%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV158+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:58:16 AM UTC 2026
% Result : Theorem 7.35s 7.40s
% Output : Refutation 7.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 98
% Syntax : Number of formulae : 198 ( 125 unt; 0 typ; 0 def)
% Number of atoms : 580 ( 173 equ; 0 cnn)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 2674 ( 10 ~; 34 |; 216 &;2282 @)
% ( 5 <=>; 127 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 46 usr; 21 con; 0-4 aty)
% Number of variables : 345 ( 0 ^; 345 !; 0 ?; 345 :)
% Comments :
%------------------------------------------------------------------------------
thf(pv84_decl,type,
pv84: $i ).
thf(sum_decl,type,
sum: $i > $i > $i > $i ).
thf(n0_decl,type,
n0: $i ).
thf(n4_decl,type,
n4: $i ).
thf(divide_decl,type,
divide: $i > $i > $i ).
thf(times_decl,type,
times: $i > $i > $i ).
thf(exp_decl,type,
exp: $i > $i ).
thf(minus_decl,type,
minus: $i > $i > $i ).
thf(a_select2_decl,type,
a_select2: $i > $i > $i ).
thf(x_decl,type,
x: $i ).
thf(pv10_decl,type,
pv10: $i ).
thf(mu_decl,type,
mu: $i ).
thf(tptp_sum_index_decl,type,
tptp_sum_index: $i ).
thf(tptp_minus_2_decl,type,
tptp_minus_2: $i ).
thf(sigma_decl,type,
sigma: $i ).
thf(rho_decl,type,
rho: $i ).
thf(sqrt_decl,type,
sqrt: $i > $i ).
thf(n2_decl,type,
n2: $i ).
thf(tptp_pi_decl,type,
tptp_pi: $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(pv47_decl,type,
pv47: $i ).
thf(n135299_decl,type,
n135299: $i ).
thf(pred_decl,type,
pred: $i > $i ).
thf(a_select3_decl,type,
a_select3: $i > $i > $i > $i ).
thf(q_decl,type,
q: $i ).
thf(n1_decl,type,
n1: $i ).
thf(plus_decl,type,
plus: $i > $i > $i ).
thf(n3_decl,type,
n3: $i ).
thf(succ_decl,type,
succ: $i > $i ).
thf(gt_decl,type,
gt: $i > $i > $o ).
thf(n5_decl,type,
n5: $i ).
thf(tptp_minus_1_decl,type,
tptp_minus_1: $i ).
thf(lt_decl,type,
lt: $i > $i > $o ).
thf(tptp_update2_decl,type,
tptp_update2: $i > $i > $i > $i ).
thf(tptp_const_array2_decl,type,
tptp_const_array2: $i > $i > $i > $i ).
thf(dim_decl,type,
dim: $i > $i > $i ).
thf(tptp_mmul_decl,type,
tptp_mmul: $i > $i > $i ).
thf(trans_decl,type,
trans: $i > $i ).
thf(tptp_update3_decl,type,
tptp_update3: $i > $i > $i > $i > $i ).
thf(tptp_madd_decl,type,
tptp_madd: $i > $i > $i ).
thf(geq_decl,type,
geq: $i > $i > $o ).
thf(uniform_int_rnd_decl,type,
uniform_int_rnd: $i > $i > $i ).
thf(tptp_msub_decl,type,
tptp_msub: $i > $i > $i ).
thf(tptp_float_0_0_decl,type,
tptp_float_0_0: $i ).
thf(tptp_const_array1_decl,type,
tptp_const_array1: $i > $i > $i ).
thf(inv_decl,type,
inv: $i > $i ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ gt ) )
=> ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt1) ).
thf(153,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ gt ) )
=> ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(27,axiom,
n1 @ ( n4 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_1) ).
thf(174,plain,
n1 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ minus ) @ leq ) )
=> ( B @ ( n0 @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_minus) ).
thf(537,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ minus ) @ leq ) )
=> ( B @ ( n0 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( n5 @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_5_l) ).
thf(129,plain,
! [A: $i] :
( ( A @ ( n5 @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( B @ a_select3 ) ) )
= ( D @ ( E @ ( B @ a_select3 ) ) ) ) )
& ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( A @ a_select3 ) ) )
= ( D @ ( E @ ( A @ a_select3 ) ) ) ) ) )
=> ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( B @ ( A @ tptp_madd ) @ a_select3 ) ) )
= ( D @ ( E @ ( B @ ( A @ tptp_madd ) @ a_select3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_add) ).
thf(442,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( B @ a_select3 ) ) )
= ( D @ ( E @ ( B @ a_select3 ) ) ) ) )
& ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( A @ a_select3 ) ) )
= ( D @ ( E @ ( A @ a_select3 ) ) ) ) ) )
=> ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( B @ ( A @ tptp_madd ) @ a_select3 ) ) )
= ( D @ ( E @ ( B @ ( A @ tptp_madd ) @ a_select3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ lt ) )
<=> ( A @ ( B @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lt_gt) ).
thf(138,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ gt ) )
=> ( B @ ( A @ lt ) ) )
& ( ( B @ ( A @ lt ) )
=> ( A @ ( B @ gt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(47,axiom,
! [A: $i] :
( ( ( n0 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( A = n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_0) ).
thf(249,plain,
! [A: $i] :
( ( ( n0 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( A = n0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(75,axiom,
( ( n0 @ succ @ succ @ succ )
= n3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_3) ).
thf(518,plain,
( ( n0 @ succ @ succ @ succ )
= n3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(83,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ succ @ leq ) )
=> ( A @ ( B @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ_gt) ).
thf(555,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ succ @ leq ) )
=> ( A @ ( B @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(52,axiom,
n0 @ ( n5 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_0) ).
thf(352,plain,
n0 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(96,axiom,
! [A: $i] :
( ( ( n5 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n5 )
| ( A = n4 )
| ( A = n3 )
| ( A = n2 )
| ( A = n1 )
| ( A = n0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_5) ).
thf(582,plain,
! [A: $i] :
( ( ( n5 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n5 )
| ( A = n4 )
| ( A = n3 )
| ( A = n2 )
| ( A = n1 )
| ( A = n0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( A @ ( B @ succ @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ_gt_equiv) ).
thf(511,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ succ @ gt ) )
=> ( B @ ( A @ leq ) ) )
& ( ( B @ ( A @ leq ) )
=> ( A @ ( B @ succ @ gt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_leq) ).
thf(570,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ succ @ pred )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pred_succ) ).
thf(184,plain,
! [A: $i] :
( ( A @ succ @ pred )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(99,axiom,
( ( n0 @ succ @ succ )
= n2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_2) ).
thf(587,plain,
( ( n0 @ succ @ succ )
= n2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(6,axiom,
tptp_minus_1 @ ( n3 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_tptp_minus_1) ).
thf(125,plain,
tptp_minus_1 @ ( n3 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(38,axiom,
tptp_minus_2 @ ( n5 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_tptp_minus_2) ).
thf(196,plain,
tptp_minus_2 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(21,axiom,
( ( n0 @ succ )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_1) ).
thf(157,plain,
( ( n0 @ succ )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(60,axiom,
! [A: $i] :
( tptp_float_0_0
= ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_plus_base_float) ).
thf(421,plain,
! [A: $i] :
( tptp_float_0_0
= ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(17,axiom,
n5 @ ( n135299 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_135299_5) ).
thf(152,plain,
n5 @ ( n135299 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(24,axiom,
tptp_minus_1 @ ( n2 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_2_tptp_minus_1) ).
thf(164,plain,
tptp_minus_1 @ ( n2 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(53,axiom,
tptp_minus_2 @ ( n2 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_2_tptp_minus_2) ).
thf(353,plain,
tptp_minus_2 @ ( n2 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(14,axiom,
! [A: $i] :
( ( n3 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_3_r) ).
thf(147,plain,
! [A: $i] :
( ( n3 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9,axiom,
! [A: $i] :
~ ( A @ ( A @ gt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_gt) ).
thf(132,plain,
! [A: $i] :
~ ( A @ ( A @ gt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(63,axiom,
n2 @ ( n5 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_2) ).
thf(428,plain,
n2 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( B @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( B @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( A @ a_select3 ) ) )
= ( C @ ( D @ ( A @ a_select3 ) ) ) ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( B @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( A @ trans @ a_select3 ) ) )
= ( C @ ( D @ ( A @ trans @ a_select3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_trans) ).
thf(233,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( B @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( B @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( A @ a_select3 ) ) )
= ( C @ ( D @ ( A @ a_select3 ) ) ) ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( B @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( A @ trans @ a_select3 ) ) )
= ( C @ ( D @ ( A @ trans @ a_select3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( B @ a_select3 ) ) )
= ( D @ ( E @ ( B @ a_select3 ) ) ) ) )
& ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( A @ a_select3 ) ) )
= ( D @ ( E @ ( A @ a_select3 ) ) ) ) ) )
=> ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( B @ ( A @ tptp_msub ) @ a_select3 ) ) )
= ( D @ ( E @ ( B @ ( A @ tptp_msub ) @ a_select3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_sub) ).
thf(366,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( B @ a_select3 ) ) )
= ( D @ ( E @ ( B @ a_select3 ) ) ) ) )
& ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( A @ a_select3 ) ) )
= ( D @ ( E @ ( A @ a_select3 ) ) ) ) ) )
=> ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( B @ ( A @ tptp_msub ) @ a_select3 ) ) )
= ( D @ ( E @ ( B @ ( A @ tptp_msub ) @ a_select3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( ( A != B )
& ( B @ ( A @ leq ) ) )
=> ( A @ ( B @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt2) ).
thf(349,plain,
! [A: $i,B: $i] :
( ( ( A != B )
& ( B @ ( A @ leq ) ) )
=> ( A @ ( B @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(86,axiom,
! [A: $i] : ( A @ ( A @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_leq) ).
thf(561,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(61,axiom,
n0 @ ( n3 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_0) ).
thf(424,plain,
n0 @ ( n3 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( F @ ( D @ leq ) )
& ( D @ ( E @ leq ) )
& ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) )
=> ( ( D @ ( A @ ( G @ ( F @ ( E @ dim ) @ ( C @ ( B @ dim ) @ tptp_const_array2 ) ) @ a_select3 ) ) )
= G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',const_array2_select) ).
thf(192,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( F @ ( D @ leq ) )
& ( D @ ( E @ leq ) )
& ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) )
=> ( ( D @ ( A @ ( G @ ( F @ ( E @ dim ) @ ( C @ ( B @ dim ) @ tptp_const_array2 ) ) @ a_select3 ) ) )
= G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(64,axiom,
! [A: $i] :
( ( n4 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_4_r) ).
thf(429,plain,
! [A: $i] :
( ( n4 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(25,axiom,
n3 @ ( n135299 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_135299_3) ).
thf(165,plain,
n3 @ ( n135299 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ ( n2 @ plus ) )
= ( A @ succ @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_2_l) ).
thf(252,plain,
! [A: $i] :
( ( A @ ( n2 @ plus ) )
= ( A @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( ( D @ ( F @ leq ) )
& ( F @ ( n0 @ leq ) )
& ( D @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) ) )
=> ( ( F @ ( E @ ( B @ a_select3 ) ) )
= ( E @ ( F @ ( B @ a_select3 ) ) ) ) )
=> ! [E: $i,F: $i] :
( ( ( C @ ( F @ leq ) )
& ( F @ ( n0 @ leq ) )
& ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) ) )
=> ( ( F @ ( E @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) )
= ( E @ ( F @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_aba2) ).
thf(197,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( ( D @ ( F @ leq ) )
& ( F @ ( n0 @ leq ) )
& ( D @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) ) )
=> ( ( F @ ( E @ ( B @ a_select3 ) ) )
= ( E @ ( F @ ( B @ a_select3 ) ) ) ) )
=> ! [E: $i,F: $i] :
( ( ( C @ ( F @ leq ) )
& ( F @ ( n0 @ leq ) )
& ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) ) )
=> ( ( F @ ( E @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) )
= ( E @ ( F @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(42,axiom,
tptp_minus_2 @ ( n1 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1_tptp_minus_2) ).
thf(229,plain,
tptp_minus_2 @ ( n1 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(88,axiom,
n0 @ ( n4 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_0) ).
thf(566,plain,
n0 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(20,axiom,
n1 @ ( n3 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_1) ).
thf(156,plain,
n1 @ ( n3 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_plus_base) ).
thf(188,plain,
! [A: $i] :
( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( B @ pred @ ( A @ leq ) )
<=> ( A @ ( B @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt_pred) ).
thf(356,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ gt ) )
=> ( B @ pred @ ( A @ leq ) ) )
& ( ( B @ pred @ ( A @ leq ) )
=> ( A @ ( B @ gt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ geq ) )
<=> ( A @ ( B @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_geq) ).
thf(343,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ leq ) )
=> ( B @ ( A @ geq ) ) )
& ( ( B @ ( A @ geq ) )
=> ( A @ ( B @ leq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(98,axiom,
tptp_minus_2 @ ( n135299 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_135299_tptp_minus_2) ).
thf(586,plain,
tptp_minus_2 @ ( n135299 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(62,axiom,
! [A: $i] :
( ( ( n1 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n1 )
| ( A = n0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_1) ).
thf(425,plain,
! [A: $i] :
( ( ( n1 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n1 )
| ( A = n0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) )
& ! [E: $i] :
( ( ( B @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) ) )
=> ( ( E @ ( C @ a_select2 ) )
= D ) ) )
=> ( ( A @ ( D @ ( B @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sel2_update_3) ).
thf(166,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) )
& ! [E: $i] :
( ( ( B @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) ) )
=> ( ( E @ ( C @ a_select2 ) )
= D ) ) )
=> ( ( A @ ( D @ ( B @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( B @ ( A @ tptp_update2 ) ) @ a_select2 ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sel2_update_1) ).
thf(161,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( B @ ( A @ tptp_update2 ) ) @ a_select2 ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(92,axiom,
! [A: $i] :
( ( ( n4 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n4 )
| ( A = n3 )
| ( A = n2 )
| ( A = n1 )
| ( A = n0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_4) ).
thf(573,plain,
! [A: $i] :
( ( ( n4 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n4 )
| ( A = n3 )
| ( A = n2 )
| ( A = n1 )
| ( A = n0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(29,axiom,
n2 @ ( n4 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_2) ).
thf(180,plain,
n2 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(36,axiom,
n0 @ ( n135299 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_135299_0) ).
thf(191,plain,
n0 @ ( n135299 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(94,axiom,
n0 @ ( n1 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1_0) ).
thf(579,plain,
n0 @ ( n1 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(91,axiom,
n4 @ ( n5 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_4) ).
thf(572,plain,
n4 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ gt ) )
& ( B @ ( A @ gt ) ) )
=> ( C @ ( A @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_gt) ).
thf(144,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ gt ) )
& ( B @ ( A @ gt ) ) )
=> ( C @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(30,axiom,
n4 @ ( n135299 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_135299_4) ).
thf(181,plain,
n4 @ ( n135299 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(81,axiom,
! [A: $i] :
( ( ( n2 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n2 )
| ( A = n1 )
| ( A = n0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_2) ).
thf(540,plain,
! [A: $i] :
( ( ( n2 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n2 )
| ( A = n1 )
| ( A = n0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(22,axiom,
( ( n0 @ succ @ succ @ succ @ succ )
= n4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_4) ).
thf(159,plain,
( ( n0 @ succ @ succ @ succ @ succ )
= n4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(34,axiom,
tptp_minus_2 @ ( n0 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_0_tptp_minus_2) ).
thf(187,plain,
tptp_minus_2 @ ( n0 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ pred @ succ )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_pred) ).
thf(230,plain,
! [A: $i] :
( ( A @ pred @ succ )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(45,axiom,
tptp_minus_1 @ ( n0 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_0_tptp_minus_1) ).
thf(245,plain,
tptp_minus_1 @ ( n0 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(71,axiom,
tptp_minus_1 @ ( n135299 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_135299_tptp_minus_1) ).
thf(509,plain,
tptp_minus_1 @ ( n135299 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(56,axiom,
n1 @ ( n135299 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_135299_1) ).
thf(362,plain,
n1 @ ( n135299 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(89,axiom,
! [A: $i] :
( ( ( n3 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n3 )
| ( A = n2 )
| ( A = n1 )
| ( A = n0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_3) ).
thf(567,plain,
! [A: $i] :
( ( ( n3 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n3 )
| ( A = n2 )
| ( A = n1 )
| ( A = n0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( A @ ( n0 @ leq ) )
=> ( A @ ( A @ ( B @ uniform_int_rnd ) @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniform_int_rand_ranges_hi) ).
thf(494,plain,
! [A: $i,B: $i] :
( ( A @ ( n0 @ leq ) )
=> ( A @ ( A @ ( B @ uniform_int_rnd ) @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( B @ succ @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ) ).
thf(535,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( B @ succ @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( B @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( C @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) )
& ! [G: $i,H: $i] :
( ( ( D @ ( H @ leq ) )
& ( C @ ( G @ leq ) )
& ( H @ ( n0 @ leq ) )
& ( G @ ( n0 @ leq ) ) )
=> ( ( H @ ( G @ ( E @ a_select3 ) ) )
= F ) ) )
=> ( ( B @ ( A @ ( F @ ( D @ ( C @ ( E @ tptp_update3 ) ) ) @ a_select3 ) ) )
= F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sel3_update_3) ).
thf(520,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( B @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( C @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) )
& ! [G: $i,H: $i] :
( ( ( D @ ( H @ leq ) )
& ( C @ ( G @ leq ) )
& ( H @ ( n0 @ leq ) )
& ( G @ ( n0 @ leq ) ) )
=> ( ( H @ ( G @ ( E @ a_select3 ) ) )
= F ) ) )
=> ( ( B @ ( A @ ( F @ ( D @ ( C @ ( E @ tptp_update3 ) ) ) @ a_select3 ) ) )
= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(19,axiom,
tptp_minus_2 @ ( n3 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_tptp_minus_2) ).
thf(155,plain,
tptp_minus_2 @ ( n3 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( B @ succ @ ( A @ succ @ leq ) )
<=> ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ_succ) ).
thf(223,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ leq ) )
=> ( B @ succ @ ( A @ succ @ leq ) ) )
& ( ( B @ succ @ ( A @ succ @ leq ) )
=> ( B @ ( A @ leq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) )
=> ( ( A @ ( D @ ( C @ ( B @ dim ) @ tptp_const_array1 ) @ a_select2 ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',const_array1_select) ).
thf(438,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) )
=> ( ( A @ ( D @ ( C @ ( B @ dim ) @ tptp_const_array1 ) @ a_select2 ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(10,axiom,
! [A: $i] :
( ( n5 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_5_r) ).
thf(135,plain,
! [A: $i] :
( ( n5 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(87,axiom,
! [A: $i] :
( ( A @ ( n1 @ plus ) )
= ( A @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_1_l) ).
thf(563,plain,
! [A: $i] :
( ( A @ ( n1 @ plus ) )
= ( A @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ! [I: $i,J: $i] :
( ( ( G @ ( J @ leq ) )
& ( J @ ( n0 @ leq ) )
& ( G @ ( I @ leq ) )
& ( I @ ( n0 @ leq ) ) )
=> ( ( J @ ( I @ ( F @ a_select3 ) ) )
= ( I @ ( J @ ( F @ a_select3 ) ) ) ) )
& ! [I: $i,J: $i] :
( ( ( G @ ( J @ leq ) )
& ( J @ ( n0 @ leq ) )
& ( G @ ( I @ leq ) )
& ( I @ ( n0 @ leq ) ) )
=> ( ( J @ ( I @ ( A @ a_select3 ) ) )
= ( I @ ( J @ ( A @ a_select3 ) ) ) ) )
& ! [I: $i,J: $i] :
( ( ( H @ ( J @ leq ) )
& ( J @ ( n0 @ leq ) )
& ( H @ ( I @ leq ) )
& ( I @ ( n0 @ leq ) ) )
=> ( ( J @ ( I @ ( D @ a_select3 ) ) )
= ( I @ ( J @ ( D @ a_select3 ) ) ) ) ) )
=> ! [I: $i,J: $i] :
( ( ( G @ ( J @ leq ) )
& ( J @ ( n0 @ leq ) )
& ( G @ ( I @ leq ) )
& ( I @ ( n0 @ leq ) ) )
=> ( ( J @ ( I @ ( B @ trans @ ( E @ trans @ ( F @ tptp_mmul ) @ ( E @ tptp_mmul ) @ ( C @ trans @ ( D @ tptp_mmul ) @ ( C @ tptp_mmul ) @ tptp_madd ) @ tptp_mmul ) @ ( B @ tptp_mmul ) @ ( A @ tptp_madd ) @ a_select3 ) ) )
= ( I @ ( J @ ( B @ trans @ ( E @ trans @ ( F @ tptp_mmul ) @ ( E @ tptp_mmul ) @ ( C @ trans @ ( D @ tptp_mmul ) @ ( C @ tptp_mmul ) @ tptp_madd ) @ tptp_mmul ) @ ( B @ tptp_mmul ) @ ( A @ tptp_madd ) @ a_select3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_joseph_update) ).
thf(255,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ! [I: $i,J: $i] :
( ( ( G @ ( J @ leq ) )
& ( J @ ( n0 @ leq ) )
& ( G @ ( I @ leq ) )
& ( I @ ( n0 @ leq ) ) )
=> ( ( J @ ( I @ ( F @ a_select3 ) ) )
= ( I @ ( J @ ( F @ a_select3 ) ) ) ) )
& ! [I: $i,J: $i] :
( ( ( G @ ( J @ leq ) )
& ( J @ ( n0 @ leq ) )
& ( G @ ( I @ leq ) )
& ( I @ ( n0 @ leq ) ) )
=> ( ( J @ ( I @ ( A @ a_select3 ) ) )
= ( I @ ( J @ ( A @ a_select3 ) ) ) ) )
& ! [I: $i,J: $i] :
( ( ( H @ ( J @ leq ) )
& ( J @ ( n0 @ leq ) )
& ( H @ ( I @ leq ) )
& ( I @ ( n0 @ leq ) ) )
=> ( ( J @ ( I @ ( D @ a_select3 ) ) )
= ( I @ ( J @ ( D @ a_select3 ) ) ) ) ) )
=> ! [I: $i,J: $i] :
( ( ( G @ ( J @ leq ) )
& ( J @ ( n0 @ leq ) )
& ( G @ ( I @ leq ) )
& ( I @ ( n0 @ leq ) ) )
=> ( ( J @ ( I @ ( B @ trans @ ( E @ trans @ ( F @ tptp_mmul ) @ ( E @ tptp_mmul ) @ ( C @ trans @ ( D @ tptp_mmul ) @ ( C @ tptp_mmul ) @ tptp_madd ) @ tptp_mmul ) @ ( B @ tptp_mmul ) @ ( A @ tptp_madd ) @ a_select3 ) ) )
= ( I @ ( J @ ( B @ trans @ ( E @ trans @ ( F @ tptp_mmul ) @ ( E @ tptp_mmul ) @ ( C @ trans @ ( D @ tptp_mmul ) @ ( C @ tptp_mmul ) @ tptp_madd ) @ tptp_mmul ) @ ( B @ tptp_mmul ) @ ( A @ tptp_madd ) @ a_select3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(5,axiom,
! [A: $i] : ( A @ ( A @ succ @ gt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_succ) ).
thf(123,plain,
! [A: $i] : ( A @ ( A @ succ @ gt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(84,axiom,
! [A: $i] :
( ( A @ ( n4 @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_4_l) ).
thf(557,plain,
! [A: $i] :
( ( A @ ( n4 @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(95,axiom,
( ( n0 @ succ @ succ @ succ @ succ @ succ )
= n5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_5) ).
thf(580,plain,
( ( n0 @ succ @ succ @ succ @ succ @ succ )
= n5 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(15,axiom,
n2 @ ( n3 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_2) ).
thf(150,plain,
n2 @ ( n3 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(31,axiom,
n3 @ ( n4 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_3) ).
thf(182,plain,
n3 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(97,axiom,
n1 @ ( n5 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_1) ).
thf(585,plain,
n1 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(93,axiom,
! [A: $i] :
( ( n2 @ ( A @ plus ) )
= ( A @ succ @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_2_r) ).
thf(576,plain,
! [A: $i] :
( ( n2 @ ( A @ plus ) )
= ( A @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( B @ ( C @ a_select2 ) )
= D )
& ( A != B ) )
=> ( ( B @ ( E @ ( A @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sel2_update_2) ).
thf(175,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( B @ ( C @ a_select2 ) )
= D )
& ( A != B ) )
=> ( ( B @ ( E @ ( A @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( B @ a_select3 ) ) )
= ( D @ ( E @ ( B @ a_select3 ) ) ) ) )
=> ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) )
= ( D @ ( E @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_aba1) ).
thf(497,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( B @ a_select3 ) ) )
= ( D @ ( E @ ( B @ a_select3 ) ) ) ) )
=> ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) )
= ( D @ ( E @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( A @ ( n0 @ leq ) )
=> ( A @ ( B @ uniform_int_rnd ) @ ( n0 @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniform_int_rand_ranges_lo) ).
thf(363,plain,
! [A: $i,B: $i] :
( ( A @ ( n0 @ leq ) )
=> ( A @ ( B @ uniform_int_rnd ) @ ( n0 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(80,axiom,
tptp_minus_1 @ ( n1 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1_tptp_minus_1) ).
thf(539,plain,
tptp_minus_1 @ ( n1 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(74,axiom,
tptp_minus_2 @ ( n4 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_tptp_minus_2) ).
thf(517,plain,
tptp_minus_2 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( D @ ( C @ ( B @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sel3_update_1) ).
thf(418,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( D @ ( C @ ( B @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( n3 @ plus ) )
= ( A @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_3_l) ).
thf(119,plain,
! [A: $i] :
( ( A @ ( n3 @ plus ) )
= ( A @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(46,axiom,
! [A: $i] :
( ( n1 @ ( A @ minus ) )
= ( A @ pred ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pred_minus_1) ).
thf(246,plain,
! [A: $i] :
( ( n1 @ ( A @ minus ) )
= ( A @ pred ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( D @ ( C @ ( E @ a_select3 ) ) )
= F )
& ( B = D )
& ( A != C ) )
=> ( ( D @ ( C @ ( G @ ( B @ ( A @ ( E @ tptp_update3 ) ) ) @ a_select3 ) ) )
= F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sel3_update_2) ).
thf(433,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( D @ ( C @ ( E @ a_select3 ) ) )
= F )
& ( B = D )
& ( A != C ) )
=> ( ( D @ ( C @ ( G @ ( B @ ( A @ ( E @ tptp_update3 ) ) ) @ a_select3 ) ) )
= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(72,axiom,
tptp_minus_1 @ ( n4 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_tptp_minus_1) ).
thf(510,plain,
tptp_minus_1 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(16,axiom,
n1 @ ( n2 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_2_1) ).
thf(151,plain,
n1 @ ( n2 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(65,axiom,
n2 @ ( n135299 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_135299_2) ).
thf(432,plain,
n2 @ ( n135299 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(13,axiom,
tptp_minus_1 @ ( n5 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_tptp_minus_1) ).
thf(146,plain,
tptp_minus_1 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(32,axiom,
tptp_minus_2 @ ( tptp_minus_1 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_tptp_minus_1_tptp_minus_2) ).
thf(183,plain,
tptp_minus_2 @ ( tptp_minus_1 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( B @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( B @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( A @ a_select3 ) ) )
= ( C @ ( D @ ( A @ a_select3 ) ) ) ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( B @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( B @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_update_diagonal) ).
thf(210,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( B @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( B @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( A @ a_select3 ) ) )
= ( C @ ( D @ ( A @ a_select3 ) ) ) ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( B @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( B @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ( A @ ( B @ gt ) )
| ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
thf(126,plain,
! [A: $i,B: $i] :
( ( A = B )
| ( A @ ( B @ gt ) )
| ( B @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(77,axiom,
! [A: $i] :
( ( n1 @ ( A @ plus ) )
= ( A @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_1_r) ).
thf(532,plain,
! [A: $i] :
( ( n1 @ ( A @ plus ) )
= ( A @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(4,axiom,
n3 @ ( n5 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_3) ).
thf(122,plain,
n3 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(54,axiom,
( ( tptp_minus_1 @ succ )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_tptp_minus_1) ).
thf(354,plain,
( ( tptp_minus_1 @ succ )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( B @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( B @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( A @ a_select3 ) ) )
= ( C @ ( D @ ( A @ a_select3 ) ) ) ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( B @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( A @ inv @ a_select3 ) ) )
= ( C @ ( D @ ( A @ inv @ a_select3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_inv) ).
thf(543,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( B @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( B @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( A @ a_select3 ) ) )
= ( C @ ( D @ ( A @ a_select3 ) ) ) ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( B @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( A @ inv @ a_select3 ) ) )
= ( C @ ( D @ ( A @ inv @ a_select3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(85,axiom,
n0 @ ( n2 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_2_0) ).
thf(560,plain,
n0 @ ( n2 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(1,conjecture,
( ( ! [A: $i] :
( ( ( pv10 @ pred @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( tptp_sum_index @ ( A @ ( q @ a_select3 ) ) @ ( n4 @ ( n0 @ sum ) ) )
= n1 ) )
& ! [A: $i] :
( ( ( pv47 @ pred @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( pv10 @ ( q @ a_select3 ) ) )
= ( tptp_sum_index @ ( sigma @ a_select2 ) @ ( tptp_pi @ ( n2 @ times ) @ sqrt @ times ) @ ( tptp_sum_index @ ( rho @ a_select2 ) @ ( tptp_sum_index @ ( sigma @ a_select2 ) @ ( tptp_sum_index @ ( sigma @ a_select2 ) @ times ) @ ( tptp_minus_2 @ ( tptp_sum_index @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ ( tptp_sum_index @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ times ) @ divide ) @ divide ) @ exp @ times ) @ divide ) @ ( n4 @ ( n0 @ sum ) ) @ ( A @ ( sigma @ a_select2 ) @ ( tptp_pi @ ( n2 @ times ) @ sqrt @ times ) @ ( A @ ( rho @ a_select2 ) @ ( A @ ( sigma @ a_select2 ) @ ( A @ ( sigma @ a_select2 ) @ times ) @ ( tptp_minus_2 @ ( A @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ ( A @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ times ) @ divide ) @ divide ) @ exp @ times ) @ divide ) @ divide ) ) ) )
& ( n4 @ ( pv47 @ leq ) )
& ( n135299 @ ( pv10 @ leq ) )
& ( pv47 @ ( n0 @ leq ) )
& ( pv10 @ ( n0 @ leq ) )
& ( pv84
= ( tptp_sum_index @ ( sigma @ a_select2 ) @ ( tptp_pi @ ( n2 @ times ) @ sqrt @ times ) @ ( tptp_sum_index @ ( rho @ a_select2 ) @ ( tptp_sum_index @ ( sigma @ a_select2 ) @ ( tptp_sum_index @ ( sigma @ a_select2 ) @ times ) @ ( tptp_minus_2 @ ( tptp_sum_index @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ ( tptp_sum_index @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ times ) @ divide ) @ divide ) @ exp @ times ) @ divide ) @ ( n4 @ ( n0 @ sum ) ) ) ) )
=> ! [A: $i] :
( ( ( pv47 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( pv47 = A )
=> ( ( pv84 @ ( pv47 @ ( sigma @ a_select2 ) @ ( tptp_pi @ ( n2 @ times ) @ sqrt @ times ) @ ( pv47 @ ( rho @ a_select2 ) @ ( pv47 @ ( sigma @ a_select2 ) @ ( pv47 @ ( sigma @ a_select2 ) @ times ) @ ( tptp_minus_2 @ ( pv47 @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ ( pv47 @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ times ) @ divide ) @ divide ) @ exp @ times ) @ divide ) @ divide ) )
= ( tptp_sum_index @ ( sigma @ a_select2 ) @ ( tptp_pi @ ( n2 @ times ) @ sqrt @ times ) @ ( tptp_sum_index @ ( rho @ a_select2 ) @ ( tptp_sum_index @ ( sigma @ a_select2 ) @ ( tptp_sum_index @ ( sigma @ a_select2 ) @ times ) @ ( tptp_minus_2 @ ( tptp_sum_index @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ ( tptp_sum_index @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ times ) @ divide ) @ divide ) @ exp @ times ) @ divide ) @ ( n4 @ ( n0 @ sum ) ) @ ( A @ ( sigma @ a_select2 ) @ ( tptp_pi @ ( n2 @ times ) @ sqrt @ times ) @ ( A @ ( rho @ a_select2 ) @ ( A @ ( sigma @ a_select2 ) @ ( A @ ( sigma @ a_select2 ) @ times ) @ ( tptp_minus_2 @ ( A @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ ( A @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ times ) @ divide ) @ divide ) @ exp @ times ) @ divide ) @ divide ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_norm_0008) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i] :
( ( ( pv10 @ pred @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( tptp_sum_index @ ( A @ ( q @ a_select3 ) ) @ ( n4 @ ( n0 @ sum ) ) )
= n1 ) )
& ! [A: $i] :
( ( ( pv47 @ pred @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( pv10 @ ( q @ a_select3 ) ) )
= ( tptp_sum_index @ ( sigma @ a_select2 ) @ ( tptp_pi @ ( n2 @ times ) @ sqrt @ times ) @ ( tptp_sum_index @ ( rho @ a_select2 ) @ ( tptp_sum_index @ ( sigma @ a_select2 ) @ ( tptp_sum_index @ ( sigma @ a_select2 ) @ times ) @ ( tptp_minus_2 @ ( tptp_sum_index @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ ( tptp_sum_index @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ times ) @ divide ) @ divide ) @ exp @ times ) @ divide ) @ ( n4 @ ( n0 @ sum ) ) @ ( A @ ( sigma @ a_select2 ) @ ( tptp_pi @ ( n2 @ times ) @ sqrt @ times ) @ ( A @ ( rho @ a_select2 ) @ ( A @ ( sigma @ a_select2 ) @ ( A @ ( sigma @ a_select2 ) @ times ) @ ( tptp_minus_2 @ ( A @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ ( A @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ times ) @ divide ) @ divide ) @ exp @ times ) @ divide ) @ divide ) ) ) )
& ( n4 @ ( pv47 @ leq ) )
& ( n135299 @ ( pv10 @ leq ) )
& ( pv47 @ ( n0 @ leq ) )
& ( pv10 @ ( n0 @ leq ) )
& ( pv84
= ( tptp_sum_index @ ( sigma @ a_select2 ) @ ( tptp_pi @ ( n2 @ times ) @ sqrt @ times ) @ ( tptp_sum_index @ ( rho @ a_select2 ) @ ( tptp_sum_index @ ( sigma @ a_select2 ) @ ( tptp_sum_index @ ( sigma @ a_select2 ) @ times ) @ ( tptp_minus_2 @ ( tptp_sum_index @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ ( tptp_sum_index @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ times ) @ divide ) @ divide ) @ exp @ times ) @ divide ) @ ( n4 @ ( n0 @ sum ) ) ) ) )
=> ! [A: $i] :
( ( ( pv47 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( pv47 = A )
=> ( ( pv84 @ ( pv47 @ ( sigma @ a_select2 ) @ ( tptp_pi @ ( n2 @ times ) @ sqrt @ times ) @ ( pv47 @ ( rho @ a_select2 ) @ ( pv47 @ ( sigma @ a_select2 ) @ ( pv47 @ ( sigma @ a_select2 ) @ times ) @ ( tptp_minus_2 @ ( pv47 @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ ( pv47 @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ times ) @ divide ) @ divide ) @ exp @ times ) @ divide ) @ divide ) )
= ( tptp_sum_index @ ( sigma @ a_select2 ) @ ( tptp_pi @ ( n2 @ times ) @ sqrt @ times ) @ ( tptp_sum_index @ ( rho @ a_select2 ) @ ( tptp_sum_index @ ( sigma @ a_select2 ) @ ( tptp_sum_index @ ( sigma @ a_select2 ) @ times ) @ ( tptp_minus_2 @ ( tptp_sum_index @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ ( tptp_sum_index @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ times ) @ divide ) @ divide ) @ exp @ times ) @ divide ) @ ( n4 @ ( n0 @ sum ) ) @ ( A @ ( sigma @ a_select2 ) @ ( tptp_pi @ ( n2 @ times ) @ sqrt @ times ) @ ( A @ ( rho @ a_select2 ) @ ( A @ ( sigma @ a_select2 ) @ ( A @ ( sigma @ a_select2 ) @ times ) @ ( tptp_minus_2 @ ( A @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ ( A @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ times ) @ divide ) @ divide ) @ exp @ times ) @ divide ) @ divide ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(100,plain,
~ ( ( ! [A: $i] :
( ( ( pv10 @ pred @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( tptp_sum_index @ ( A @ ( q @ a_select3 ) ) @ ( n4 @ ( n0 @ sum ) ) )
= n1 ) )
& ! [A: $i] :
( ( ( pv47 @ pred @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( pv10 @ ( q @ a_select3 ) ) )
= ( tptp_sum_index @ ( sigma @ a_select2 ) @ ( tptp_pi @ ( n2 @ times ) @ sqrt @ times ) @ ( tptp_sum_index @ ( rho @ a_select2 ) @ ( tptp_sum_index @ ( sigma @ a_select2 ) @ ( tptp_sum_index @ ( sigma @ a_select2 ) @ times ) @ ( tptp_minus_2 @ ( tptp_sum_index @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ ( tptp_sum_index @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ times ) @ divide ) @ divide ) @ exp @ times ) @ divide ) @ ( n4 @ ( n0 @ sum ) ) @ ( A @ ( sigma @ a_select2 ) @ ( tptp_pi @ ( n2 @ times ) @ sqrt @ times ) @ ( A @ ( rho @ a_select2 ) @ ( A @ ( sigma @ a_select2 ) @ ( A @ ( sigma @ a_select2 ) @ times ) @ ( tptp_minus_2 @ ( A @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ ( A @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ times ) @ divide ) @ divide ) @ exp @ times ) @ divide ) @ divide ) ) ) )
& ( n4 @ ( pv47 @ leq ) )
& ( n135299 @ ( pv10 @ leq ) )
& ( pv47 @ ( n0 @ leq ) )
& ( pv10 @ ( n0 @ leq ) )
& ( pv84
= ( tptp_sum_index @ ( sigma @ a_select2 ) @ ( tptp_pi @ ( n2 @ times ) @ sqrt @ times ) @ ( tptp_sum_index @ ( rho @ a_select2 ) @ ( tptp_sum_index @ ( sigma @ a_select2 ) @ ( tptp_sum_index @ ( sigma @ a_select2 ) @ times ) @ ( tptp_minus_2 @ ( tptp_sum_index @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ ( tptp_sum_index @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ times ) @ divide ) @ divide ) @ exp @ times ) @ divide ) @ ( n4 @ ( n0 @ sum ) ) ) ) )
=> ! [A: $i] :
( ( ( pv47 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( pv47 = A )
=> ( ( pv84 @ ( pv47 @ ( sigma @ a_select2 ) @ ( tptp_pi @ ( n2 @ times ) @ sqrt @ times ) @ ( pv47 @ ( rho @ a_select2 ) @ ( pv47 @ ( sigma @ a_select2 ) @ ( pv47 @ ( sigma @ a_select2 ) @ times ) @ ( tptp_minus_2 @ ( pv47 @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ ( pv47 @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ times ) @ divide ) @ divide ) @ exp @ times ) @ divide ) @ divide ) )
= ( tptp_sum_index @ ( sigma @ a_select2 ) @ ( tptp_pi @ ( n2 @ times ) @ sqrt @ times ) @ ( tptp_sum_index @ ( rho @ a_select2 ) @ ( tptp_sum_index @ ( sigma @ a_select2 ) @ ( tptp_sum_index @ ( sigma @ a_select2 ) @ times ) @ ( tptp_minus_2 @ ( tptp_sum_index @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ ( tptp_sum_index @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ times ) @ divide ) @ divide ) @ exp @ times ) @ divide ) @ ( n4 @ ( n0 @ sum ) ) @ ( A @ ( sigma @ a_select2 ) @ ( tptp_pi @ ( n2 @ times ) @ sqrt @ times ) @ ( A @ ( rho @ a_select2 ) @ ( A @ ( sigma @ a_select2 ) @ ( A @ ( sigma @ a_select2 ) @ times ) @ ( tptp_minus_2 @ ( A @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ ( A @ ( mu @ a_select2 ) @ ( pv10 @ ( x @ a_select2 ) @ minus ) @ times ) @ divide ) @ divide ) @ exp @ times ) @ divide ) @ divide ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(589,plain,
$false,
inference(e,[status(thm)],[153,174,537,129,442,138,249,518,555,352,582,511,570,184,587,125,196,157,421,152,164,353,147,132,428,233,366,349,561,424,192,429,165,252,197,229,566,156,188,356,343,586,425,166,161,573,180,191,579,572,144,181,540,159,187,230,245,509,362,567,494,535,520,155,223,438,135,563,255,123,557,580,150,182,585,576,175,497,363,539,517,418,119,246,433,510,151,432,146,183,210,126,532,122,354,543,560,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV158+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/5.43 % Computer : n009.cluster.edu
% 0.15/5.43 % Model : x86_64 x86_64
% 0.15/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.43 % Memory : 8046.5625MB
% 0.15/5.43 % OS : Linux 6.8.0-71-generic
% 0.15/5.43 % CPULimit : 300
% 0.15/5.43 % WCLimit : 300
% 0.15/5.43 % DateTime : Sat Sep 26 13:17:05 UTC 2026
% 0.15/5.43 % CPUTime :
% 0.15/5.43 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.19/5.75 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/5.90 % [INFO] Parsing done (152ms).
% 0.19/5.91 % [INFO] Running in sequential loop mode.
% 1.73/6.11 % [INFO] eprover registered as external prover.
% 1.73/6.12 % [INFO] Scanning for conjecture ...
% 2.27/6.21 % [INFO] Found a conjecture (or negated_conjecture) and 99 axioms. Running axiom selection ...
% 2.27/6.29 % [INFO] Axiom selection finished. Selected 97 axioms (removed 2 axioms).
% 2.62/6.36 % [INFO] Problem is first-order (TPTP FOF).
% 2.62/6.37 % [INFO] Type checking passed.
% 2.62/6.37 % [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 ...
% 7.35/7.40 % External prover 'e' found a proof!
% 7.35/7.40 % [INFO] Killing All external provers ...
% 7.35/7.40 % Time passed: 1856ms (effective reasoning time: 1485ms)
% 7.35/7.40 % 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)>
% 7.35/7.40 % Axioms used in derivation (97): sel3_update_2, gt_2_tptp_minus_1, gt_3_1, sel2_update_2, succ_plus_5_l, lt_gt, gt_135299_tptp_minus_2, 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, gt_5_4, leq_gt2, gt_1_tptp_minus_2, 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_4_tptp_minus_2, gt_135299_0, 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, gt_tptp_minus_1_tptp_minus_2, 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_3_tptp_minus_2, gt_135299_3, finite_domain_0, leq_succ, gt_0_tptp_minus_2, gt_5_tptp_minus_2, leq_minus, gt_2_tptp_minus_2
% 7.35/7.40 % No. of inferences in proof: 198
% 7.35/7.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1856 ms resp. 1485 ms w/o parsing
% 7.70/7.56 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.70/7.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------