%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV203+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 : n017.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 08:58:24 AM UTC 2026
% Result : Theorem 81.68s 18.95s
% Output : Refutation 83.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 99
% Syntax : Number of formulae : 649 ( 341 unt; 0 typ; 8 def)
% Number of atoms : 2022 ( 890 equ; 0 cnn)
% Maximal formula atoms : 51 ( 3 avg)
% Number of connectives : 6734 ( 775 ~; 588 |; 429 &;4790 @)
% ( 5 <=>; 147 =>; 0 <=; 0 <~>)
% Maximal formula depth : 46 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 49 usr; 23 con; 0-4 aty)
% Number of variables : 879 ( 14 ^; 855 !; 2 ?; 879 :)
% ( 0 !>; 0 ?*; 0 @-; 8 @+)
% 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(pv5_decl,type,
pv5: $i ).
thf(n998_decl,type,
n998: $i ).
thf(gt_decl,type,
gt: $i > $i > $o ).
thf(pred_decl,type,
pred: $i > $i ).
thf(z_defuse_decl,type,
z_defuse: $i ).
thf(succ_decl,type,
succ: $i > $i ).
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(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(lt_decl,type,
lt: $i > $i > $o ).
thf(tptp_const_array1_decl,type,
tptp_const_array1: $i > $i > $i ).
thf(inv_decl,type,
inv: $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( pv5 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ~ ( ( pv5 = B )
& ( n2 = A ) )
& ~ ( ( pv5 = B )
& ( n1 = A ) )
& ~ ( ( pv5 = B )
& ( n0 = A ) ) )
=> ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( ( pv5 @ ( A @ leq ) )
& ( n2 @ ( sk1 @ leq ) )
& ( A @ ( n0 @ leq ) )
& ( sk1 @ ( n0 @ leq ) ) )
=> ( ( ~ ( ( pv5 = A )
& ( n2 = sk1 ) )
& ~ ( ( pv5 = A )
& ( n1 = sk1 ) )
& ~ ( ( pv5 = A )
& ( n0 = sk1 ) ) )
=> ( ( A @ ( sk1 @ ( z_defuse @ a_select3 ) ) )
= use ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ! [E: $i] :
( ( ( A @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( A @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( B @ a_select3 ) ) )
= ( D @ ( E @ ( B @ a_select3 ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( ( A @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( A @ ( C @ ( B @ ( A @ sk3 ) ) @ leq ) )
& ( C @ ( B @ ( A @ sk3 ) ) @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ sk3 ) ) @ ( B @ a_select3 ) ) )
= ( C @ ( B @ ( A @ sk3 ) ) @ ( D @ ( B @ a_select3 ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ! [D: $i] :
( ( ( A @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( A @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( B @ a_select3 ) ) )
= ( C @ ( D @ ( B @ a_select3 ) ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( ( A @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) )
& ( A @ ( B @ ( A @ sk5 ) @ leq ) )
& ( B @ ( A @ sk5 ) @ ( n0 @ leq ) ) )
=> ( ( C @ ( B @ ( A @ sk5 ) @ ( B @ a_select3 ) ) )
= ( B @ ( A @ sk5 ) @ ( C @ ( B @ a_select3 ) ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ! [D: $i] :
( ( ( A @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( A @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( B @ a_select3 ) ) )
= ( C @ ( D @ ( B @ a_select3 ) ) ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( ( A @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) )
& ( A @ ( B @ ( A @ sk7 ) @ leq ) )
& ( B @ ( A @ sk7 ) @ ( n0 @ leq ) ) )
=> ( ( C @ ( B @ ( A @ sk7 ) @ ( B @ a_select3 ) ) )
= ( B @ ( A @ sk7 ) @ ( C @ ( B @ a_select3 ) ) ) ) ) ) ) ).
thf(90,axiom,
n2 @ ( n4 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_2) ).
thf(629,plain,
n2 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(24,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(240,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)],[24]) ).
thf(241,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ( D @ ( C @ ( A @ trans @ a_select3 ) ) )
= ( C @ ( D @ ( A @ trans @ a_select3 ) ) ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( ( A @ ( B @ sk8 ) @ ( A @ ( B @ sk7 ) @ ( A @ a_select3 ) ) )
!= ( A @ ( B @ sk7 ) @ ( A @ ( B @ sk8 ) @ ( A @ a_select3 ) ) ) ) )
& ( ( ( D @ ( C @ ( A @ trans @ a_select3 ) ) )
= ( C @ ( D @ ( A @ trans @ a_select3 ) ) ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( B @ ( A @ ( B @ sk8 ) @ leq ) ) )
& ( ( ( D @ ( C @ ( A @ trans @ a_select3 ) ) )
= ( C @ ( D @ ( A @ trans @ a_select3 ) ) ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( A @ ( B @ sk8 ) @ ( n0 @ leq ) ) )
& ( ( ( D @ ( C @ ( A @ trans @ a_select3 ) ) )
= ( C @ ( D @ ( A @ trans @ a_select3 ) ) ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( B @ ( A @ ( B @ sk7 ) @ leq ) ) )
& ( ( ( D @ ( C @ ( A @ trans @ a_select3 ) ) )
= ( C @ ( D @ ( A @ trans @ a_select3 ) ) ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( A @ ( B @ sk7 ) @ ( n0 @ leq ) ) ) ),
inference(cnf,[status(esa)],[240]) ).
thf(245,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ trans @ a_select3 ) ) )
= ( C @ ( D @ ( A @ trans @ a_select3 ) ) ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( A @ ( B @ sk7 ) @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[241]) ).
thf(249,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( A @ ( B @ sk7 ) @ ( n0 @ leq ) )
| ( ( D @ ( C @ ( A @ trans @ a_select3 ) ) )
= ( C @ ( D @ ( A @ trans @ a_select3 ) ) ) ) ),
inference(lifteq,[status(thm)],[245]) ).
thf(60,axiom,
n1 @ ( n998 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_998_1) ).
thf(555,plain,
n1 @ ( n998 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(36,axiom,
( ( tptp_minus_1 @ succ )
= n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_tptp_minus_1) ).
thf(365,plain,
( ( tptp_minus_1 @ succ )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(1,conjecture,
( ( ! [A: $i,B: $i] :
( ( ( pv5 @ pred @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use ) )
& ! [A: $i,B: $i] :
( ( ( pv5 @ pred @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( u_defuse @ a_select3 ) ) )
= use ) )
& ( n0 @ ( pv5 @ gt ) )
& ( n998 @ ( pv5 @ leq ) )
& ( pv5 @ ( n0 @ leq ) )
& ( ( 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] :
( ( ( pv5 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ~ ( ( pv5 = B )
& ( n2 = A ) )
& ~ ( ( pv5 = B )
& ( n1 = A ) )
& ~ ( ( pv5 = B )
& ( n0 = A ) ) )
=> ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_inuse_0014) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i,B: $i] :
( ( ( pv5 @ pred @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use ) )
& ! [A: $i,B: $i] :
( ( ( pv5 @ pred @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( u_defuse @ a_select3 ) ) )
= use ) )
& ( n0 @ ( pv5 @ gt ) )
& ( n998 @ ( pv5 @ leq ) )
& ( pv5 @ ( n0 @ leq ) )
& ( ( 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] :
( ( ( pv5 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ~ ( ( pv5 = B )
& ( n2 = A ) )
& ~ ( ( pv5 = B )
& ( n1 = A ) )
& ~ ( ( pv5 = B )
& ( n0 = A ) ) )
=> ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(93,plain,
~ ( ( ! [A: $i,B: $i] :
( ( ( pv5 @ pred @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use ) )
& ! [A: $i,B: $i] :
( ( ( pv5 @ pred @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( u_defuse @ a_select3 ) ) )
= use ) )
& ( n0 @ ( pv5 @ gt ) )
& ( n998 @ ( pv5 @ leq ) )
& ( pv5 @ ( n0 @ leq ) )
& ( ( 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] :
( ( ( pv5 @ ( B @ leq ) )
& ( n2 @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( ~ ( ( pv5 = B )
& ( n2 = A ) )
& ~ ( ( pv5 = B )
& ( n1 = A ) )
& ~ ( ( pv5 = B )
& ( n0 = A ) ) )
=> ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(94,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( z_defuse @ a_select3 ) ) )
!= use )
& ( ( pv5 != sk2 )
| ( n2 != sk1 ) )
& ( ( pv5 != sk2 )
| ( n1 != sk1 ) )
& ( ( pv5 != sk2 )
| ( n0 != sk1 ) )
& ( pv5 @ ( sk2 @ leq ) )
& ( n2 @ ( sk1 @ leq ) )
& ( sk2 @ ( n0 @ leq ) )
& ( sk1 @ ( n0 @ leq ) )
& ( ( ( D @ ( C @ ( z_defuse @ a_select3 ) ) )
= use )
| ~ ( pv5 @ pred @ ( D @ leq ) )
| ~ ( n2 @ ( C @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( C @ ( n0 @ leq ) ) )
& ( ( ( B @ ( A @ ( u_defuse @ a_select3 ) ) )
= use )
| ~ ( pv5 @ pred @ ( B @ leq ) )
| ~ ( n2 @ ( A @ leq ) )
| ~ ( B @ ( n0 @ leq ) )
| ~ ( A @ ( n0 @ leq ) ) )
& ( n0 @ ( pv5 @ gt ) )
& ( n998 @ ( pv5 @ leq ) )
& ( pv5 @ ( n0 @ leq ) )
& ( ( 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 ) ),
inference(cnf,[status(esa)],[93]) ).
thf(130,plain,
( ( n0 @ ( rho_defuse @ a_select2 ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(138,plain,
( ( n0 @ ( rho_defuse @ a_select2 ) )
= use ),
inference(lifteq,[status(thm)],[130]) ).
thf(366,plain,
( ( tptp_minus_1 @ succ )
= n0 ),
inference(lifteq,[status(thm)],[365]) ).
thf(92,axiom,
! [A: $i] :
( ( A @ succ @ pred )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pred_succ) ).
thf(631,plain,
! [A: $i] :
( ( A @ succ @ pred )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(632,plain,
! [A: $i] :
( ( A @ succ @ pred )
= A ),
inference(cnf,[status(esa)],[631]) ).
thf(633,plain,
! [A: $i] :
( ( A @ succ @ pred )
= A ),
inference(lifteq,[status(thm)],[632]) ).
thf(6073,plain,
! [A: $i] :
( ( ( tptp_minus_1 @ succ )
!= ( A @ succ ) )
| ( ( n0 @ pred )
= A ) ),
inference(paramod_ordered,[status(thm)],[366,633]) ).
thf(6074,plain,
( ( n0 @ pred )
= tptp_minus_1 ),
inference(pattern_uni,[status(thm)],[6073:[bind(A,$thf( tptp_minus_1 ))]]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ succ @ ( A @ succ @ leq ) )
<=> ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_succ) ).
thf(231,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)],[22]) ).
thf(232,plain,
( ! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( B @ succ @ ( A @ succ @ leq ) ) )
& ! [A: $i,B: $i] :
( ( B @ succ @ ( A @ succ @ leq ) )
=> ( B @ ( A @ leq ) ) ) ),
inference(miniscope,[status(thm)],[231]) ).
thf(233,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ succ @ ( C @ succ @ leq ) )
| ~ ( D @ ( C @ leq ) ) )
& ( ( B @ ( A @ leq ) )
| ~ ( B @ succ @ ( A @ succ @ leq ) ) ) ),
inference(cnf,[status(esa)],[232]) ).
thf(234,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( B @ succ @ ( A @ succ @ leq ) ) ),
inference(cnfConj,[status(thm)],[233]) ).
thf(4,axiom,
n1 @ ( n2 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_2_1) ).
thf(170,plain,
n1 @ ( n2 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(115,plain,
pv5 @ ( n0 @ leq ),
inference(cnfConj,[status(thm)],[94]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ lt ) )
<=> ( A @ ( B @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lt_gt) ).
thf(449,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)],[49]) ).
thf(40,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(379,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)],[40]) ).
thf(99,plain,
pv5 @ ( sk2 @ leq ),
inference(cnfConj,[status(thm)],[94]) ).
thf(235,plain,
! [B: $i,A: $i] :
( ( B @ succ @ ( A @ succ @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnfConj,[status(thm)],[233]) ).
thf(236,plain,
! [B: $i,A: $i] :
( ( B @ succ @ ( A @ succ @ leq ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[235]) ).
thf(13685,plain,
! [B: $i,A: $i] :
( ( ( pv5 @ ( sk2 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ succ @ ( A @ succ @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[99,236]) ).
thf(13686,plain,
! [B: $i,A: $i] :
( ( ( pv5 @ ( sk2 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ succ @ ( A @ succ @ leq ) ) ),
inference(simp,[status(thm)],[13685]) ).
thf(13687,plain,
pv5 @ succ @ ( sk2 @ succ @ leq ),
inference(pattern_uni,[status(thm)],[13686:[bind(A,$thf( sk2 )),bind(B,$thf( pv5 ))]]) ).
thf(111,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use )
| ~ ( pv5 @ pred @ ( B @ leq ) )
| ~ ( n2 @ ( A @ leq ) )
| ~ ( B @ ( n0 @ leq ) )
| ~ ( A @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(166,plain,
! [B: $i,A: $i] :
( ~ ( pv5 @ pred @ ( B @ leq ) )
| ~ ( n2 @ ( A @ leq ) )
| ~ ( B @ ( n0 @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use ) ),
inference(lifteq,[status(thm)],[111]) ).
thf(167,plain,
! [B: $i,A: $i] :
( ~ ( pv5 @ pred @ ( B @ leq ) )
| ~ ( n2 @ ( A @ leq ) )
| ~ ( B @ ( n0 @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
= use ) ),
inference(simp,[status(thm)],[166]) ).
thf(113,plain,
( ( sk2 @ ( sk1 @ ( z_defuse @ a_select3 ) ) )
!= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(157,plain,
( ( sk2 @ ( sk1 @ ( z_defuse @ a_select3 ) ) )
!= use ),
inference(lifteq,[status(thm)],[113]) ).
thf(2521,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
!= ( sk2 @ ( sk1 @ ( z_defuse @ a_select3 ) ) ) )
| ( use != use )
| ~ ( pv5 @ pred @ ( B @ leq ) )
| ~ ( n2 @ ( A @ leq ) )
| ~ ( B @ ( n0 @ leq ) )
| ~ ( A @ ( n0 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[167,157]) ).
thf(2522,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( z_defuse @ a_select3 ) ) )
!= ( sk2 @ ( sk1 @ ( z_defuse @ a_select3 ) ) ) )
| ~ ( pv5 @ pred @ ( B @ leq ) )
| ~ ( n2 @ ( A @ leq ) )
| ~ ( B @ ( n0 @ leq ) )
| ~ ( A @ ( n0 @ leq ) ) ),
inference(simp,[status(thm)],[2521]) ).
thf(2523,plain,
( ~ ( pv5 @ pred @ ( sk2 @ leq ) )
| ~ ( n2 @ ( sk1 @ leq ) )
| ~ ( sk2 @ ( n0 @ leq ) )
| ~ ( sk1 @ ( n0 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[2522:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(114,plain,
n2 @ ( sk1 @ leq ),
inference(cnfConj,[status(thm)],[94]) ).
thf(100,plain,
sk2 @ ( n0 @ leq ),
inference(cnfConj,[status(thm)],[94]) ).
thf(134,plain,
sk1 @ ( n0 @ leq ),
inference(cnfConj,[status(thm)],[94]) ).
thf(2775,plain,
( ~ ( pv5 @ pred @ ( sk2 @ leq ) )
| ~ $true
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[2523,114,100,134]) ).
thf(2776,plain,
~ ( pv5 @ pred @ ( sk2 @ leq ) ),
inference(simp,[status(thm)],[2775]) ).
thf(57,axiom,
( ( n0 @ succ @ succ @ succ )
= n3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_3) ).
thf(538,plain,
( ( n0 @ succ @ succ @ succ )
= n3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(539,plain,
( ( n0 @ succ @ succ @ succ )
= n3 ),
inference(lifteq,[status(thm)],[538]) ).
thf(6,axiom,
( ( n0 @ succ )
= n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_1) ).
thf(172,plain,
( ( n0 @ succ )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(173,plain,
( ( n0 @ succ )
= n1 ),
inference(lifteq,[status(thm)],[172]) ).
thf(2659,plain,
( ( n1 @ succ @ succ )
= n3 ),
inference(rewrite,[status(thm)],[539,173]) ).
thf(85,axiom,
n0 @ ( n1 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_1_0) ).
thf(613,plain,
n0 @ ( n1 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(38,axiom,
! [A: $i] :
~ ( A @ ( A @ gt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_gt) ).
thf(373,plain,
! [A: $i] :
~ ( A @ ( A @ gt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(374,plain,
~ ? [A: $i] : ( A @ ( A @ gt ) ),
inference(miniscope,[status(thm)],[373]) ).
thf(375,plain,
! [A: $i] :
~ ( A @ ( A @ gt ) ),
inference(cnf,[status(esa)],[374]) ).
thf(2096,plain,
! [A: $i] :
( ( ( n0 @ ( n1 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[613,375]) ).
thf(2097,plain,
! [A: $i] :
( ( n0 @ ( n1 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[2096]) ).
thf(2098,plain,
! [A: $i] :
( ( n0 != A )
| ( n1 != A ) ),
inference(simp,[status(thm)],[2097]) ).
thf(2099,plain,
n1 != n0,
inference(simp,[status(thm)],[2098]) ).
thf(243,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ trans @ a_select3 ) ) )
= ( C @ ( D @ ( A @ trans @ a_select3 ) ) ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( B @ ( A @ ( B @ sk8 ) @ leq ) ) ),
inference(cnfConj,[status(thm)],[241]) ).
thf(247,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( B @ ( A @ ( B @ sk8 ) @ leq ) )
| ( ( D @ ( C @ ( A @ trans @ a_select3 ) ) )
= ( C @ ( D @ ( A @ trans @ a_select3 ) ) ) ) ),
inference(lifteq,[status(thm)],[243]) ).
thf(86,axiom,
( ( n0 @ succ @ succ @ succ @ succ @ succ )
= n5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_5) ).
thf(614,plain,
( ( n0 @ succ @ succ @ succ @ succ @ succ )
= n5 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(13,axiom,
n3 @ ( n4 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_3) ).
thf(189,plain,
n3 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(646,plain,
! [A: $i] :
( ( ( n3 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[189,375]) ).
thf(647,plain,
! [A: $i] :
( ( n3 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[646]) ).
thf(667,plain,
! [A: $i] :
( ( n3 != A )
| ( n4 != A ) ),
inference(simp,[status(thm)],[647]) ).
thf(677,plain,
n4 != n3,
inference(simp,[status(thm)],[667]) ).
thf(13692,plain,
! [B: $i,A: $i] :
( ( ( n2 @ ( sk1 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ succ @ ( A @ succ @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[114,236]) ).
thf(13693,plain,
! [B: $i,A: $i] :
( ( ( n2 @ ( sk1 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ succ @ ( A @ succ @ leq ) ) ),
inference(simp,[status(thm)],[13692]) ).
thf(13694,plain,
n2 @ succ @ ( sk1 @ succ @ leq ),
inference(pattern_uni,[status(thm)],[13693:[bind(A,$thf( sk1 )),bind(B,$thf( n2 ))]]) ).
thf(75,axiom,
( ( n0 @ succ @ succ )
= n2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_2) ).
thf(592,plain,
( ( n0 @ succ @ succ )
= n2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(593,plain,
( ( n0 @ succ @ succ )
= n2 ),
inference(lifteq,[status(thm)],[592]) ).
thf(2650,plain,
( ( n1 @ succ )
= n2 ),
inference(rewrite,[status(thm)],[593,173]) ).
thf(2666,plain,
( ( ( n1 @ succ )
!= ( n1 @ succ ) )
| ( ( n2 @ succ )
= n3 ) ),
inference(paramod_ordered,[status(thm)],[2650,2659]) ).
thf(2667,plain,
( ( n2 @ succ )
= n3 ),
inference(pattern_uni,[status(thm)],[2666:[]]) ).
thf(16597,plain,
n3 @ ( sk1 @ succ @ leq ),
inference(rewrite,[status(thm)],[13694,2667]) ).
thf(16684,plain,
! [B: $i,A: $i] :
( ( ( n3 @ ( sk1 @ succ @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ succ @ ( A @ succ @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16597,236]) ).
thf(16685,plain,
! [B: $i,A: $i] :
( ( ( n3 @ ( sk1 @ succ @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ succ @ ( A @ succ @ leq ) ) ),
inference(simp,[status(thm)],[16684]) ).
thf(16686,plain,
n3 @ succ @ ( sk1 @ succ @ succ @ leq ),
inference(pattern_uni,[status(thm)],[16685:[bind(A,$thf( sk1 @ succ )),bind(B,$thf( n3 ))]]) ).
thf(7,axiom,
( ( n0 @ succ @ succ @ succ @ succ )
= n4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_4) ).
thf(174,plain,
( ( n0 @ succ @ succ @ succ @ succ )
= n4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(175,plain,
( ( n0 @ succ @ succ @ succ @ succ )
= n4 ),
inference(lifteq,[status(thm)],[174]) ).
thf(2698,plain,
( ( n1 @ succ @ succ @ succ )
= n4 ),
inference(rewrite,[status(thm)],[175,173]) ).
thf(2706,plain,
( ( ( n1 @ succ @ succ )
!= ( n1 @ succ @ succ ) )
| ( ( n3 @ succ )
= n4 ) ),
inference(paramod_ordered,[status(thm)],[2659,2698]) ).
thf(2707,plain,
( ( n3 @ succ )
= n4 ),
inference(pattern_uni,[status(thm)],[2706:[]]) ).
thf(19521,plain,
n4 @ ( sk1 @ succ @ succ @ leq ),
inference(rewrite,[status(thm)],[16686,2707]) ).
thf(125,plain,
n998 @ ( pv5 @ leq ),
inference(cnfConj,[status(thm)],[94]) ).
thf(13499,plain,
! [B: $i,A: $i] :
( ( ( n998 @ ( pv5 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ succ @ ( A @ succ @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[125,236]) ).
thf(13500,plain,
! [B: $i,A: $i] :
( ( ( n998 @ ( pv5 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ succ @ ( A @ succ @ leq ) ) ),
inference(simp,[status(thm)],[13499]) ).
thf(13501,plain,
n998 @ succ @ ( pv5 @ succ @ leq ),
inference(pattern_uni,[status(thm)],[13500:[bind(A,$thf( pv5 )),bind(B,$thf( n998 ))]]) ).
thf(131,plain,
( ( n4 @ ( xinit_mean_defuse @ a_select2 ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(142,plain,
( ( n4 @ ( xinit_mean_defuse @ a_select2 ) )
= use ),
inference(lifteq,[status(thm)],[131]) ).
thf(74,axiom,
n0 @ ( n4 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_0) ).
thf(591,plain,
n0 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(1864,plain,
! [A: $i] :
( ( ( n0 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[591,375]) ).
thf(1865,plain,
! [A: $i] :
( ( n0 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[1864]) ).
thf(1866,plain,
! [A: $i] :
( ( n0 != A )
| ( n4 != A ) ),
inference(simp,[status(thm)],[1865]) ).
thf(1867,plain,
n4 != n0,
inference(simp,[status(thm)],[1866]) ).
thf(46,axiom,
n2 @ ( n5 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_2) ).
thf(442,plain,
n2 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(1272,plain,
! [A: $i] :
( ( ( n2 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[442,375]) ).
thf(1273,plain,
! [A: $i] :
( ( n2 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[1272]) ).
thf(1274,plain,
! [A: $i] :
( ( n2 != A )
| ( n5 != A ) ),
inference(simp,[status(thm)],[1273]) ).
thf(1275,plain,
n5 != n2,
inference(simp,[status(thm)],[1274]) ).
thf(124,plain,
( ( n5 @ ( xinit_mean_defuse @ a_select2 ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(153,plain,
( ( n5 @ ( xinit_mean_defuse @ a_select2 ) )
= use ),
inference(lifteq,[status(thm)],[124]) ).
thf(615,plain,
( ( n0 @ succ @ succ @ succ @ succ @ succ )
= n5 ),
inference(lifteq,[status(thm)],[614]) ).
thf(2941,plain,
( ( n1 @ succ @ succ @ succ @ succ )
= n5 ),
inference(rewrite,[status(thm)],[615,173]) ).
thf(2957,plain,
( ( ( n1 @ succ @ succ @ succ )
!= ( n1 @ succ @ succ @ succ ) )
| ( ( n4 @ succ )
= n5 ) ),
inference(paramod_ordered,[status(thm)],[2698,2941]) ).
thf(2958,plain,
( ( n4 @ succ )
= n5 ),
inference(pattern_uni,[status(thm)],[2957:[]]) ).
thf(2783,plain,
( ( ( pv5 @ pred @ ( sk2 @ leq ) )
!= ( pv5 @ ( sk2 @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[99,2776]) ).
thf(2784,plain,
( ( pv5 @ pred @ ( sk2 @ leq ) )
!= ( pv5 @ ( sk2 @ leq ) ) ),
inference(simp,[status(thm)],[2783]) ).
thf(2793,plain,
( ( ( pv5 @ pred )
!= pv5 )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[2784]) ).
thf(2795,plain,
( ( pv5 @ pred )
!= pv5 ),
inference(simp,[status(thm)],[2793]) ).
thf(6099,plain,
! [A: $i] :
( ( ( A @ succ @ pred )
!= ( pv5 @ pred ) )
| ( A != pv5 ) ),
inference(paramod_ordered,[status(thm)],[633,2795]) ).
thf(6109,plain,
( ( pv5 @ succ )
!= pv5 ),
inference(simp,[status(thm)],[6099]) ).
thf(6246,plain,
( ( ( pv5 @ succ )
!= ( n4 @ succ ) )
| ( pv5 != n5 ) ),
inference(paramod_ordered,[status(thm)],[2958,6109]) ).
thf(6268,plain,
( ( pv5 != n4 )
| ( pv5 != n5 ) ),
inference(simp,[status(thm)],[6246]) ).
thf(64,axiom,
tptp_minus_1 @ ( n1 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_1_tptp_minus_1) ).
thf(563,plain,
tptp_minus_1 @ ( n1 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(1647,plain,
! [A: $i] :
( ( ( tptp_minus_1 @ ( n1 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[563,375]) ).
thf(1648,plain,
! [A: $i] :
( ( tptp_minus_1 @ ( n1 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[1647]) ).
thf(1649,plain,
! [A: $i] :
( ( tptp_minus_1 != A )
| ( n1 != A ) ),
inference(simp,[status(thm)],[1648]) ).
thf(1650,plain,
tptp_minus_1 != n1,
inference(simp,[status(thm)],[1649]) ).
thf(13479,plain,
! [B: $i,A: $i] :
( ( ( pv5 @ ( n0 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ succ @ ( A @ succ @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[115,236]) ).
thf(13480,plain,
! [B: $i,A: $i] :
( ( ( pv5 @ ( n0 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ succ @ ( A @ succ @ leq ) ) ),
inference(simp,[status(thm)],[13479]) ).
thf(13481,plain,
pv5 @ succ @ ( n0 @ succ @ leq ),
inference(pattern_uni,[status(thm)],[13480:[bind(A,$thf( n0 )),bind(B,$thf( pv5 ))]]) ).
thf(13923,plain,
pv5 @ succ @ ( n1 @ leq ),
inference(rewrite,[status(thm)],[13481,173]) ).
thf(76,axiom,
n2 @ ( n998 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_998_2) ).
thf(594,plain,
n2 @ ( n998 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(1868,plain,
! [A: $i] :
( ( ( n2 @ ( n998 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[594,375]) ).
thf(1869,plain,
! [A: $i] :
( ( n2 @ ( n998 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[1868]) ).
thf(1870,plain,
! [A: $i] :
( ( n2 != A )
| ( n998 != A ) ),
inference(simp,[status(thm)],[1869]) ).
thf(1871,plain,
n998 != n2,
inference(simp,[status(thm)],[1870]) ).
thf(6065,plain,
! [A: $i] :
( ( ( n2 @ succ )
!= ( A @ succ ) )
| ( ( n3 @ pred )
= A ) ),
inference(paramod_ordered,[status(thm)],[2667,633]) ).
thf(6066,plain,
( ( n3 @ pred )
= n2 ),
inference(pattern_uni,[status(thm)],[6065:[bind(A,$thf( n2 ))]]) ).
thf(55,axiom,
tptp_minus_1 @ ( n4 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_tptp_minus_1) ).
thf(531,plain,
tptp_minus_1 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(1276,plain,
! [A: $i] :
( ( ( tptp_minus_1 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[531,375]) ).
thf(1277,plain,
! [A: $i] :
( ( tptp_minus_1 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[1276]) ).
thf(1278,plain,
! [A: $i] :
( ( tptp_minus_1 != A )
| ( n4 != A ) ),
inference(simp,[status(thm)],[1277]) ).
thf(1279,plain,
tptp_minus_1 != n4,
inference(simp,[status(thm)],[1278]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
= n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_plus_base) ).
thf(194,plain,
! [A: $i] :
( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(195,plain,
! [A: $i] :
( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
= n0 ),
inference(cnf,[status(esa)],[194]) ).
thf(196,plain,
! [A: $i] :
( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
= n0 ),
inference(lifteq,[status(thm)],[195]) ).
thf(12,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(184,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)],[12]) ).
thf(14000,plain,
! [B: $i,A: $i] :
( ( ( pv5 @ succ @ ( n1 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ succ @ ( A @ succ @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13923,236]) ).
thf(14001,plain,
! [B: $i,A: $i] :
( ( ( pv5 @ succ @ ( n1 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ succ @ ( A @ succ @ leq ) ) ),
inference(simp,[status(thm)],[14000]) ).
thf(14002,plain,
pv5 @ succ @ succ @ ( n1 @ succ @ leq ),
inference(pattern_uni,[status(thm)],[14001:[bind(A,$thf( n1 )),bind(B,$thf( pv5 @ succ ))]]) ).
thf(18671,plain,
pv5 @ succ @ succ @ ( n2 @ leq ),
inference(rewrite,[status(thm)],[14002,2650]) ).
thf(72,axiom,
! [A: $i] : ( A @ ( A @ leq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_leq) ).
thf(586,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(587,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(cnf,[status(esa)],[586]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ gt ) )
=> ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt1) ).
thf(619,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ gt ) )
=> ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(47,axiom,
! [A: $i] :
( ( n4 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_4_r) ).
thf(443,plain,
! [A: $i] :
( ( n4 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(444,plain,
! [A: $i] :
( ( n4 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
inference(cnf,[status(esa)],[443]) ).
thf(445,plain,
! [A: $i] :
( ( n4 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
inference(lifteq,[status(thm)],[444]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ ( n2 @ plus ) )
= ( A @ succ @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_2_l) ).
thf(259,plain,
! [A: $i] :
( ( A @ ( n2 @ plus ) )
= ( A @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(260,plain,
! [A: $i] :
( ( A @ ( n2 @ plus ) )
= ( A @ succ @ succ ) ),
inference(cnf,[status(esa)],[259]) ).
thf(261,plain,
! [A: $i] :
( ( A @ ( n2 @ plus ) )
= ( A @ succ @ succ ) ),
inference(lifteq,[status(thm)],[260]) ).
thf(12980,plain,
! [B: $i,A: $i] :
( ( ( n4 @ ( A @ plus ) )
!= ( B @ ( n2 @ plus ) ) )
| ( ( A @ succ @ succ @ succ @ succ )
= ( B @ succ @ succ ) ) ),
inference(paramod_ordered,[status(thm)],[445,261]) ).
thf(12981,plain,
( ( n2 @ succ @ succ @ succ @ succ )
= ( n4 @ succ @ succ ) ),
inference(pattern_uni,[status(thm)],[12980:[bind(A,$thf( n2 )),bind(B,$thf( n4 ))]]) ).
thf(13282,plain,
( ( n3 @ succ @ succ @ succ )
= ( n5 @ succ ) ),
inference(rewrite,[status(thm)],[12981,2667,2958]) ).
thf(79,axiom,
! [A: $i] : ( A @ ( A @ succ @ gt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_succ) ).
thf(600,plain,
! [A: $i] : ( A @ ( A @ succ @ gt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(601,plain,
! [A: $i] : ( A @ ( A @ succ @ gt ) ),
inference(cnf,[status(esa)],[600]) ).
thf(13333,plain,
! [A: $i] :
( ( ( n3 @ succ @ succ @ succ )
!= ( A @ succ ) )
| ( A @ ( n5 @ succ @ gt ) ) ),
inference(paramod_ordered,[status(thm)],[13282,601]) ).
thf(13334,plain,
n3 @ succ @ succ @ ( n5 @ succ @ gt ),
inference(pattern_uni,[status(thm)],[13333:[bind(A,$thf( n3 @ succ @ succ ))]]) ).
thf(2971,plain,
( ( ( n1 @ succ )
!= ( n1 @ succ ) )
| ( ( n2 @ succ @ succ @ succ )
= n5 ) ),
inference(paramod_ordered,[status(thm)],[2650,2941]) ).
thf(2972,plain,
( ( n2 @ succ @ succ @ succ )
= n5 ),
inference(pattern_uni,[status(thm)],[2971:[]]) ).
thf(4569,plain,
( ( n3 @ succ @ succ )
= n5 ),
inference(rewrite,[status(thm)],[2972,2667]) ).
thf(18627,plain,
n5 @ ( n5 @ succ @ gt ),
inference(rewrite,[status(thm)],[13334,4569]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ( A != B )
& ( B @ ( A @ leq ) ) )
=> ( A @ ( B @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt2) ).
thf(357,plain,
! [A: $i,B: $i] :
( ( ( A != B )
& ( B @ ( A @ leq ) ) )
=> ( A @ ( B @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(51,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(460,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)],[51]) ).
thf(6070,plain,
! [A: $i] :
( ( ( n1 @ succ )
!= ( A @ succ ) )
| ( ( n2 @ pred )
= A ) ),
inference(paramod_ordered,[status(thm)],[2650,633]) ).
thf(6071,plain,
( ( n2 @ pred )
= n1 ),
inference(pattern_uni,[status(thm)],[6070:[bind(A,$thf( n1 ))]]) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( B @ succ @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ) ).
thf(559,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( B @ succ @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(6057,plain,
! [A: $i] :
( ( ( n0 @ succ )
!= ( A @ succ ) )
| ( ( n1 @ pred )
= A ) ),
inference(paramod_ordered,[status(thm)],[173,633]) ).
thf(6058,plain,
( ( n1 @ pred )
= n0 ),
inference(pattern_uni,[status(thm)],[6057:[bind(A,$thf( n0 ))]]) ).
thf(4677,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( pv5 @ pred @ ( sk2 @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[587,2776]) ).
thf(4678,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
!= ( pv5 @ pred @ ( sk2 @ leq ) ) ),
inference(simp,[status(thm)],[4677]) ).
thf(4733,plain,
! [A: $i] :
( ( A
!= ( pv5 @ pred ) )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[4678]) ).
thf(4751,plain,
( ( pv5 @ pred )
!= sk2 ),
inference(simp,[status(thm)],[4733]) ).
thf(6124,plain,
( ( ( pv5 @ pred )
!= ( n1 @ pred ) )
| ( sk2 != n0 ) ),
inference(paramod_ordered,[status(thm)],[6058,4751]) ).
thf(6149,plain,
( ( pv5 != n1 )
| ( sk2 != n0 ) ),
inference(simp,[status(thm)],[6124]) ).
thf(109,plain,
( ( n1 @ ( xinit_noise_defuse @ a_select2 ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(152,plain,
( ( n1 @ ( xinit_noise_defuse @ a_select2 ) )
= use ),
inference(lifteq,[status(thm)],[109]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ pred @ succ )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_pred) ).
thf(237,plain,
! [A: $i] :
( ( A @ pred @ succ )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(238,plain,
! [A: $i] :
( ( A @ pred @ succ )
= A ),
inference(cnf,[status(esa)],[237]) ).
thf(239,plain,
! [A: $i] :
( ( A @ pred @ succ )
= A ),
inference(lifteq,[status(thm)],[238]) ).
thf(5030,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ succ @ gt ) )
!= ( B @ ( B @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[601,375]) ).
thf(5031,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ succ @ gt ) )
!= ( B @ ( B @ gt ) ) ),
inference(simp,[status(thm)],[5030]) ).
thf(5042,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( A @ succ )
!= B ) ),
inference(simp,[status(thm)],[5031]) ).
thf(5046,plain,
! [A: $i] :
( ( A @ succ )
!= A ),
inference(simp,[status(thm)],[5042]) ).
thf(5073,plain,
! [B: $i,A: $i] :
( ( ( A @ pred @ succ )
!= ( B @ succ ) )
| ( A != B ) ),
inference(paramod_ordered,[status(thm)],[239,5046]) ).
thf(5074,plain,
! [A: $i] :
( ( A @ pred )
!= A ),
inference(pattern_uni,[status(thm)],[5073:[bind(A,$thf( C )),bind(B,$thf( C @ pred ))]]) ).
thf(5077,plain,
! [A: $i] :
( ( A @ pred )
!= A ),
inference(simp,[status(thm)],[5074]) ).
thf(82,axiom,
tptp_minus_1 @ ( n3 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_tptp_minus_1) ).
thf(606,plain,
tptp_minus_1 @ ( n3 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(2785,plain,
( ( ( pv5 @ pred @ ( sk2 @ leq ) )
!= ( n2 @ ( sk1 @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[114,2776]) ).
thf(2786,plain,
( ( pv5 @ pred @ ( sk2 @ leq ) )
!= ( n2 @ ( sk1 @ leq ) ) ),
inference(simp,[status(thm)],[2785]) ).
thf(2794,plain,
( ( ( pv5 @ pred )
!= n2 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[2786]) ).
thf(9,axiom,
tptp_minus_1 @ ( n2 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_2_tptp_minus_1) ).
thf(179,plain,
tptp_minus_1 @ ( n2 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(39,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(376,plain,
! [A: $i,B: $i] :
( ( A @ ( n0 @ leq ) )
=> ( A @ ( B @ uniform_int_rnd ) @ ( n0 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(6161,plain,
( ( ( pv5 @ pred )
!= ( n3 @ pred ) )
| ( sk2 != n2 ) ),
inference(paramod_ordered,[status(thm)],[6066,4751]) ).
thf(6187,plain,
( ( pv5 != n3 )
| ( sk2 != n2 ) ),
inference(simp,[status(thm)],[6161]) ).
thf(44,axiom,
n0 @ ( n3 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_0) ).
thf(438,plain,
n0 @ ( n3 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(1148,plain,
! [A: $i] :
( ( ( n0 @ ( n3 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[438,375]) ).
thf(1149,plain,
! [A: $i] :
( ( n0 @ ( n3 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[1148]) ).
thf(1150,plain,
! [A: $i] :
( ( n0 != A )
| ( n3 != A ) ),
inference(simp,[status(thm)],[1149]) ).
thf(1151,plain,
n3 != n0,
inference(simp,[status(thm)],[1150]) ).
thf(13758,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( n0 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ succ @ ( A @ succ @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[100,236]) ).
thf(13759,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( n0 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ succ @ ( A @ succ @ leq ) ) ),
inference(simp,[status(thm)],[13758]) ).
thf(13760,plain,
sk2 @ succ @ ( n0 @ succ @ leq ),
inference(pattern_uni,[status(thm)],[13759:[bind(A,$thf( n0 )),bind(B,$thf( sk2 ))]]) ).
thf(16974,plain,
sk2 @ succ @ ( n1 @ leq ),
inference(rewrite,[status(thm)],[13760,173]) ).
thf(17061,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ succ @ ( n1 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ succ @ ( A @ succ @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16974,236]) ).
thf(17062,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ succ @ ( n1 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ succ @ ( A @ succ @ leq ) ) ),
inference(simp,[status(thm)],[17061]) ).
thf(17063,plain,
sk2 @ succ @ succ @ ( n1 @ succ @ leq ),
inference(pattern_uni,[status(thm)],[17062:[bind(A,$thf( n1 )),bind(B,$thf( sk2 @ succ ))]]) ).
thf(22043,plain,
sk2 @ succ @ succ @ ( n2 @ leq ),
inference(rewrite,[status(thm)],[17063,2650]) ).
thf(107,plain,
( ( n4 @ ( sigma_defuse @ a_select2 ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(164,plain,
( ( n4 @ ( sigma_defuse @ a_select2 ) )
= use ),
inference(lifteq,[status(thm)],[107]) ).
thf(18,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(201,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)],[18]) ).
thf(202,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 ) ) ) ) )
=> ! [C: $i,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(miniscope,[status(thm)],[201]) ).
thf(203,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ( F @ ( E @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) )
= ( E @ ( F @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) ) )
| ~ ( D @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ( ( A @ ( B @ ( C @ sk4 ) ) @ ( A @ ( B @ ( C @ sk3 ) ) @ ( B @ a_select3 ) ) )
!= ( A @ ( B @ ( C @ sk3 ) ) @ ( A @ ( B @ ( C @ sk4 ) ) @ ( B @ a_select3 ) ) ) ) )
& ( ( ( F @ ( E @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) )
= ( E @ ( F @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) ) )
| ~ ( D @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ( C @ ( A @ ( B @ ( C @ sk4 ) ) @ 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 ) ) ) )
| ~ ( D @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ( A @ ( B @ ( C @ sk4 ) ) @ ( 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 ) ) ) )
| ~ ( D @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ( C @ ( A @ ( B @ ( C @ sk3 ) ) @ 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 ) ) ) )
| ~ ( D @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ( A @ ( B @ ( C @ sk3 ) ) @ ( n0 @ leq ) ) ) ),
inference(cnf,[status(esa)],[202]) ).
thf(204,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) )
= ( E @ ( F @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) ) )
| ~ ( D @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ( A @ ( B @ ( C @ sk4 ) ) @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[203]) ).
thf(211,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ( A @ ( B @ ( C @ sk4 ) ) @ ( 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(lifteq,[status(thm)],[204]) ).
thf(6155,plain,
( ( ( pv5 @ pred )
!= ( n3 @ pred ) )
| ~ ( n2 @ ( sk2 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[6066,2776]) ).
thf(6189,plain,
( ( pv5 != n3 )
| ~ ( n2 @ ( sk2 @ leq ) ) ),
inference(simp,[status(thm)],[6155]) ).
thf(26,axiom,
! [A: $i] :
( ( n1 @ ( A @ minus ) )
= ( A @ pred ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pred_minus_1) ).
thf(253,plain,
! [A: $i] :
( ( n1 @ ( A @ minus ) )
= ( A @ pred ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(132,plain,
( ( n3 @ ( xinit_mean_defuse @ a_select2 ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(147,plain,
( ( n3 @ ( xinit_mean_defuse @ a_select2 ) )
= use ),
inference(lifteq,[status(thm)],[132]) ).
thf(2779,plain,
( ( ( pv5 @ pred @ ( sk2 @ leq ) )
!= ( n998 @ ( pv5 @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[125,2776]) ).
thf(2780,plain,
( ( pv5 @ pred @ ( sk2 @ leq ) )
!= ( n998 @ ( pv5 @ leq ) ) ),
inference(simp,[status(thm)],[2779]) ).
thf(2792,plain,
( ( ( pv5 @ pred )
!= n998 )
| ( sk2 != pv5 ) ),
inference(simp,[status(thm)],[2780]) ).
thf(6091,plain,
! [A: $i] :
( ( ( A @ succ @ pred )
!= ( pv5 @ pred ) )
| ( A != n998 )
| ( sk2 != pv5 ) ),
inference(paramod_ordered,[status(thm)],[633,2792]) ).
thf(6103,plain,
( ( ( n998 @ succ )
!= pv5 )
| ( sk2 != pv5 ) ),
inference(simp,[status(thm)],[6091]) ).
thf(5040,plain,
! [B: $i,A: $i] :
( ( ( A @ pred @ succ )
!= ( B @ succ ) )
| ( B @ ( A @ gt ) ) ),
inference(paramod_ordered,[status(thm)],[239,601]) ).
thf(5041,plain,
! [A: $i] : ( A @ pred @ ( A @ gt ) ),
inference(pattern_uni,[status(thm)],[5040:[bind(A,$thf( C )),bind(B,$thf( C @ pred ))]]) ).
thf(5045,plain,
! [A: $i] : ( A @ pred @ ( A @ gt ) ),
inference(simp,[status(thm)],[5041]) ).
thf(80,axiom,
n4 @ ( n5 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_4) ).
thf(602,plain,
n4 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(71,axiom,
n4 @ ( n998 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_998_4) ).
thf(585,plain,
n4 @ ( n998 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(1860,plain,
! [A: $i] :
( ( ( n4 @ ( n998 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[585,375]) ).
thf(1861,plain,
! [A: $i] :
( ( n4 @ ( n998 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[1860]) ).
thf(1862,plain,
! [A: $i] :
( ( n4 != A )
| ( n998 != A ) ),
inference(simp,[status(thm)],[1861]) ).
thf(1863,plain,
n998 != n4,
inference(simp,[status(thm)],[1862]) ).
thf(244,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ trans @ a_select3 ) ) )
= ( C @ ( D @ ( A @ trans @ a_select3 ) ) ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( A @ ( B @ sk8 ) @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[241]) ).
thf(248,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( A @ ( B @ sk8 ) @ ( n0 @ leq ) )
| ( ( D @ ( C @ ( A @ trans @ a_select3 ) ) )
= ( C @ ( D @ ( A @ trans @ a_select3 ) ) ) ) ),
inference(lifteq,[status(thm)],[244]) ).
thf(45,axiom,
! [A: $i] :
( ( ( n1 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n1 )
| ( A = n0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_1) ).
thf(439,plain,
! [A: $i] :
( ( ( n1 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n1 )
| ( A = n0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(656,plain,
! [A: $i] :
( ( ( n1 @ ( n2 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[170,375]) ).
thf(657,plain,
! [A: $i] :
( ( n1 @ ( n2 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[656]) ).
thf(668,plain,
! [A: $i] :
( ( n1 != A )
| ( n2 != A ) ),
inference(simp,[status(thm)],[657]) ).
thf(678,plain,
n2 != n1,
inference(simp,[status(thm)],[668]) ).
thf(2781,plain,
( ( ( pv5 @ pred @ ( sk2 @ leq ) )
!= ( sk1 @ ( n0 @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[134,2776]) ).
thf(2782,plain,
( ( pv5 @ pred @ ( sk2 @ leq ) )
!= ( sk1 @ ( n0 @ leq ) ) ),
inference(simp,[status(thm)],[2781]) ).
thf(2790,plain,
( ( ( pv5 @ pred )
!= sk1 )
| ( sk2 != n0 ) ),
inference(simp,[status(thm)],[2782]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ minus ) @ leq ) )
=> ( B @ ( n0 @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_minus) ).
thf(561,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ minus ) @ leq ) )
=> ( B @ ( n0 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(91,axiom,
n1 @ ( n5 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_1) ).
thf(630,plain,
n1 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(129,plain,
( ( n2 @ ( sigma_defuse @ a_select2 ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(137,plain,
( ( n2 @ ( sigma_defuse @ a_select2 ) )
= use ),
inference(lifteq,[status(thm)],[129]) ).
thf(126,plain,
( ( n2 @ ( rho_defuse @ a_select2 ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(165,plain,
( ( n2 @ ( rho_defuse @ a_select2 ) )
= use ),
inference(lifteq,[status(thm)],[126]) ).
thf(78,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(598,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(108,plain,
( ( pv5 != sk2 )
| ( n0 != sk1 ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(160,plain,
( ( sk2 != pv5 )
| ( sk1 != n0 ) ),
inference(lifteq,[status(thm)],[108]) ).
thf(6072,plain,
! [A: $i] :
( ( ( A @ succ @ pred )
!= ( pv5 @ pred ) )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[633,4751]) ).
thf(6112,plain,
( ( sk2 @ succ )
!= pv5 ),
inference(simp,[status(thm)],[6072]) ).
thf(6280,plain,
( ( ( sk2 @ succ )
!= ( n4 @ succ ) )
| ( pv5 != n5 ) ),
inference(paramod_ordered,[status(thm)],[2958,6112]) ).
thf(6303,plain,
( ( sk2 != n4 )
| ( pv5 != n5 ) ),
inference(simp,[status(thm)],[6280]) ).
thf(25,axiom,
tptp_minus_1 @ ( n0 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_0_tptp_minus_1) ).
thf(252,plain,
tptp_minus_1 @ ( n0 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(17,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(197,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)],[17]) ).
thf(19,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(214,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)],[19]) ).
thf(215,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] :
( ( ( B @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( B @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( B @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ! [F: $i] :
( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) ) ) ),
inference(miniscope,[status(thm)],[214]) ).
thf(216,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) )
| ~ ( B @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( ( A @ ( B @ sk6 ) @ ( A @ ( B @ sk5 ) @ ( A @ a_select3 ) ) )
!= ( A @ ( B @ sk5 ) @ ( A @ ( B @ sk6 ) @ ( A @ a_select3 ) ) ) ) )
& ( ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) )
| ~ ( B @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( B @ ( A @ ( B @ sk6 ) @ leq ) ) )
& ( ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) )
| ~ ( B @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( A @ ( B @ sk6 ) @ ( n0 @ leq ) ) )
& ( ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) )
| ~ ( B @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( B @ ( A @ ( B @ sk5 ) @ leq ) ) )
& ( ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) )
| ~ ( B @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( A @ ( B @ sk5 ) @ ( n0 @ leq ) ) ) ),
inference(cnf,[status(esa)],[215]) ).
thf(219,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) )
| ~ ( B @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( ( A @ ( B @ sk6 ) @ ( A @ ( B @ sk5 ) @ ( A @ a_select3 ) ) )
!= ( A @ ( B @ sk5 ) @ ( A @ ( B @ sk6 ) @ ( A @ a_select3 ) ) ) ) ),
inference(cnfConj,[status(thm)],[216]) ).
thf(225,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $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 ) ) ) )
| ( ( A @ ( B @ sk5 ) @ ( A @ ( B @ sk6 ) @ ( A @ a_select3 ) ) )
!= ( A @ ( B @ sk6 ) @ ( A @ ( B @ sk5 ) @ ( A @ a_select3 ) ) ) ) ),
inference(lifteq,[status(thm)],[219]) ).
thf(897,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
!= ( sk2 @ ( sk1 @ ( z_defuse @ a_select3 ) ) ) )
| ( ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
!= use )
| ~ ( B @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( ( A @ ( B @ sk5 ) @ ( A @ ( B @ sk6 ) @ ( A @ a_select3 ) ) )
!= ( A @ ( B @ sk6 ) @ ( A @ ( B @ sk5 ) @ ( A @ a_select3 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[225,157]) ).
thf(1037,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D != sk2 )
| ( C != sk1 )
| ( ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) )
!= z_defuse )
| ( ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
!= use )
| ~ ( B @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( ( A @ ( B @ sk6 ) )
!= ( A @ ( B @ sk5 ) ) )
| ( ( A @ ( B @ sk6 ) )
!= ( A @ ( B @ sk5 ) ) )
| ( A != A ) ),
inference(simp,[status(thm)],[897]) ).
thf(1060,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( C @ ( A @ tptp_update3 ) ) ) )
!= z_defuse )
| ( ( sk1 @ ( sk2 @ ( D @ ( C @ ( C @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
!= use )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ~ ( B @ ( sk2 @ leq ) )
| ~ ( sk2 @ ( n0 @ leq ) )
| ~ ( B @ ( sk1 @ leq ) )
| ~ ( sk1 @ ( n0 @ leq ) )
| ( ( A @ ( B @ sk6 ) )
!= ( A @ ( B @ sk5 ) ) ) ),
inference(simp,[status(thm)],[1037]) ).
thf(1280,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( C @ ( A @ tptp_update3 ) ) ) )
!= z_defuse )
| ( ( sk1 @ ( sk2 @ ( D @ ( C @ ( C @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
!= use )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ~ ( B @ ( sk2 @ leq ) )
| ~ $true
| ~ ( B @ ( sk1 @ leq ) )
| ~ $true
| ( ( A @ ( B @ sk6 ) )
!= ( A @ ( B @ sk5 ) ) ) ),
inference(rewrite,[status(thm)],[1060,100,134]) ).
thf(1281,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( C @ ( A @ tptp_update3 ) ) ) )
!= z_defuse )
| ( ( sk1 @ ( sk2 @ ( D @ ( C @ ( C @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
!= use )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ~ ( B @ ( sk2 @ leq ) )
| ~ ( B @ ( sk1 @ leq ) )
| ( ( A @ ( B @ sk6 ) )
!= ( A @ ( B @ sk5 ) ) ) ),
inference(simp,[status(thm)],[1280]) ).
thf(220,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) )
| ~ ( B @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( B @ ( A @ ( B @ sk5 ) @ leq ) ) ),
inference(cnfConj,[status(thm)],[216]) ).
thf(224,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( B @ ( A @ ( B @ sk5 ) @ leq ) )
| ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) ) ),
inference(lifteq,[status(thm)],[220]) ).
thf(66,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(566,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)],[66]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ ( n3 @ plus ) )
= ( A @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_3_l) ).
thf(227,plain,
! [A: $i] :
( ( A @ ( n3 @ plus ) )
= ( A @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(228,plain,
! [A: $i] :
( ( A @ ( n3 @ plus ) )
= ( A @ succ @ succ @ succ ) ),
inference(cnf,[status(esa)],[227]) ).
thf(229,plain,
! [A: $i] :
( ( A @ ( n3 @ plus ) )
= ( A @ succ @ succ @ succ ) ),
inference(lifteq,[status(thm)],[228]) ).
thf(43,axiom,
n0 @ ( n998 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_998_0) ).
thf(437,plain,
n0 @ ( n998 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(844,plain,
! [A: $i] :
( ( ( n0 @ ( n998 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[437,375]) ).
thf(845,plain,
! [A: $i] :
( ( n0 @ ( n998 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[844]) ).
thf(846,plain,
! [A: $i] :
( ( n0 != A )
| ( n998 != A ) ),
inference(simp,[status(thm)],[845]) ).
thf(847,plain,
n998 != n0,
inference(simp,[status(thm)],[846]) ).
thf(34,axiom,
n3 @ ( n998 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_998_3) ).
thf(361,plain,
n3 @ ( n998 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(1399,plain,
! [A: $i] :
( ( ( n1 @ ( n998 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[555,375]) ).
thf(1400,plain,
! [A: $i] :
( ( n1 @ ( n998 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[1399]) ).
thf(1401,plain,
! [A: $i] :
( ( n1 != A )
| ( n998 != A ) ),
inference(simp,[status(thm)],[1400]) ).
thf(1402,plain,
n998 != n1,
inference(simp,[status(thm)],[1401]) ).
thf(105,plain,
( ( n0 @ ( xinit_mean_defuse @ a_select2 ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(156,plain,
( ( n0 @ ( xinit_mean_defuse @ a_select2 ) )
= use ),
inference(lifteq,[status(thm)],[105]) ).
thf(185,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B @ ( C @ a_select2 ) )
= D )
& ( A != B ) )
=> ! [E: $i] :
( ( B @ ( E @ ( A @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D ) ),
inference(miniscope,[status(thm)],[184]) ).
thf(186,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( E @ ( A @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D )
| ( ( B @ ( C @ a_select2 ) )
!= D )
| ( A = B ) ),
inference(cnf,[status(esa)],[185]) ).
thf(187,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( E @ ( A @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D )
| ( ( B @ ( C @ a_select2 ) )
!= D )
| ( A = B ) ),
inference(lifteq,[status(thm)],[186]) ).
thf(188,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ ( A @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= ( B @ ( C @ a_select2 ) ) )
| ( A = B ) ),
inference(simp,[status(thm)],[187]) ).
thf(31,axiom,
tptp_minus_1 @ ( n998 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_998_tptp_minus_1) ).
thf(356,plain,
tptp_minus_1 @ ( n998 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(3,axiom,
n2 @ ( n3 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_2) ).
thf(169,plain,
n2 @ ( n3 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(119,plain,
( ( n0 @ ( xinit_noise_defuse @ a_select2 ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(141,plain,
( ( n0 @ ( xinit_noise_defuse @ a_select2 ) )
= use ),
inference(lifteq,[status(thm)],[119]) ).
thf(84,axiom,
! [A: $i] :
( ( n3 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_3_r) ).
thf(610,plain,
! [A: $i] :
( ( n3 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
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 @ 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(519,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)],[54]) ).
thf(67,axiom,
tptp_minus_1 @ ( n5 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_tptp_minus_1) ).
thf(578,plain,
tptp_minus_1 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(18779,plain,
! [B: $i,A: $i] :
( ( ( pv5 @ succ @ succ @ ( n2 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ succ @ ( A @ succ @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18671,236]) ).
thf(18780,plain,
! [B: $i,A: $i] :
( ( ( pv5 @ succ @ succ @ ( n2 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ succ @ ( A @ succ @ leq ) ) ),
inference(simp,[status(thm)],[18779]) ).
thf(18781,plain,
pv5 @ succ @ succ @ succ @ ( n2 @ succ @ leq ),
inference(pattern_uni,[status(thm)],[18780:[bind(A,$thf( n2 )),bind(B,$thf( pv5 @ succ @ succ ))]]) ).
thf(23480,plain,
pv5 @ succ @ succ @ succ @ ( n3 @ leq ),
inference(rewrite,[status(thm)],[18781,2667]) ).
thf(6075,plain,
! [A: $i] :
( ( ( A @ succ @ pred )
!= ( pv5 @ pred ) )
| ( A != sk1 )
| ( sk2 != n0 ) ),
inference(paramod_ordered,[status(thm)],[633,2790]) ).
thf(6101,plain,
( ( ( sk1 @ succ )
!= pv5 )
| ( sk2 != n0 ) ),
inference(simp,[status(thm)],[6075]) ).
thf(27,axiom,
! [A: $i] :
( ( ( n0 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( A = n0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_0) ).
thf(256,plain,
! [A: $i] :
( ( ( n0 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( A = n0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(15,axiom,
def != use,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',defuse) ).
thf(191,plain,
def != use,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(192,plain,
def != use,
inference(polarity_switch,[status(thm)],[191]) ).
thf(193,plain,
def != use,
inference(lifteq,[status(thm)],[192]) ).
thf(73,axiom,
! [A: $i] :
( ( A @ ( n1 @ plus ) )
= ( A @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_1_l) ).
thf(588,plain,
! [A: $i] :
( ( A @ ( n1 @ plus ) )
= ( A @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(589,plain,
! [A: $i] :
( ( A @ ( n1 @ plus ) )
= ( A @ succ ) ),
inference(cnf,[status(esa)],[588]) ).
thf(590,plain,
! [A: $i] :
( ( A @ ( n1 @ plus ) )
= ( A @ succ ) ),
inference(lifteq,[status(thm)],[589]) ).
thf(648,plain,
! [A: $i] :
( ( ( tptp_minus_1 @ ( n2 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[179,375]) ).
thf(649,plain,
! [A: $i] :
( ( tptp_minus_1 @ ( n2 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[648]) ).
thf(669,plain,
! [A: $i] :
( ( tptp_minus_1 != A )
| ( n2 != A ) ),
inference(simp,[status(thm)],[649]) ).
thf(679,plain,
tptp_minus_1 != n2,
inference(simp,[status(thm)],[669]) ).
thf(208,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) )
= ( E @ ( F @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) ) )
| ~ ( D @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ( C @ ( A @ ( B @ ( C @ sk4 ) ) @ leq ) ) ),
inference(cnfConj,[status(thm)],[203]) ).
thf(212,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ( C @ ( A @ ( B @ ( C @ sk4 ) ) @ 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(lifteq,[status(thm)],[208]) ).
thf(14367,plain,
! [B: $i,A: $i] :
( ( ( n998 @ succ @ ( pv5 @ succ @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ succ @ ( A @ succ @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13501,236]) ).
thf(14368,plain,
! [B: $i,A: $i] :
( ( ( n998 @ succ @ ( pv5 @ succ @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ succ @ ( A @ succ @ leq ) ) ),
inference(simp,[status(thm)],[14367]) ).
thf(14369,plain,
n998 @ succ @ succ @ ( pv5 @ succ @ succ @ leq ),
inference(pattern_uni,[status(thm)],[14368:[bind(A,$thf( pv5 @ succ )),bind(B,$thf( n998 @ succ ))]]) ).
thf(6180,plain,
( ( ( pv5 @ pred )
!= ( n3 @ pred ) )
| ( pv5 != n2 ) ),
inference(paramod_ordered,[status(thm)],[6066,2795]) ).
thf(6186,plain,
( ( pv5 != n3 )
| ( pv5 != n2 ) ),
inference(simp,[status(thm)],[6180]) ).
thf(61,axiom,
! [A: $i] :
( ( n1 @ ( A @ plus ) )
= ( A @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_1_r) ).
thf(556,plain,
! [A: $i] :
( ( n1 @ ( A @ plus ) )
= ( A @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(557,plain,
! [A: $i] :
( ( n1 @ ( A @ plus ) )
= ( A @ succ ) ),
inference(cnf,[status(esa)],[556]) ).
thf(558,plain,
! [A: $i] :
( ( n1 @ ( A @ plus ) )
= ( A @ succ ) ),
inference(lifteq,[status(thm)],[557]) ).
thf(21,axiom,
n3 @ ( n5 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_3) ).
thf(230,plain,
n3 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(654,plain,
! [A: $i] :
( ( ( n3 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[230,375]) ).
thf(655,plain,
! [A: $i] :
( ( n3 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[654]) ).
thf(664,plain,
! [A: $i] :
( ( n3 != A )
| ( n5 != A ) ),
inference(simp,[status(thm)],[655]) ).
thf(674,plain,
n5 != n3,
inference(simp,[status(thm)],[664]) ).
thf(33,axiom,
n0 @ ( n5 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_0) ).
thf(360,plain,
n0 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(133,plain,
( ( n1 @ ( rho_defuse @ a_select2 ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(148,plain,
( ( n1 @ ( rho_defuse @ a_select2 ) )
= use ),
inference(lifteq,[status(thm)],[133]) ).
thf(112,plain,
( ( n5 @ ( sigma_defuse @ a_select2 ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(161,plain,
( ( n5 @ ( sigma_defuse @ a_select2 ) )
= use ),
inference(lifteq,[status(thm)],[112]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ( A @ ( B @ gt ) )
| ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality) ).
thf(180,plain,
! [A: $i,B: $i] :
( ( A = B )
| ( A @ ( B @ gt ) )
| ( B @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(116,plain,
( ( pv5 != sk2 )
| ( n1 != sk1 ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(149,plain,
( ( sk2 != pv5 )
| ( sk1 != n1 ) ),
inference(lifteq,[status(thm)],[116]) ).
thf(70,axiom,
n0 @ ( n2 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_2_0) ).
thf(584,plain,
n0 @ ( n2 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(6196,plain,
( ( ( pv5 @ pred )
!= ( n2 @ pred ) )
| ~ ( n1 @ ( sk2 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[6071,2776]) ).
thf(6234,plain,
( ( pv5 != n2 )
| ~ ( n1 @ ( sk2 @ leq ) ) ),
inference(simp,[status(thm)],[6196]) ).
thf(8,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(176,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( B @ ( A @ tptp_update2 ) ) @ a_select2 ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6092,plain,
! [A: $i] :
( ( ( n3 @ succ )
!= ( A @ succ ) )
| ( ( n4 @ pred )
= A ) ),
inference(paramod_ordered,[status(thm)],[2707,633]) ).
thf(6093,plain,
( ( n4 @ pred )
= n3 ),
inference(pattern_uni,[status(thm)],[6092:[bind(A,$thf( n3 ))]]) ).
thf(6923,plain,
( ( ( pv5 @ pred )
!= ( n4 @ pred ) )
| ~ ( n3 @ ( sk2 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[6093,2776]) ).
thf(6959,plain,
( ( pv5 != n4 )
| ~ ( n3 @ ( sk2 @ leq ) ) ),
inference(simp,[status(thm)],[6923]) ).
thf(769,plain,
! [A: $i] :
( ( ( n3 @ ( n998 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[361,375]) ).
thf(770,plain,
! [A: $i] :
( ( n3 @ ( n998 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[769]) ).
thf(771,plain,
! [A: $i] :
( ( n3 != A )
| ( n998 != A ) ),
inference(simp,[status(thm)],[770]) ).
thf(772,plain,
n998 != n3,
inference(simp,[status(thm)],[771]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ succ @ leq ) )
=> ( A @ ( B @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_gt) ).
thf(579,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ succ @ leq ) )
=> ( A @ ( B @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(118,plain,
n0 @ ( pv5 @ gt ),
inference(cnfConj,[status(thm)],[94]) ).
thf(13592,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( n0 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ succ @ ( A @ succ @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[134,236]) ).
thf(13593,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( n0 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ succ @ ( A @ succ @ leq ) ) ),
inference(simp,[status(thm)],[13592]) ).
thf(13594,plain,
sk1 @ succ @ ( n0 @ succ @ leq ),
inference(pattern_uni,[status(thm)],[13593:[bind(A,$thf( n0 )),bind(B,$thf( sk1 ))]]) ).
thf(14667,plain,
sk1 @ succ @ ( n1 @ leq ),
inference(rewrite,[status(thm)],[13594,173]) ).
thf(110,plain,
( ( n0 @ ( n1 @ ( u_defuse @ a_select3 ) ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(144,plain,
( ( n0 @ ( n1 @ ( u_defuse @ a_select3 ) ) )
= use ),
inference(lifteq,[status(thm)],[110]) ).
thf(17370,plain,
( ( ( n3 @ ( sk1 @ succ @ leq ) )
!= ( n3 @ ( sk2 @ leq ) ) )
| ( pv5 != n4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16597,6959]) ).
thf(17371,plain,
( ( ( n3 @ ( sk1 @ succ @ leq ) )
!= ( n3 @ ( sk2 @ leq ) ) )
| ( pv5 != n4 ) ),
inference(simp,[status(thm)],[17370]) ).
thf(17423,plain,
( ( n3 != n3 )
| ( ( sk1 @ succ )
!= sk2 )
| ( pv5 != n4 ) ),
inference(simp,[status(thm)],[17371]) ).
thf(17438,plain,
( ( ( sk1 @ succ )
!= sk2 )
| ( pv5 != n4 ) ),
inference(simp,[status(thm)],[17423]) ).
thf(19971,plain,
! [A: $i] :
( ( ( A @ pred @ succ )
!= ( sk1 @ succ ) )
| ( A != sk2 )
| ( pv5 != n4 ) ),
inference(paramod_ordered,[status(thm)],[239,17438]) ).
thf(19973,plain,
( ( ( sk2 @ pred )
!= sk1 )
| ( pv5 != n4 ) ),
inference(simp,[status(thm)],[19971]) ).
thf(701,plain,
! [A: $i] :
( ( ( tptp_minus_1 @ ( n998 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[356,375]) ).
thf(702,plain,
! [A: $i] :
( ( tptp_minus_1 @ ( n998 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[701]) ).
thf(703,plain,
! [A: $i] :
( ( tptp_minus_1 != A )
| ( n998 != A ) ),
inference(simp,[status(thm)],[702]) ).
thf(704,plain,
tptp_minus_1 != n998,
inference(simp,[status(thm)],[703]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ geq ) )
<=> ( A @ ( B @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_geq) ).
thf(350,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)],[30]) ).
thf(58,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(540,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)],[58]) ).
thf(103,plain,
( ( n3 @ ( xinit_noise_defuse @ a_select2 ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(159,plain,
( ( n3 @ ( xinit_noise_defuse @ a_select2 ) )
= use ),
inference(lifteq,[status(thm)],[103]) ).
thf(14076,plain,
( ( ( pv5 @ succ )
!= ( n3 @ succ ) )
| ( n4 @ ( n1 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[2707,13923]) ).
thf(14166,plain,
( ( pv5 != n3 )
| ( n4 @ ( n1 @ leq ) ) ),
inference(simp,[status(thm)],[14076]) ).
thf(11,axiom,
n1 @ ( n4 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_1) ).
thf(183,plain,
n1 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(662,plain,
! [A: $i] :
( ( ( n1 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[183,375]) ).
thf(663,plain,
! [A: $i] :
( ( n1 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[662]) ).
thf(671,plain,
! [A: $i] :
( ( n1 != A )
| ( n4 != A ) ),
inference(simp,[status(thm)],[663]) ).
thf(681,plain,
n4 != n1,
inference(simp,[status(thm)],[671]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ ( n5 @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_5_l) ).
thf(362,plain,
! [A: $i] :
( ( A @ ( n5 @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(42,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(434,plain,
! [A: $i] :
( tptp_float_0_0
= ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
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(616,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(83,axiom,
! [A: $i] :
( ( n2 @ ( A @ plus ) )
= ( A @ succ @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_2_r) ).
thf(607,plain,
! [A: $i] :
( ( n2 @ ( A @ plus ) )
= ( A @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(608,plain,
! [A: $i] :
( ( n2 @ ( A @ plus ) )
= ( A @ succ @ succ ) ),
inference(cnf,[status(esa)],[607]) ).
thf(609,plain,
! [A: $i] :
( ( n2 @ ( A @ plus ) )
= ( A @ succ @ succ ) ),
inference(lifteq,[status(thm)],[608]) ).
thf(207,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) )
= ( E @ ( F @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) ) )
| ~ ( D @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ( C @ ( A @ ( B @ ( C @ sk3 ) ) @ leq ) ) ),
inference(cnfConj,[status(thm)],[203]) ).
thf(213,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ( C @ ( A @ ( B @ ( C @ sk3 ) ) @ 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(lifteq,[status(thm)],[207]) ).
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(621,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(127,plain,
( ( n0 @ ( n2 @ ( u_defuse @ a_select3 ) ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(140,plain,
( ( n0 @ ( n2 @ ( u_defuse @ a_select3 ) ) )
= use ),
inference(lifteq,[status(thm)],[127]) ).
thf(698,plain,
( ( ( sk2 @ ( sk1 @ ( z_defuse @ a_select3 ) ) )
!= ( n0 @ ( n2 @ ( u_defuse @ a_select3 ) ) ) )
| ( use != use ) ),
inference(paramod_ordered,[status(thm)],[140,157]) ).
thf(699,plain,
( ( sk2 @ ( sk1 @ ( z_defuse @ a_select3 ) ) )
!= ( n0 @ ( n2 @ ( u_defuse @ a_select3 ) ) ) ),
inference(simp,[status(thm)],[698]) ).
thf(700,plain,
( ( sk2 != n0 )
| ( sk1 != n2 )
| ( z_defuse != u_defuse ) ),
inference(simp,[status(thm)],[699]) ).
thf(128,plain,
( ( n1 @ ( xinit_mean_defuse @ a_select2 ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(155,plain,
( ( n1 @ ( xinit_mean_defuse @ a_select2 ) )
= use ),
inference(lifteq,[status(thm)],[128]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( B @ pred @ ( A @ leq ) )
<=> ( A @ ( B @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt_pred) ).
thf(367,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)],[37]) ).
thf(59,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(552,plain,
! [A: $i] :
( ( ( n2 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n2 )
| ( A = n1 )
| ( A = n0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(682,plain,
! [A: $i] :
( ( ( tptp_minus_1 @ ( n0 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[252,375]) ).
thf(683,plain,
! [A: $i] :
( ( tptp_minus_1 @ ( n0 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[682]) ).
thf(684,plain,
! [A: $i] :
( ( tptp_minus_1 != A )
| ( n0 != A ) ),
inference(simp,[status(thm)],[683]) ).
thf(685,plain,
tptp_minus_1 != n0,
inference(simp,[status(thm)],[684]) ).
thf(765,plain,
! [A: $i] :
( ( ( n0 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[360,375]) ).
thf(766,plain,
! [A: $i] :
( ( n0 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[765]) ).
thf(767,plain,
! [A: $i] :
( ( n0 != A )
| ( n5 != A ) ),
inference(simp,[status(thm)],[766]) ).
thf(768,plain,
n5 != n0,
inference(simp,[status(thm)],[767]) ).
thf(6119,plain,
( ( ( pv5 @ pred )
!= ( n1 @ pred ) )
| ~ ( n0 @ ( sk2 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[6058,2776]) ).
thf(6151,plain,
( ( pv5 != n1 )
| ~ ( n0 @ ( sk2 @ leq ) ) ),
inference(simp,[status(thm)],[6119]) ).
thf(6257,plain,
( ( ( pv5 @ succ )
!= ( n3 @ succ ) )
| ( pv5 != n4 ) ),
inference(paramod_ordered,[status(thm)],[2707,6109]) ).
thf(6270,plain,
( ( pv5 != n3 )
| ( pv5 != n4 ) ),
inference(simp,[status(thm)],[6257]) ).
thf(50,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(455,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)],[50]) ).
thf(221,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) )
| ~ ( B @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( A @ ( B @ sk5 ) @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[216]) ).
thf(223,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( A @ ( B @ sk5 ) @ ( n0 @ leq ) )
| ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) ) ),
inference(lifteq,[status(thm)],[221]) ).
thf(218,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) )
| ~ ( B @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( B @ ( A @ ( B @ sk6 ) @ leq ) ) ),
inference(cnfConj,[status(thm)],[216]) ).
thf(226,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( B @ ( A @ ( B @ sk6 ) @ leq ) )
| ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) ) ),
inference(lifteq,[status(thm)],[218]) ).
thf(41,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(431,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)],[41]) ).
thf(101,plain,
( ( pv5 != sk2 )
| ( n2 != sk1 ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(135,plain,
( ( sk2 != pv5 )
| ( sk1 != n2 ) ),
inference(lifteq,[status(thm)],[101]) ).
thf(650,plain,
! [A: $i] :
( ( ( n2 @ ( n3 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[169,375]) ).
thf(651,plain,
! [A: $i] :
( ( n2 @ ( n3 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[650]) ).
thf(665,plain,
! [A: $i] :
( ( n2 != A )
| ( n3 != A ) ),
inference(simp,[status(thm)],[651]) ).
thf(675,plain,
n3 != n2,
inference(simp,[status(thm)],[665]) ).
thf(6203,plain,
( ( ( pv5 @ pred )
!= ( n2 @ pred ) )
| ( sk2 != n1 ) ),
inference(paramod_ordered,[status(thm)],[6071,4751]) ).
thf(6225,plain,
( ( pv5 != n2 )
| ( sk2 != n1 ) ),
inference(simp,[status(thm)],[6203]) ).
thf(254,plain,
! [A: $i] :
( ( n1 @ ( A @ minus ) )
= ( A @ pred ) ),
inference(cnf,[status(esa)],[253]) ).
thf(255,plain,
! [A: $i] :
( ( n1 @ ( A @ minus ) )
= ( A @ pred ) ),
inference(lifteq,[status(thm)],[254]) ).
thf(206,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) )
= ( E @ ( F @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) ) )
| ~ ( D @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ( ( A @ ( B @ ( C @ sk4 ) ) @ ( A @ ( B @ ( C @ sk3 ) ) @ ( B @ a_select3 ) ) )
!= ( A @ ( B @ ( C @ sk3 ) ) @ ( A @ ( B @ ( C @ sk4 ) ) @ ( B @ a_select3 ) ) ) ) ),
inference(cnfConj,[status(thm)],[203]) ).
thf(209,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( D @ ( 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 ) ) ) )
| ( ( A @ ( B @ ( C @ sk3 ) ) @ ( A @ ( B @ ( C @ sk4 ) ) @ ( B @ a_select3 ) ) )
!= ( A @ ( B @ ( C @ sk4 ) ) @ ( A @ ( B @ ( C @ sk3 ) ) @ ( B @ a_select3 ) ) ) ) ),
inference(lifteq,[status(thm)],[206]) ).
thf(13930,plain,
( ( ( pv5 @ succ )
!= ( n2 @ succ ) )
| ( n3 @ ( n1 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[2667,13923]) ).
thf(14175,plain,
( ( pv5 != n2 )
| ( n3 @ ( n1 @ leq ) ) ),
inference(simp,[status(thm)],[13930]) ).
thf(53,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(516,plain,
! [A: $i,B: $i] :
( ( A @ ( n0 @ leq ) )
=> ( A @ ( A @ ( B @ uniform_int_rnd ) @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(13368,plain,
! [A: $i] :
( ( ( n3 @ succ @ succ @ succ )
!= ( A @ succ ) )
| ( ( n5 @ succ )
!= A ) ),
inference(paramod_ordered,[status(thm)],[13282,5046]) ).
thf(13369,plain,
( ( n3 @ succ @ succ )
!= ( n5 @ succ ) ),
inference(pattern_uni,[status(thm)],[13368:[bind(A,$thf( n3 @ succ @ succ ))]]) ).
thf(13431,plain,
( ( n5 @ succ )
!= n5 ),
inference(rewrite,[status(thm)],[13369,4569]) ).
thf(16288,plain,
! [B: $i,A: $i] :
( ( ( pv5 @ succ @ ( sk2 @ succ @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ succ @ ( A @ succ @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13687,236]) ).
thf(16289,plain,
! [B: $i,A: $i] :
( ( ( pv5 @ succ @ ( sk2 @ succ @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ succ @ ( A @ succ @ leq ) ) ),
inference(simp,[status(thm)],[16288]) ).
thf(16290,plain,
pv5 @ succ @ succ @ ( sk2 @ succ @ succ @ leq ),
inference(pattern_uni,[status(thm)],[16289:[bind(A,$thf( sk2 @ succ )),bind(B,$thf( pv5 @ succ ))]]) ).
thf(123,plain,
( ( n0 @ ( n0 @ ( u_defuse @ a_select3 ) ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(162,plain,
( ( n0 @ ( n0 @ ( u_defuse @ a_select3 ) ) )
= use ),
inference(lifteq,[status(thm)],[123]) ).
thf(2315,plain,
! [A: $i] :
( ( ( n2 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[629,375]) ).
thf(2316,plain,
! [A: $i] :
( ( n2 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[2315]) ).
thf(2317,plain,
! [A: $i] :
( ( n2 != A )
| ( n4 != A ) ),
inference(simp,[status(thm)],[2316]) ).
thf(2318,plain,
n4 != n2,
inference(simp,[status(thm)],[2317]) ).
thf(652,plain,
! [A: $i] :
( ( ( n0 @ ( pv5 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[118,375]) ).
thf(653,plain,
! [A: $i] :
( ( n0 @ ( pv5 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[652]) ).
thf(670,plain,
! [A: $i] :
( ( n0 != A )
| ( pv5 != A ) ),
inference(simp,[status(thm)],[653]) ).
thf(680,plain,
pv5 != n0,
inference(simp,[status(thm)],[670]) ).
thf(106,plain,
( ( n4 @ ( xinit_noise_defuse @ a_select2 ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(145,plain,
( ( n4 @ ( xinit_noise_defuse @ a_select2 ) )
= use ),
inference(lifteq,[status(thm)],[106]) ).
thf(2264,plain,
( ( ( sk2 @ ( sk1 @ ( z_defuse @ a_select3 ) ) )
!= ( n0 @ ( n0 @ ( u_defuse @ a_select3 ) ) ) )
| ( use != use ) ),
inference(paramod_ordered,[status(thm)],[162,157]) ).
thf(2265,plain,
( ( sk2 @ ( sk1 @ ( z_defuse @ a_select3 ) ) )
!= ( n0 @ ( n0 @ ( u_defuse @ a_select3 ) ) ) ),
inference(simp,[status(thm)],[2264]) ).
thf(2298,plain,
( ( sk2 != n0 )
| ( sk1 != n0 )
| ( z_defuse != u_defuse ) ),
inference(simp,[status(thm)],[2265]) ).
thf(117,plain,
( ( n5 @ ( xinit_defuse @ a_select2 ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(150,plain,
( ( n5 @ ( xinit_defuse @ a_select2 ) )
= use ),
inference(lifteq,[status(thm)],[117]) ).
thf(5,axiom,
n1 @ ( n3 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_1) ).
thf(171,plain,
n1 @ ( n3 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(658,plain,
! [A: $i] :
( ( ( n1 @ ( n3 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[171,375]) ).
thf(659,plain,
! [A: $i] :
( ( n1 @ ( n3 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[658]) ).
thf(672,plain,
! [A: $i] :
( ( n1 != A )
| ( n3 != A ) ),
inference(simp,[status(thm)],[659]) ).
thf(673,plain,
n3 != n1,
inference(simp,[status(thm)],[672]) ).
thf(181,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( A @ ( B @ gt ) )
| ( B @ ( A @ gt ) ) ),
inference(cnf,[status(esa)],[180]) ).
thf(182,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ( B @ ( A @ gt ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[181]) ).
thf(2319,plain,
! [A: $i] :
( ( ( n1 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[630,375]) ).
thf(2320,plain,
! [A: $i] :
( ( n1 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[2319]) ).
thf(2321,plain,
! [A: $i] :
( ( n1 != A )
| ( n5 != A ) ),
inference(simp,[status(thm)],[2320]) ).
thf(2322,plain,
n5 != n1,
inference(simp,[status(thm)],[2321]) ).
thf(1676,plain,
! [A: $i] :
( ( ( n0 @ ( n2 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[584,375]) ).
thf(1677,plain,
! [A: $i] :
( ( n0 @ ( n2 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[1676]) ).
thf(1678,plain,
! [A: $i] :
( ( n0 != A )
| ( n2 != A ) ),
inference(simp,[status(thm)],[1677]) ).
thf(1679,plain,
n2 != n0,
inference(simp,[status(thm)],[1678]) ).
thf(96,plain,
( ( n3 @ ( xinit_defuse @ a_select2 ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(154,plain,
( ( n3 @ ( xinit_defuse @ a_select2 ) )
= use ),
inference(lifteq,[status(thm)],[96]) ).
thf(6159,plain,
( ( ( pv5 @ pred )
!= ( n3 @ pred ) )
| ( n2 != n2 )
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[6066,2794]) ).
thf(6160,plain,
( ( ( pv5 @ pred )
!= ( n3 @ pred ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[6159]) ).
thf(6193,plain,
( ( pv5 != n3 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[6160]) ).
thf(48,axiom,
! [A: $i] :
( ( n5 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_5_r) ).
thf(446,plain,
! [A: $i] :
( ( n5 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(611,plain,
! [A: $i] :
( ( n3 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ ) ),
inference(cnf,[status(esa)],[610]) ).
thf(612,plain,
! [A: $i] :
( ( n3 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ ) ),
inference(lifteq,[status(thm)],[611]) ).
thf(120,plain,
( ( n2 @ ( xinit_mean_defuse @ a_select2 ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(143,plain,
( ( n2 @ ( xinit_mean_defuse @ a_select2 ) )
= use ),
inference(lifteq,[status(thm)],[120]) ).
thf(435,plain,
! [A: $i] :
( tptp_float_0_0
= ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) ) ),
inference(cnf,[status(esa)],[434]) ).
thf(436,plain,
! [A: $i] :
( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
= tptp_float_0_0 ),
inference(lifteq,[status(thm)],[435]) ).
thf(4671,plain,
tptp_float_0_0 = n0,
inference(rewrite,[status(thm)],[436,196]) ).
thf(77,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(595,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)],[77]) ).
thf(69,axiom,
! [A: $i] :
( ( A @ ( n4 @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_4_l) ).
thf(581,plain,
! [A: $i] :
( ( A @ ( n4 @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(1651,plain,
! [A: $i] :
( ( ( tptp_minus_1 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[578,375]) ).
thf(1652,plain,
! [A: $i] :
( ( tptp_minus_1 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[1651]) ).
thf(1653,plain,
! [A: $i] :
( ( tptp_minus_1 != A )
| ( n5 != A ) ),
inference(simp,[status(thm)],[1652]) ).
thf(1654,plain,
tptp_minus_1 != n5,
inference(simp,[status(thm)],[1653]) ).
thf(6076,plain,
! [A: $i] :
( ( ( n4 @ succ )
!= ( A @ succ ) )
| ( ( n5 @ pred )
= A ) ),
inference(paramod_ordered,[status(thm)],[2958,633]) ).
thf(6077,plain,
( ( n5 @ pred )
= n4 ),
inference(pattern_uni,[status(thm)],[6076:[bind(A,$thf( n4 ))]]) ).
thf(98,plain,
( ( n4 @ ( xinit_defuse @ a_select2 ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(158,plain,
( ( n4 @ ( xinit_defuse @ a_select2 ) )
= use ),
inference(lifteq,[status(thm)],[98]) ).
thf(6871,plain,
( ( ( pv5 @ pred )
!= ( n5 @ pred ) )
| ~ ( n4 @ ( sk2 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[6077,2776]) ).
thf(6910,plain,
( ( pv5 != n5 )
| ~ ( n4 @ ( sk2 @ leq ) ) ),
inference(simp,[status(thm)],[6871]) ).
thf(95,plain,
( ( n1 @ ( sigma_defuse @ a_select2 ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(139,plain,
( ( n1 @ ( sigma_defuse @ a_select2 ) )
= use ),
inference(lifteq,[status(thm)],[95]) ).
thf(2092,plain,
! [A: $i] :
( ( ( tptp_minus_1 @ ( n3 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[606,375]) ).
thf(2093,plain,
! [A: $i] :
( ( tptp_minus_1 @ ( n3 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[2092]) ).
thf(2094,plain,
! [A: $i] :
( ( tptp_minus_1 != A )
| ( n3 != A ) ),
inference(simp,[status(thm)],[2093]) ).
thf(2095,plain,
tptp_minus_1 != n3,
inference(simp,[status(thm)],[2094]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( u_defuse @ a_select3 ) ) )
= use )
| ~ ( pv5 @ pred @ ( B @ leq ) )
| ~ ( n2 @ ( A @ leq ) )
| ~ ( B @ ( n0 @ leq ) )
| ~ ( A @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(151,plain,
! [B: $i,A: $i] :
( ~ ( pv5 @ pred @ ( B @ leq ) )
| ~ ( n2 @ ( A @ leq ) )
| ~ ( B @ ( n0 @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( ( B @ ( A @ ( u_defuse @ a_select3 ) ) )
= use ) ),
inference(lifteq,[status(thm)],[102]) ).
thf(13945,plain,
( ( ( pv5 @ succ )
!= ( n4 @ succ ) )
| ( n5 @ ( n1 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[2958,13923]) ).
thf(14170,plain,
( ( pv5 != n4 )
| ( n5 @ ( n1 @ leq ) ) ),
inference(simp,[status(thm)],[13945]) ).
thf(121,plain,
( ( n5 @ ( xinit_noise_defuse @ a_select2 ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(146,plain,
( ( n5 @ ( xinit_noise_defuse @ a_select2 ) )
= use ),
inference(lifteq,[status(thm)],[121]) ).
thf(6222,plain,
( ( ( pv5 @ pred )
!= ( n2 @ pred ) )
| ( pv5 != n1 ) ),
inference(paramod_ordered,[status(thm)],[6071,2795]) ).
thf(6237,plain,
( ( pv5 != n2 )
| ( pv5 != n1 ) ),
inference(simp,[status(thm)],[6222]) ).
thf(14,axiom,
n5 @ ( n998 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_998_5) ).
thf(190,plain,
n5 @ ( n998 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(122,plain,
( ( n3 @ ( sigma_defuse @ a_select2 ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(168,plain,
( ( n3 @ ( sigma_defuse @ a_select2 ) )
= use ),
inference(lifteq,[status(thm)],[122]) ).
thf(29,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(262,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)],[29]) ).
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(603,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(65,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(564,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ gt ) )
& ( B @ ( A @ gt ) ) )
=> ( C @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(205,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) )
= ( E @ ( F @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) ) )
| ~ ( D @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ( A @ ( B @ ( C @ sk3 ) ) @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[203]) ).
thf(210,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ( A @ ( B @ ( C @ sk3 ) ) @ ( 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(lifteq,[status(thm)],[205]) ).
thf(97,plain,
( ( n0 @ ( sigma_defuse @ a_select2 ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(136,plain,
( ( n0 @ ( sigma_defuse @ a_select2 ) )
= use ),
inference(lifteq,[status(thm)],[97]) ).
thf(198,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( D @ leq ) )
& ( D @ ( E @ leq ) )
& ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) )
=> ! [G: $i] :
( ( D @ ( A @ ( G @ ( F @ ( E @ dim ) @ ( C @ ( B @ dim ) @ tptp_const_array2 ) ) @ a_select3 ) ) )
= G ) ),
inference(miniscope,[status(thm)],[197]) ).
thf(199,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( G @ ( F @ ( E @ dim ) @ ( C @ ( B @ dim ) @ tptp_const_array2 ) ) @ a_select3 ) ) )
= G )
| ~ ( F @ ( D @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( C @ ( A @ leq ) )
| ~ ( A @ ( B @ leq ) ) ),
inference(cnf,[status(esa)],[198]) ).
thf(200,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $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(lifteq,[status(thm)],[199]) ).
thf(5139,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( G @ ( F @ ( E @ dim ) @ ( C @ ( B @ dim ) @ tptp_const_array2 ) ) @ a_select3 ) ) )
!= ( sk2 @ ( sk1 @ ( z_defuse @ a_select3 ) ) ) )
| ( G != use )
| ~ ( F @ ( D @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( C @ ( A @ leq ) )
| ~ ( A @ ( B @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[200,157]) ).
thf(5240,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D != sk2 )
| ( A != sk1 )
| ( ( use @ ( F @ ( E @ dim ) @ ( C @ ( B @ dim ) @ tptp_const_array2 ) ) )
!= z_defuse )
| ~ ( F @ ( D @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( C @ ( A @ leq ) )
| ~ ( A @ ( B @ leq ) ) ),
inference(simp,[status(thm)],[5139]) ).
thf(5300,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( use @ ( D @ ( C @ dim ) @ ( B @ ( A @ dim ) @ tptp_const_array2 ) ) )
!= z_defuse )
| ~ ( D @ ( sk2 @ leq ) )
| ~ ( sk2 @ ( C @ leq ) )
| ~ ( B @ ( sk1 @ leq ) )
| ~ ( sk1 @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[5240]) ).
thf(6291,plain,
( ( ( sk2 @ succ )
!= ( n3 @ succ ) )
| ( pv5 != n4 ) ),
inference(paramod_ordered,[status(thm)],[2707,6112]) ).
thf(6294,plain,
( ( sk2 != n3 )
| ( pv5 != n4 ) ),
inference(simp,[status(thm)],[6291]) ).
thf(2088,plain,
! [A: $i] :
( ( ( n4 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[602,375]) ).
thf(2089,plain,
! [A: $i] :
( ( n4 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[2088]) ).
thf(2090,plain,
! [A: $i] :
( ( n4 != A )
| ( n5 != A ) ),
inference(simp,[status(thm)],[2089]) ).
thf(2091,plain,
n5 != n4,
inference(simp,[status(thm)],[2090]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( A @ ( B @ succ @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_gt_equiv) ).
thf(532,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)],[56]) ).
thf(14744,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ succ @ ( n1 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ succ @ ( A @ succ @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14667,236]) ).
thf(14745,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ succ @ ( n1 @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( B @ succ @ ( A @ succ @ leq ) ) ),
inference(simp,[status(thm)],[14744]) ).
thf(14746,plain,
sk1 @ succ @ succ @ ( n1 @ succ @ leq ),
inference(pattern_uni,[status(thm)],[14745:[bind(A,$thf( n1 )),bind(B,$thf( sk1 @ succ ))]]) ).
thf(19096,plain,
sk1 @ succ @ succ @ ( n2 @ leq ),
inference(rewrite,[status(thm)],[14746,2650]) ).
thf(833,plain,
( ( ( sk2 @ ( sk1 @ ( z_defuse @ a_select3 ) ) )
!= ( n0 @ ( n1 @ ( u_defuse @ a_select3 ) ) ) )
| ( use != use ) ),
inference(paramod_ordered,[status(thm)],[144,157]) ).
thf(834,plain,
( ( sk2 @ ( sk1 @ ( z_defuse @ a_select3 ) ) )
!= ( n0 @ ( n1 @ ( u_defuse @ a_select3 ) ) ) ),
inference(simp,[status(thm)],[833]) ).
thf(839,plain,
( ( sk2 != n0 )
| ( sk1 != n1 )
| ( z_defuse != u_defuse ) ),
inference(simp,[status(thm)],[834]) ).
thf(52,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(464,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)],[52]) ).
thf(104,plain,
( ( n2 @ ( xinit_noise_defuse @ a_select2 ) )
= use ),
inference(cnfConj,[status(thm)],[94]) ).
thf(163,plain,
( ( n2 @ ( xinit_noise_defuse @ a_select2 ) )
= use ),
inference(lifteq,[status(thm)],[104]) ).
thf(177,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ tptp_update2 ) ) @ a_select2 ) )
= C ),
inference(cnf,[status(esa)],[176]) ).
thf(178,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ tptp_update2 ) ) @ a_select2 ) )
= C ),
inference(lifteq,[status(thm)],[177]) ).
thf(660,plain,
! [A: $i] :
( ( ( n5 @ ( n998 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[190,375]) ).
thf(661,plain,
! [A: $i] :
( ( n5 @ ( n998 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[660]) ).
thf(666,plain,
! [A: $i] :
( ( n5 != A )
| ( n998 != A ) ),
inference(simp,[status(thm)],[661]) ).
thf(676,plain,
n998 != n5,
inference(simp,[status(thm)],[666]) ).
thf(217,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) )
| ~ ( B @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( A @ ( B @ sk6 ) @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[216]) ).
thf(222,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( A @ ( B @ sk6 ) @ ( n0 @ leq ) )
| ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) ) ),
inference(lifteq,[status(thm)],[217]) ).
thf(33185,plain,
$false,
inference(e,[status(thm)],[629,249,555,365,138,6074,234,170,115,449,379,13687,2776,2659,2099,247,614,677,19521,13501,142,1867,1275,538,153,174,6268,1650,13923,2698,2667,1871,6066,125,1279,196,184,18671,587,619,18627,357,460,157,6071,559,189,6149,152,5077,261,93,606,2794,179,591,443,376,2650,6187,1151,22043,164,211,6189,253,147,4751,6103,5045,602,1863,248,439,678,201,6058,366,2790,561,630,16597,137,165,598,160,2958,6303,252,197,1281,224,566,229,847,361,13282,1402,156,188,356,169,141,610,519,578,23480,6101,256,225,193,590,679,212,14369,173,6186,134,237,558,674,586,633,360,148,2941,161,180,149,375,601,584,6234,176,191,6959,772,579,118,259,14667,445,144,19973,236,704,350,540,159,14166,172,681,6112,230,362,434,616,631,4569,609,213,621,700,240,155,367,552,594,140,685,768,6151,6270,455,223,226,438,431,167,135,563,675,6225,255,209,14175,516,13431,16290,162,531,2318,680,194,145,2298,150,16974,673,182,585,6093,2322,1679,613,154,600,6193,446,612,143,4671,17438,595,231,99,556,581,1654,2792,6077,158,114,6910,171,139,588,2707,2095,214,151,14170,146,6237,190,183,168,262,373,603,564,210,239,136,5300,6294,437,2091,2795,532,19096,839,464,5046,442,607,163,200,6109,178,227,676,222,592,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV203+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
% 0.12/0.40 % Computer : n017.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sat Sep 26 13:15:03 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 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
% 0.83/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.36/1.24 % [INFO] Parsing done (253ms).
% 1.36/1.25 % [INFO] Running in sequential loop mode.
% 2.26/1.64 % [INFO] eprover registered as external prover.
% 2.26/1.65 % [INFO] Scanning for conjecture ...
% 2.67/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 91 axioms. Running axiom selection ...
% 2.90/1.94 % [INFO] Axiom selection finished. Selected 90 axioms (removed 1 axioms).
% 2.90/2.02 % [INFO] Problem is first-order (TPTP FOF).
% 3.21/2.04 % [INFO] Type checking passed.
% 3.21/2.04 % [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 ...
% 81.68/18.94 % External prover 'e' found a proof!
% 81.68/18.94 % [INFO] Killing All external provers ...
% 81.68/18.94 % Time passed: 18391ms (effective reasoning time: 17684ms)
% 81.68/18.94 % 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)>
% 81.68/18.95 % 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
% 81.68/18.95 % No. of inferences in proof: 641
% 81.68/18.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 18391 ms resp. 17684 ms w/o parsing
% 83.36/19.17 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 83.36/19.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------