TSTP Solution File: SWV125+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV125+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:13:58 EDT 2023
% Result : Theorem 11.24s 3.96s
% Output : Refutation 11.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 161
% Syntax : Number of formulae : 283 ( 167 unt; 41 typ; 0 def)
% Number of atoms : 2543 ( 180 equ; 0 cnn)
% Maximal formula atoms : 654 ( 10 avg)
% Number of connectives : 9053 ( 58 ~; 46 |;1995 &;6694 @)
% ( 5 <=>; 255 =>; 0 <=; 0 <~>)
% Maximal formula depth : 117 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 41 usr; 20 con; 0-4 aty)
% Number of variables : 342 ( 0 ^; 342 !; 0 ?; 342 :)
% Comments :
%------------------------------------------------------------------------------
thf(geq_type,type,
geq: $i > $i > $o ).
thf(minus_type,type,
minus: $i > $i > $i ).
thf(n4_type,type,
n4: $i ).
thf(n1_type,type,
n1: $i ).
thf(n0_type,type,
n0: $i ).
thf(n1000_type,type,
n1000: $i ).
thf(n7_type,type,
n7: $i ).
thf(true_type,type,
true: $o ).
thf(leq_type,type,
leq: $i > $i > $o ).
thf(n2_type,type,
n2: $i ).
thf(n3_type,type,
n3: $i ).
thf(n5_type,type,
n5: $i ).
thf(n6_type,type,
n6: $i ).
thf(pv5_type,type,
pv5: $i ).
thf(pv21_type,type,
pv21: $i ).
thf(n588_type,type,
n588: $i ).
thf(pv31_type,type,
pv31: $i ).
thf(pv32_type,type,
pv32: $i ).
thf(gt_type,type,
gt: $i > $i > $o ).
thf(pv23_type,type,
pv23: $i ).
thf(a_select2_type,type,
a_select2: $i > $i > $i ).
thf(sigma_type,type,
sigma: $i ).
thf(pred_type,type,
pred: $i > $i ).
thf(succ_type,type,
succ: $i > $i ).
thf(a_select3_type,type,
a_select3: $i > $i > $i > $i ).
thf(tptp_update3_type,type,
tptp_update3: $i > $i > $i > $i > $i ).
thf(tptp_minus_1_type,type,
tptp_minus_1: $i ).
thf(tptp_update2_type,type,
tptp_update2: $i > $i > $i > $i ).
thf(sum_type,type,
sum: $i > $i > $i > $i ).
thf(tptp_const_array2_type,type,
tptp_const_array2: $i > $i > $i > $i ).
thf(dim_type,type,
dim: $i > $i > $i ).
thf(tptp_mmul_type,type,
tptp_mmul: $i > $i > $i ).
thf(trans_type,type,
trans: $i > $i ).
thf(plus_type,type,
plus: $i > $i > $i ).
thf(tptp_madd_type,type,
tptp_madd: $i > $i > $i ).
thf(uniform_int_rnd_type,type,
uniform_int_rnd: $i > $i > $i ).
thf(tptp_msub_type,type,
tptp_msub: $i > $i > $i ).
thf(tptp_float_0_0_type,type,
tptp_float_0_0: $i ).
thf(lt_type,type,
lt: $i > $i > $o ).
thf(tptp_const_array1_type,type,
tptp_const_array1: $i > $i > $i ).
thf(inv_type,type,
inv: $i > $i ).
thf(115,axiom,
! [A: $i] :
( ( plus @ A @ n3 )
= ( succ @ ( succ @ ( succ @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_3_r) ).
thf(670,plain,
! [A: $i] :
( ( plus @ A @ n3 )
= ( succ @ ( succ @ ( succ @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(44,axiom,
gt @ n7 @ n4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_7_4) ).
thf(315,plain,
gt @ n7 @ n4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(35,axiom,
gt @ n588 @ n7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_588_7) ).
thf(268,plain,
gt @ n588 @ n7,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(100,axiom,
gt @ n7 @ n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_7_2) ).
thf(645,plain,
gt @ n7 @ n2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( ( leq @ n0 @ E )
& ( leq @ E @ B ) )
=> ( ( a_select2 @ C @ E )
= D ) )
& ( leq @ n0 @ A )
& ( leq @ A @ B ) )
=> ( ( a_select2 @ ( tptp_update2 @ C @ B @ D ) @ A )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sel2_update_3) ).
thf(234,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( ( leq @ n0 @ E )
& ( leq @ E @ B ) )
=> ( ( a_select2 @ C @ E )
= D ) )
& ( leq @ n0 @ A )
& ( leq @ A @ B ) )
=> ( ( a_select2 @ ( tptp_update2 @ C @ B @ D ) @ A )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(113,axiom,
gt @ n3 @ tptp_minus_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_tptp_minus_1) ).
thf(666,plain,
gt @ n3 @ tptp_minus_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(8,axiom,
gt @ n588 @ tptp_minus_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_588_tptp_minus_1) ).
thf(217,plain,
gt @ n588 @ tptp_minus_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [A: $i] :
( ( pred @ ( succ @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pred_succ) ).
thf(202,plain,
! [A: $i] :
( ( pred @ ( succ @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( ( leq @ n0 @ E )
& ( leq @ E @ D )
& ( leq @ n0 @ F )
& ( leq @ F @ D ) )
=> ( ( a_select3 @ B @ E @ F )
= ( a_select3 @ B @ F @ E ) ) )
=> ! [E: $i,F: $i] :
( ( ( leq @ n0 @ E )
& ( leq @ E @ C )
& ( leq @ n0 @ F )
& ( leq @ F @ C ) )
=> ( ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ E @ F )
= ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ F @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_aba2) ).
thf(269,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( ( leq @ n0 @ E )
& ( leq @ E @ D )
& ( leq @ n0 @ F )
& ( leq @ F @ D ) )
=> ( ( a_select3 @ B @ E @ F )
= ( a_select3 @ B @ F @ E ) ) )
=> ! [E: $i,F: $i] :
( ( ( leq @ n0 @ E )
& ( leq @ E @ C )
& ( leq @ n0 @ F )
& ( leq @ F @ C ) )
=> ( ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ E @ F )
= ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ F @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(119,axiom,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n5 ) )
=> ( ( A = n0 )
| ( A = n1 )
| ( A = n2 )
| ( A = n3 )
| ( A = n4 )
| ( A = n5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_5) ).
thf(677,plain,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n5 ) )
=> ( ( A = n0 )
| ( A = n1 )
| ( A = n2 )
| ( A = n3 )
| ( A = n4 )
| ( A = n5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(47,axiom,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n0 ) )
=> ( A = n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_0) ).
thf(320,plain,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n0 ) )
=> ( A = n0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(104,axiom,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n3 ) )
=> ( ( A = n0 )
| ( A = n1 )
| ( A = n2 )
| ( A = n3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_3) ).
thf(651,plain,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n3 ) )
=> ( ( A = n0 )
| ( A = n1 )
| ( A = n2 )
| ( A = n3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(29,axiom,
gt @ n1000 @ n5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1000_5) ).
thf(257,plain,
gt @ n1000 @ n5,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( leq @ n0 @ A )
=> ( leq @ ( uniform_int_rnd @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniform_int_rand_ranges_hi) ).
thf(570,plain,
! [A: $i,B: $i] :
( ( leq @ n0 @ A )
=> ( leq @ ( uniform_int_rnd @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(90,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( leq @ n0 @ C )
& ( leq @ C @ B )
& ( leq @ n0 @ D )
& ( leq @ D @ B ) )
=> ( ( a_select3 @ A @ C @ D )
= ( a_select3 @ A @ D @ C ) ) )
=> ! [C: $i,D: $i] :
( ( ( leq @ n0 @ C )
& ( leq @ C @ B )
& ( leq @ n0 @ D )
& ( leq @ D @ B ) )
=> ( ( a_select3 @ ( inv @ A ) @ C @ D )
= ( a_select3 @ ( inv @ A ) @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_inv) ).
thf(619,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( leq @ n0 @ C )
& ( leq @ C @ B )
& ( leq @ n0 @ D )
& ( leq @ D @ B ) )
=> ( ( a_select3 @ A @ C @ D )
= ( a_select3 @ A @ D @ C ) ) )
=> ! [C: $i,D: $i] :
( ( ( leq @ n0 @ C )
& ( leq @ C @ B )
& ( leq @ n0 @ D )
& ( leq @ D @ B ) )
=> ( ( a_select3 @ ( inv @ A ) @ C @ D )
= ( a_select3 @ ( inv @ A ) @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(83,axiom,
gt @ n1000 @ n6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1000_6) ).
thf(606,plain,
gt @ n1000 @ n6,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( a_select2 @ ( tptp_update2 @ A @ B @ C ) @ B )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sel2_update_1) ).
thf(228,plain,
! [A: $i,B: $i,C: $i] :
( ( a_select2 @ ( tptp_update2 @ A @ B @ C ) @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(45,axiom,
gt @ n0 @ tptp_minus_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_0_tptp_minus_1) ).
thf(316,plain,
gt @ n0 @ tptp_minus_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( leq @ B @ A )
& ( leq @ A @ C )
& ( leq @ E @ D )
& ( leq @ D @ F ) )
=> ( ( a_select3 @ ( tptp_const_array2 @ ( dim @ B @ C ) @ ( dim @ E @ F ) @ G ) @ A @ D )
= G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',const_array2_select) ).
thf(261,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( leq @ B @ A )
& ( leq @ A @ C )
& ( leq @ E @ D )
& ( leq @ D @ F ) )
=> ( ( a_select3 @ ( tptp_const_array2 @ ( dim @ B @ C ) @ ( dim @ E @ F ) @ G ) @ A @ D )
= G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(7,axiom,
gt @ n2 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_2_1) ).
thf(216,plain,
gt @ n2 @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(80,axiom,
( ( succ @ ( succ @ ( succ @ n0 ) ) )
= n3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_3) ).
thf(591,plain,
( ( succ @ ( succ @ ( succ @ n0 ) ) )
= n3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( A != C )
& ( B = D )
& ( ( a_select3 @ E @ C @ D )
= F ) )
=> ( ( a_select3 @ ( tptp_update3 @ E @ A @ B @ G ) @ C @ D )
= F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sel3_update_2) ).
thf(211,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( A != C )
& ( B = D )
& ( ( a_select3 @ E @ C @ D )
= F ) )
=> ( ( a_select3 @ ( tptp_update3 @ E @ A @ B @ G ) @ C @ D )
= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(101,axiom,
( ( succ @ ( succ @ n0 ) )
= n2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_2) ).
thf(646,plain,
( ( succ @ ( succ @ n0 ) )
= n2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(25,axiom,
gt @ n4 @ n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_2) ).
thf(253,plain,
gt @ n4 @ n2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(11,axiom,
gt @ n6 @ n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_6_2) ).
thf(221,plain,
gt @ n6 @ n2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(38,axiom,
! [A: $i] :
( ( plus @ n3 @ A )
= ( succ @ ( succ @ ( succ @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_3_l) ).
thf(293,plain,
! [A: $i] :
( ( plus @ n3 @ A )
= ( succ @ ( succ @ ( succ @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(109,axiom,
gt @ n5 @ n4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_4) ).
thf(660,plain,
gt @ n5 @ n4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(32,axiom,
gt @ n588 @ n4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_588_4) ).
thf(265,plain,
gt @ n588 @ n4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(19,axiom,
gt @ n588 @ n6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_588_6) ).
thf(233,plain,
gt @ n588 @ n6,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(110,axiom,
gt @ n7 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_7_0) ).
thf(661,plain,
gt @ n7 @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(40,axiom,
gt @ n1000 @ n588,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1000_588) ).
thf(297,plain,
gt @ n1000 @ n588,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(55,axiom,
gt @ n6 @ n3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_6_3) ).
thf(424,plain,
gt @ n6 @ n3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(91,axiom,
gt @ n5 @ tptp_minus_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_tptp_minus_1) ).
thf(630,plain,
gt @ n5 @ tptp_minus_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(59,axiom,
! [A: $i] :
~ ( gt @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_gt) ).
thf(435,plain,
! [A: $i] :
~ ( gt @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(63,axiom,
! [A: $i] :
( tptp_float_0_0
= ( sum @ n0 @ tptp_minus_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_plus_base_float) ).
thf(493,plain,
! [A: $i] :
( tptp_float_0_0
= ( sum @ n0 @ tptp_minus_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(49,axiom,
! [A: $i] :
( ( plus @ n2 @ A )
= ( succ @ ( succ @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_2_l) ).
thf(324,plain,
! [A: $i] :
( ( plus @ n2 @ A )
= ( succ @ ( succ @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(14,axiom,
( ( succ @ n0 )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_1) ).
thf(224,plain,
( ( succ @ n0 )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ A @ D @ E )
= ( a_select3 @ A @ E @ D ) ) )
& ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ B @ D @ E )
= ( a_select3 @ B @ E @ D ) ) ) )
=> ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ ( tptp_madd @ A @ B ) @ D @ E )
= ( a_select3 @ ( tptp_madd @ A @ B ) @ E @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_add) ).
thf(519,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ A @ D @ E )
= ( a_select3 @ A @ E @ D ) ) )
& ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ B @ D @ E )
= ( a_select3 @ B @ E @ D ) ) ) )
=> ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ ( tptp_madd @ A @ B ) @ D @ E )
= ( a_select3 @ ( tptp_madd @ A @ B ) @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(46,axiom,
! [A: $i] :
( ( minus @ A @ n1 )
= ( pred @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pred_minus_1) ).
thf(317,plain,
! [A: $i] :
( ( minus @ A @ n1 )
= ( pred @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(88,axiom,
gt @ n1 @ tptp_minus_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1_tptp_minus_1) ).
thf(615,plain,
gt @ n1 @ tptp_minus_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ! [G: $i,H: $i] :
( ( ( leq @ n0 @ G )
& ( leq @ n0 @ H )
& ( leq @ G @ C )
& ( leq @ H @ D ) )
=> ( ( a_select3 @ E @ G @ H )
= F ) )
& ( leq @ n0 @ A )
& ( leq @ A @ C )
& ( leq @ n0 @ B )
& ( leq @ B @ D ) )
=> ( ( a_select3 @ ( tptp_update3 @ E @ C @ D @ F ) @ A @ B )
= F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sel3_update_3) ).
thf(593,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ! [G: $i,H: $i] :
( ( ( leq @ n0 @ G )
& ( leq @ n0 @ H )
& ( leq @ G @ C )
& ( leq @ H @ D ) )
=> ( ( a_select3 @ E @ G @ H )
= F ) )
& ( leq @ n0 @ A )
& ( leq @ A @ C )
& ( leq @ n0 @ B )
& ( leq @ B @ D ) )
=> ( ( a_select3 @ ( tptp_update3 @ E @ C @ D @ F ) @ A @ B )
= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(86,axiom,
! [A: $i] :
( ( plus @ A @ n1 )
= ( succ @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_1_r) ).
thf(610,plain,
! [A: $i] :
( ( plus @ A @ n1 )
= ( succ @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( ( leq @ A @ B )
& ( A != B ) )
=> ( gt @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt2) ).
thf(420,plain,
! [A: $i,B: $i] :
( ( ( leq @ A @ B )
& ( A != B ) )
=> ( gt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(28,axiom,
gt @ n1000 @ tptp_minus_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1000_tptp_minus_1) ).
thf(256,plain,
gt @ n1000 @ tptp_minus_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(95,axiom,
! [A: $i] : ( leq @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_leq) ).
thf(637,plain,
! [A: $i] : ( leq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(79,axiom,
gt @ n1000 @ n3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1000_3) ).
thf(590,plain,
gt @ n1000 @ n3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( leq @ B @ A )
& ( leq @ A @ C ) )
=> ( ( a_select2 @ ( tptp_const_array1 @ ( dim @ B @ C ) @ D ) @ A )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',const_array1_select) ).
thf(515,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( leq @ B @ A )
& ( leq @ A @ C ) )
=> ( ( a_select2 @ ( tptp_const_array1 @ ( dim @ B @ C ) @ D ) @ A )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( leq @ A @ B )
& ( leq @ B @ C ) )
=> ( leq @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_leq) ).
thf(654,plain,
! [A: $i,B: $i,C: $i] :
( ( ( leq @ A @ B )
& ( leq @ B @ C ) )
=> ( leq @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(22,axiom,
gt @ n4 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_1) ).
thf(244,plain,
gt @ n4 @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(33,axiom,
gt @ n6 @ n5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_6_5) ).
thf(266,plain,
gt @ n6 @ n5,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(93,axiom,
! [A: $i] :
( ( plus @ n4 @ A )
= ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_4_l) ).
thf(633,plain,
! [A: $i] :
( ( plus @ n4 @ A )
= ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(4,axiom,
! [A: $i] :
( ( succ @ ( pred @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_pred) ).
thf(205,plain,
! [A: $i] :
( ( succ @ ( pred @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(70,axiom,
gt @ n1000 @ n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1000_2) ).
thf(508,plain,
gt @ n1000 @ n2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(117,axiom,
gt @ n6 @ n4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_6_4) ).
thf(674,plain,
gt @ n6 @ n4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(111,axiom,
gt @ n1000 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1000_0) ).
thf(662,plain,
gt @ n1000 @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( leq @ ( succ @ A ) @ ( succ @ B ) )
<=> ( leq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ_succ) ).
thf(298,plain,
! [A: $i,B: $i] :
( ( ( leq @ ( succ @ A ) @ ( succ @ B ) )
=> ( leq @ A @ B ) )
& ( ( leq @ A @ B )
=> ( leq @ ( succ @ A ) @ ( succ @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(56,axiom,
( ( succ @ tptp_minus_1 )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_tptp_minus_1) ).
thf(425,plain,
( ( succ @ tptp_minus_1 )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ ( pred @ B ) )
<=> ( gt @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt_pred) ).
thf(430,plain,
! [A: $i,B: $i] :
( ( ( leq @ A @ ( pred @ B ) )
=> ( gt @ B @ A ) )
& ( ( gt @ B @ A )
=> ( leq @ A @ ( pred @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ B @ D @ E )
= ( a_select3 @ B @ E @ D ) ) )
=> ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ D @ E )
= ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ E @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_aba1) ).
thf(573,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ B @ D @ E )
= ( a_select3 @ B @ E @ D ) ) )
=> ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ D @ E )
= ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(39,axiom,
gt @ n5 @ n3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_3) ).
thf(296,plain,
gt @ n5 @ n3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(77,axiom,
gt @ n4 @ tptp_minus_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_tptp_minus_1) ).
thf(584,plain,
gt @ n4 @ tptp_minus_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(54,axiom,
gt @ n5 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_0) ).
thf(423,plain,
gt @ n5 @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( leq @ n0 @ C )
& ( leq @ C @ B )
& ( leq @ n0 @ D )
& ( leq @ D @ B ) )
=> ( ( a_select3 @ A @ C @ D )
= ( a_select3 @ A @ D @ C ) ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( leq @ n0 @ C )
& ( leq @ C @ B )
& ( leq @ n0 @ D )
& ( leq @ D @ B )
& ( leq @ n0 @ E )
& ( leq @ E @ B ) )
=> ( ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ C @ D )
= ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_update_diagonal) ).
thf(281,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( leq @ n0 @ C )
& ( leq @ C @ B )
& ( leq @ n0 @ D )
& ( leq @ D @ B ) )
=> ( ( a_select3 @ A @ C @ D )
= ( a_select3 @ A @ D @ C ) ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( leq @ n0 @ C )
& ( leq @ C @ B )
& ( leq @ n0 @ D )
& ( leq @ D @ B )
& ( leq @ n0 @ E )
& ( leq @ E @ B ) )
=> ( ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ C @ D )
= ( a_select3 @ ( tptp_update3 @ A @ E @ E @ F ) @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(98,axiom,
! [A: $i] :
( ( plus @ n1 @ A )
= ( succ @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_1_l) ).
thf(641,plain,
! [A: $i] :
( ( plus @ n1 @ A )
= ( succ @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(66,axiom,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n1 ) )
=> ( ( A = n0 )
| ( A = n1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_1) ).
thf(498,plain,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n1 ) )
=> ( ( A = n0 )
| ( A = n1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( leq @ ( minus @ A @ B ) @ A )
=> ( leq @ n0 @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_minus) ).
thf(604,plain,
! [A: $i,B: $i] :
( ( leq @ ( minus @ A @ B ) @ A )
=> ( leq @ n0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(121,axiom,
gt @ n1000 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1000_1) ).
thf(681,plain,
gt @ n1000 @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( gt @ B @ A )
=> ( leq @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt1) ).
thf(219,plain,
! [A: $i,B: $i] :
( ( gt @ B @ A )
=> ( leq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(52,axiom,
true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ttrue) ).
thf(419,plain,
true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A != B )
& ( ( a_select2 @ C @ B )
= D ) )
=> ( ( a_select2 @ ( tptp_update2 @ C @ A @ E ) @ B )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sel2_update_2) ).
thf(245,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A != B )
& ( ( a_select2 @ C @ B )
= D ) )
=> ( ( a_select2 @ ( tptp_update2 @ C @ A @ E ) @ B )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( a_select3 @ ( tptp_update3 @ A @ B @ C @ D ) @ B @ C )
= D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sel3_update_1) ).
thf(208,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( a_select3 @ ( tptp_update3 @ A @ B @ C @ D ) @ B @ C )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(71,axiom,
gt @ n7 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_7_1) ).
thf(509,plain,
gt @ n7 @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(103,axiom,
( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) ) )
= n6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_6) ).
thf(649,plain,
( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) ) )
= n6 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(89,axiom,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n2 ) )
=> ( ( A = n0 )
| ( A = n1 )
| ( A = n2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_2) ).
thf(616,plain,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n2 ) )
=> ( ( A = n0 )
| ( A = n1 )
| ( A = n2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(42,axiom,
gt @ n7 @ n3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_7_3) ).
thf(303,plain,
gt @ n7 @ n3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(92,axiom,
! [A: $i,B: $i] :
( ( leq @ ( succ @ A ) @ B )
=> ( gt @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ_gt) ).
thf(631,plain,
! [A: $i,B: $i] :
( ( leq @ ( succ @ A ) @ B )
=> ( gt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(48,axiom,
gt @ n588 @ n5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_588_5) ).
thf(323,plain,
gt @ n588 @ n5,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(94,axiom,
gt @ n2 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_2_0) ).
thf(636,plain,
gt @ n2 @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(15,axiom,
( ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) )
= n4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_4) ).
thf(226,plain,
( ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) )
= n4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(34,axiom,
gt @ n588 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_588_1) ).
thf(267,plain,
gt @ n588 @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( gt @ A @ B )
| ( gt @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
thf(241,plain,
! [A: $i,B: $i] :
( ( gt @ A @ B )
| ( gt @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(107,axiom,
gt @ n1000 @ n4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1000_4) ).
thf(658,plain,
gt @ n1000 @ n4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(13,axiom,
gt @ n7 @ n5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_7_5) ).
thf(223,plain,
gt @ n7 @ n5,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( gt @ A @ B )
& ( gt @ B @ C ) )
=> ( gt @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_gt) ).
thf(608,plain,
! [A: $i,B: $i,C: $i] :
( ( ( gt @ A @ B )
& ( gt @ B @ C ) )
=> ( gt @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(69,axiom,
! [A: $i] :
( ( plus @ A @ n5 )
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_5_r) ).
thf(505,plain,
! [A: $i] :
( ( plus @ A @ n5 )
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( leq @ n0 @ A )
=> ( leq @ n0 @ ( uniform_int_rnd @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniform_int_rand_ranges_lo) ).
thf(438,plain,
! [A: $i,B: $i] :
( ( leq @ n0 @ A )
=> ( leq @ n0 @ ( uniform_int_rnd @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(118,axiom,
( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) )
= n5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_5) ).
thf(675,plain,
( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) )
= n5 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(120,axiom,
gt @ n5 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_1) ).
thf(680,plain,
gt @ n5 @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(112,axiom,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n4 ) )
=> ( ( A = n0 )
| ( A = n1 )
| ( A = n2 )
| ( A = n3 )
| ( A = n4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_4) ).
thf(663,plain,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n4 ) )
=> ( ( A = n0 )
| ( A = n1 )
| ( A = n2 )
| ( A = n3 )
| ( A = n4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(27,axiom,
gt @ n4 @ n3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_3) ).
thf(255,plain,
gt @ n4 @ n3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(102,axiom,
gt @ n1000 @ n7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1000_7) ).
thf(648,plain,
gt @ n1000 @ n7,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(97,axiom,
gt @ n7 @ n6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_7_6) ).
thf(640,plain,
gt @ n7 @ n6,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( geq @ A @ B )
<=> ( leq @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_geq) ).
thf(414,plain,
! [A: $i,B: $i] :
( ( ( geq @ A @ B )
=> ( leq @ B @ A ) )
& ( ( leq @ B @ A )
=> ( geq @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ! [I: $i,J: $i] :
( ( ( leq @ n0 @ I )
& ( leq @ I @ H )
& ( leq @ n0 @ J )
& ( leq @ J @ H ) )
=> ( ( a_select3 @ D @ I @ J )
= ( a_select3 @ D @ J @ I ) ) )
& ! [I: $i,J: $i] :
( ( ( leq @ n0 @ I )
& ( leq @ I @ G )
& ( leq @ n0 @ J )
& ( leq @ J @ G ) )
=> ( ( a_select3 @ A @ I @ J )
= ( a_select3 @ A @ J @ I ) ) )
& ! [I: $i,J: $i] :
( ( ( leq @ n0 @ I )
& ( leq @ I @ G )
& ( leq @ n0 @ J )
& ( leq @ J @ G ) )
=> ( ( a_select3 @ F @ I @ J )
= ( a_select3 @ F @ J @ I ) ) ) )
=> ! [I: $i,J: $i] :
( ( ( leq @ n0 @ I )
& ( leq @ I @ G )
& ( leq @ n0 @ J )
& ( leq @ J @ G ) )
=> ( ( a_select3 @ ( tptp_madd @ A @ ( tptp_mmul @ B @ ( tptp_mmul @ ( tptp_madd @ ( tptp_mmul @ C @ ( tptp_mmul @ D @ ( trans @ C ) ) ) @ ( tptp_mmul @ E @ ( tptp_mmul @ F @ ( trans @ E ) ) ) ) @ ( trans @ B ) ) ) ) @ I @ J )
= ( a_select3 @ ( tptp_madd @ A @ ( tptp_mmul @ B @ ( tptp_mmul @ ( tptp_madd @ ( tptp_mmul @ C @ ( tptp_mmul @ D @ ( trans @ C ) ) ) @ ( tptp_mmul @ E @ ( tptp_mmul @ F @ ( trans @ E ) ) ) ) @ ( trans @ B ) ) ) ) @ J @ I ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_joseph_update) ).
thf(327,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ! [I: $i,J: $i] :
( ( ( leq @ n0 @ I )
& ( leq @ I @ H )
& ( leq @ n0 @ J )
& ( leq @ J @ H ) )
=> ( ( a_select3 @ D @ I @ J )
= ( a_select3 @ D @ J @ I ) ) )
& ! [I: $i,J: $i] :
( ( ( leq @ n0 @ I )
& ( leq @ I @ G )
& ( leq @ n0 @ J )
& ( leq @ J @ G ) )
=> ( ( a_select3 @ A @ I @ J )
= ( a_select3 @ A @ J @ I ) ) )
& ! [I: $i,J: $i] :
( ( ( leq @ n0 @ I )
& ( leq @ I @ G )
& ( leq @ n0 @ J )
& ( leq @ J @ G ) )
=> ( ( a_select3 @ F @ I @ J )
= ( a_select3 @ F @ J @ I ) ) ) )
=> ! [I: $i,J: $i] :
( ( ( leq @ n0 @ I )
& ( leq @ I @ G )
& ( leq @ n0 @ J )
& ( leq @ J @ G ) )
=> ( ( a_select3 @ ( tptp_madd @ A @ ( tptp_mmul @ B @ ( tptp_mmul @ ( tptp_madd @ ( tptp_mmul @ C @ ( tptp_mmul @ D @ ( trans @ C ) ) ) @ ( tptp_mmul @ E @ ( tptp_mmul @ F @ ( trans @ E ) ) ) ) @ ( trans @ B ) ) ) ) @ I @ J )
= ( a_select3 @ ( tptp_madd @ A @ ( tptp_mmul @ B @ ( tptp_mmul @ ( tptp_madd @ ( tptp_mmul @ C @ ( tptp_mmul @ D @ ( trans @ C ) ) ) @ ( tptp_mmul @ E @ ( tptp_mmul @ F @ ( trans @ E ) ) ) ) @ ( trans @ B ) ) ) ) @ J @ I ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(116,axiom,
gt @ n1 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1_0) ).
thf(673,plain,
gt @ n1 @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(61,axiom,
gt @ n588 @ n3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_588_3) ).
thf(441,plain,
gt @ n588 @ n3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( gt @ ( succ @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ_gt_equiv) ).
thf(585,plain,
! [A: $i,B: $i] :
( ( ( leq @ A @ B )
=> ( gt @ ( succ @ B ) @ A ) )
& ( ( gt @ ( succ @ B ) @ A )
=> ( leq @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(68,axiom,
! [A: $i] :
( ( plus @ A @ n4 )
= ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_4_r) ).
thf(502,plain,
! [A: $i] :
( ( plus @ A @ n4 )
= ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(106,axiom,
! [A: $i] : ( gt @ ( succ @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_succ) ).
thf(656,plain,
! [A: $i] : ( gt @ ( succ @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
=> ( leq @ A @ ( succ @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ) ).
thf(613,plain,
! [A: $i,B: $i] :
( ( leq @ A @ B )
=> ( leq @ A @ ( succ @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(65,axiom,
gt @ n7 @ tptp_minus_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_7_tptp_minus_1) ).
thf(497,plain,
gt @ n7 @ tptp_minus_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(9,axiom,
gt @ n3 @ n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_2) ).
thf(218,plain,
gt @ n3 @ n2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(24,axiom,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n6 ) )
=> ( ( A = n0 )
| ( A = n1 )
| ( A = n2 )
| ( A = n3 )
| ( A = n4 )
| ( A = n5 )
| ( A = n6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_6) ).
thf(250,plain,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n6 ) )
=> ( ( A = n0 )
| ( A = n1 )
| ( A = n2 )
| ( A = n3 )
| ( A = n4 )
| ( A = n5 )
| ( A = n6 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(17,axiom,
gt @ n2 @ tptp_minus_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_2_tptp_minus_1) ).
thf(231,plain,
gt @ n2 @ tptp_minus_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( leq @ n0 @ C )
& ( leq @ C @ B )
& ( leq @ n0 @ D )
& ( leq @ D @ B ) )
=> ( ( a_select3 @ A @ C @ D )
= ( a_select3 @ A @ D @ C ) ) )
=> ! [C: $i,D: $i] :
( ( ( leq @ n0 @ C )
& ( leq @ C @ B )
& ( leq @ n0 @ D )
& ( leq @ D @ B ) )
=> ( ( a_select3 @ ( trans @ A ) @ C @ D )
= ( a_select3 @ ( trans @ A ) @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_trans) ).
thf(304,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( leq @ n0 @ C )
& ( leq @ C @ B )
& ( leq @ n0 @ D )
& ( leq @ D @ B ) )
=> ( ( a_select3 @ A @ C @ D )
= ( a_select3 @ A @ D @ C ) ) )
=> ! [C: $i,D: $i] :
( ( ( leq @ n0 @ C )
& ( leq @ C @ B )
& ( leq @ n0 @ D )
& ( leq @ D @ B ) )
=> ( ( a_select3 @ ( trans @ A ) @ C @ D )
= ( a_select3 @ ( trans @ A ) @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(30,axiom,
! [A: $i] :
( ( sum @ n0 @ tptp_minus_1 @ A )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_plus_base) ).
thf(258,plain,
! [A: $i] :
( ( sum @ n0 @ tptp_minus_1 @ A )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( lt @ A @ B )
<=> ( gt @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lt_gt) ).
thf(510,plain,
! [A: $i,B: $i] :
( ( ( lt @ A @ B )
=> ( gt @ B @ A ) )
& ( ( gt @ B @ A )
=> ( lt @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(114,axiom,
! [A: $i] :
( ( plus @ A @ n2 )
= ( succ @ ( succ @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_2_r) ).
thf(667,plain,
! [A: $i] :
( ( plus @ A @ n2 )
= ( succ @ ( succ @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(57,axiom,
! [A: $i] :
( ( plus @ n5 @ A )
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_5_l) ).
thf(427,plain,
! [A: $i] :
( ( plus @ n5 @ A )
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(99,axiom,
gt @ n4 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_0) ).
thf(644,plain,
gt @ n4 @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ A @ D @ E )
= ( a_select3 @ A @ E @ D ) ) )
& ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ B @ D @ E )
= ( a_select3 @ B @ E @ D ) ) ) )
=> ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ ( tptp_msub @ A @ B ) @ D @ E )
= ( a_select3 @ ( tptp_msub @ A @ B ) @ E @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_sub) ).
thf(442,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ A @ D @ E )
= ( a_select3 @ A @ E @ D ) ) )
& ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ B @ D @ E )
= ( a_select3 @ B @ E @ D ) ) ) )
=> ! [D: $i,E: $i] :
( ( ( leq @ n0 @ D )
& ( leq @ D @ C )
& ( leq @ n0 @ E )
& ( leq @ E @ C ) )
=> ( ( a_select3 @ ( tptp_msub @ A @ B ) @ D @ E )
= ( a_select3 @ ( tptp_msub @ A @ B ) @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(67,axiom,
gt @ n5 @ n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_2) ).
thf(501,plain,
gt @ n5 @ n2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(84,axiom,
gt @ n588 @ n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_588_2) ).
thf(607,plain,
gt @ n588 @ n2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(26,axiom,
gt @ n6 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_6_1) ).
thf(254,plain,
gt @ n6 @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(1,conjecture,
( ( ( geq @ ( minus @ n4 @ n1 ) @ n0 )
& ( geq @ ( minus @ n1000 @ n1 ) @ n0 ) )
=> ! [A: $i] :
( ( ( geq @ n7 @ n0 )
& ( geq @ ( minus @ n1000 @ n1 ) @ n0 ) )
=> ! [B: $i] :
( ( true
=> true )
& ( true
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n0 @ ( minus @ n1000 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 ) ) )
& ( ( ( leq @ n0 @ pv5 )
& ( leq @ n0 @ pv21 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv21 @ ( minus @ n6 @ n1 ) ) )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ pv21 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv21 @ n5 )
& ( leq @ pv21 @ ( minus @ n6 @ n1 ) ) ) )
& ( ( ( leq @ n0 @ pv5 )
& ( leq @ n0 @ pv31 )
& ( leq @ n0 @ pv32 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv31 @ ( minus @ n6 @ n1 ) )
& ( leq @ pv32 @ ( minus @ n6 @ n1 ) ) )
=> ( ( ( pv31 != pv32 )
=> ( ( leq @ n0 @ pv5 )
& ( leq @ n0 @ pv31 )
& ( leq @ n0 @ pv32 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv31 @ ( minus @ n6 @ n1 ) )
& ( leq @ pv32 @ ( minus @ n6 @ n1 ) ) ) )
& ( ( pv31 = pv32 )
=> ( ( leq @ n0 @ pv5 )
& ( leq @ n0 @ pv31 )
& ( leq @ n0 @ pv32 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv31 @ ( minus @ n6 @ n1 ) )
& ( leq @ pv32 @ ( minus @ n6 @ n1 ) ) ) ) ) )
& ( ( ( leq @ n0 @ pv5 )
& ( leq @ n0 @ pv31 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv31 @ ( minus @ n6 @ n1 ) ) )
=> ( ( leq @ n0 @ pv5 )
& ( leq @ n0 @ pv31 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv31 @ ( minus @ n6 @ n1 ) ) ) )
& ( ( ( leq @ n0 @ pv5 )
& ( leq @ n0 @ pv31 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv31 @ ( minus @ n6 @ n1 ) ) )
=> ( ( leq @ n0 @ pv5 )
& ( leq @ pv5 @ n588 ) ) )
& ( ( ( leq @ n0 @ pv5 )
& ( leq @ pv5 @ n588 ) )
=> true )
& ( ( ( leq @ n0 @ pv5 )
& ( leq @ pv5 @ n588 ) )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) )
& ( ~ ( gt @ pv5 @ n0 )
=> ( ( ~ ( gt @ pv5 @ n0 )
=> ( ( ~ ( gt @ pv5 @ n0 )
=> ( ( ~ ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) )
& ( ~ ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) ) ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n2 @ n7 )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n5 @ n7 )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) )
& ( ~ ( gt @ pv5 @ n0 )
=> ( ( ~ ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) )
& ( ~ ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) ) ) ) ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) )
& ( ~ ( gt @ pv5 @ n0 )
=> ( ( ~ ( gt @ pv5 @ n0 )
=> ( ( ~ ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) )
& ( ~ ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) ) ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n2 @ n7 )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n5 @ n7 )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) )
& ( ~ ( gt @ pv5 @ n0 )
=> ( ( ~ ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) )
& ( ~ ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ( leq @ n0 @ pv5 )
& ( leq @ pv5 @ n588 ) )
=> ( ( leq @ n0 @ pv5 )
& ( leq @ pv5 @ n588 ) ) )
& ( ( ( leq @ n0 @ pv23 )
& ( leq @ pv23 @ ( minus @ n6 @ n1 ) ) )
=> ( ( leq @ n0 @ ( a_select2 @ sigma @ pv23 ) )
=> true ) )
& ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( ( geq @ ( minus @ n4 @ n1 ) @ n0 )
& ( geq @ ( minus @ n1000 @ n1 ) @ n0 ) )
=> true ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thruster_array_0001) ).
thf(2,negated_conjecture,
~ ( ( ( geq @ ( minus @ n4 @ n1 ) @ n0 )
& ( geq @ ( minus @ n1000 @ n1 ) @ n0 ) )
=> ! [A: $i] :
( ( ( geq @ n7 @ n0 )
& ( geq @ ( minus @ n1000 @ n1 ) @ n0 ) )
=> ! [B: $i] :
( ( true
=> true )
& ( true
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n0 @ ( minus @ n1000 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 ) ) )
& ( ( ( leq @ n0 @ pv5 )
& ( leq @ n0 @ pv21 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv21 @ ( minus @ n6 @ n1 ) ) )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ pv21 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv21 @ n5 )
& ( leq @ pv21 @ ( minus @ n6 @ n1 ) ) ) )
& ( ( ( leq @ n0 @ pv5 )
& ( leq @ n0 @ pv31 )
& ( leq @ n0 @ pv32 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv31 @ ( minus @ n6 @ n1 ) )
& ( leq @ pv32 @ ( minus @ n6 @ n1 ) ) )
=> ( ( ( pv31 != pv32 )
=> ( ( leq @ n0 @ pv5 )
& ( leq @ n0 @ pv31 )
& ( leq @ n0 @ pv32 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv31 @ ( minus @ n6 @ n1 ) )
& ( leq @ pv32 @ ( minus @ n6 @ n1 ) ) ) )
& ( ( pv31 = pv32 )
=> ( ( leq @ n0 @ pv5 )
& ( leq @ n0 @ pv31 )
& ( leq @ n0 @ pv32 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv31 @ ( minus @ n6 @ n1 ) )
& ( leq @ pv32 @ ( minus @ n6 @ n1 ) ) ) ) ) )
& ( ( ( leq @ n0 @ pv5 )
& ( leq @ n0 @ pv31 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv31 @ ( minus @ n6 @ n1 ) ) )
=> ( ( leq @ n0 @ pv5 )
& ( leq @ n0 @ pv31 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv31 @ ( minus @ n6 @ n1 ) ) ) )
& ( ( ( leq @ n0 @ pv5 )
& ( leq @ n0 @ pv31 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv31 @ ( minus @ n6 @ n1 ) ) )
=> ( ( leq @ n0 @ pv5 )
& ( leq @ pv5 @ n588 ) ) )
& ( ( ( leq @ n0 @ pv5 )
& ( leq @ pv5 @ n588 ) )
=> true )
& ( ( ( leq @ n0 @ pv5 )
& ( leq @ pv5 @ n588 ) )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) )
& ( ~ ( gt @ pv5 @ n0 )
=> ( ( ~ ( gt @ pv5 @ n0 )
=> ( ( ~ ( gt @ pv5 @ n0 )
=> ( ( ~ ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) )
& ( ~ ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) ) ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n2 @ n7 )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n5 @ n7 )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) )
& ( ~ ( gt @ pv5 @ n0 )
=> ( ( ~ ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) )
& ( ~ ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) ) ) ) ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) )
& ( ~ ( gt @ pv5 @ n0 )
=> ( ( ~ ( gt @ pv5 @ n0 )
=> ( ( ~ ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) )
& ( ~ ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) ) ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n2 @ n7 )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n5 @ n7 )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) )
& ( ~ ( gt @ pv5 @ n0 )
=> ( ( ~ ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) )
& ( ~ ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ( leq @ n0 @ pv5 )
& ( leq @ pv5 @ n588 ) )
=> ( ( leq @ n0 @ pv5 )
& ( leq @ pv5 @ n588 ) ) )
& ( ( ( leq @ n0 @ pv23 )
& ( leq @ pv23 @ ( minus @ n6 @ n1 ) ) )
=> ( ( leq @ n0 @ ( a_select2 @ sigma @ pv23 ) )
=> true ) )
& ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( ( geq @ ( minus @ n4 @ n1 ) @ n0 )
& ( geq @ ( minus @ n1000 @ n1 ) @ n0 ) )
=> true ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(122,plain,
~ ( ( ( geq @ ( minus @ n4 @ n1 ) @ n0 )
& ( geq @ ( minus @ n1000 @ n1 ) @ n0 ) )
=> ( ( ( geq @ n7 @ n0 )
& ( geq @ ( minus @ n1000 @ n1 ) @ n0 ) )
=> ( ( true
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n0 @ ( minus @ n1000 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 ) ) )
& ( ( ( leq @ n0 @ pv5 )
& ( leq @ n0 @ pv21 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv21 @ ( minus @ n6 @ n1 ) ) )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ pv21 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv21 @ n5 )
& ( leq @ pv21 @ ( minus @ n6 @ n1 ) ) ) )
& ( ( ( leq @ n0 @ pv5 )
& ( leq @ n0 @ pv31 )
& ( leq @ n0 @ pv32 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv31 @ ( minus @ n6 @ n1 ) )
& ( leq @ pv32 @ ( minus @ n6 @ n1 ) ) )
=> ( ( ( pv31 != pv32 )
=> ( ( leq @ n0 @ pv5 )
& ( leq @ n0 @ pv31 )
& ( leq @ n0 @ pv32 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv31 @ ( minus @ n6 @ n1 ) )
& ( leq @ pv32 @ ( minus @ n6 @ n1 ) ) ) )
& ( ( pv31 = pv32 )
=> ( ( leq @ n0 @ pv5 )
& ( leq @ n0 @ pv31 )
& ( leq @ n0 @ pv32 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv31 @ ( minus @ n6 @ n1 ) )
& ( leq @ pv32 @ ( minus @ n6 @ n1 ) ) ) ) ) )
& ( ( ( leq @ n0 @ pv5 )
& ( leq @ n0 @ pv31 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv31 @ ( minus @ n6 @ n1 ) ) )
=> ( ( leq @ n0 @ pv5 )
& ( leq @ pv5 @ n588 ) ) )
& ( ( ( leq @ n0 @ pv5 )
& ( leq @ pv5 @ n588 ) )
=> true )
& ( ( ( leq @ n0 @ pv5 )
& ( leq @ pv5 @ n588 ) )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) )
& ( ~ ( gt @ pv5 @ n0 )
=> ( ( ~ ( gt @ pv5 @ n0 )
=> ( ( ~ ( gt @ pv5 @ n0 )
=> ( ( ~ ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) )
& ( ~ ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) ) ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n2 @ n7 )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n5 @ n7 )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) )
& ( ~ ( gt @ pv5 @ n0 )
=> ( ( ~ ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) )
& ( ~ ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) ) ) ) ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) )
& ( ~ ( gt @ pv5 @ n0 )
=> ( ( ~ ( gt @ pv5 @ n0 )
=> ( ( ~ ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) )
& ( ~ ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) ) ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n2 @ n7 )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n5 @ n7 )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) )
& ( ~ ( gt @ pv5 @ n0 )
=> ( ( ~ ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) )
& ( ~ ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) )
& ( ( gt @ pv5 @ n0 )
=> ( ( leq @ n0 @ n0 )
& ( leq @ n0 @ n1 )
& ( leq @ n0 @ n2 )
& ( leq @ n0 @ n3 )
& ( leq @ n0 @ n4 )
& ( leq @ n0 @ n5 )
& ( leq @ n0 @ n6 )
& ( leq @ n0 @ n7 )
& ( leq @ n0 @ pv5 )
& ( leq @ n0 @ ( minus @ n4 @ n1 ) )
& ( leq @ n0 @ ( minus @ n6 @ n1 ) )
& ( leq @ n1 @ n7 )
& ( leq @ n1 @ ( minus @ n4 @ n1 ) )
& ( leq @ n1 @ ( minus @ n6 @ n1 ) )
& ( leq @ n2 @ n7 )
& ( leq @ n2 @ ( minus @ n4 @ n1 ) )
& ( leq @ n2 @ ( minus @ n6 @ n1 ) )
& ( leq @ n3 @ n7 )
& ( leq @ n3 @ ( minus @ n4 @ n1 ) )
& ( leq @ n3 @ ( minus @ n6 @ n1 ) )
& ( leq @ n4 @ n7 )
& ( leq @ n4 @ ( minus @ n6 @ n1 ) )
& ( leq @ n5 @ n7 )
& ( leq @ n5 @ ( minus @ n6 @ n1 ) )
& ( leq @ n6 @ n7 )
& ( leq @ n7 @ n7 )
& ( leq @ pv5 @ n588 )
& ( leq @ pv5 @ ( minus @ n1000 @ n1 ) ) ) ) ) ) ) ) ) ) ) )
& ( ( ( leq @ n0 @ pv23 )
& ( leq @ pv23 @ ( minus @ n6 @ n1 ) ) )
=> ( ( leq @ n0 @ ( a_select2 @ sigma @ pv23 ) )
=> true ) )
& ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( geq @ ( minus @ n6 @ n1 ) @ n0 )
=> ( ( ( geq @ ( minus @ n4 @ n1 ) @ n0 )
& ( geq @ ( minus @ n1000 @ n1 ) @ n0 ) )
=> true ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(108,axiom,
gt @ n6 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_6_0) ).
thf(659,plain,
gt @ n6 @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(96,axiom,
gt @ n588 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_588_0) ).
thf(639,plain,
gt @ n588 @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(12,axiom,
gt @ n3 @ n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_1) ).
thf(222,plain,
gt @ n3 @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(64,axiom,
gt @ n3 @ n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_0) ).
thf(496,plain,
gt @ n3 @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(18,axiom,
gt @ n6 @ tptp_minus_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_6_tptp_minus_1) ).
thf(232,plain,
gt @ n6 @ tptp_minus_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(809,plain,
$false,
inference(cvc4,[status(thm)],[670,315,268,645,234,666,217,202,269,677,320,651,257,570,619,606,228,316,261,216,591,211,646,253,221,293,660,265,233,661,297,424,630,435,493,324,224,519,317,615,593,610,420,256,637,590,515,654,244,266,633,205,508,674,662,298,425,430,573,296,584,423,281,641,498,604,681,219,419,245,208,509,649,616,303,631,323,636,226,267,241,658,223,608,505,438,675,680,663,255,648,640,414,327,673,441,585,502,656,613,497,218,250,231,304,258,510,667,427,644,442,501,607,254,122,659,639,222,496,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV125+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n026.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 19 02:41:36 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.98/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.63/1.12 % [INFO] Parsing done (226ms).
% 1.63/1.12 % [INFO] Running in sequential loop mode.
% 2.31/1.33 % [INFO] eprover registered as external prover.
% 2.31/1.33 % [INFO] cvc4 registered as external prover.
% 2.31/1.34 % [INFO] Scanning for conjecture ...
% 3.07/1.65 % [INFO] Found a conjecture and 120 axioms. Running axiom selection ...
% 3.37/1.76 % [INFO] Axiom selection finished. Selected 119 axioms (removed 1 axioms).
% 3.83/1.81 % [INFO] Problem is first-order (TPTP FOF).
% 3.87/1.82 % [INFO] Type checking passed.
% 3.87/1.83 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 11.24/3.96 % External prover 'cvc4' found a proof!
% 11.24/3.96 % [INFO] Killing All external provers ...
% 11.24/3.96 % Time passed: 3443ms (effective reasoning time: 2833ms)
% 11.24/3.96 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 11.24/3.96 % Axioms used in derivation (119): gt_6_0, gt_0_tptp_minus_1, sel3_update_2, gt_6_1, sel2_update_2, succ_plus_5_l, lt_gt, gt_1000_4, gt_5_tptp_minus_1, succ_plus_3_r, gt_4_3, transitivity_gt, gt_588_6, gt_6_4, matrix_symm_inv, gt_1000_3, matrix_symm_trans, finite_domain_1, gt_5_0, const_array2_select, finite_domain_6, gt_2_tptp_minus_1, gt_6_tptp_minus_1, gt_1000_7, sel3_update_3, leq_geq, gt_1_0, leq_gt2, gt_5_4, succ_plus_1_l, gt_588_5, gt_3_2, matrix_symm_add, leq_succ_gt, gt_7_3, finite_domain_5, pred_minus_1, gt_7_6, gt_6_5, successor_3, gt_3_tptp_minus_1, matrix_symm_update_diagonal, gt_1000_2, sel2_update_1, ttrue, matrix_symm_sub, gt_588_2, gt_4_2, gt_5_3, successor_4, gt_succ, gt_1000_6, succ_plus_4_l, reflexivity_leq, successor_2, leq_gt1, gt_1_tptp_minus_1, finite_domain_2, matrix_symm_aba1, finite_domain_4, gt_7_0, matrix_symm_aba2, gt_1000_tptp_minus_1, gt_1000_588, succ_tptp_minus_1, succ_plus_5_r, leq_succ_succ, sum_plus_base_float, succ_plus_2_l, gt_1000_1, gt_3_1, gt_4_1, gt_2_0, gt_5_2, gt_588_0, const_array1_select, leq_gt_pred, matrix_symm_joseph_update, gt_588_3, succ_pred, totality, successor_6, transitivity_leq, finite_domain_3, uniform_int_rand_ranges_lo, gt_6_3, gt_588_7, sel3_update_1, successor_1, gt_1000_0, gt_7_1, sum_plus_base, irreflexivity_gt, gt_588_tptp_minus_1, successor_5, gt_1000_5, gt_3_0, sel2_update_3, gt_7_5, pred_succ, succ_plus_1_r, succ_plus_3_l, gt_4_tptp_minus_1, gt_588_1, succ_plus_4_r, gt_7_tptp_minus_1, gt_4_0, succ_plus_2_r, gt_6_2, leq_succ_gt_equiv, gt_5_1, uniform_int_rand_ranges_hi, gt_2_1, gt_7_4, gt_588_4, finite_domain_0, leq_succ, gt_7_2, leq_minus
% 11.24/3.96 % No. of inferences in proof: 242
% 11.24/3.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3443 ms resp. 2833 ms w/o parsing
% 11.69/4.08 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.69/4.08 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------