TSTP Solution File: SWV163+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV163+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.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 12:14:06 EDT 2023
% Result : Theorem 6.19s 2.40s
% Output : Refutation 6.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 129
% Syntax : Number of formulae : 221 ( 109 unt; 39 typ; 0 def)
% Number of atoms : 543 ( 164 equ; 0 cnn)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 1982 ( 10 ~; 34 |; 201 &;1611 @)
% ( 5 <=>; 121 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 39 usr; 15 con; 0-4 aty)
% Number of variables : 342 ( 0 ^; 342 !; 0 ?; 342 :)
% Comments :
%------------------------------------------------------------------------------
thf(leq_type,type,
leq: $i > $i > $o ).
thf(n0_type,type,
n0: $i ).
thf(pv10_type,type,
pv10: $i ).
thf(n135299_type,type,
n135299: $i ).
thf(pred_type,type,
pred: $i > $i ).
thf(sum_type,type,
sum: $i > $i > $i > $i ).
thf(n4_type,type,
n4: $i ).
thf(a_select3_type,type,
a_select3: $i > $i > $i > $i ).
thf(q_type,type,
q: $i ).
thf(tptp_sum_index_type,type,
tptp_sum_index: $i ).
thf(n1_type,type,
n1: $i ).
thf(tptp_minus_1_type,type,
tptp_minus_1: $i ).
thf(divide_type,type,
divide: $i > $i > $i ).
thf(sqrt_type,type,
sqrt: $i > $i ).
thf(times_type,type,
times: $i > $i > $i ).
thf(minus_type,type,
minus: $i > $i > $i ).
thf(center_type,type,
center: $i ).
thf(a_select2_type,type,
a_select2: $i > $i > $i ).
thf(x_type,type,
x: $i ).
thf(plus_type,type,
plus: $i > $i > $i ).
thf(n3_type,type,
n3: $i ).
thf(succ_type,type,
succ: $i > $i ).
thf(gt_type,type,
gt: $i > $i > $o ).
thf(n5_type,type,
n5: $i ).
thf(n2_type,type,
n2: $i ).
thf(lt_type,type,
lt: $i > $i > $o ).
thf(tptp_update2_type,type,
tptp_update2: $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(tptp_update3_type,type,
tptp_update3: $i > $i > $i > $i > $i ).
thf(tptp_madd_type,type,
tptp_madd: $i > $i > $i ).
thf(geq_type,type,
geq: $i > $i > $o ).
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(tptp_const_array1_type,type,
tptp_const_array1: $i > $i > $i ).
thf(inv_type,type,
inv: $i > $i ).
thf(33,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/sandbox2/benchmark/theBenchmark.p',matrix_symm_aba2) ).
thf(173,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)],[33]) ).
thf(44,axiom,
gt @ n5 @ n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_0) ).
thf(318,plain,
gt @ n5 @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(62,axiom,
gt @ n4 @ tptp_minus_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_tptp_minus_1) ).
thf(470,plain,
gt @ n4 @ tptp_minus_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( gt @ B @ A )
=> ( leq @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt1) ).
thf(138,plain,
! [A: $i,B: $i] :
( ( gt @ B @ A )
=> ( leq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3,axiom,
! [A: $i] :
( ( plus @ n3 @ A )
= ( succ @ ( succ @ ( succ @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_3_l) ).
thf(101,plain,
! [A: $i] :
( ( plus @ n3 @ A )
= ( succ @ ( succ @ ( succ @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(76,axiom,
! [A: $i] : ( leq @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_leq) ).
thf(518,plain,
! [A: $i] : ( leq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(78,axiom,
gt @ n4 @ n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_0) ).
thf(523,plain,
gt @ n4 @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(9,axiom,
gt @ n3 @ n2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_2) ).
thf(115,plain,
gt @ n3 @ n2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(39,axiom,
! [A: $i] :
( ( minus @ A @ n1 )
= ( pred @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pred_minus_1) ).
thf(217,plain,
! [A: $i] :
( ( minus @ A @ n1 )
= ( pred @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(72,axiom,
gt @ n5 @ tptp_minus_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_tptp_minus_1) ).
thf(511,plain,
gt @ n5 @ tptp_minus_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(36,axiom,
! [A: $i] :
( ( succ @ ( pred @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_pred) ).
thf(202,plain,
! [A: $i] :
( ( succ @ ( pred @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(51,axiom,
! [A: $i] :
( tptp_float_0_0
= ( sum @ n0 @ tptp_minus_1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_plus_base_float) ).
thf(384,plain,
! [A: $i] :
( tptp_float_0_0
= ( sum @ n0 @ tptp_minus_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(83,axiom,
gt @ n3 @ tptp_minus_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_tptp_minus_1) ).
thf(533,plain,
gt @ n3 @ tptp_minus_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(71,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/sandbox2/benchmark/theBenchmark.p',matrix_symm_inv) ).
thf(500,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)],[71]) ).
thf(58,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/sandbox2/benchmark/theBenchmark.p',matrix_symm_add) ).
thf(404,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)],[58]) ).
thf(34,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/sandbox2/benchmark/theBenchmark.p',matrix_symm_update_diagonal) ).
thf(185,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)],[34]) ).
thf(13,axiom,
! [A: $i] :
~ ( gt @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_gt) ).
thf(125,plain,
! [A: $i] :
~ ( gt @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(89,axiom,
gt @ n4 @ n3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_3) ).
thf(542,plain,
gt @ n4 @ n3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(26,axiom,
gt @ n4 @ n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_1) ).
thf(157,plain,
gt @ n4 @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(38,axiom,
gt @ n0 @ tptp_minus_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_0_tptp_minus_1) ).
thf(216,plain,
gt @ n0 @ tptp_minus_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ ( pred @ B ) )
<=> ( gt @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt_pred) ).
thf(321,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)],[46]) ).
thf(6,axiom,
! [A: $i] :
( ( plus @ A @ n5 )
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_5_r) ).
thf(106,plain,
! [A: $i] :
( ( plus @ A @ n5 )
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(74,axiom,
! [A: $i] :
( ( plus @ n4 @ A )
= ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_4_l) ).
thf(514,plain,
! [A: $i] :
( ( plus @ n4 @ A )
= ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
=> ( leq @ A @ ( succ @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ) ).
thf(492,plain,
! [A: $i,B: $i] :
( ( leq @ A @ B )
=> ( leq @ A @ ( succ @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(29,axiom,
gt @ n135299 @ n4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135299_4) ).
thf(164,plain,
gt @ n135299 @ n4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( gt @ A @ B )
& ( gt @ B @ C ) )
=> ( gt @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_gt) ).
thf(133,plain,
! [A: $i,B: $i,C: $i] :
( ( ( gt @ A @ B )
& ( gt @ B @ C ) )
=> ( gt @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( gt @ A @ B )
| ( gt @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality) ).
thf(116,plain,
! [A: $i,B: $i] :
( ( gt @ A @ B )
| ( gt @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( leq @ A @ B )
& ( leq @ B @ C ) )
=> ( leq @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_leq) ).
thf(527,plain,
! [A: $i,B: $i,C: $i] :
( ( ( leq @ A @ B )
& ( leq @ B @ C ) )
=> ( leq @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( leq @ ( succ @ A ) @ B )
=> ( gt @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_gt) ).
thf(512,plain,
! [A: $i,B: $i] :
( ( leq @ ( succ @ A ) @ B )
=> ( gt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(81,axiom,
gt @ n5 @ n4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_4) ).
thf(529,plain,
gt @ n5 @ n4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(91,axiom,
( ( succ @ ( succ @ n0 ) )
= n2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_2) ).
thf(546,plain,
( ( succ @ ( succ @ n0 ) )
= n2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( a_select3 @ ( tptp_update3 @ A @ B @ C @ D ) @ B @ C )
= D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sel3_update_1) ).
thf(381,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)],[50]) ).
thf(40,axiom,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n0 ) )
=> ( A = n0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_0) ).
thf(220,plain,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n0 ) )
=> ( A = n0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(84,axiom,
gt @ n1 @ n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_1_0) ).
thf(534,plain,
gt @ n1 @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(17,axiom,
gt @ n135299 @ n5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135299_5) ).
thf(137,plain,
gt @ n135299 @ n5,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(30,axiom,
! [A: $i] :
( ( sum @ n0 @ tptp_minus_1 @ A )
= n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_plus_base) ).
thf(165,plain,
! [A: $i] :
( ( sum @ n0 @ tptp_minus_1 @ A )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1,conjecture,
( ( ( leq @ n0 @ pv10 )
& ( leq @ pv10 @ n135299 )
& ! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ ( pred @ pv10 ) ) )
=> ( ( sum @ n0 @ n4 @ ( a_select3 @ q @ A @ tptp_sum_index ) )
= n1 ) ) )
=> ! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ tptp_minus_1 ) )
=> ( ( a_select3 @ q @ pv10 @ A )
= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ A @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ A @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ n4 @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ tptp_sum_index @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ tptp_sum_index @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_norm_0013) ).
thf(2,negated_conjecture,
~ ( ( ( leq @ n0 @ pv10 )
& ( leq @ pv10 @ n135299 )
& ! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ ( pred @ pv10 ) ) )
=> ( ( sum @ n0 @ n4 @ ( a_select3 @ q @ A @ tptp_sum_index ) )
= n1 ) ) )
=> ! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ tptp_minus_1 ) )
=> ( ( a_select3 @ q @ pv10 @ A )
= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ A @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ A @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ n4 @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ tptp_sum_index @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ tptp_sum_index @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(92,plain,
~ ( ( ( leq @ n0 @ pv10 )
& ( leq @ pv10 @ n135299 )
& ! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ ( pred @ pv10 ) ) )
=> ( ( sum @ n0 @ n4 @ ( a_select3 @ q @ A @ tptp_sum_index ) )
= n1 ) ) )
=> ! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ tptp_minus_1 ) )
=> ( ( a_select3 @ q @ pv10 @ A )
= ( divide @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ A @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ A @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) @ ( sum @ n0 @ n4 @ ( sqrt @ ( times @ ( minus @ ( a_select3 @ center @ tptp_sum_index @ n0 ) @ ( a_select2 @ x @ pv10 ) ) @ ( minus @ ( a_select3 @ center @ tptp_sum_index @ n0 ) @ ( a_select2 @ x @ pv10 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( leq @ ( succ @ A ) @ ( succ @ B ) )
<=> ( leq @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_succ) ).
thf(197,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)],[35]) ).
thf(53,axiom,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n1 ) )
=> ( ( A = n0 )
| ( A = n1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_1) ).
thf(388,plain,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n1 ) )
=> ( ( A = n0 )
| ( A = n1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(32,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/sandbox2/benchmark/theBenchmark.p',const_array2_select) ).
thf(169,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)],[32]) ).
thf(20,axiom,
( ( succ @ n0 )
= n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_1) ).
thf(141,plain,
( ( succ @ n0 )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(86,axiom,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n5 ) )
=> ( ( A = n0 )
| ( A = n1 )
| ( A = n2 )
| ( A = n3 )
| ( A = n4 )
| ( A = n5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_5) ).
thf(537,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)],[86]) ).
thf(64,axiom,
( ( succ @ ( succ @ ( succ @ n0 ) ) )
= n3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_3) ).
thf(476,plain,
( ( succ @ ( succ @ ( succ @ n0 ) ) )
= n3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(66,axiom,
! [A: $i] :
( ( plus @ A @ n1 )
= ( succ @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_1_r) ).
thf(489,plain,
! [A: $i] :
( ( plus @ A @ n1 )
= ( succ @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(7,axiom,
! [A: $i] :
( ( plus @ A @ n2 )
= ( succ @ ( succ @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_2_r) ).
thf(109,plain,
! [A: $i] :
( ( plus @ A @ n2 )
= ( succ @ ( succ @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( gt @ ( succ @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_gt_equiv) ).
thf(471,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)],[63]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( lt @ A @ B )
<=> ( gt @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lt_gt) ).
thf(128,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)],[14]) ).
thf(5,axiom,
gt @ n5 @ n2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_2) ).
thf(105,plain,
gt @ n5 @ n2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
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] :
( ( ( 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/sandbox2/benchmark/theBenchmark.p',matrix_symm_trans) ).
thf(205,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)],[37]) ).
thf(88,axiom,
gt @ n5 @ n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_1) ).
thf(541,plain,
gt @ n5 @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(82,axiom,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n4 ) )
=> ( ( A = n0 )
| ( A = n1 )
| ( A = n2 )
| ( A = n3 )
| ( A = n4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_4) ).
thf(530,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)],[82]) ).
thf(23,axiom,
gt @ n2 @ tptp_minus_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_2_tptp_minus_1) ).
thf(148,plain,
gt @ n2 @ tptp_minus_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(24,axiom,
gt @ n135299 @ n3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135299_3) ).
thf(149,plain,
gt @ n135299 @ n3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(54,axiom,
! [A: $i] :
( ( plus @ A @ n4 )
= ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_4_r) ).
thf(391,plain,
! [A: $i] :
( ( plus @ A @ n4 )
= ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(87,axiom,
gt @ n2 @ n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_2_1) ).
thf(540,plain,
gt @ n2 @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(52,axiom,
gt @ n3 @ n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_0) ).
thf(387,plain,
gt @ n3 @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( leq @ ( minus @ A @ B ) @ A )
=> ( leq @ n0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_minus) ).
thf(494,plain,
! [A: $i,B: $i] :
( ( leq @ ( minus @ A @ B ) @ A )
=> ( leq @ n0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(85,axiom,
( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) )
= n5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_5) ).
thf(535,plain,
( ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) )
= n5 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(19,axiom,
gt @ n3 @ n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_1) ).
thf(140,plain,
gt @ n3 @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(77,axiom,
! [A: $i] :
( ( plus @ n1 @ A )
= ( succ @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_1_l) ).
thf(520,plain,
! [A: $i] :
( ( plus @ n1 @ A )
= ( succ @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(49,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/sandbox2/benchmark/theBenchmark.p',matrix_symm_sub) ).
thf(330,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)],[49]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( leq @ n0 @ A )
=> ( leq @ ( uniform_int_rnd @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniform_int_rand_ranges_hi) ).
thf(455,plain,
! [A: $i,B: $i] :
( ( leq @ n0 @ A )
=> ( leq @ ( uniform_int_rnd @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(41,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/sandbox2/benchmark/theBenchmark.p',matrix_symm_joseph_update) ).
thf(223,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)],[41]) ).
thf(55,axiom,
gt @ n135299 @ n2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135299_2) ).
thf(394,plain,
gt @ n135299 @ n2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(16,axiom,
! [A: $i] : ( gt @ ( succ @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_succ) ).
thf(135,plain,
! [A: $i] : ( gt @ ( succ @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(8,axiom,
! [A: $i] :
( ( plus @ A @ n3 )
= ( succ @ ( succ @ ( succ @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_3_r) ).
thf(112,plain,
! [A: $i] :
( ( plus @ A @ n3 )
= ( succ @ ( succ @ ( succ @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(60,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/sandbox2/benchmark/theBenchmark.p',matrix_symm_aba1) ).
thf(458,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)],[60]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( a_select2 @ ( tptp_update2 @ A @ B @ C ) @ B )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sel2_update_1) ).
thf(145,plain,
! [A: $i,B: $i,C: $i] :
( ( a_select2 @ ( tptp_update2 @ A @ B @ C ) @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(25,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/sandbox2/benchmark/theBenchmark.p',sel2_update_3) ).
thf(150,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)],[25]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( leq @ n0 @ A )
=> ( leq @ n0 @ ( uniform_int_rnd @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniform_int_rand_ranges_lo) ).
thf(327,plain,
! [A: $i,B: $i] :
( ( leq @ n0 @ A )
=> ( leq @ n0 @ ( uniform_int_rnd @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( geq @ A @ B )
<=> ( leq @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_geq) ).
thf(310,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)],[42]) ).
thf(21,axiom,
( ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) )
= n4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_4) ).
thf(143,plain,
( ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) )
= n4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(70,axiom,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n2 ) )
=> ( ( A = n0 )
| ( A = n1 )
| ( A = n2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_2) ).
thf(497,plain,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n2 ) )
=> ( ( A = n0 )
| ( A = n1 )
| ( A = n2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(79,axiom,
! [A: $i] :
( ( ( leq @ n0 @ A )
& ( leq @ A @ n3 ) )
=> ( ( A = n0 )
| ( A = n1 )
| ( A = n2 )
| ( A = n3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_3) ).
thf(524,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)],[79]) ).
thf(4,axiom,
gt @ n5 @ n3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_3) ).
thf(104,plain,
gt @ n5 @ n3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(75,axiom,
gt @ n2 @ n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_2_0) ).
thf(517,plain,
gt @ n2 @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(45,axiom,
( ( succ @ tptp_minus_1 )
= n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_tptp_minus_1) ).
thf(319,plain,
( ( succ @ tptp_minus_1 )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(27,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/sandbox2/benchmark/theBenchmark.p',sel2_update_2) ).
thf(158,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)],[27]) ).
thf(11,axiom,
! [A: $i] :
( ( plus @ n2 @ A )
= ( succ @ ( succ @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_2_l) ).
thf(119,plain,
! [A: $i] :
( ( plus @ n2 @ A )
= ( succ @ ( succ @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(65,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/sandbox2/benchmark/theBenchmark.p',sel3_update_3) ).
thf(478,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)],[65]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( ( leq @ A @ B )
& ( A != B ) )
=> ( gt @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt2) ).
thf(315,plain,
! [A: $i,B: $i] :
( ( ( leq @ A @ B )
& ( A != B ) )
=> ( gt @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(31,axiom,
gt @ n135299 @ n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135299_0) ).
thf(168,plain,
gt @ n135299 @ n0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(47,axiom,
gt @ n135299 @ n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135299_1) ).
thf(326,plain,
gt @ n135299 @ n1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(57,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/sandbox2/benchmark/theBenchmark.p',const_array1_select) ).
thf(400,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)],[57]) ).
thf(56,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/sandbox2/benchmark/theBenchmark.p',sel3_update_2) ).
thf(395,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)],[56]) ).
thf(28,axiom,
gt @ n4 @ n2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_2) ).
thf(163,plain,
gt @ n4 @ n2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(12,axiom,
! [A: $i] :
( ( plus @ n5 @ A )
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_5_l) ).
thf(122,plain,
! [A: $i] :
( ( plus @ n5 @ A )
= ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(61,axiom,
gt @ n135299 @ tptp_minus_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135299_tptp_minus_1) ).
thf(469,plain,
gt @ n135299 @ tptp_minus_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(90,axiom,
! [A: $i] :
( ( pred @ ( succ @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pred_succ) ).
thf(543,plain,
! [A: $i] :
( ( pred @ ( succ @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(69,axiom,
gt @ n1 @ tptp_minus_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_1_tptp_minus_1) ).
thf(496,plain,
gt @ n1 @ tptp_minus_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(548,plain,
$false,
inference(e,[status(thm)],[173,318,470,138,101,518,523,115,217,511,202,384,533,500,404,185,125,542,157,216,321,106,514,492,164,133,116,527,512,529,546,381,220,534,137,165,92,197,388,169,141,537,476,489,109,471,128,105,205,541,530,148,149,391,540,387,494,535,140,520,330,455,223,394,135,112,458,145,150,327,310,143,497,524,104,517,319,158,119,478,315,168,326,400,395,163,122,469,543,496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV163+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n023.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % 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 02:32:45 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.95/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.28/0.99 % [INFO] Parsing done (141ms).
% 1.28/1.00 % [INFO] Running in sequential loop mode.
% 1.80/1.19 % [INFO] eprover registered as external prover.
% 1.80/1.19 % [INFO] cvc4 registered as external prover.
% 1.89/1.19 % [INFO] Scanning for conjecture ...
% 2.03/1.27 % [INFO] Found a conjecture and 91 axioms. Running axiom selection ...
% 2.24/1.33 % [INFO] Axiom selection finished. Selected 89 axioms (removed 2 axioms).
% 2.45/1.41 % [INFO] Problem is first-order (TPTP FOF).
% 2.45/1.42 % [INFO] Type checking passed.
% 2.45/1.42 % [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 ...
% 6.19/2.39 % External prover 'e' found a proof!
% 6.19/2.39 % [INFO] Killing All external provers ...
% 6.19/2.39 % Time passed: 1866ms (effective reasoning time: 1390ms)
% 6.19/2.39 % 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)>
% 6.19/2.40 % Axioms used in derivation (89): sel3_update_2, gt_2_tptp_minus_1, gt_135299_0, gt_3_1, leq_minus, sel2_update_2, succ_plus_5_l, lt_gt, gt_5_tptp_minus_1, succ_plus_3_r, gt_4_3, transitivity_gt, matrix_symm_inv, matrix_symm_trans, finite_domain_1, gt_5_0, const_array2_select, gt_135299_4, sel3_update_3, leq_geq, gt_1_0, leq_gt2, gt_5_4, succ_plus_1_l, gt_3_2, matrix_symm_add, leq_succ_gt, finite_domain_5, pred_minus_1, successor_3, gt_3_tptp_minus_1, matrix_symm_update_diagonal, sel2_update_1, gt_135299_5, gt_4_2, matrix_symm_sub, gt_5_3, successor_4, gt_succ, succ_plus_4_l, reflexivity_leq, successor_2, leq_gt1, gt_1_tptp_minus_1, finite_domain_2, matrix_symm_aba1, finite_domain_4, matrix_symm_aba2, succ_tptp_minus_1, succ_plus_5_r, gt_0_tptp_minus_1, gt_135299_2, leq_succ_succ, sum_plus_base_float, succ_plus_2_l, gt_4_1, gt_2_0, gt_5_2, const_array1_select, leq_gt_pred, matrix_symm_joseph_update, succ_pred, totality, gt_135299_1, transitivity_leq, finite_domain_3, uniform_int_rand_ranges_lo, gt_135299_tptp_minus_1, sel3_update_1, successor_1, sum_plus_base, irreflexivity_gt, successor_5, gt_3_0, sel2_update_3, pred_succ, succ_plus_1_r, succ_plus_3_l, gt_4_tptp_minus_1, succ_plus_4_r, gt_4_0, succ_plus_2_r, leq_succ_gt_equiv, gt_5_1, uniform_int_rand_ranges_hi, gt_2_1, gt_135299_3, finite_domain_0, leq_succ
% 6.19/2.40 % No. of inferences in proof: 182
% 6.19/2.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1866 ms resp. 1390 ms w/o parsing
% 6.67/2.47 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.67/2.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------