%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV210+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:58:25 AM UTC 2026
% Result : Theorem 9.48s 4.43s
% Output : Refutation 9.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 91
% Syntax : Number of formulae : 184 ( 111 unt; 0 typ; 0 def)
% Number of atoms : 647 ( 250 equ; 0 cnn)
% Maximal formula atoms : 42 ( 3 avg)
% Number of connectives : 2173 ( 12 ~; 34 |; 300 &;1698 @)
% ( 5 <=>; 124 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 40 usr; 19 con; 0-4 aty)
% Number of variables : 354 ( 0 ^; 354 !; 0 ?; 354 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_select2_decl,type,
a_select2: $i > $i > $i ).
thf(rho_defuse_decl,type,
rho_defuse: $i ).
thf(n0_decl,type,
n0: $i ).
thf(use_decl,type,
use: $i ).
thf(n1_decl,type,
n1: $i ).
thf(n2_decl,type,
n2: $i ).
thf(sigma_defuse_decl,type,
sigma_defuse: $i ).
thf(n3_decl,type,
n3: $i ).
thf(n4_decl,type,
n4: $i ).
thf(n5_decl,type,
n5: $i ).
thf(a_select3_decl,type,
a_select3: $i > $i > $i > $i ).
thf(u_defuse_decl,type,
u_defuse: $i ).
thf(xinit_defuse_decl,type,
xinit_defuse: $i ).
thf(xinit_mean_defuse_decl,type,
xinit_mean_defuse: $i ).
thf(xinit_noise_defuse_decl,type,
xinit_noise_defuse: $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(n998_decl,type,
n998: $i ).
thf(z_defuse_decl,type,
z_defuse: $i ).
thf(gt_decl,type,
gt: $i > $i > $o ).
thf(pred_decl,type,
pred: $i > $i ).
thf(succ_decl,type,
succ: $i > $i ).
thf(lt_decl,type,
lt: $i > $i > $o ).
thf(tptp_update2_decl,type,
tptp_update2: $i > $i > $i > $i ).
thf(tptp_minus_1_decl,type,
tptp_minus_1: $i ).
thf(def_decl,type,
def: $i ).
thf(sum_decl,type,
sum: $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(plus_decl,type,
plus: $i > $i > $i ).
thf(minus_decl,type,
minus: $i > $i > $i ).
thf(tptp_madd_decl,type,
tptp_madd: $i > $i > $i ).
thf(geq_decl,type,
geq: $i > $i > $o ).
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(uniform_int_rnd_decl,type,
uniform_int_rnd: $i > $i > $i ).
thf(inv_decl,type,
inv: $i > $i ).
thf(13,axiom,
( ( n0 @ succ )
= n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_1) ).
thf(185,plain,
( ( n0 @ succ )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( A @ ( B @ succ @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_gt_equiv) ).
thf(527,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)],[58]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ succ @ leq ) )
=> ( A @ ( B @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_gt) ).
thf(572,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ succ @ leq ) )
=> ( A @ ( B @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(32,axiom,
! [A: $i] :
( ( ( n0 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( A = n0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_0) ).
thf(263,plain,
! [A: $i] :
( ( ( n0 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( A = n0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(78,axiom,
! [A: $i] :
( ( ( n3 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n3 )
| ( A = n2 )
| ( A = n1 )
| ( A = n0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_3) ).
thf(588,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)],[78]) ).
thf(23,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/sandbox2/benchmark/theBenchmark.p',const_array2_select) ).
thf(207,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)],[23]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( ( A != B )
& ( B @ ( A @ leq ) ) )
=> ( A @ ( B @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt2) ).
thf(364,plain,
! [A: $i,B: $i] :
( ( ( A != B )
& ( B @ ( A @ leq ) ) )
=> ( A @ ( B @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(29,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/sandbox2/benchmark/theBenchmark.p',matrix_symm_trans) ).
thf(247,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)],[29]) ).
thf(34,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/sandbox2/benchmark/theBenchmark.p',matrix_symm_joseph_update) ).
thf(269,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)],[34]) ).
thf(82,axiom,
tptp_minus_1 @ ( n3 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_tptp_minus_1) ).
thf(597,plain,
tptp_minus_1 @ ( n3 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(48,axiom,
! [A: $i] :
( ( ( n1 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n1 )
| ( A = n0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_1) ).
thf(440,plain,
! [A: $i] :
( ( ( n1 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n1 )
| ( A = n0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( A @ ( n0 @ leq ) )
=> ( A @ ( A @ ( B @ uniform_int_rnd ) @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniform_int_rand_ranges_hi) ).
thf(511,plain,
! [A: $i,B: $i] :
( ( A @ ( n0 @ leq ) )
=> ( A @ ( A @ ( B @ uniform_int_rnd ) @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(59,axiom,
( ( n0 @ succ @ succ @ succ )
= n3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_3) ).
thf(533,plain,
( ( n0 @ succ @ succ @ succ )
= n3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(62,axiom,
n1 @ ( n998 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_998_1) ).
thf(550,plain,
n1 @ ( n998 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(12,axiom,
n1 @ ( n3 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_1) ).
thf(184,plain,
n1 @ ( n3 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(41,axiom,
( ( tptp_minus_1 @ succ )
= n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_tptp_minus_1) ).
thf(372,plain,
( ( tptp_minus_1 @ succ )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(77,axiom,
n2 @ ( n998 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_998_2) ).
thf(587,plain,
n2 @ ( n998 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ geq ) )
<=> ( A @ ( B @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_geq) ).
thf(357,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)],[35]) ).
thf(67,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/sandbox2/benchmark/theBenchmark.p',matrix_symm_inv) ).
thf(559,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)],[67]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( B @ ( A @ tptp_update2 ) ) @ a_select2 ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sel2_update_1) ).
thf(189,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( B @ ( A @ tptp_update2 ) ) @ a_select2 ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1,conjecture,
( ( ! [A: $i,B: $i] :
( ( ( n998 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use ) )
& ! [A: $i,B: $i] :
( ( ( n998 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( u_defuse @ a_select3 ) ) )
= use ) )
& ( ( n5 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n5 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n5 @ ( xinit_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( xinit_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( xinit_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( n2 @ ( u_defuse @ a_select3 ) ) )
= use )
& ( ( n0 @ ( n1 @ ( u_defuse @ a_select3 ) ) )
= use )
& ( ( n0 @ ( n0 @ ( u_defuse @ a_select3 ) ) )
= use )
& ( ( n5 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( rho_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( rho_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( rho_defuse @ a_select2 ) )
= use ) )
=> ! [A: $i,B: $i] :
( ( ( n998 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_inuse_0021) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i,B: $i] :
( ( ( n998 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use ) )
& ! [A: $i,B: $i] :
( ( ( n998 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( u_defuse @ a_select3 ) ) )
= use ) )
& ( ( n5 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n5 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n5 @ ( xinit_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( xinit_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( xinit_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( n2 @ ( u_defuse @ a_select3 ) ) )
= use )
& ( ( n0 @ ( n1 @ ( u_defuse @ a_select3 ) ) )
= use )
& ( ( n0 @ ( n0 @ ( u_defuse @ a_select3 ) ) )
= use )
& ( ( n5 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( rho_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( rho_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( rho_defuse @ a_select2 ) )
= use ) )
=> ! [A: $i,B: $i] :
( ( ( n998 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(93,plain,
~ ( ( ! [A: $i,B: $i] :
( ( ( n998 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use ) )
& ! [A: $i,B: $i] :
( ( ( n998 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( u_defuse @ a_select3 ) ) )
= use ) )
& ( ( n5 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( xinit_noise_defuse @ a_select2 ) )
= use )
& ( ( n5 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( xinit_mean_defuse @ a_select2 ) )
= use )
& ( ( n5 @ ( xinit_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( xinit_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( xinit_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( n2 @ ( u_defuse @ a_select3 ) ) )
= use )
& ( ( n0 @ ( n1 @ ( u_defuse @ a_select3 ) ) )
= use )
& ( ( n0 @ ( n0 @ ( u_defuse @ a_select3 ) ) )
= use )
& ( ( n5 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n4 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n3 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( sigma_defuse @ a_select2 ) )
= use )
& ( ( n2 @ ( rho_defuse @ a_select2 ) )
= use )
& ( ( n1 @ ( rho_defuse @ a_select2 ) )
= use )
& ( ( n0 @ ( rho_defuse @ a_select2 ) )
= use ) )
=> ! [A: $i,B: $i] :
( ( ( n998 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_leq) ).
thf(591,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(49,axiom,
n2 @ ( n5 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_2) ).
thf(443,plain,
n2 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(24,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/sandbox2/benchmark/theBenchmark.p',matrix_symm_aba2) ).
thf(211,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)],[24]) ).
thf(56,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/sandbox2/benchmark/theBenchmark.p',matrix_symm_aba1) ).
thf(514,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)],[56]) ).
thf(70,axiom,
! [A: $i] :
( ( A @ ( n4 @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_4_l) ).
thf(574,plain,
! [A: $i] :
( ( A @ ( n4 @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(43,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/sandbox2/benchmark/theBenchmark.p',matrix_symm_sub) ).
thf(380,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)],[43]) ).
thf(47,axiom,
n0 @ ( n3 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_0) ).
thf(439,plain,
n0 @ ( n3 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(21,axiom,
def != use,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',defuse) ).
thf(201,plain,
def != use,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(31,axiom,
! [A: $i] :
( ( n1 @ ( A @ minus ) )
= ( A @ pred ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pred_minus_1) ).
thf(260,plain,
! [A: $i] :
( ( n1 @ ( A @ minus ) )
= ( A @ pred ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(16,axiom,
tptp_minus_1 @ ( n2 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_2_tptp_minus_1) ).
thf(192,plain,
tptp_minus_1 @ ( n2 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(83,axiom,
! [A: $i] :
( ( n2 @ ( A @ plus ) )
= ( A @ succ @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_2_r) ).
thf(598,plain,
! [A: $i] :
( ( n2 @ ( A @ plus ) )
= ( A @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ( A @ ( B @ gt ) )
| ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality) ).
thf(160,plain,
! [A: $i,B: $i] :
( ( A = B )
| ( A @ ( B @ gt ) )
| ( B @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(45,axiom,
! [A: $i] :
( tptp_float_0_0
= ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_plus_base_float) ).
thf(435,plain,
! [A: $i] :
( tptp_float_0_0
= ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(63,axiom,
! [A: $i] :
( ( n1 @ ( A @ plus ) )
= ( A @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_1_r) ).
thf(551,plain,
! [A: $i] :
( ( n1 @ ( A @ plus ) )
= ( A @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(25,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/sandbox2/benchmark/theBenchmark.p',matrix_symm_update_diagonal) ).
thf(224,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)],[25]) ).
thf(72,axiom,
n4 @ ( n998 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_998_4) ).
thf(578,plain,
n4 @ ( n998 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(6,axiom,
! [A: $i] :
~ ( A @ ( A @ gt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_gt) ).
thf(169,plain,
! [A: $i] :
~ ( A @ ( A @ gt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(80,axiom,
n4 @ ( n5 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_4) ).
thf(593,plain,
n4 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ gt ) )
=> ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt1) ).
thf(610,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ gt ) )
=> ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( B @ succ @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ) ).
thf(554,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( B @ succ @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(17,axiom,
n1 @ ( n4 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_1) ).
thf(193,plain,
n1 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(57,axiom,
tptp_minus_1 @ ( n4 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_tptp_minus_1) ).
thf(526,plain,
tptp_minus_1 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(61,axiom,
! [A: $i] :
( ( ( n2 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n2 )
| ( A = n1 )
| ( A = n0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_2) ).
thf(547,plain,
! [A: $i] :
( ( ( n2 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n2 )
| ( A = n1 )
| ( A = n0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(92,axiom,
! [A: $i,B: $i] :
( ( A @ ( n0 @ leq ) )
=> ( A @ ( B @ uniform_int_rnd ) @ ( n0 @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniform_int_rand_ranges_lo) ).
thf(622,plain,
! [A: $i,B: $i] :
( ( A @ ( n0 @ leq ) )
=> ( A @ ( B @ uniform_int_rnd ) @ ( n0 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(86,axiom,
( ( n0 @ succ @ succ @ succ @ succ @ succ )
= n5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_5) ).
thf(605,plain,
( ( n0 @ succ @ succ @ succ @ succ @ succ )
= n5 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ ( n3 @ plus ) )
= ( A @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_3_l) ).
thf(237,plain,
! [A: $i] :
( ( A @ ( n3 @ plus ) )
= ( A @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ ( n2 @ plus ) )
= ( A @ succ @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_2_l) ).
thf(266,plain,
! [A: $i] :
( ( A @ ( n2 @ plus ) )
= ( A @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(66,axiom,
tptp_minus_1 @ ( n1 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_1_tptp_minus_1) ).
thf(558,plain,
tptp_minus_1 @ ( n1 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ pred @ succ )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_pred) ).
thf(166,plain,
! [A: $i] :
( ( A @ pred @ succ )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [A: $i] : ( A @ ( A @ succ @ gt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_succ) ).
thf(180,plain,
! [A: $i] : ( A @ ( A @ succ @ gt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(50,axiom,
! [A: $i] :
( ( n4 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_4_r) ).
thf(444,plain,
! [A: $i] :
( ( n4 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(84,axiom,
! [A: $i] :
( ( n3 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_3_r) ).
thf(601,plain,
! [A: $i] :
( ( n3 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(75,axiom,
n0 @ ( n4 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_0) ).
thf(584,plain,
n0 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(71,axiom,
n0 @ ( n2 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_2_0) ).
thf(577,plain,
n0 @ ( n2 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(73,axiom,
! [A: $i] : ( A @ ( A @ leq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_leq) ).
thf(579,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
= n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_plus_base) ).
thf(204,plain,
! [A: $i] :
( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(30,axiom,
tptp_minus_1 @ ( n0 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_0_tptp_minus_1) ).
thf(259,plain,
tptp_minus_1 @ ( n0 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(85,axiom,
n0 @ ( n1 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_1_0) ).
thf(604,plain,
n0 @ ( n1 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(14,axiom,
( ( n0 @ succ @ succ @ succ @ succ )
= n4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_4) ).
thf(187,plain,
( ( n0 @ succ @ succ @ succ @ succ )
= n4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ lt ) )
<=> ( A @ ( B @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lt_gt) ).
thf(172,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)],[7]) ).
thf(38,axiom,
n0 @ ( n5 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_0) ).
thf(367,plain,
n0 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(60,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/sandbox2/benchmark/theBenchmark.p',sel3_update_3) ).
thf(535,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)],[60]) ).
thf(81,axiom,
! [A: $i] :
( ( ( n4 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n4 )
| ( A = n3 )
| ( A = n2 )
| ( A = n1 )
| ( A = n0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_4) ).
thf(594,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)],[81]) ).
thf(91,axiom,
n1 @ ( n5 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_1) ).
thf(621,plain,
n1 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(27,axiom,
n3 @ ( n5 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_3) ).
thf(240,plain,
n3 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(53,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/sandbox2/benchmark/theBenchmark.p',const_array1_select) ).
thf(455,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)],[53]) ).
thf(46,axiom,
n0 @ ( n998 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_998_0) ).
thf(438,plain,
n0 @ ( n998 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B @ succ @ ( A @ succ @ leq ) )
<=> ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_succ) ).
thf(241,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)],[28]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( B @ pred @ ( A @ leq ) )
<=> ( A @ ( B @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt_pred) ).
thf(374,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)],[42]) ).
thf(18,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/sandbox2/benchmark/theBenchmark.p',sel2_update_2) ).
thf(194,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)],[18]) ).
thf(19,axiom,
n3 @ ( n4 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_3) ).
thf(199,plain,
n3 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(10,axiom,
n2 @ ( n3 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_2) ).
thf(182,plain,
n2 @ ( n3 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(76,axiom,
( ( n0 @ succ @ succ )
= n2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_2) ).
thf(585,plain,
( ( n0 @ succ @ succ )
= n2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(68,axiom,
tptp_minus_1 @ ( n5 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_tptp_minus_1) ).
thf(571,plain,
tptp_minus_1 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(89,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/sandbox2/benchmark/theBenchmark.p',sel2_update_3) ).
thf(612,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)],[89]) ).
thf(52,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/sandbox2/benchmark/theBenchmark.p',sel3_update_2) ).
thf(450,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)],[52]) ).
thf(74,axiom,
! [A: $i] :
( ( A @ ( n1 @ plus ) )
= ( A @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_1_l) ).
thf(581,plain,
! [A: $i] :
( ( A @ ( n1 @ plus ) )
= ( A @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(39,axiom,
n3 @ ( n998 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_998_3) ).
thf(368,plain,
n3 @ ( n998 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(36,axiom,
tptp_minus_1 @ ( n998 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_998_tptp_minus_1) ).
thf(363,plain,
tptp_minus_1 @ ( n998 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ minus ) @ leq ) )
=> ( B @ ( n0 @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_minus) ).
thf(556,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ minus ) @ leq ) )
=> ( B @ ( n0 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(90,axiom,
n2 @ ( n4 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_2) ).
thf(620,plain,
n2 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(51,axiom,
! [A: $i] :
( ( n5 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_5_r) ).
thf(447,plain,
! [A: $i] :
( ( n5 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( D @ ( C @ ( B @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sel3_update_1) ).
thf(432,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)],[44]) ).
thf(11,axiom,
n1 @ ( n2 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_2_1) ).
thf(183,plain,
n1 @ ( n2 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(54,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/sandbox2/benchmark/theBenchmark.p',matrix_symm_add) ).
thf(459,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)],[54]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ gt ) )
& ( B @ ( A @ gt ) ) )
=> ( C @ ( A @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_gt) ).
thf(178,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ gt ) )
& ( B @ ( A @ gt ) ) )
=> ( C @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ succ @ pred )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pred_succ) ).
thf(163,plain,
! [A: $i] :
( ( A @ succ @ pred )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(20,axiom,
n5 @ ( n998 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_998_5) ).
thf(200,plain,
n5 @ ( n998 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ ( n5 @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_5_l) ).
thf(369,plain,
! [A: $i] :
( ( A @ ( n5 @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(87,axiom,
! [A: $i] :
( ( ( n5 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n5 )
| ( A = n4 )
| ( A = n3 )
| ( A = n2 )
| ( A = n1 )
| ( A = n0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_5) ).
thf(607,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)],[87]) ).
thf(629,plain,
$false,
inference(e,[status(thm)],[185,527,572,263,588,207,364,247,269,597,440,511,533,550,184,372,587,357,559,189,93,591,443,211,514,574,380,439,201,260,192,598,160,435,551,224,578,169,593,610,554,193,526,547,622,605,237,266,558,166,180,444,601,584,577,579,204,259,604,187,172,367,535,594,621,240,455,438,241,374,194,199,182,585,571,612,450,581,368,363,556,620,447,432,183,459,178,163,200,369,607]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV210+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.39 % Computer : n003.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 13:21:39 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.31/1.26 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.09/1.68 % [INFO] Parsing done (415ms).
% 2.51/1.70 % [INFO] Running in sequential loop mode.
% 3.40/2.31 % [INFO] eprover registered as external prover.
% 3.40/2.32 % [INFO] Scanning for conjecture ...
% 3.78/2.53 % [INFO] Found a conjecture (or negated_conjecture) and 91 axioms. Running axiom selection ...
% 3.99/2.65 % [INFO] Axiom selection finished. Selected 90 axioms (removed 1 axioms).
% 4.22/2.76 % [INFO] Problem is first-order (TPTP FOF).
% 4.22/2.78 % [INFO] Type checking passed.
% 4.22/2.78 % [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 ...
% 9.48/4.42 % External prover 'e' found a proof!
% 9.48/4.42 % [INFO] Killing All external provers ...
% 9.48/4.43 % Time passed: 3814ms (effective reasoning time: 2713ms)
% 9.48/4.43 % 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)>
% 9.48/4.43 % Axioms used in derivation (90): sel3_update_2, gt_2_tptp_minus_1, gt_998_5, gt_0_tptp_minus_1, gt_3_1, leq_minus, gt_998_4, sel2_update_2, succ_plus_5_l, lt_gt, gt_998_1, 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, 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, gt_998_0, sel2_update_1, 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_998_2, leq_succ_succ, sum_plus_base_float, succ_plus_2_l, gt_4_1, gt_2_0, gt_5_2, const_array1_select, defuse, leq_gt_pred, matrix_symm_joseph_update, succ_pred, totality, transitivity_leq, finite_domain_3, uniform_int_rand_ranges_lo, 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_998_3, 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_998_tptp_minus_1, finite_domain_0, leq_succ
% 9.48/4.43 % No. of inferences in proof: 184
% 9.48/4.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3814 ms resp. 2713 ms w/o parsing
% 9.84/4.56 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.84/4.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------