%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV131+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 : n003.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 10:55:06 AM UTC 2026
% Result : Theorem 1.66s 0.50s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 33
% Syntax : Number of formulae : 319 ( 205 unt; 0 typ; 0 def)
% Number of atoms : 1573 ( 458 equ; 0 cnn)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 2407 ( 374 ~; 292 |; 51 &;1579 @)
% ( 15 <=>; 96 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 39 usr; 19 con; 0-4 aty)
% Number of variables : 400 ( 0 ^; 400 !; 0 ?; 400 :)
% 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_loopcounter,type,
loopcounter: $i ).
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_plus,type,
plus: $i > $i > $i ).
thf(tp_pred,type,
pred: $i > $i ).
thf(tp_pv1341,type,
pv1341: $i ).
thf(tp_s_best7,type,
s_best7: $i ).
thf(tp_s_sworst7,type,
s_sworst7: $i ).
thf(tp_s_worst7,type,
s_worst7: $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_float_0_001,type,
tptp_float_0_001: $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(1,axiom,
( ( succ @ ( succ @ ( succ @ n0 ) ) )
= n3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_3) ).
thf(8,axiom,
! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_1) ).
thf(9,axiom,
! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_0) ).
thf(12,axiom,
gt @ n5 @ n3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_3) ).
thf(13,axiom,
gt @ n4 @ n3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_3) ).
thf(14,axiom,
gt @ n3 @ n2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_2) ).
thf(17,axiom,
gt @ n3 @ n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_1) ).
thf(21,axiom,
gt @ n3 @ n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_0) ).
thf(22,axiom,
gt @ n2 @ n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_2_0) ).
thf(23,axiom,
gt @ n1 @ n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_1_0) ).
thf(24,axiom,
gt @ n5 @ n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_0) ).
thf(25,axiom,
gt @ n4 @ n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_0) ).
thf(26,axiom,
gt @ n3 @ tptp_minus_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_tptp_minus_1) ).
thf(29,axiom,
gt @ n0 @ tptp_minus_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_0_tptp_minus_1) ).
thf(41,axiom,
! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_minus) ).
thf(42,axiom,
! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ Y )
=> ( gt @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_gt) ).
thf(43,axiom,
! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_succ) ).
thf(70,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(71,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(72,axiom,
! [X: $i,Y: $i] :
( ( leq @ X @ Y )
<=> ( gt @ ( succ @ Y ) @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_gt_equiv) ).
thf(73,axiom,
! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ) ).
thf(74,axiom,
! [X: $i] : ( gt @ ( succ @ X ) @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_succ) ).
thf(75,axiom,
! [X: $i,Y: $i] :
( ( leq @ X @ ( pred @ Y ) )
<=> ( gt @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt_pred) ).
thf(76,axiom,
! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt2) ).
thf(77,axiom,
! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt1) ).
thf(78,axiom,
! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_geq) ).
thf(79,axiom,
! [X: $i,Y: $i] :
( ( lt @ X @ Y )
<=> ( gt @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lt_gt) ).
thf(80,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(81,axiom,
! [X: $i] : ( leq @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_leq) ).
thf(82,axiom,
! [X: $i] :
~ ( gt @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_gt) ).
thf(83,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( gt @ X @ Y )
& ( gt @ Y @ Z ) )
=> ( gt @ X @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_gt) ).
thf(84,axiom,
! [X: $i,Y: $i] :
( ( gt @ X @ Y )
| ( gt @ Y @ X )
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality) ).
thf(85,conjecture,
( ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
& ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ n0 @ s_best7 ) )
& ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ n0 @ s_sworst7 ) )
& ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ n0 @ s_worst7 ) )
& ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ s_best7 @ n3 ) )
& ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ s_sworst7 @ n3 ) )
& ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ s_worst7 @ n3 ) )
& ( ( gt @ loopcounter @ n0 )
=> ( leq @ n0 @ s_best7 ) )
& ( ( gt @ loopcounter @ n0 )
=> ( leq @ n0 @ s_sworst7 ) )
& ( ( gt @ loopcounter @ n0 )
=> ( leq @ n0 @ s_worst7 ) )
& ( ( gt @ loopcounter @ n0 )
=> ( leq @ s_best7 @ n3 ) )
& ( ( gt @ loopcounter @ n0 )
=> ( leq @ s_sworst7 @ n3 ) )
& ( ( gt @ loopcounter @ n0 )
=> ( leq @ s_worst7 @ n3 ) ) )
=> ( leq @ n0 @ s_best7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gauss_array_0001) ).
thf(86,negated_conjecture,
( ( ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
& ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ n0 @ s_best7 ) )
& ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ n0 @ s_sworst7 ) )
& ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ n0 @ s_worst7 ) )
& ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ s_best7 @ n3 ) )
& ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ s_sworst7 @ n3 ) )
& ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ s_worst7 @ n3 ) )
& ( ( gt @ loopcounter @ n0 )
=> ( leq @ n0 @ s_best7 ) )
& ( ( gt @ loopcounter @ n0 )
=> ( leq @ n0 @ s_sworst7 ) )
& ( ( gt @ loopcounter @ n0 )
=> ( leq @ n0 @ s_worst7 ) )
& ( ( gt @ loopcounter @ n0 )
=> ( leq @ s_best7 @ n3 ) )
& ( ( gt @ loopcounter @ n0 )
=> ( leq @ s_sworst7 @ n3 ) )
& ( ( gt @ loopcounter @ n0 )
=> ( leq @ s_worst7 @ n3 ) ) )
=> ( leq @ n0 @ s_best7 ) )
= $false ),
inference(negate_conjecture,[status(cth)],[85]) ).
thf(87,plain,
( ( ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
& ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ n0 @ s_best7 ) )
& ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ n0 @ s_sworst7 ) )
& ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ n0 @ s_worst7 ) )
& ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ s_best7 @ n3 ) )
& ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ s_sworst7 @ n3 ) )
& ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ s_worst7 @ n3 ) )
& ( ( gt @ loopcounter @ n0 )
=> ( leq @ n0 @ s_best7 ) )
& ( ( gt @ loopcounter @ n0 )
=> ( leq @ n0 @ s_sworst7 ) )
& ( ( gt @ loopcounter @ n0 )
=> ( leq @ n0 @ s_worst7 ) )
& ( ( gt @ loopcounter @ n0 )
=> ( leq @ s_best7 @ n3 ) )
& ( ( gt @ loopcounter @ n0 )
=> ( leq @ s_sworst7 @ n3 ) )
& ( ( gt @ loopcounter @ n0 )
=> ( leq @ s_worst7 @ n3 ) ) )
=> ( leq @ n0 @ s_best7 ) )
= $false ),
inference(unfold_def,[status(thm)],[86]) ).
thf(88,plain,
( ( ( succ @ ( succ @ ( succ @ n0 ) ) )
= n3 )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(89,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(90,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(91,plain,
( ( gt @ n5 @ n3 )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(92,plain,
( ( gt @ n4 @ n3 )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(93,plain,
( ( gt @ n3 @ n2 )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(94,plain,
( ( gt @ n3 @ n1 )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(95,plain,
( ( gt @ n3 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(96,plain,
( ( gt @ n2 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(97,plain,
( ( gt @ n1 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(98,plain,
( ( gt @ n5 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(99,plain,
( ( gt @ n4 @ n0 )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(100,plain,
( ( gt @ n3 @ tptp_minus_1 )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(101,plain,
( ( gt @ n0 @ tptp_minus_1 )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(102,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(103,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ Y )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(104,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(105,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(106,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(107,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
<=> ( gt @ ( succ @ Y ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(108,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(109,plain,
( ( ! [X: $i] : ( gt @ ( succ @ X ) @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(110,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ ( pred @ Y ) )
<=> ( gt @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(111,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(112,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(113,plain,
( ( ! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(114,plain,
( ( ! [X: $i,Y: $i] :
( ( lt @ X @ Y )
<=> ( gt @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(115,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(116,plain,
( ( ! [X: $i] : ( leq @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(117,plain,
( ( ! [X: $i] :
~ ( gt @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(118,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( gt @ X @ Y )
& ( gt @ Y @ Z ) )
=> ( gt @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(119,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ X @ Y )
| ( gt @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(120,plain,
( ( ~ ( leq @ tptp_float_0_001 @ pv1341 ) )
= $true ),
inference(standard_cnf,[status(thm)],[87]) ).
thf(121,plain,
( ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ n0 @ s_best7 ) )
= $true ),
inference(standard_cnf,[status(thm)],[87]) ).
thf(122,plain,
( ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ n0 @ s_sworst7 ) )
= $true ),
inference(standard_cnf,[status(thm)],[87]) ).
thf(123,plain,
( ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ n0 @ s_worst7 ) )
= $true ),
inference(standard_cnf,[status(thm)],[87]) ).
thf(124,plain,
( ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ s_best7 @ n3 ) )
= $true ),
inference(standard_cnf,[status(thm)],[87]) ).
thf(125,plain,
( ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ s_sworst7 @ n3 ) )
= $true ),
inference(standard_cnf,[status(thm)],[87]) ).
thf(126,plain,
( ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ s_worst7 @ n3 ) )
= $true ),
inference(standard_cnf,[status(thm)],[87]) ).
thf(127,plain,
( ( ( gt @ loopcounter @ n0 )
=> ( leq @ n0 @ s_best7 ) )
= $true ),
inference(standard_cnf,[status(thm)],[87]) ).
thf(128,plain,
( ( ( gt @ loopcounter @ n0 )
=> ( leq @ n0 @ s_sworst7 ) )
= $true ),
inference(standard_cnf,[status(thm)],[87]) ).
thf(129,plain,
( ( ( gt @ loopcounter @ n0 )
=> ( leq @ n0 @ s_worst7 ) )
= $true ),
inference(standard_cnf,[status(thm)],[87]) ).
thf(130,plain,
( ( ( gt @ loopcounter @ n0 )
=> ( leq @ s_best7 @ n3 ) )
= $true ),
inference(standard_cnf,[status(thm)],[87]) ).
thf(131,plain,
( ( ( gt @ loopcounter @ n0 )
=> ( leq @ s_sworst7 @ n3 ) )
= $true ),
inference(standard_cnf,[status(thm)],[87]) ).
thf(132,plain,
( ( ( gt @ loopcounter @ n0 )
=> ( leq @ s_worst7 @ n3 ) )
= $true ),
inference(standard_cnf,[status(thm)],[87]) ).
thf(133,plain,
( ( leq @ n0 @ s_best7 )
= $false ),
inference(standard_cnf,[status(thm)],[87]) ).
thf(134,plain,
( ( ~ ( leq @ n0 @ s_best7 ) )
= $true ),
inference(polarity_switch,[status(thm)],[133]) ).
thf(135,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ X @ Y )
| ( gt @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(136,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( gt @ X @ Y )
& ( gt @ Y @ Z ) )
=> ( gt @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(137,plain,
( ( ! [X: $i] :
~ ( gt @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(138,plain,
( ( ! [X: $i] : ( leq @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(139,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(140,plain,
( ( ! [X: $i,Y: $i] :
( ( lt @ X @ Y )
<=> ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(141,plain,
( ( ! [X: $i,Y: $i] :
( ( geq @ X @ Y )
<=> ( leq @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(142,plain,
( ( ! [X: $i,Y: $i] :
( ( gt @ Y @ X )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(143,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( X != Y ) )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(144,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ ( pred @ Y ) )
<=> ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(145,plain,
( ( ! [X: $i] : ( gt @ ( succ @ X ) @ X ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(146,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
=> ( leq @ X @ ( succ @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(147,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
<=> ( gt @ ( succ @ Y ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(148,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(149,plain,
( ( ! [X: $i,C: $i] :
( ( leq @ n0 @ X )
=> ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(150,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ ( succ @ Y ) )
<=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(151,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( succ @ X ) @ Y )
=> ( gt @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(152,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ ( minus @ X @ Y ) @ X )
=> ( leq @ n0 @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(153,plain,
( ( gt @ n0 @ tptp_minus_1 )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(154,plain,
( ( gt @ n3 @ tptp_minus_1 )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(155,plain,
( ( gt @ n4 @ n0 )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(156,plain,
( ( gt @ n5 @ n0 )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(157,plain,
( ( gt @ n1 @ n0 )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(158,plain,
( ( gt @ n2 @ n0 )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(159,plain,
( ( gt @ n3 @ n0 )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(160,plain,
( ( gt @ n3 @ n1 )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(161,plain,
( ( gt @ n3 @ n2 )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(162,plain,
( ( gt @ n4 @ n3 )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(163,plain,
( ( gt @ n5 @ n3 )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(164,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n0 ) )
=> ( X = n0 ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(165,plain,
( ( ! [X: $i] :
( ( ( leq @ n0 @ X )
& ( leq @ X @ n1 ) )
=> ( ( X = n0 )
| ( X = n1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(166,plain,
( ( ( succ @ ( succ @ ( succ @ n0 ) ) )
= n3 )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(167,plain,
( ( ( gt @ loopcounter @ n0 )
=> ( leq @ s_worst7 @ n3 ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(168,plain,
( ( ( gt @ loopcounter @ n0 )
=> ( leq @ s_sworst7 @ n3 ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(169,plain,
( ( ( gt @ loopcounter @ n0 )
=> ( leq @ s_best7 @ n3 ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(170,plain,
( ( ( gt @ loopcounter @ n0 )
=> ( leq @ n0 @ s_worst7 ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(171,plain,
( ( ( gt @ loopcounter @ n0 )
=> ( leq @ n0 @ s_sworst7 ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(172,plain,
( ( ( gt @ loopcounter @ n0 )
=> ( leq @ n0 @ s_best7 ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(173,plain,
( ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ s_worst7 @ n3 ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(174,plain,
( ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ s_sworst7 @ n3 ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(175,plain,
( ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ s_best7 @ n3 ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(176,plain,
( ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ n0 @ s_worst7 ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(177,plain,
( ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ n0 @ s_sworst7 ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(178,plain,
( ( ~ ( leq @ tptp_float_0_001 @ pv1341 )
=> ( leq @ n0 @ s_best7 ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(179,plain,
( ( ~ ( leq @ tptp_float_0_001 @ pv1341 ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(180,plain,
( ( ~ ( leq @ n0 @ s_best7 ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(181,plain,
( ( ~ ~ ( leq @ tptp_float_0_001 @ pv1341 )
| ( leq @ n0 @ s_sworst7 ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(182,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ n0 @ ( uniform_int_rnd @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(183,plain,
( ( ~ ~ ( leq @ tptp_float_0_001 @ pv1341 )
| ( leq @ s_worst7 @ n3 ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(184,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( leq @ SX0 @ SX1 )
| ( gt @ ( succ @ SX1 ) @ SX0 ) )
| ~ ( ~ ( gt @ ( succ @ SX1 ) @ SX0 )
| ( leq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(185,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( leq @ SX1 @ SX2 ) )
| ( leq @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(186,plain,
( ( ~ ~ ( leq @ tptp_float_0_001 @ pv1341 )
| ( leq @ n0 @ s_best7 ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(187,plain,
( ( ~ ( gt @ loopcounter @ n0 )
| ( leq @ n0 @ s_worst7 ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(188,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ ( succ @ SX0 ) @ SX1 )
| ( gt @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(189,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n1 ) )
| ( SX0 = n0 )
| ( SX0 = n1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(190,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ SX0 @ SX1 )
| ( leq @ SX0 @ ( succ @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(191,plain,
( ( ~ ( gt @ loopcounter @ n0 )
| ( leq @ s_worst7 @ n3 ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(192,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( leq @ n0 @ SX0 )
| ~ ( leq @ SX0 @ n0 ) )
| ( SX0 = n0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(193,plain,
( ( ~ ~ ( leq @ tptp_float_0_001 @ pv1341 )
| ( leq @ s_sworst7 @ n3 ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(194,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( gt @ SX0 @ SX1 )
| ~ ( gt @ SX1 @ SX2 ) )
| ( gt @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(195,plain,
( ( ~ ~ ( leq @ tptp_float_0_001 @ pv1341 )
| ( leq @ s_best7 @ n3 ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(196,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ n0 @ SX0 )
| ( leq @ ( uniform_int_rnd @ SX1 @ SX0 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(197,plain,
( ( ~ ( gt @ loopcounter @ n0 )
| ( leq @ s_best7 @ n3 ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(198,plain,
( ( ~ ( gt @ loopcounter @ n0 )
| ( leq @ n0 @ s_sworst7 ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(199,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( leq @ SX0 @ ( pred @ SX1 ) )
| ( gt @ SX1 @ SX0 ) )
| ~ ( ~ ( gt @ SX1 @ SX0 )
| ( leq @ SX0 @ ( pred @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(200,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( gt @ SX1 @ SX0 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(201,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)],[150]) ).
thf(202,plain,
( ( ~ ( gt @ loopcounter @ n0 )
| ( leq @ n0 @ s_best7 ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(203,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( gt @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(204,plain,
( ( ~ ~ ( leq @ tptp_float_0_001 @ pv1341 )
| ( leq @ n0 @ s_worst7 ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(205,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( lt @ SX0 @ SX1 )
| ( gt @ SX1 @ SX0 ) )
| ~ ( ~ ( gt @ SX1 @ SX0 )
| ( lt @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(206,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( leq @ ( minus @ SX0 @ SX1 ) @ SX0 )
| ( leq @ n0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(207,plain,
( ( ~ ( gt @ loopcounter @ n0 )
| ( leq @ s_sworst7 @ n3 ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(208,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( geq @ SX0 @ SX1 )
| ( leq @ SX1 @ SX0 ) )
| ~ ( ~ ( leq @ SX1 @ SX0 )
| ( geq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(209,plain,
! [SV1: $i] :
( ( ! [SY37: $i] :
( ( gt @ SV1 @ SY37 )
| ( gt @ SY37 @ SV1 )
| ( SV1 = SY37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(210,plain,
! [SV2: $i] :
( ( ~ ( gt @ SV2 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(211,plain,
! [SV3: $i] :
( ( leq @ SV3 @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(212,plain,
! [SV4: $i] :
( ( gt @ ( succ @ SV4 ) @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(213,plain,
( ( leq @ tptp_float_0_001 @ pv1341 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(214,plain,
( ( leq @ n0 @ s_best7 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(215,plain,
( ( ( ~ ~ ( leq @ tptp_float_0_001 @ pv1341 ) )
= $true )
| ( ( leq @ n0 @ s_sworst7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(216,plain,
! [SV5: $i] :
( ( ! [SY38: $i] :
( ~ ( leq @ n0 @ SV5 )
| ( leq @ n0 @ ( uniform_int_rnd @ SY38 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(217,plain,
( ( ( ~ ~ ( leq @ tptp_float_0_001 @ pv1341 ) )
= $true )
| ( ( leq @ s_worst7 @ n3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(218,plain,
! [SV6: $i] :
( ( ! [SY39: $i] :
~ ( ~ ( ~ ( leq @ SV6 @ SY39 )
| ( gt @ ( succ @ SY39 ) @ SV6 ) )
| ~ ( ~ ( gt @ ( succ @ SY39 ) @ SV6 )
| ( leq @ SV6 @ SY39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(219,plain,
! [SV7: $i] :
( ( ! [SY40: $i,SY41: $i] :
( ~ ~ ( ~ ( leq @ SV7 @ SY40 )
| ~ ( leq @ SY40 @ SY41 ) )
| ( leq @ SV7 @ SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(220,plain,
( ( ( ~ ~ ( leq @ tptp_float_0_001 @ pv1341 ) )
= $true )
| ( ( leq @ n0 @ s_best7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(221,plain,
( ( ( ~ ( gt @ loopcounter @ n0 ) )
= $true )
| ( ( leq @ n0 @ s_worst7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(222,plain,
! [SV8: $i] :
( ( ! [SY42: $i] :
( ~ ( leq @ ( succ @ SV8 ) @ SY42 )
| ( gt @ SY42 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(223,plain,
! [SV9: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV9 )
| ~ ( leq @ SV9 @ n1 ) )
| ( SV9 = n0 )
| ( SV9 = n1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(224,plain,
! [SV10: $i] :
( ( ! [SY43: $i] :
( ~ ( leq @ SV10 @ SY43 )
| ( leq @ SV10 @ ( succ @ SY43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(225,plain,
( ( ( ~ ( gt @ loopcounter @ n0 ) )
= $true )
| ( ( leq @ s_worst7 @ n3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(226,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ( leq @ n0 @ SV11 )
| ~ ( leq @ SV11 @ n0 ) )
| ( SV11 = n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(227,plain,
( ( ( ~ ~ ( leq @ tptp_float_0_001 @ pv1341 ) )
= $true )
| ( ( leq @ s_sworst7 @ n3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(228,plain,
! [SV12: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ~ ~ ( ~ ( gt @ SV12 @ SY44 )
| ~ ( gt @ SY44 @ SY45 ) )
| ( gt @ SV12 @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(229,plain,
( ( ( ~ ~ ( leq @ tptp_float_0_001 @ pv1341 ) )
= $true )
| ( ( leq @ s_best7 @ n3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(230,plain,
! [SV13: $i] :
( ( ! [SY46: $i] :
( ~ ( leq @ n0 @ SV13 )
| ( leq @ ( uniform_int_rnd @ SY46 @ SV13 ) @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(231,plain,
( ( ( ~ ( gt @ loopcounter @ n0 ) )
= $true )
| ( ( leq @ s_best7 @ n3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(232,plain,
( ( ( ~ ( gt @ loopcounter @ n0 ) )
= $true )
| ( ( leq @ n0 @ s_sworst7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(233,plain,
! [SV14: $i] :
( ( ! [SY47: $i] :
~ ( ~ ( ~ ( leq @ SV14 @ ( pred @ SY47 ) )
| ( gt @ SY47 @ SV14 ) )
| ~ ( ~ ( gt @ SY47 @ SV14 )
| ( leq @ SV14 @ ( pred @ SY47 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(234,plain,
! [SV15: $i] :
( ( ! [SY48: $i] :
( ~ ( gt @ SY48 @ SV15 )
| ( leq @ SV15 @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(235,plain,
! [SV16: $i] :
( ( ! [SY49: $i] :
~ ( ~ ( ~ ( leq @ ( succ @ SV16 ) @ ( succ @ SY49 ) )
| ( leq @ SV16 @ SY49 ) )
| ~ ( ~ ( leq @ SV16 @ SY49 )
| ( leq @ ( succ @ SV16 ) @ ( succ @ SY49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(236,plain,
( ( ( ~ ( gt @ loopcounter @ n0 ) )
= $true )
| ( ( leq @ n0 @ s_best7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(237,plain,
! [SV17: $i] :
( ( ! [SY50: $i] :
( ~ ~ ( ~ ( leq @ SV17 @ SY50 )
| ~ ( ( SV17 != SY50 ) ) )
| ( gt @ SY50 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(238,plain,
( ( ( ~ ~ ( leq @ tptp_float_0_001 @ pv1341 ) )
= $true )
| ( ( leq @ n0 @ s_worst7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(239,plain,
! [SV18: $i] :
( ( ! [SY51: $i] :
~ ( ~ ( ~ ( lt @ SV18 @ SY51 )
| ( gt @ SY51 @ SV18 ) )
| ~ ( ~ ( gt @ SY51 @ SV18 )
| ( lt @ SV18 @ SY51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(240,plain,
! [SV19: $i] :
( ( ! [SY52: $i] :
( ~ ( leq @ ( minus @ SV19 @ SY52 ) @ SV19 )
| ( leq @ n0 @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(241,plain,
( ( ( ~ ( gt @ loopcounter @ n0 ) )
= $true )
| ( ( leq @ s_sworst7 @ n3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(242,plain,
! [SV20: $i] :
( ( ! [SY53: $i] :
~ ( ~ ( ~ ( geq @ SV20 @ SY53 )
| ( leq @ SY53 @ SV20 ) )
| ~ ( ~ ( leq @ SY53 @ SV20 )
| ( geq @ SV20 @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(243,plain,
! [SV21: $i,SV1: $i] :
( ( ( gt @ SV1 @ SV21 )
| ( gt @ SV21 @ SV1 )
| ( SV1 = SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(244,plain,
! [SV2: $i] :
( ( gt @ SV2 @ SV2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(245,plain,
( ( ( ~ ( leq @ tptp_float_0_001 @ pv1341 ) )
= $false )
| ( ( leq @ n0 @ s_sworst7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(246,plain,
! [SV22: $i,SV5: $i] :
( ( ~ ( leq @ n0 @ SV5 )
| ( leq @ n0 @ ( uniform_int_rnd @ SV22 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(247,plain,
( ( ( ~ ( leq @ tptp_float_0_001 @ pv1341 ) )
= $false )
| ( ( leq @ s_worst7 @ n3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(248,plain,
! [SV23: $i,SV6: $i] :
( ( ~ ( ~ ( ~ ( leq @ SV6 @ SV23 )
| ( gt @ ( succ @ SV23 ) @ SV6 ) )
| ~ ( ~ ( gt @ ( succ @ SV23 ) @ SV6 )
| ( leq @ SV6 @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(249,plain,
! [SV24: $i,SV7: $i] :
( ( ! [SY54: $i] :
( ~ ~ ( ~ ( leq @ SV7 @ SV24 )
| ~ ( leq @ SV24 @ SY54 ) )
| ( leq @ SV7 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(250,plain,
( ( ( ~ ( leq @ tptp_float_0_001 @ pv1341 ) )
= $false )
| ( ( leq @ n0 @ s_best7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(251,plain,
( ( ( gt @ loopcounter @ n0 )
= $false )
| ( ( leq @ n0 @ s_worst7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(252,plain,
! [SV25: $i,SV8: $i] :
( ( ~ ( leq @ ( succ @ SV8 ) @ SV25 )
| ( gt @ SV25 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(253,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV9 )
| ~ ( leq @ SV9 @ n1 ) ) )
= $true )
| ( ( ( SV9 = n0 )
| ( SV9 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(254,plain,
! [SV26: $i,SV10: $i] :
( ( ~ ( leq @ SV10 @ SV26 )
| ( leq @ SV10 @ ( succ @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(255,plain,
( ( ( gt @ loopcounter @ n0 )
= $false )
| ( ( leq @ s_worst7 @ n3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(256,plain,
! [SV11: $i] :
( ( ( ~ ~ ( ~ ( leq @ n0 @ SV11 )
| ~ ( leq @ SV11 @ n0 ) ) )
= $true )
| ( ( SV11 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(257,plain,
( ( ( ~ ( leq @ tptp_float_0_001 @ pv1341 ) )
= $false )
| ( ( leq @ s_sworst7 @ n3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(258,plain,
! [SV27: $i,SV12: $i] :
( ( ! [SY55: $i] :
( ~ ~ ( ~ ( gt @ SV12 @ SV27 )
| ~ ( gt @ SV27 @ SY55 ) )
| ( gt @ SV12 @ SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(259,plain,
( ( ( ~ ( leq @ tptp_float_0_001 @ pv1341 ) )
= $false )
| ( ( leq @ s_best7 @ n3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(260,plain,
! [SV28: $i,SV13: $i] :
( ( ~ ( leq @ n0 @ SV13 )
| ( leq @ ( uniform_int_rnd @ SV28 @ SV13 ) @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(261,plain,
( ( ( gt @ loopcounter @ n0 )
= $false )
| ( ( leq @ s_best7 @ n3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(262,plain,
( ( ( gt @ loopcounter @ n0 )
= $false )
| ( ( leq @ n0 @ s_sworst7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(263,plain,
! [SV29: $i,SV14: $i] :
( ( ~ ( ~ ( ~ ( leq @ SV14 @ ( pred @ SV29 ) )
| ( gt @ SV29 @ SV14 ) )
| ~ ( ~ ( gt @ SV29 @ SV14 )
| ( leq @ SV14 @ ( pred @ SV29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(264,plain,
! [SV15: $i,SV30: $i] :
( ( ~ ( gt @ SV30 @ SV15 )
| ( leq @ SV15 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(265,plain,
! [SV31: $i,SV16: $i] :
( ( ~ ( ~ ( ~ ( leq @ ( succ @ SV16 ) @ ( succ @ SV31 ) )
| ( leq @ SV16 @ SV31 ) )
| ~ ( ~ ( leq @ SV16 @ SV31 )
| ( leq @ ( succ @ SV16 ) @ ( succ @ SV31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(266,plain,
( ( ( gt @ loopcounter @ n0 )
= $false )
| ( ( leq @ n0 @ s_best7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(267,plain,
! [SV32: $i,SV17: $i] :
( ( ~ ~ ( ~ ( leq @ SV17 @ SV32 )
| ~ ( ( SV17 != SV32 ) ) )
| ( gt @ SV32 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(268,plain,
( ( ( ~ ( leq @ tptp_float_0_001 @ pv1341 ) )
= $false )
| ( ( leq @ n0 @ s_worst7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(269,plain,
! [SV33: $i,SV18: $i] :
( ( ~ ( ~ ( ~ ( lt @ SV18 @ SV33 )
| ( gt @ SV33 @ SV18 ) )
| ~ ( ~ ( gt @ SV33 @ SV18 )
| ( lt @ SV18 @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(270,plain,
! [SV34: $i,SV19: $i] :
( ( ~ ( leq @ ( minus @ SV19 @ SV34 ) @ SV19 )
| ( leq @ n0 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(271,plain,
( ( ( gt @ loopcounter @ n0 )
= $false )
| ( ( leq @ s_sworst7 @ n3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(272,plain,
! [SV35: $i,SV20: $i] :
( ( ~ ( ~ ( ~ ( geq @ SV20 @ SV35 )
| ( leq @ SV35 @ SV20 ) )
| ~ ( ~ ( leq @ SV35 @ SV20 )
| ( geq @ SV20 @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(273,plain,
! [SV21: $i,SV1: $i] :
( ( ( ( gt @ SV1 @ SV21 )
| ( gt @ SV21 @ SV1 ) )
= $true )
| ( ( SV1 = SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(274,plain,
( ( ( leq @ tptp_float_0_001 @ pv1341 )
= $true )
| ( ( leq @ n0 @ s_sworst7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(275,plain,
! [SV22: $i,SV5: $i] :
( ( ( ~ ( leq @ n0 @ SV5 ) )
= $true )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV22 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(276,plain,
( ( ( leq @ tptp_float_0_001 @ pv1341 )
= $true )
| ( ( leq @ s_worst7 @ n3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(277,plain,
! [SV23: $i,SV6: $i] :
( ( ~ ( ~ ( leq @ SV6 @ SV23 )
| ( gt @ ( succ @ SV23 ) @ SV6 ) )
| ~ ( ~ ( gt @ ( succ @ SV23 ) @ SV6 )
| ( leq @ SV6 @ SV23 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(278,plain,
! [SV36: $i,SV24: $i,SV7: $i] :
( ( ~ ~ ( ~ ( leq @ SV7 @ SV24 )
| ~ ( leq @ SV24 @ SV36 ) )
| ( leq @ SV7 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(279,plain,
( ( ( leq @ tptp_float_0_001 @ pv1341 )
= $true )
| ( ( leq @ n0 @ s_best7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(280,plain,
! [SV25: $i,SV8: $i] :
( ( ( ~ ( leq @ ( succ @ SV8 ) @ SV25 ) )
= $true )
| ( ( gt @ SV25 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(281,plain,
! [SV9: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV9 )
| ~ ( leq @ SV9 @ n1 ) ) )
= $false )
| ( ( ( SV9 = n0 )
| ( SV9 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(282,plain,
! [SV26: $i,SV10: $i] :
( ( ( ~ ( leq @ SV10 @ SV26 ) )
= $true )
| ( ( leq @ SV10 @ ( succ @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(283,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ( leq @ n0 @ SV11 )
| ~ ( leq @ SV11 @ n0 ) ) )
= $false )
| ( ( SV11 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(284,plain,
( ( ( leq @ tptp_float_0_001 @ pv1341 )
= $true )
| ( ( leq @ s_sworst7 @ n3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(285,plain,
! [SV37: $i,SV27: $i,SV12: $i] :
( ( ~ ~ ( ~ ( gt @ SV12 @ SV27 )
| ~ ( gt @ SV27 @ SV37 ) )
| ( gt @ SV12 @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(286,plain,
( ( ( leq @ tptp_float_0_001 @ pv1341 )
= $true )
| ( ( leq @ s_best7 @ n3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(287,plain,
! [SV28: $i,SV13: $i] :
( ( ( ~ ( leq @ n0 @ SV13 ) )
= $true )
| ( ( leq @ ( uniform_int_rnd @ SV28 @ SV13 ) @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(288,plain,
! [SV29: $i,SV14: $i] :
( ( ~ ( ~ ( leq @ SV14 @ ( pred @ SV29 ) )
| ( gt @ SV29 @ SV14 ) )
| ~ ( ~ ( gt @ SV29 @ SV14 )
| ( leq @ SV14 @ ( pred @ SV29 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(289,plain,
! [SV15: $i,SV30: $i] :
( ( ( ~ ( gt @ SV30 @ SV15 ) )
= $true )
| ( ( leq @ SV15 @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(290,plain,
! [SV31: $i,SV16: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV16 ) @ ( succ @ SV31 ) )
| ( leq @ SV16 @ SV31 ) )
| ~ ( ~ ( leq @ SV16 @ SV31 )
| ( leq @ ( succ @ SV16 ) @ ( succ @ SV31 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(291,plain,
! [SV32: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV17 @ SV32 )
| ~ ( ( SV17 != SV32 ) ) ) )
= $true )
| ( ( gt @ SV32 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[267]) ).
thf(292,plain,
( ( ( leq @ tptp_float_0_001 @ pv1341 )
= $true )
| ( ( leq @ n0 @ s_worst7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(293,plain,
! [SV33: $i,SV18: $i] :
( ( ~ ( ~ ( lt @ SV18 @ SV33 )
| ( gt @ SV33 @ SV18 ) )
| ~ ( ~ ( gt @ SV33 @ SV18 )
| ( lt @ SV18 @ SV33 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(294,plain,
! [SV34: $i,SV19: $i] :
( ( ( ~ ( leq @ ( minus @ SV19 @ SV34 ) @ SV19 ) )
= $true )
| ( ( leq @ n0 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(295,plain,
! [SV35: $i,SV20: $i] :
( ( ~ ( ~ ( geq @ SV20 @ SV35 )
| ( leq @ SV35 @ SV20 ) )
| ~ ( ~ ( leq @ SV35 @ SV20 )
| ( geq @ SV20 @ SV35 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(296,plain,
! [SV21: $i,SV1: $i] :
( ( ( gt @ SV1 @ SV21 )
= $true )
| ( ( gt @ SV21 @ SV1 )
= $true )
| ( ( SV1 = SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(297,plain,
! [SV22: $i,SV5: $i] :
( ( ( leq @ n0 @ SV5 )
= $false )
| ( ( leq @ n0 @ ( uniform_int_rnd @ SV22 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(298,plain,
! [SV23: $i,SV6: $i] :
( ( ~ ( ~ ( leq @ SV6 @ SV23 )
| ( gt @ ( succ @ SV23 ) @ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[277]) ).
thf(299,plain,
! [SV6: $i,SV23: $i] :
( ( ~ ( ~ ( gt @ ( succ @ SV23 ) @ SV6 )
| ( leq @ SV6 @ SV23 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[277]) ).
thf(300,plain,
! [SV36: $i,SV24: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV7 @ SV24 )
| ~ ( leq @ SV24 @ SV36 ) ) )
= $true )
| ( ( leq @ SV7 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(301,plain,
! [SV25: $i,SV8: $i] :
( ( ( leq @ ( succ @ SV8 ) @ SV25 )
= $false )
| ( ( gt @ SV25 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(302,plain,
! [SV9: $i] :
( ( ( ~ ( leq @ n0 @ SV9 )
| ~ ( leq @ SV9 @ n1 ) )
= $true )
| ( ( ( SV9 = n0 )
| ( SV9 = n1 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(303,plain,
! [SV26: $i,SV10: $i] :
( ( ( leq @ SV10 @ SV26 )
= $false )
| ( ( leq @ SV10 @ ( succ @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(304,plain,
! [SV11: $i] :
( ( ( ~ ( leq @ n0 @ SV11 )
| ~ ( leq @ SV11 @ n0 ) )
= $true )
| ( ( SV11 = n0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(305,plain,
! [SV37: $i,SV27: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( gt @ SV12 @ SV27 )
| ~ ( gt @ SV27 @ SV37 ) ) )
= $true )
| ( ( gt @ SV12 @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(306,plain,
! [SV28: $i,SV13: $i] :
( ( ( leq @ n0 @ SV13 )
= $false )
| ( ( leq @ ( uniform_int_rnd @ SV28 @ SV13 ) @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(307,plain,
! [SV29: $i,SV14: $i] :
( ( ~ ( ~ ( leq @ SV14 @ ( pred @ SV29 ) )
| ( gt @ SV29 @ SV14 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(308,plain,
! [SV14: $i,SV29: $i] :
( ( ~ ( ~ ( gt @ SV29 @ SV14 )
| ( leq @ SV14 @ ( pred @ SV29 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(309,plain,
! [SV15: $i,SV30: $i] :
( ( ( gt @ SV30 @ SV15 )
= $false )
| ( ( leq @ SV15 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(310,plain,
! [SV31: $i,SV16: $i] :
( ( ~ ( ~ ( leq @ ( succ @ SV16 ) @ ( succ @ SV31 ) )
| ( leq @ SV16 @ SV31 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(311,plain,
! [SV31: $i,SV16: $i] :
( ( ~ ( ~ ( leq @ SV16 @ SV31 )
| ( leq @ ( succ @ SV16 ) @ ( succ @ SV31 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(312,plain,
! [SV32: $i,SV17: $i] :
( ( ( ~ ( ~ ( leq @ SV17 @ SV32 )
| ~ ( ( SV17 != SV32 ) ) ) )
= $false )
| ( ( gt @ SV32 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(313,plain,
! [SV33: $i,SV18: $i] :
( ( ~ ( ~ ( lt @ SV18 @ SV33 )
| ( gt @ SV33 @ SV18 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(314,plain,
! [SV18: $i,SV33: $i] :
( ( ~ ( ~ ( gt @ SV33 @ SV18 )
| ( lt @ SV18 @ SV33 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(315,plain,
! [SV34: $i,SV19: $i] :
( ( ( leq @ ( minus @ SV19 @ SV34 ) @ SV19 )
= $false )
| ( ( leq @ n0 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(316,plain,
! [SV35: $i,SV20: $i] :
( ( ~ ( ~ ( geq @ SV20 @ SV35 )
| ( leq @ SV35 @ SV20 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[295]) ).
thf(317,plain,
! [SV20: $i,SV35: $i] :
( ( ~ ( ~ ( leq @ SV35 @ SV20 )
| ( geq @ SV20 @ SV35 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[295]) ).
thf(318,plain,
! [SV23: $i,SV6: $i] :
( ( ~ ( leq @ SV6 @ SV23 )
| ( gt @ ( succ @ SV23 ) @ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[298]) ).
thf(319,plain,
! [SV6: $i,SV23: $i] :
( ( ~ ( gt @ ( succ @ SV23 ) @ SV6 )
| ( leq @ SV6 @ SV23 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(320,plain,
! [SV36: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( ~ ( leq @ SV7 @ SV24 )
| ~ ( leq @ SV24 @ SV36 ) ) )
= $false )
| ( ( leq @ SV7 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(321,plain,
! [SV9: $i] :
( ( ( ~ ( leq @ n0 @ SV9 ) )
= $true )
| ( ( ~ ( leq @ SV9 @ n1 ) )
= $true )
| ( ( ( SV9 = n0 )
| ( SV9 = n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(322,plain,
! [SV11: $i] :
( ( ( ~ ( leq @ n0 @ SV11 ) )
= $true )
| ( ( ~ ( leq @ SV11 @ n0 ) )
= $true )
| ( ( SV11 = n0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(323,plain,
! [SV37: $i,SV27: $i,SV12: $i] :
( ( ( ~ ( ~ ( gt @ SV12 @ SV27 )
| ~ ( gt @ SV27 @ SV37 ) ) )
= $false )
| ( ( gt @ SV12 @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(324,plain,
! [SV29: $i,SV14: $i] :
( ( ~ ( leq @ SV14 @ ( pred @ SV29 ) )
| ( gt @ SV29 @ SV14 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(325,plain,
! [SV14: $i,SV29: $i] :
( ( ~ ( gt @ SV29 @ SV14 )
| ( leq @ SV14 @ ( pred @ SV29 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(326,plain,
! [SV31: $i,SV16: $i] :
( ( ~ ( leq @ ( succ @ SV16 ) @ ( succ @ SV31 ) )
| ( leq @ SV16 @ SV31 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(327,plain,
! [SV31: $i,SV16: $i] :
( ( ~ ( leq @ SV16 @ SV31 )
| ( leq @ ( succ @ SV16 ) @ ( succ @ SV31 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(328,plain,
! [SV32: $i,SV17: $i] :
( ( ( ~ ( leq @ SV17 @ SV32 )
| ~ ( ( SV17 != SV32 ) ) )
= $true )
| ( ( gt @ SV32 @ SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[312]) ).
thf(329,plain,
! [SV33: $i,SV18: $i] :
( ( ~ ( lt @ SV18 @ SV33 )
| ( gt @ SV33 @ SV18 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[313]) ).
thf(330,plain,
! [SV18: $i,SV33: $i] :
( ( ~ ( gt @ SV33 @ SV18 )
| ( lt @ SV18 @ SV33 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[314]) ).
thf(331,plain,
! [SV35: $i,SV20: $i] :
( ( ~ ( geq @ SV20 @ SV35 )
| ( leq @ SV35 @ SV20 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(332,plain,
! [SV20: $i,SV35: $i] :
( ( ~ ( leq @ SV35 @ SV20 )
| ( geq @ SV20 @ SV35 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[317]) ).
thf(333,plain,
! [SV23: $i,SV6: $i] :
( ( ( ~ ( leq @ SV6 @ SV23 ) )
= $true )
| ( ( gt @ ( succ @ SV23 ) @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(334,plain,
! [SV6: $i,SV23: $i] :
( ( ( ~ ( gt @ ( succ @ SV23 ) @ SV6 ) )
= $true )
| ( ( leq @ SV6 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(335,plain,
! [SV36: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( leq @ SV7 @ SV24 )
| ~ ( leq @ SV24 @ SV36 ) )
= $true )
| ( ( leq @ SV7 @ SV36 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(336,plain,
! [SV9: $i] :
( ( ( leq @ n0 @ SV9 )
= $false )
| ( ( ~ ( leq @ SV9 @ n1 ) )
= $true )
| ( ( ( SV9 = n0 )
| ( SV9 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(337,plain,
! [SV11: $i] :
( ( ( leq @ n0 @ SV11 )
= $false )
| ( ( ~ ( leq @ SV11 @ n0 ) )
= $true )
| ( ( SV11 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(338,plain,
! [SV37: $i,SV27: $i,SV12: $i] :
( ( ( ~ ( gt @ SV12 @ SV27 )
| ~ ( gt @ SV27 @ SV37 ) )
= $true )
| ( ( gt @ SV12 @ SV37 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[323]) ).
thf(339,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ( leq @ SV14 @ ( pred @ SV29 ) ) )
= $true )
| ( ( gt @ SV29 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(340,plain,
! [SV14: $i,SV29: $i] :
( ( ( ~ ( gt @ SV29 @ SV14 ) )
= $true )
| ( ( leq @ SV14 @ ( pred @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(341,plain,
! [SV31: $i,SV16: $i] :
( ( ( ~ ( leq @ ( succ @ SV16 ) @ ( succ @ SV31 ) ) )
= $true )
| ( ( leq @ SV16 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(342,plain,
! [SV31: $i,SV16: $i] :
( ( ( ~ ( leq @ SV16 @ SV31 ) )
= $true )
| ( ( leq @ ( succ @ SV16 ) @ ( succ @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(343,plain,
! [SV32: $i,SV17: $i] :
( ( ( ~ ( leq @ SV17 @ SV32 ) )
= $true )
| ( ( ~ ( ( SV17 != SV32 ) ) )
= $true )
| ( ( gt @ SV32 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(344,plain,
! [SV33: $i,SV18: $i] :
( ( ( ~ ( lt @ SV18 @ SV33 ) )
= $true )
| ( ( gt @ SV33 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(345,plain,
! [SV18: $i,SV33: $i] :
( ( ( ~ ( gt @ SV33 @ SV18 ) )
= $true )
| ( ( lt @ SV18 @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[330]) ).
thf(346,plain,
! [SV35: $i,SV20: $i] :
( ( ( ~ ( geq @ SV20 @ SV35 ) )
= $true )
| ( ( leq @ SV35 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(347,plain,
! [SV20: $i,SV35: $i] :
( ( ( ~ ( leq @ SV35 @ SV20 ) )
= $true )
| ( ( geq @ SV20 @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(348,plain,
! [SV23: $i,SV6: $i] :
( ( ( leq @ SV6 @ SV23 )
= $false )
| ( ( gt @ ( succ @ SV23 ) @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(349,plain,
! [SV6: $i,SV23: $i] :
( ( ( gt @ ( succ @ SV23 ) @ SV6 )
= $false )
| ( ( leq @ SV6 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(350,plain,
! [SV36: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( leq @ SV7 @ SV24 ) )
= $true )
| ( ( ~ ( leq @ SV24 @ SV36 ) )
= $true )
| ( ( leq @ SV7 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(351,plain,
! [SV9: $i] :
( ( ( leq @ SV9 @ n1 )
= $false )
| ( ( leq @ n0 @ SV9 )
= $false )
| ( ( ( SV9 = n0 )
| ( SV9 = n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(352,plain,
! [SV11: $i] :
( ( ( leq @ SV11 @ n0 )
= $false )
| ( ( leq @ n0 @ SV11 )
= $false )
| ( ( SV11 = n0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(353,plain,
! [SV37: $i,SV27: $i,SV12: $i] :
( ( ( ~ ( gt @ SV12 @ SV27 ) )
= $true )
| ( ( ~ ( gt @ SV27 @ SV37 ) )
= $true )
| ( ( gt @ SV12 @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(354,plain,
! [SV29: $i,SV14: $i] :
( ( ( leq @ SV14 @ ( pred @ SV29 ) )
= $false )
| ( ( gt @ SV29 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(355,plain,
! [SV14: $i,SV29: $i] :
( ( ( gt @ SV29 @ SV14 )
= $false )
| ( ( leq @ SV14 @ ( pred @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(356,plain,
! [SV31: $i,SV16: $i] :
( ( ( leq @ ( succ @ SV16 ) @ ( succ @ SV31 ) )
= $false )
| ( ( leq @ SV16 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(357,plain,
! [SV31: $i,SV16: $i] :
( ( ( leq @ SV16 @ SV31 )
= $false )
| ( ( leq @ ( succ @ SV16 ) @ ( succ @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(358,plain,
! [SV32: $i,SV17: $i] :
( ( ( leq @ SV17 @ SV32 )
= $false )
| ( ( ~ ( ( SV17 != SV32 ) ) )
= $true )
| ( ( gt @ SV32 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(359,plain,
! [SV33: $i,SV18: $i] :
( ( ( lt @ SV18 @ SV33 )
= $false )
| ( ( gt @ SV33 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(360,plain,
! [SV18: $i,SV33: $i] :
( ( ( gt @ SV33 @ SV18 )
= $false )
| ( ( lt @ SV18 @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(361,plain,
! [SV35: $i,SV20: $i] :
( ( ( geq @ SV20 @ SV35 )
= $false )
| ( ( leq @ SV35 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(362,plain,
! [SV20: $i,SV35: $i] :
( ( ( leq @ SV35 @ SV20 )
= $false )
| ( ( geq @ SV20 @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(363,plain,
! [SV36: $i,SV24: $i,SV7: $i] :
( ( ( leq @ SV7 @ SV24 )
= $false )
| ( ( ~ ( leq @ SV24 @ SV36 ) )
= $true )
| ( ( leq @ SV7 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(364,plain,
! [SV9: $i] :
( ( ( SV9 = n0 )
= $true )
| ( ( SV9 = n1 )
= $true )
| ( ( leq @ n0 @ SV9 )
= $false )
| ( ( leq @ SV9 @ n1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(365,plain,
! [SV37: $i,SV27: $i,SV12: $i] :
( ( ( gt @ SV12 @ SV27 )
= $false )
| ( ( ~ ( gt @ SV27 @ SV37 ) )
= $true )
| ( ( gt @ SV12 @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(366,plain,
! [SV32: $i,SV17: $i] :
( ( ( SV17 != SV32 )
= $false )
| ( ( leq @ SV17 @ SV32 )
= $false )
| ( ( gt @ SV32 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(367,plain,
! [SV7: $i,SV36: $i,SV24: $i] :
( ( ( leq @ SV24 @ SV36 )
= $false )
| ( ( leq @ SV7 @ SV24 )
= $false )
| ( ( leq @ SV7 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(368,plain,
! [SV12: $i,SV37: $i,SV27: $i] :
( ( ( gt @ SV27 @ SV37 )
= $false )
| ( ( gt @ SV12 @ SV27 )
= $false )
| ( ( gt @ SV12 @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(369,plain,
! [SV32: $i,SV17: $i] :
( ( ( SV17 = SV32 )
= $true )
| ( ( leq @ SV17 @ SV32 )
= $false )
| ( ( gt @ SV32 @ SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[366]) ).
thf(370,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[153,369,368,367,364,362,361,360,359,357,356,355,354,352,349,348,315,309,306,303,301,297,296,292,286,284,279,276,274,271,266,262,261,255,251,244,214,213,212,211,166,163,162,161,160,159,158,157,156,155,154]) ).
thf(371,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[370]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV131+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.20 % Computer : n003.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % OS : Linux 6.8.0-71-generic
% 0.11/0.20 % CPULimit : 300
% 0.11/0.20 % WCLimit : 300
% 0.11/0.20 % DateTime : Tue Oct 6 16:21:25 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.66/0.50
% 1.66/0.50 No.of.Axioms: 32
% 1.66/0.50
% 1.66/0.50 Length.of.Defs: 0
% 1.66/0.50
% 1.66/0.50 Contains.Choice.Funs: false
% 1.66/0.50 .......
% 1.66/0.50
% 1.66/0.50 ********************************
% 1.66/0.50 * All subproblems solved! *
% 1.66/0.50 ********************************
% 1.66/0.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:45,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:370,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.66/0.50
% 1.66/0.50 %**** Beginning of derivation protocol ****
% 1.66/0.50 % SZS output start CNFRefutation
% See solution above
% 1.66/0.50
% 1.66/0.50 %**** End of derivation protocol ****
% 1.66/0.50 %**** no. of clauses in derivation: 319 ****
% 1.66/0.50 %**** clause counter: 370 ****
% 1.66/0.50
% 1.66/0.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:45,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:370,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------