq @ SV31 @ n1 ) )
= $true )
| ( ( ( SV31 = n0 )
| ( SV31 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(331,plain,
! [SV32: $i] :
( ( ( ~ ( leq @ n0 @ SV32 ) )
= $true )
| ( ( ~ ( leq @ SV32 @ n2 ) )
= $true )
| ( ( ( SV32 = n0 )
| ( SV32 = n1 )
| ( SV32 = n2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(332,plain,
! [SV42: $i,SV33: $i] :
( ( ( ~ ( leq @ SV33 @ SV42 )
| ~ ( ( SV33 != SV42 ) ) )
= $true )
| ( ( gt @ SV42 @ SV33 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(333,plain,
! [SV43: $i,SV34: $i] :
( ( ~ ( leq @ ( succ @ SV34 ) @ ( succ @ SV43 ) )
| ( leq @ SV34 @ SV43 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[321]) ).
thf(334,plain,
! [SV43: $i,SV34: $i] :
( ( ~ ( leq @ SV34 @ SV43 )
| ( leq @ ( succ @ SV34 ) @ ( succ @ SV43 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[322]) ).
thf(335,plain,
! [SV48: $i,SV46: $i,SV37: $i] :
( ( ( ~ ( ~ ( leq @ SV37 @ SV46 )
| ~ ( leq @ SV46 @ SV48 ) ) )
= $false )
| ( ( leq @ SV37 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(336,plain,
! [SV28: $i] :
( ( ( leq @ n0 @ SV28 )
= $false )
| ( ( ~ ( leq @ SV28 @ n0 ) )
= $true )
| ( ( SV28 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(337,plain,
! [SV40: $i,SV29: $i] :
( ( ( ~ ( geq @ SV29 @ SV40 ) )
= $true )
| ( ( leq @ SV40 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(338,plain,
! [SV29: $i,SV40: $i] :
( ( ( ~ ( leq @ SV40 @ SV29 ) )
= $true )
| ( ( geq @ SV29 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(339,plain,
! [SV31: $i] :
( ( ( leq @ n0 @ SV31 )
= $false )
| ( ( ~ ( leq @ SV31 @ n1 ) )
= $true )
| ( ( ( SV31 = n0 )
| ( SV31 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(340,plain,
! [SV32: $i] :
( ( ( leq @ n0 @ SV32 )
= $false )
| ( ( ~ ( leq @ SV32 @ n2 ) )
= $true )
| ( ( ( SV32 = n0 )
| ( SV32 = n1 )
| ( SV32 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(341,plain,
! [SV42: $i,SV33: $i] :
( ( ( ~ ( leq @ SV33 @ SV42 ) )
= $true )
| ( ( ~ ( ( SV33 != SV42 ) ) )
= $true )
| ( ( gt @ SV42 @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(342,plain,
! [SV43: $i,SV34: $i] :
( ( ( ~ ( leq @ ( succ @ SV34 ) @ ( succ @ SV43 ) ) )
= $true )
| ( ( leq @ SV34 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(343,plain,
! [SV43: $i,SV34: $i] :
( ( ( ~ ( leq @ SV34 @ SV43 ) )
= $true )
| ( ( leq @ ( succ @ SV34 ) @ ( succ @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[334]) ).
thf(344,plain,
! [SV48: $i,SV46: $i,SV37: $i] :
( ( ( ~ ( leq @ SV37 @ SV46 )
| ~ ( leq @ SV46 @ SV48 ) )
= $true )
| ( ( leq @ SV37 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(345,plain,
! [SV28: $i] :
( ( ( leq @ SV28 @ n0 )
= $false )
| ( ( leq @ n0 @ SV28 )
= $false )
| ( ( SV28 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(346,plain,
! [SV40: $i,SV29: $i] :
( ( ( geq @ SV29 @ SV40 )
= $false )
| ( ( leq @ SV40 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(347,plain,
! [SV29: $i,SV40: $i] :
( ( ( leq @ SV40 @ SV29 )
= $false )
| ( ( geq @ SV29 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(348,plain,
! [SV31: $i] :
( ( ( leq @ SV31 @ n1 )
= $false )
| ( ( leq @ n0 @ SV31 )
= $false )
| ( ( ( SV31 = n0 )
| ( SV31 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(349,plain,
! [SV32: $i] :
( ( ( leq @ SV32 @ n2 )
= $false )
| ( ( leq @ n0 @ SV32 )
= $false )
| ( ( ( SV32 = n0 )
| ( SV32 = n1 )
| ( SV32 = n2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(350,plain,
! [SV42: $i,SV33: $i] :
( ( ( leq @ SV33 @ SV42 )
= $false )
| ( ( ~ ( ( SV33 != SV42 ) ) )
= $true )
| ( ( gt @ SV42 @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(351,plain,
! [SV43: $i,SV34: $i] :
( ( ( leq @ ( succ @ SV34 ) @ ( succ @ SV43 ) )
= $false )
| ( ( leq @ SV34 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(352,plain,
! [SV43: $i,SV34: $i] :
( ( ( leq @ SV34 @ SV43 )
= $false )
| ( ( leq @ ( succ @ SV34 ) @ ( succ @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(353,plain,
! [SV48: $i,SV46: $i,SV37: $i] :
( ( ( ~ ( leq @ SV37 @ SV46 ) )
= $true )
| ( ( ~ ( leq @ SV46 @ SV48 ) )
= $true )
| ( ( leq @ SV37 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(354,plain,
! [SV31: $i] :
( ( ( SV31 = n0 )
= $true )
| ( ( SV31 = n1 )
= $true )
| ( ( leq @ n0 @ SV31 )
= $false )
| ( ( leq @ SV31 @ n1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(355,plain,
! [SV32: $i] :
( ( ( ( SV32 = n0 )
| ( SV32 = n1 ) )
= $true )
| ( ( SV32 = n2 )
= $true )
| ( ( leq @ n0 @ SV32 )
= $false )
| ( ( leq @ SV32 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(356,plain,
! [SV42: $i,SV33: $i] :
( ( ( SV33 != SV42 )
= $false )
| ( ( leq @ SV33 @ SV42 )
= $false )
| ( ( gt @ SV42 @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(357,plain,
! [SV48: $i,SV46: $i,SV37: $i] :
( ( ( leq @ SV37 @ SV46 )
= $false )
| ( ( ~ ( leq @ SV46 @ SV48 ) )
= $true )
| ( ( leq @ SV37 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(358,plain,
! [SV32: $i] :
( ( ( SV32 = n0 )
= $true )
| ( ( SV32 = n1 )
= $true )
| ( ( SV32 = n2 )
= $true )
| ( ( leq @ n0 @ SV32 )
= $false )
| ( ( leq @ SV32 @ n2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[355]) ).
thf(359,plain,
! [SV42: $i,SV33: $i] :
( ( ( SV33 = SV42 )
= $true )
| ( ( leq @ SV33 @ SV42 )
= $false )
| ( ( gt @ SV42 @ SV33 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[356]) ).
thf(360,plain,
! [SV37: $i,SV48: $i,SV46: $i] :
( ( ( leq @ SV46 @ SV48 )
= $false )
| ( ( leq @ SV37 @ SV46 )
= $false )
| ( ( leq @ SV37 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(361,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[252,360,359,358,354,352,351,347,346,345,326,324,323,317,313,276,275,274,260,259,258,254,253]) ).
thf(362,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[361,240]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV070+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n004.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 16:17:54 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.70/0.37
% 0.70/0.37 No.of.Axioms: 18
% 0.70/0.37
% 0.70/0.37 Length.of.Defs: 0
% 0.70/0.37
% 0.70/0.37 Contains.Choice.Funs: false
% 0.70/0.37 .......
% 0.70/0.37
% 0.70/0.37 ********************************
% 0.70/0.37 * All subproblems solved! *
% 0.70/0.37 ********************************
% 0.70/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:20,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:361,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.70/0.37
% 0.70/0.37 %**** Beginning of derivation protocol ****
% 0.70/0.37 % SZS output start CNFRefutation
% See solution above
% 0.70/0.38
% 0.70/0.38 %**** End of derivation protocol ****
% 0.70/0.38 %**** no. of clauses in derivation: 289 ****
% 0.70/0.38 %**** clause counter: 361 ****
% 0.70/0.38
% 0.70/0.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:20,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:361,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------