%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV053+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 : n011.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 08:58:01 AM UTC 2026
% Result : Theorem 90.05s 22.03s
% Output : Refutation 92.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 97
% Syntax : Number of formulae : 762 ( 270 unt; 0 typ; 7 def)
% Number of atoms : 2932 (1316 equ; 0 cnn)
% Maximal formula atoms : 73 ( 3 avg)
% Number of connectives : 13307 (1496 ~;1310 |; 292 &;10060 @)
% ( 5 <=>; 144 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 47 usr; 21 con; 0-4 aty)
% Number of variables : 936 ( 8 ^; 920 !; 1 ?; 936 :)
% ( 0 !>; 0 ?*; 0 @-; 7 @+)
% Comments :
%------------------------------------------------------------------------------
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(n0_decl,type,
n0: $i ).
thf(pv10_decl,type,
pv10: $i ).
thf(pv12_decl,type,
pv12: $i ).
thf(minus_decl,type,
minus: $i > $i > $i ).
thf(n135300_decl,type,
n135300: $i ).
thf(n1_decl,type,
n1: $i ).
thf(n5_decl,type,
n5: $i ).
thf(a_select3_decl,type,
a_select3: $i > $i > $i > $i ).
thf(q_decl,type,
q: $i ).
thf(divide_decl,type,
divide: $i > $i > $i ).
thf(sqrt_decl,type,
sqrt: $i > $i ).
thf(times_decl,type,
times: $i > $i > $i ).
thf(center_decl,type,
center: $i ).
thf(a_select2_decl,type,
a_select2: $i > $i > $i ).
thf(x_decl,type,
x: $i ).
thf(sum_decl,type,
sum: $i > $i > $i > $i ).
thf(pv71_decl,type,
pv71: $i ).
thf(plus_decl,type,
plus: $i > $i > $i ).
thf(n3_decl,type,
n3: $i ).
thf(succ_decl,type,
succ: $i > $i ).
thf(pred_decl,type,
pred: $i > $i ).
thf(gt_decl,type,
gt: $i > $i > $o ).
thf(tptp_minus_1_decl,type,
tptp_minus_1: $i ).
thf(n2_decl,type,
n2: $i ).
thf(n4_decl,type,
n4: $i ).
thf(lt_decl,type,
lt: $i > $i > $o ).
thf(tptp_update2_decl,type,
tptp_update2: $i > $i > $i > $i ).
thf(tptp_const_array2_decl,type,
tptp_const_array2: $i > $i > $i > $i ).
thf(dim_decl,type,
dim: $i > $i > $i ).
thf(tptp_mmul_decl,type,
tptp_mmul: $i > $i > $i ).
thf(trans_decl,type,
trans: $i > $i ).
thf(tptp_update3_decl,type,
tptp_update3: $i > $i > $i > $i > $i ).
thf(tptp_madd_decl,type,
tptp_madd: $i > $i > $i ).
thf(geq_decl,type,
geq: $i > $i > $o ).
thf(uniform_int_rnd_decl,type,
uniform_int_rnd: $i > $i > $i ).
thf(tptp_msub_decl,type,
tptp_msub: $i > $i > $i ).
thf(tptp_float_0_0_decl,type,
tptp_float_0_0: $i ).
thf(tptp_const_array1_decl,type,
tptp_const_array1: $i > $i > $i ).
thf(inv_decl,type,
inv: $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( ( n1 @ ( pv12 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ! [B: $i] :
( ( A @ ( pv10 @ ( q @ a_select3 ) ) )
= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( B @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( B @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
( ( sk1 @ ( pv10 @ ( q @ a_select3 ) ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( ( n1 @ ( pv10 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ! [B: $i] :
( ( B @ ( A @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
( ( A @ ( sk3 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
!= n1 ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i,C: $i,D: $i] :
@+[E: $i] :
~ ( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) ) )
=> ( ( E @ ( B @ a_select2 ) )
= A ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [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(sk9_def,definition,
( sk9
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( ( A @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) )
& ( A @ ( B @ ( A @ sk8 ) @ leq ) )
& ( B @ ( A @ sk8 ) @ ( n0 @ leq ) ) )
=> ( ( C @ ( B @ ( A @ sk8 ) @ ( B @ a_select3 ) ) )
= ( B @ ( A @ sk8 ) @ ( C @ ( B @ a_select3 ) ) ) ) ) ) ) ).
thf(1,conjecture,
( ( ! [A: $i,B: $i] :
( ( ( n1 @ ( pv10 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( pv12 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( pv10 @ ( q @ a_select3 ) ) )
= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( B @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( B @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) ) )
& ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
& ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
& ( pv12 @ ( n0 @ leq ) )
& ( pv10 @ ( n0 @ leq ) ) )
=> ( ! [A: $i,B: $i] :
( ( ( n1 @ ( pv10 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( pv12 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( pv10 @ ( q @ a_select3 ) ) )
= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( B @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( B @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) ) )
& ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
& ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
& ( pv12 @ ( n0 @ leq ) )
& ( pv10 @ ( n0 @ leq ) )
& ( n0
= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_norm_0031) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i,B: $i] :
( ( ( n1 @ ( pv10 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( pv12 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( pv10 @ ( q @ a_select3 ) ) )
= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( B @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( B @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) ) )
& ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
& ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
& ( pv12 @ ( n0 @ leq ) )
& ( pv10 @ ( n0 @ leq ) ) )
=> ( ! [A: $i,B: $i] :
( ( ( n1 @ ( pv10 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( pv12 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( pv10 @ ( q @ a_select3 ) ) )
= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( B @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( B @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) ) )
& ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
& ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
& ( pv12 @ ( n0 @ leq ) )
& ( pv10 @ ( n0 @ leq ) )
& ( n0
= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(92,plain,
~ ( ( ! [A: $i,B: $i] :
( ( ( n1 @ ( pv10 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( pv12 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( pv10 @ ( q @ a_select3 ) ) )
= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( B @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( B @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) ) )
& ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
& ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
& ( pv12 @ ( n0 @ leq ) )
& ( pv10 @ ( n0 @ leq ) ) )
=> ( ! [A: $i,B: $i] :
( ( ( n1 @ ( pv10 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( pv12 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( pv10 @ ( q @ a_select3 ) ) )
= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( B @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( B @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) ) )
& ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
& ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
& ( pv12 @ ( n0 @ leq ) )
& ( pv10 @ ( n0 @ leq ) )
& ( n0
= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(93,plain,
~ ( ( ! [A: $i] :
( ( ( n1 @ ( pv10 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ! [B: $i] :
( ( B @ ( A @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) )
& ! [A: $i] :
( ( ( n1 @ ( pv12 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ! [B: $i] :
( ( A @ ( pv10 @ ( q @ a_select3 ) ) )
= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( B @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( B @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) ) )
& ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
& ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
& ( pv12 @ ( n0 @ leq ) )
& ( pv10 @ ( n0 @ leq ) ) )
=> ( ! [A: $i] :
( ( ( n1 @ ( pv10 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ! [B: $i] :
( ( B @ ( A @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) )
& ! [A: $i] :
( ( ( n1 @ ( pv12 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ! [B: $i] :
( ( A @ ( pv10 @ ( q @ a_select3 ) ) )
= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( B @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( B @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) ) )
& ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
& ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
& ( pv12 @ ( n0 @ leq ) )
& ( pv10 @ ( n0 @ leq ) )
& ( n0
= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) ) ) ),
inference(miniscope,[status(thm)],[92]) ).
thf(94,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ( sk4 @ ( sk3 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
!= n1 )
| ( ( sk1 @ ( pv10 @ ( q @ a_select3 ) ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) )
| ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( n0
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) ) )
& ( ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ( ( sk1 @ ( pv10 @ ( q @ a_select3 ) ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) )
| ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( n0
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) ) )
& ( ( sk3 @ ( n0 @ leq ) )
| ( ( sk1 @ ( pv10 @ ( q @ a_select3 ) ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) )
| ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( n0
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) ) )
& ( ( ( sk4 @ ( sk3 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
!= n1 )
| ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( n0
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) ) )
& ( ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( n0
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) ) )
& ( ( sk3 @ ( n0 @ leq ) )
| ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( n0
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) ) )
& ( ( ( sk4 @ ( sk3 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
!= n1 )
| ( sk1 @ ( n0 @ leq ) )
| ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( n0
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) ) )
& ( ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ( sk1 @ ( n0 @ leq ) )
| ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( n0
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) ) )
& ( ( sk3 @ ( n0 @ leq ) )
| ( sk1 @ ( n0 @ leq ) )
| ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( n0
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) ) )
& ( ( ( D @ ( C @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 )
| ~ ( n1 @ ( pv10 @ minus ) @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) ) )
& ( ( ( A @ ( pv10 @ ( q @ a_select3 ) ) )
= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( B @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( B @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) )
| ~ ( n1 @ ( pv12 @ minus ) @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) ) )
& ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
& ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
& ( pv12 @ ( n0 @ leq ) )
& ( pv10 @ ( n0 @ leq ) ) ),
inference(cnf,[status(esa)],[93]) ).
thf(100,plain,
pv10 @ ( n0 @ leq ),
inference(cnfConj,[status(thm)],[94]) ).
thf(101,plain,
pv12 @ ( n0 @ leq ),
inference(cnfConj,[status(thm)],[94]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 )
| ~ ( n1 @ ( pv10 @ minus ) @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(117,plain,
! [B: $i,A: $i] :
( ~ ( n1 @ ( pv10 @ minus ) @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( ( B @ ( A @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(lifteq,[status(thm)],[96]) ).
thf(118,plain,
! [B: $i,A: $i] :
( ~ ( n1 @ ( pv10 @ minus ) @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( ( B @ ( A @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[117]) ).
thf(922,plain,
! [B: $i,A: $i] :
( ( ( pv12 @ ( n0 @ leq ) )
!= ( A @ ( n0 @ leq ) ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( A @ leq ) )
| ~ $true
| ( ( B @ ( A @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[101,118]) ).
thf(923,plain,
! [B: $i,A: $i] :
( ( ( pv12 @ ( n0 @ leq ) )
!= ( A @ ( n0 @ leq ) ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( A @ leq ) )
| ( ( B @ ( A @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[922]) ).
thf(924,plain,
! [A: $i] :
( ~ ( n1 @ ( pv10 @ minus ) @ ( pv12 @ leq ) )
| ( ( A @ ( pv12 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(pattern_uni,[status(thm)],[923:[bind(A,$thf( pv12 ))]]) ).
thf(969,plain,
! [A: $i] :
( ~ ( n1 @ ( pv10 @ minus ) @ ( pv12 @ leq ) )
| ( ( A @ ( pv12 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[924]) ).
thf(1320,plain,
! [A: $i] :
( ( ( n1 @ ( pv10 @ minus ) @ ( pv12 @ leq ) )
!= ( pv10 @ ( n0 @ leq ) ) )
| ~ $true
| ( ( A @ ( pv12 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[100,969]) ).
thf(1321,plain,
! [A: $i] :
( ( ( n1 @ ( pv10 @ minus ) @ ( pv12 @ leq ) )
!= ( pv10 @ ( n0 @ leq ) ) )
| ( ( A @ ( pv12 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[1320]) ).
thf(1337,plain,
! [A: $i] :
( ( ( n1 @ ( pv10 @ minus ) )
!= pv10 )
| ( pv12 != n0 )
| ( ( A @ ( pv12 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[1321]) ).
thf(10,axiom,
tptp_minus_1 @ ( n2 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_2_tptp_minus_1) ).
thf(138,plain,
tptp_minus_1 @ ( n2 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(86,axiom,
n1 @ ( n2 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_2_1) ).
thf(576,plain,
n1 @ ( n2 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ lt ) )
<=> ( A @ ( B @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lt_gt) ).
thf(156,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)],[18]) ).
thf(157,plain,
( ! [A: $i,B: $i] :
( ( A @ ( B @ gt ) )
=> ( B @ ( A @ lt ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ lt ) )
=> ( A @ ( B @ gt ) ) ) ),
inference(miniscope,[status(thm)],[156]) ).
thf(158,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ lt ) )
| ~ ( C @ ( D @ gt ) ) )
& ( ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ lt ) ) ) ),
inference(cnf,[status(esa)],[157]) ).
thf(160,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lt ) )
| ~ ( A @ ( B @ gt ) ) ),
inference(cnfConj,[status(thm)],[158]) ).
thf(161,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lt ) )
| ~ ( A @ ( B @ gt ) ) ),
inference(simp,[status(thm)],[160]) ).
thf(15535,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( n2 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[576,161]) ).
thf(15536,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( n2 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15535]) ).
thf(15537,plain,
n2 @ ( n1 @ lt ),
inference(pattern_uni,[status(thm)],[15536:[bind(A,$thf( n1 )),bind(B,$thf( n2 ))]]) ).
thf(76,axiom,
! [A: $i] : ( A @ ( A @ leq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_leq) ).
thf(555,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(98,plain,
( ( sk3 @ ( n0 @ leq ) )
| ( ( sk1 @ ( pv10 @ ( q @ a_select3 ) ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) )
| ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( n0
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(113,plain,
( ( sk3 @ ( n0 @ leq ) )
| ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( ( sk1 @ ( pv10 @ ( q @ a_select3 ) ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(lifteq,[status(thm)],[98]) ).
thf(104,plain,
n1 @ ( n5 @ minus ) @ ( pv12 @ leq ),
inference(cnfConj,[status(thm)],[94]) ).
thf(106,plain,
n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ),
inference(cnfConj,[status(thm)],[94]) ).
thf(1410,plain,
( ( sk3 @ ( n0 @ leq ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ( ( sk1 @ ( pv10 @ ( q @ a_select3 ) ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(rewrite,[status(thm)],[113,100,101,104,106]) ).
thf(1411,plain,
( ( sk3 @ ( n0 @ leq ) )
| ( ( sk1 @ ( pv10 @ ( q @ a_select3 ) ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(simp,[status(thm)],[1410]) ).
thf(25,axiom,
( ( n0 @ succ @ succ @ succ @ succ )
= n4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_4) ).
thf(172,plain,
( ( n0 @ succ @ succ @ succ @ succ )
= n4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(173,plain,
( ( n0 @ succ @ succ @ succ @ succ )
= n4 ),
inference(lifteq,[status(thm)],[172]) ).
thf(24,axiom,
( ( n0 @ succ )
= n1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_1) ).
thf(170,plain,
( ( n0 @ succ )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(171,plain,
( ( n0 @ succ )
= n1 ),
inference(lifteq,[status(thm)],[170]) ).
thf(6176,plain,
( ( n1 @ succ @ succ @ succ )
= n4 ),
inference(rewrite,[status(thm)],[173,171]) ).
thf(84,axiom,
( ( n0 @ succ @ succ @ succ @ succ @ succ )
= n5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_5) ).
thf(571,plain,
( ( n0 @ succ @ succ @ succ @ succ @ succ )
= n5 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(572,plain,
( ( n0 @ succ @ succ @ succ @ succ @ succ )
= n5 ),
inference(lifteq,[status(thm)],[571]) ).
thf(6517,plain,
( ( n1 @ succ @ succ @ succ @ succ )
= n5 ),
inference(rewrite,[status(thm)],[572,171]) ).
thf(6530,plain,
( ( ( n1 @ succ @ succ @ succ )
!= ( n1 @ succ @ succ @ succ ) )
| ( ( n4 @ succ )
= n5 ) ),
inference(paramod_ordered,[status(thm)],[6176,6517]) ).
thf(6531,plain,
( ( n4 @ succ )
= n5 ),
inference(pattern_uni,[status(thm)],[6530:[]]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ succ @ pred )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pred_succ) ).
thf(144,plain,
! [A: $i] :
( ( A @ succ @ pred )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(145,plain,
! [A: $i] :
( ( A @ succ @ pred )
= A ),
inference(cnf,[status(esa)],[144]) ).
thf(146,plain,
! [A: $i] :
( ( A @ succ @ pred )
= A ),
inference(lifteq,[status(thm)],[145]) ).
thf(14781,plain,
! [A: $i] :
( ( ( n4 @ succ )
!= ( A @ succ ) )
| ( ( n5 @ pred )
= A ) ),
inference(paramod_ordered,[status(thm)],[6531,146]) ).
thf(14782,plain,
( ( n5 @ pred )
= n4 ),
inference(pattern_uni,[status(thm)],[14781:[bind(A,$thf( n4 ))]]) ).
thf(73,axiom,
tptp_minus_1 @ ( n5 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_tptp_minus_1) ).
thf(551,plain,
tptp_minus_1 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(16,axiom,
! [A: $i] :
~ ( A @ ( A @ gt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_gt) ).
thf(150,plain,
! [A: $i] :
~ ( A @ ( A @ gt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(151,plain,
~ ? [A: $i] : ( A @ ( A @ gt ) ),
inference(miniscope,[status(thm)],[150]) ).
thf(152,plain,
! [A: $i] :
~ ( A @ ( A @ gt ) ),
inference(cnf,[status(esa)],[151]) ).
thf(3531,plain,
! [A: $i] :
( ( ( tptp_minus_1 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[551,152]) ).
thf(3532,plain,
! [A: $i] :
( ( tptp_minus_1 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[3531]) ).
thf(3533,plain,
! [A: $i] :
( ( tptp_minus_1 != A )
| ( n5 != A ) ),
inference(simp,[status(thm)],[3532]) ).
thf(3534,plain,
tptp_minus_1 != n5,
inference(simp,[status(thm)],[3533]) ).
thf(91,axiom,
( ( n0 @ succ @ succ )
= n2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_2) ).
thf(582,plain,
( ( n0 @ succ @ succ )
= n2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(1303,plain,
! [A: $i] :
( ( ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
!= ( n1 @ ( pv10 @ minus ) @ ( pv12 @ leq ) ) )
| ~ $true
| ( ( A @ ( pv12 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[104,969]) ).
thf(1304,plain,
! [A: $i] :
( ( ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
!= ( n1 @ ( pv10 @ minus ) @ ( pv12 @ leq ) ) )
| ( ( A @ ( pv12 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[1303]) ).
thf(1335,plain,
! [A: $i] :
( ( ( n1 @ ( n5 @ minus ) )
!= ( n1 @ ( pv10 @ minus ) ) )
| ( pv12 != pv12 )
| ( ( A @ ( pv12 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[1304]) ).
thf(1352,plain,
! [A: $i] :
( ( ( n1 @ ( n5 @ minus ) )
!= ( n1 @ ( pv10 @ minus ) ) )
| ( ( A @ ( pv12 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[1335]) ).
thf(2618,plain,
! [A: $i] :
( ( n1 != n1 )
| ( n5 != pv10 )
| ( ( A @ ( pv12 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[1352]) ).
thf(2808,plain,
! [A: $i] :
( ( n5 != pv10 )
| ( ( A @ ( pv12 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[2618]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
= n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_plus_base) ).
thf(192,plain,
! [A: $i] :
( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(193,plain,
! [A: $i] :
( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
= n0 ),
inference(cnf,[status(esa)],[192]) ).
thf(194,plain,
! [A: $i] :
( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
= n0 ),
inference(lifteq,[status(thm)],[193]) ).
thf(105,plain,
! [B: $i,A: $i] :
( ( ( A @ ( pv10 @ ( q @ a_select3 ) ) )
= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( B @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( B @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) )
| ~ ( n1 @ ( pv12 @ minus ) @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(112,plain,
! [B: $i,A: $i] :
( ~ ( n1 @ ( pv12 @ minus ) @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( ( A @ ( pv10 @ ( q @ a_select3 ) ) )
= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( B @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( B @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) ) ),
inference(lifteq,[status(thm)],[105]) ).
thf(97,plain,
( ( ( sk4 @ ( sk3 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
!= n1 )
| ( ( sk1 @ ( pv10 @ ( q @ a_select3 ) ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) )
| ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( n0
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(111,plain,
( ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( ( sk4 @ ( sk3 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
!= n1 )
| ( ( sk1 @ ( pv10 @ ( q @ a_select3 ) ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(lifteq,[status(thm)],[97]) ).
thf(602,plain,
( ~ $true
| ~ $true
| ~ $true
| ~ $true
| ( ( sk4 @ ( sk3 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
!= n1 )
| ( ( sk1 @ ( pv10 @ ( q @ a_select3 ) ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(rewrite,[status(thm)],[111,100,101,104,106]) ).
thf(603,plain,
( ( ( sk4 @ ( sk3 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
!= n1 )
| ( ( sk1 @ ( pv10 @ ( q @ a_select3 ) ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(simp,[status(thm)],[602]) ).
thf(1041,plain,
! [B: $i,A: $i] :
( ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( B @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( B @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( A @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) )
| ( ( sk4 @ ( sk3 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
!= n1 )
| ( ( A @ ( pv10 @ ( q @ a_select3 ) ) )
!= ( sk1 @ ( pv10 @ ( q @ a_select3 ) ) ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[112,603]) ).
thf(1042,plain,
( ( ( sk4 @ ( sk3 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
!= n1 )
| ( ( sk1 @ ( pv10 @ ( q @ a_select3 ) ) )
!= ( sk1 @ ( pv10 @ ( q @ a_select3 ) ) ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( sk1 @ ( n0 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[1041:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(1129,plain,
( ( ( sk4 @ ( sk3 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
!= n1 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( sk1 @ ( n0 @ leq ) ) ),
inference(simp,[status(thm)],[1042]) ).
thf(1202,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
!= ( sk4 @ ( sk3 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) ) )
| ( n1 != n1 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( sk1 @ ( n0 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[118,1129]) ).
thf(1203,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
!= ( sk4 @ ( sk3 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( sk1 @ ( n0 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) ) ),
inference(simp,[status(thm)],[1202]) ).
thf(1204,plain,
( ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( sk1 @ ( n0 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ~ ( sk3 @ ( n0 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[1203:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(1596,plain,
( ( ( sk3 @ ( n0 @ leq ) )
!= ( pv10 @ ( n0 @ leq ) ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( sk1 @ ( n0 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[100,1204]) ).
thf(1597,plain,
( ( ( sk3 @ ( n0 @ leq ) )
!= ( pv10 @ ( n0 @ leq ) ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( sk1 @ ( n0 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[1596]) ).
thf(1616,plain,
( ( sk3 != pv10 )
| ( n0 != n0 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( sk1 @ ( n0 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[1597]) ).
thf(1646,plain,
( ( sk3 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( sk1 @ ( n0 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[1616]) ).
thf(1690,plain,
( ( ( sk1 @ ( n0 @ leq ) )
!= ( pv10 @ ( n0 @ leq ) ) )
| ( sk3 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ $true
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[100,1646]) ).
thf(1691,plain,
( ( ( sk1 @ ( n0 @ leq ) )
!= ( pv10 @ ( n0 @ leq ) ) )
| ( sk3 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[1690]) ).
thf(1698,plain,
( ( sk1 != pv10 )
| ( n0 != n0 )
| ( sk3 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[1691]) ).
thf(1728,plain,
( ( sk1 != pv10 )
| ( sk3 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[1698]) ).
thf(2038,plain,
( ( ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
!= ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) ) )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ $true
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[106,1728]) ).
thf(2039,plain,
( ( ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
!= ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) ) )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[2038]) ).
thf(2057,plain,
( ( ( n1 @ ( n135300 @ minus ) )
!= ( n1 @ ( pv12 @ minus ) ) )
| ( sk1 != pv10 )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[2039]) ).
thf(2087,plain,
( ( ( n1 @ ( n135300 @ minus ) )
!= ( n1 @ ( pv12 @ minus ) ) )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[2057]) ).
thf(7400,plain,
! [A: $i] :
( ( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) )
| ( ( n1 @ ( n135300 @ minus ) )
!= ( n1 @ ( pv12 @ minus ) ) )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ( n0 != n0 )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[194,2087]) ).
thf(7401,plain,
! [A: $i] :
( ( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) )
| ( ( n1 @ ( n135300 @ minus ) )
!= ( n1 @ ( pv12 @ minus ) ) )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[7400]) ).
thf(7431,plain,
! [A: $i] :
( ( A
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt ) )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( n0 != n0 )
| ( n1 != n1 )
| ( n135300 != pv12 )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[7401]) ).
thf(7501,plain,
( ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( n135300 != pv12 )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[7431]) ).
thf(7589,plain,
( ( ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
!= ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( n135300 != pv12 )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,7501]) ).
thf(7590,plain,
( ( ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
!= ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( n135300 != pv12 )
| ( sk1 != pv10 )
| ( sk3 != pv10 ) ),
inference(simp,[status(thm)],[7589]) ).
thf(7596,plain,
( ( ( n1 @ ( n135300 @ minus ) )
!= ( n1 @ ( pv10 @ minus ) ) )
| ( sk3 != pv10 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( n135300 != pv12 )
| ( sk1 != pv10 )
| ( sk3 != pv10 ) ),
inference(simp,[status(thm)],[7590]) ).
thf(7599,plain,
( ( ( n1 @ ( n135300 @ minus ) )
!= ( n1 @ ( pv10 @ minus ) ) )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( n135300 != pv12 )
| ( sk1 != pv10 )
| ( sk3 != pv10 ) ),
inference(simp,[status(thm)],[7596]) ).
thf(15096,plain,
( ( n1 != n1 )
| ( n135300 != pv10 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( n135300 != pv12 )
| ( sk1 != pv10 )
| ( sk3 != pv10 ) ),
inference(simp,[status(thm)],[7599]) ).
thf(15143,plain,
( ( n135300 != pv10 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( n135300 != pv12 )
| ( sk1 != pv10 )
| ( sk3 != pv10 ) ),
inference(simp,[status(thm)],[15096]) ).
thf(42,axiom,
n0 @ ( n135300 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135300_0) ).
thf(339,plain,
n0 @ ( n135300 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(2111,plain,
! [A: $i] :
( ( ( n0 @ ( n135300 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[339,152]) ).
thf(2112,plain,
! [A: $i] :
( ( n0 @ ( n135300 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[2111]) ).
thf(2113,plain,
! [A: $i] :
( ( n0 != A )
| ( n135300 != A ) ),
inference(simp,[status(thm)],[2112]) ).
thf(2114,plain,
n135300 != n0,
inference(simp,[status(thm)],[2113]) ).
thf(583,plain,
( ( n0 @ succ @ succ )
= n2 ),
inference(lifteq,[status(thm)],[582]) ).
thf(5348,plain,
( ( n1 @ succ )
= n2 ),
inference(rewrite,[status(thm)],[583,171]) ).
thf(102,plain,
( ( sk3 @ ( n0 @ leq ) )
| ( sk1 @ ( n0 @ leq ) )
| ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( n0
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(110,plain,
( ( sk3 @ ( n0 @ leq ) )
| ( sk1 @ ( n0 @ leq ) )
| ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(lifteq,[status(thm)],[102]) ).
thf(596,plain,
( ( sk3 @ ( n0 @ leq ) )
| ( sk1 @ ( n0 @ leq ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(rewrite,[status(thm)],[110,100,101,104,106]) ).
thf(597,plain,
( ( sk3 @ ( n0 @ leq ) )
| ( sk1 @ ( n0 @ leq ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(simp,[status(thm)],[596]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ minus ) @ leq ) )
=> ( B @ ( n0 @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_minus) ).
thf(533,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ minus ) @ leq ) )
=> ( B @ ( n0 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(12,axiom,
n2 @ ( n4 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_2) ).
thf(142,plain,
n2 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ geq ) )
<=> ( A @ ( B @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_geq) ).
thf(340,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)],[43]) ).
thf(17,axiom,
! [A: $i] :
( ( n4 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_4_r) ).
thf(153,plain,
! [A: $i] :
( ( n4 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(556,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(cnf,[status(esa)],[555]) ).
thf(1573,plain,
( ( ( sk3 @ ( n0 @ leq ) )
!= ( pv12 @ ( n0 @ leq ) ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( sk1 @ ( n0 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,1204]) ).
thf(1574,plain,
( ( ( sk3 @ ( n0 @ leq ) )
!= ( pv12 @ ( n0 @ leq ) ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( sk1 @ ( n0 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[1573]) ).
thf(1627,plain,
( ( sk3 != pv12 )
| ( n0 != n0 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( sk1 @ ( n0 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[1574]) ).
thf(1651,plain,
( ( sk3 != pv12 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( sk1 @ ( n0 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[1627]) ).
thf(3538,plain,
( ( ( sk1 @ ( n0 @ leq ) )
!= ( pv12 @ ( n0 @ leq ) ) )
| ( sk3 != pv12 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ $true
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[101,1651]) ).
thf(3539,plain,
( ( ( sk1 @ ( n0 @ leq ) )
!= ( pv12 @ ( n0 @ leq ) ) )
| ( sk3 != pv12 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[3538]) ).
thf(3596,plain,
( ( sk1 != pv12 )
| ( n0 != n0 )
| ( sk3 != pv12 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[3539]) ).
thf(3627,plain,
( ( sk1 != pv12 )
| ( sk3 != pv12 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[3596]) ).
thf(7366,plain,
! [A: $i] :
( ( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) )
| ( sk1 != pv12 )
| ( sk3 != pv12 )
| ( n0 != n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[194,3627]) ).
thf(7367,plain,
! [A: $i] :
( ( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) )
| ( sk1 != pv12 )
| ( sk3 != pv12 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[7366]) ).
thf(7491,plain,
! [A: $i] :
( ( A
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt ) )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( n0 != n0 )
| ( sk1 != pv12 )
| ( sk3 != pv12 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[7367]) ).
thf(7561,plain,
( ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv12 )
| ( sk3 != pv12 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[7491]) ).
thf(17865,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv12 )
| ( sk3 != pv12 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[556,7561]) ).
thf(17866,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv12 )
| ( sk3 != pv12 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) ) ),
inference(simp,[status(thm)],[17865]) ).
thf(17887,plain,
! [A: $i] :
( ( A
!= ( n1 @ ( pv10 @ minus ) ) )
| ( A != sk3 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv12 )
| ( sk3 != pv12 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) ) ),
inference(simp,[status(thm)],[17866]) ).
thf(17907,plain,
( ( ( n1 @ ( pv10 @ minus ) )
!= sk3 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv12 )
| ( sk3 != pv12 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) ) ),
inference(simp,[status(thm)],[17887]) ).
thf(70,axiom,
tptp_minus_1 @ ( n1 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_1_tptp_minus_1) ).
thf(535,plain,
tptp_minus_1 @ ( n1 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(3527,plain,
! [A: $i] :
( ( ( tptp_minus_1 @ ( n1 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[535,152]) ).
thf(3528,plain,
! [A: $i] :
( ( tptp_minus_1 @ ( n1 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[3527]) ).
thf(3529,plain,
! [A: $i] :
( ( tptp_minus_1 != A )
| ( n1 != A ) ),
inference(simp,[status(thm)],[3528]) ).
thf(3530,plain,
tptp_minus_1 != n1,
inference(simp,[status(thm)],[3529]) ).
thf(26,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(174,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( B @ ( A @ tptp_update2 ) ) @ a_select2 ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(28,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(178,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)],[28]) ).
thf(179,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ( A @ ( D @ ( B @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D )
| ~ ( B @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( ( A @ ( B @ ( C @ ( D @ sk5 ) ) ) @ ( C @ a_select2 ) )
!= D ) )
& ( ( ( A @ ( D @ ( B @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D )
| ~ ( B @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( B @ ( A @ ( B @ ( C @ ( D @ sk5 ) ) ) @ leq ) ) )
& ( ( ( A @ ( D @ ( B @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D )
| ~ ( B @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( A @ ( B @ ( C @ ( D @ sk5 ) ) ) @ ( n0 @ leq ) ) ) ),
inference(cnf,[status(esa)],[178]) ).
thf(182,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( B @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D )
| ~ ( B @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( ( A @ ( B @ ( C @ ( D @ sk5 ) ) ) @ ( C @ a_select2 ) )
!= D ) ),
inference(cnfConj,[status(thm)],[179]) ).
thf(185,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( ( A @ ( D @ ( B @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D )
| ( ( A @ ( B @ ( C @ ( D @ sk5 ) ) ) @ ( C @ a_select2 ) )
!= D ) ),
inference(lifteq,[status(thm)],[182]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ( A @ ( B @ gt ) )
| ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality) ).
thf(139,plain,
! [A: $i,B: $i] :
( ( A = B )
| ( A @ ( B @ gt ) )
| ( B @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(140,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( A @ ( B @ gt ) )
| ( B @ ( A @ gt ) ) ),
inference(cnf,[status(esa)],[139]) ).
thf(141,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ( B @ ( A @ gt ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[140]) ).
thf(933,plain,
! [B: $i,A: $i] :
( ( ( pv10 @ ( n0 @ leq ) )
!= ( A @ ( n0 @ leq ) ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( A @ leq ) )
| ~ $true
| ( ( B @ ( A @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[100,118]) ).
thf(934,plain,
! [B: $i,A: $i] :
( ( ( pv10 @ ( n0 @ leq ) )
!= ( A @ ( n0 @ leq ) ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( A @ leq ) )
| ( ( B @ ( A @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[933]) ).
thf(935,plain,
! [A: $i] :
( ~ ( n1 @ ( pv10 @ minus ) @ ( pv10 @ leq ) )
| ( ( A @ ( pv10 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(pattern_uni,[status(thm)],[934:[bind(A,$thf( pv10 ))]]) ).
thf(953,plain,
! [A: $i] :
( ~ ( n1 @ ( pv10 @ minus ) @ ( pv10 @ leq ) )
| ( ( A @ ( pv10 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[935]) ).
thf(985,plain,
! [A: $i] :
( ( ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
!= ( n1 @ ( pv10 @ minus ) @ ( pv10 @ leq ) ) )
| ~ $true
| ( ( A @ ( pv10 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[106,953]) ).
thf(986,plain,
! [A: $i] :
( ( ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
!= ( n1 @ ( pv10 @ minus ) @ ( pv10 @ leq ) ) )
| ( ( A @ ( pv10 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[985]) ).
thf(997,plain,
! [A: $i] :
( ( ( n1 @ ( n135300 @ minus ) )
!= ( n1 @ ( pv10 @ minus ) ) )
| ( pv10 != pv10 )
| ( ( A @ ( pv10 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[986]) ).
thf(1009,plain,
! [A: $i] :
( ( ( n1 @ ( n135300 @ minus ) )
!= ( n1 @ ( pv10 @ minus ) ) )
| ( ( A @ ( pv10 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[997]) ).
thf(1822,plain,
! [A: $i] :
( ( n1 != n1 )
| ( n135300 != pv10 )
| ( ( A @ ( pv10 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[1009]) ).
thf(1915,plain,
! [A: $i] :
( ( n135300 != pv10 )
| ( ( A @ ( pv10 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[1822]) ).
thf(7331,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
!= ( B @ ( pv10 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) ) )
| ( n135300 != pv10 )
| ( n1 = n0 ) ),
inference(paramod_ordered,[status(thm)],[194,1915]) ).
thf(7471,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ ( pv10 @ ( q @ a_select3 ) ) ) )
| ( ( n1 @ ( n5 @ minus ) )
!= tptp_minus_1 )
| ( n0 != n0 )
| ( n135300 != pv10 )
| ( n1 = n0 ) ),
inference(simp,[status(thm)],[7331]) ).
thf(7541,plain,
( ( ( n1 @ ( n5 @ minus ) )
!= tptp_minus_1 )
| ( n135300 != pv10 )
| ( n1 = n0 ) ),
inference(simp,[status(thm)],[7471]) ).
thf(83,axiom,
n0 @ ( n1 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_1_0) ).
thf(570,plain,
n0 @ ( n1 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(4282,plain,
! [A: $i] :
( ( ( n0 @ ( n1 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[570,152]) ).
thf(4283,plain,
! [A: $i] :
( ( n0 @ ( n1 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[4282]) ).
thf(4284,plain,
! [A: $i] :
( ( n0 != A )
| ( n1 != A ) ),
inference(simp,[status(thm)],[4283]) ).
thf(4285,plain,
n1 != n0,
inference(simp,[status(thm)],[4284]) ).
thf(7785,plain,
( ( ( n1 @ ( n5 @ minus ) )
!= tptp_minus_1 )
| ( n135300 != pv10 ) ),
inference(simplifyReflect,[status(thm)],[7541,4285]) ).
thf(10384,plain,
! [B: $i,A: $i] :
( ( A != n135300 )
| ( ( n1 @ ( n5 @ minus ) )
!= tptp_minus_1 )
| ( B != pv10 )
| ( A @ ( B @ gt ) )
| ( B @ ( A @ gt ) ) ),
inference(paramod_ordered,[status(thm)],[141,7785]) ).
thf(10385,plain,
! [A: $i] :
( ( ( n1 @ ( n5 @ minus ) )
!= tptp_minus_1 )
| ( A != pv10 )
| ( n135300 @ ( A @ gt ) )
| ( A @ ( n135300 @ gt ) ) ),
inference(pattern_uni,[status(thm)],[10384:[bind(A,$thf( n135300 ))]]) ).
thf(13970,plain,
( ( ( n1 @ ( n5 @ minus ) )
!= tptp_minus_1 )
| ( n135300 @ ( pv10 @ gt ) )
| ( pv10 @ ( n135300 @ gt ) ) ),
inference(simp,[status(thm)],[10385]) ).
thf(7386,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
!= ( B @ ( pv12 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) ) )
| ( ( n1 @ ( n5 @ minus ) )
!= ( n1 @ ( pv10 @ minus ) ) )
| ( n1 = n0 ) ),
inference(paramod_ordered,[status(thm)],[194,1352]) ).
thf(7428,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ ( pv12 @ ( q @ a_select3 ) ) ) )
| ( ( n1 @ ( n5 @ minus ) )
!= tptp_minus_1 )
| ( n0 != n0 )
| ( n1 != n1 )
| ( n5 != pv10 )
| ( n1 = n0 ) ),
inference(simp,[status(thm)],[7386]) ).
thf(7498,plain,
( ( ( n1 @ ( n5 @ minus ) )
!= tptp_minus_1 )
| ( n5 != pv10 )
| ( n1 = n0 ) ),
inference(simp,[status(thm)],[7428]) ).
thf(7784,plain,
( ( ( n1 @ ( n5 @ minus ) )
!= tptp_minus_1 )
| ( n5 != pv10 ) ),
inference(simplifyReflect,[status(thm)],[7498,4285]) ).
thf(11528,plain,
! [B: $i,A: $i] :
( ( A != n5 )
| ( ( n1 @ ( n5 @ minus ) )
!= tptp_minus_1 )
| ( B != pv10 )
| ( A @ ( B @ gt ) )
| ( B @ ( A @ gt ) ) ),
inference(paramod_ordered,[status(thm)],[141,7784]) ).
thf(11529,plain,
! [A: $i] :
( ( ( n1 @ ( n5 @ minus ) )
!= tptp_minus_1 )
| ( A != pv10 )
| ( n5 @ ( A @ gt ) )
| ( A @ ( n5 @ gt ) ) ),
inference(pattern_uni,[status(thm)],[11528:[bind(A,$thf( n5 ))]]) ).
thf(14396,plain,
( ( ( n1 @ ( n5 @ minus ) )
!= tptp_minus_1 )
| ( n5 @ ( pv10 @ gt ) )
| ( pv10 @ ( n5 @ gt ) ) ),
inference(simp,[status(thm)],[11529]) ).
thf(1671,plain,
( ( ( sk1 @ ( n0 @ leq ) )
!= ( pv12 @ ( n0 @ leq ) ) )
| ( sk3 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ $true
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[101,1646]) ).
thf(1672,plain,
( ( ( sk1 @ ( n0 @ leq ) )
!= ( pv12 @ ( n0 @ leq ) ) )
| ( sk3 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[1671]) ).
thf(1703,plain,
( ( sk1 != pv12 )
| ( n0 != n0 )
| ( sk3 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[1672]) ).
thf(1732,plain,
( ( sk1 != pv12 )
| ( sk3 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[1703]) ).
thf(7352,plain,
! [A: $i] :
( ( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) )
| ( sk1 != pv12 )
| ( sk3 != pv10 )
| ( n0 != n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[194,1732]) ).
thf(7353,plain,
! [A: $i] :
( ( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) )
| ( sk1 != pv12 )
| ( sk3 != pv10 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[7352]) ).
thf(7405,plain,
! [A: $i] :
( ( A
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt ) )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( n0 != n0 )
| ( sk1 != pv12 )
| ( sk3 != pv10 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[7353]) ).
thf(7567,plain,
( ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv12 )
| ( sk3 != pv10 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[7405]) ).
thf(18895,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) ) )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv12 )
| ( sk3 != pv10 )
| ~ $true
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[556,7567]) ).
thf(18896,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) ) )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv12 )
| ( sk3 != pv10 )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[18895]) ).
thf(18911,plain,
! [A: $i] :
( ( A
!= ( n1 @ ( pv12 @ minus ) ) )
| ( A != sk1 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv12 )
| ( sk3 != pv10 )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[18896]) ).
thf(18933,plain,
( ( ( n1 @ ( pv12 @ minus ) )
!= sk1 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv12 )
| ( sk3 != pv10 )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[18911]) ).
thf(181,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( B @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D )
| ~ ( B @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( B @ ( A @ ( B @ ( C @ ( D @ sk5 ) ) ) @ leq ) ) ),
inference(cnfConj,[status(thm)],[179]) ).
thf(184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( B @ ( A @ ( B @ ( C @ ( D @ sk5 ) ) ) @ leq ) )
| ( ( A @ ( D @ ( B @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D ) ),
inference(lifteq,[status(thm)],[181]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ pred @ succ )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_pred) ).
thf(125,plain,
! [A: $i] :
( ( A @ pred @ succ )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(55,axiom,
n0 @ ( n3 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_0) ).
thf(424,plain,
n0 @ ( n3 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(2894,plain,
! [A: $i] :
( ( ( n0 @ ( n3 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[424,152]) ).
thf(2895,plain,
! [A: $i] :
( ( n0 @ ( n3 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[2894]) ).
thf(2896,plain,
! [A: $i] :
( ( n0 != A )
| ( n3 != A ) ),
inference(simp,[status(thm)],[2895]) ).
thf(2897,plain,
n3 != n0,
inference(simp,[status(thm)],[2896]) ).
thf(9,axiom,
n2 @ ( n3 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_2) ).
thf(137,plain,
n2 @ ( n3 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15475,plain,
! [B: $i,A: $i] :
( ( ( n2 @ ( n3 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[137,161]) ).
thf(15476,plain,
! [B: $i,A: $i] :
( ( ( n2 @ ( n3 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15475]) ).
thf(15477,plain,
n3 @ ( n2 @ lt ),
inference(pattern_uni,[status(thm)],[15476:[bind(A,$thf( n2 )),bind(B,$thf( n3 ))]]) ).
thf(54,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(421,plain,
! [A: $i] :
( tptp_float_0_0
= ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(36,axiom,
n3 @ ( n5 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_3) ).
thf(231,plain,
n3 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(2021,plain,
! [A: $i] :
( ( ( n3 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[231,152]) ).
thf(2022,plain,
! [A: $i] :
( ( n3 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[2021]) ).
thf(2023,plain,
! [A: $i] :
( ( n3 != A )
| ( n5 != A ) ),
inference(simp,[status(thm)],[2022]) ).
thf(2024,plain,
n3 != n5,
inference(simp,[status(thm)],[2023]) ).
thf(15460,plain,
! [B: $i,A: $i] :
( ( ( n2 @ ( n4 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[142,161]) ).
thf(15461,plain,
! [B: $i,A: $i] :
( ( ( n2 @ ( n4 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15460]) ).
thf(15462,plain,
n4 @ ( n2 @ lt ),
inference(pattern_uni,[status(thm)],[15461:[bind(A,$thf( n2 )),bind(B,$thf( n4 ))]]) ).
thf(20,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(163,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ gt ) )
& ( B @ ( A @ gt ) ) )
=> ( C @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(164,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ gt ) )
| ~ ( C @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
inference(cnf,[status(esa)],[163]) ).
thf(65,axiom,
( ( n0 @ succ @ succ @ succ )
= n3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_3) ).
thf(514,plain,
( ( n0 @ succ @ succ @ succ )
= n3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(515,plain,
( ( n0 @ succ @ succ @ succ )
= n3 ),
inference(lifteq,[status(thm)],[514]) ).
thf(5588,plain,
( ( n1 @ succ @ succ )
= n3 ),
inference(rewrite,[status(thm)],[515,171]) ).
thf(6187,plain,
( ( ( n1 @ succ @ succ )
!= ( n1 @ succ @ succ ) )
| ( ( n3 @ succ )
= n4 ) ),
inference(paramod_ordered,[status(thm)],[5588,6176]) ).
thf(6188,plain,
( ( n3 @ succ )
= n4 ),
inference(pattern_uni,[status(thm)],[6187:[]]) ).
thf(14779,plain,
! [A: $i] :
( ( ( n3 @ succ )
!= ( A @ succ ) )
| ( ( n4 @ pred )
= A ) ),
inference(paramod_ordered,[status(thm)],[6188,146]) ).
thf(14780,plain,
( ( n4 @ pred )
= n3 ),
inference(pattern_uni,[status(thm)],[14779:[bind(A,$thf( n3 ))]]) ).
thf(6,axiom,
tptp_minus_1 @ ( n3 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_tptp_minus_1) ).
thf(130,plain,
tptp_minus_1 @ ( n3 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(586,plain,
! [A: $i] :
( ( ( tptp_minus_1 @ ( n3 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[130,152]) ).
thf(587,plain,
! [A: $i] :
( ( tptp_minus_1 @ ( n3 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[586]) ).
thf(589,plain,
! [A: $i] :
( ( tptp_minus_1 != A )
| ( n3 != A ) ),
inference(simp,[status(thm)],[587]) ).
thf(591,plain,
tptp_minus_1 != n3,
inference(simp,[status(thm)],[589]) ).
thf(6519,plain,
( ( ( n1 @ succ )
!= ( n1 @ succ ) )
| ( ( n2 @ succ @ succ @ succ )
= n5 ) ),
inference(paramod_ordered,[status(thm)],[5348,6517]) ).
thf(6520,plain,
( ( n2 @ succ @ succ @ succ )
= n5 ),
inference(pattern_uni,[status(thm)],[6519:[]]) ).
thf(5591,plain,
( ( ( n1 @ succ )
!= ( n1 @ succ ) )
| ( ( n2 @ succ )
= n3 ) ),
inference(paramod_ordered,[status(thm)],[5348,5588]) ).
thf(5592,plain,
( ( n2 @ succ )
= n3 ),
inference(pattern_uni,[status(thm)],[5591:[]]) ).
thf(6895,plain,
( ( n3 @ succ @ succ )
= n5 ),
inference(rewrite,[status(thm)],[6520,5592]) ).
thf(50,axiom,
n1 @ ( n135300 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135300_1) ).
thf(362,plain,
n1 @ ( n135300 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(2890,plain,
! [A: $i] :
( ( ( n1 @ ( n135300 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[362,152]) ).
thf(2891,plain,
! [A: $i] :
( ( n1 @ ( n135300 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[2890]) ).
thf(2892,plain,
! [A: $i] :
( ( n1 != A )
| ( n135300 != A ) ),
inference(simp,[status(thm)],[2891]) ).
thf(2893,plain,
n1 != n135300,
inference(simp,[status(thm)],[2892]) ).
thf(1310,plain,
! [A: $i] :
( ( ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
!= ( n1 @ ( pv10 @ minus ) @ ( pv12 @ leq ) ) )
| ~ $true
| ( ( A @ ( pv12 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[106,969]) ).
thf(1311,plain,
! [A: $i] :
( ( ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
!= ( n1 @ ( pv10 @ minus ) @ ( pv12 @ leq ) ) )
| ( ( A @ ( pv12 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[1310]) ).
thf(1328,plain,
! [A: $i] :
( ( ( n1 @ ( n135300 @ minus ) )
!= ( n1 @ ( pv10 @ minus ) ) )
| ( pv12 != pv10 )
| ( ( A @ ( pv12 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[1311]) ).
thf(5802,plain,
! [A: $i] :
( ( n1 != n1 )
| ( n135300 != pv10 )
| ( pv12 != pv10 )
| ( ( A @ ( pv12 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[1328]) ).
thf(6135,plain,
! [A: $i] :
( ( n135300 != pv10 )
| ( pv12 != pv10 )
| ( ( A @ ( pv12 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[5802]) ).
thf(57,axiom,
n2 @ ( n5 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_2) ).
thf(428,plain,
n2 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(15466,plain,
! [B: $i,A: $i] :
( ( ( n2 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[428,161]) ).
thf(15467,plain,
! [B: $i,A: $i] :
( ( ( n2 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15466]) ).
thf(15468,plain,
n5 @ ( n2 @ lt ),
inference(pattern_uni,[status(thm)],[15467:[bind(A,$thf( n2 )),bind(B,$thf( n5 ))]]) ).
thf(17867,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) ) )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv12 )
| ( sk3 != pv12 )
| ~ $true
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[556,7561]) ).
thf(17868,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) ) )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv12 )
| ( sk3 != pv12 )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[17867]) ).
thf(17897,plain,
! [A: $i] :
( ( A
!= ( n1 @ ( pv12 @ minus ) ) )
| ( A != sk1 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv12 )
| ( sk3 != pv12 )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[17868]) ).
thf(17916,plain,
( ( ( n1 @ ( pv12 @ minus ) )
!= sk1 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv12 )
| ( sk3 != pv12 )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[17897]) ).
thf(15520,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n1 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[535,161]) ).
thf(15521,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n1 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15520]) ).
thf(15522,plain,
n1 @ ( tptp_minus_1 @ lt ),
inference(pattern_uni,[status(thm)],[15521:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n1 ))]]) ).
thf(126,plain,
! [A: $i] :
( ( A @ pred @ succ )
= A ),
inference(cnf,[status(esa)],[125]) ).
thf(127,plain,
! [A: $i] :
( ( A @ pred @ succ )
= A ),
inference(lifteq,[status(thm)],[126]) ).
thf(5,axiom,
! [A: $i] : ( A @ ( A @ succ @ gt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_succ) ).
thf(128,plain,
! [A: $i] : ( A @ ( A @ succ @ gt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(129,plain,
! [A: $i] : ( A @ ( A @ succ @ gt ) ),
inference(cnf,[status(esa)],[128]) ).
thf(6834,plain,
! [B: $i,A: $i] :
( ( ( A @ pred @ succ )
!= ( B @ succ ) )
| ( B @ ( A @ gt ) ) ),
inference(paramod_ordered,[status(thm)],[127,129]) ).
thf(6835,plain,
! [A: $i] : ( A @ pred @ ( A @ gt ) ),
inference(pattern_uni,[status(thm)],[6834:[bind(A,$thf( C )),bind(B,$thf( C @ pred ))]]) ).
thf(6841,plain,
! [A: $i] : ( A @ pred @ ( A @ gt ) ),
inference(simp,[status(thm)],[6835]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ ( n2 @ plus ) )
= ( A @ succ @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_2_l) ).
thf(147,plain,
! [A: $i] :
( ( A @ ( n2 @ plus ) )
= ( A @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1600,plain,
( ( ( sk1 @ ( n0 @ leq ) )
!= ( pv10 @ ( n0 @ leq ) ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ $true
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ~ ( sk3 @ ( n0 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[100,1204]) ).
thf(1601,plain,
( ( ( sk1 @ ( n0 @ leq ) )
!= ( pv10 @ ( n0 @ leq ) ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ~ ( sk3 @ ( n0 @ leq ) ) ),
inference(simp,[status(thm)],[1600]) ).
thf(1618,plain,
( ( sk1 != pv10 )
| ( n0 != n0 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ~ ( sk3 @ ( n0 @ leq ) ) ),
inference(simp,[status(thm)],[1601]) ).
thf(1647,plain,
( ( sk1 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ~ ( sk3 @ ( n0 @ leq ) ) ),
inference(simp,[status(thm)],[1618]) ).
thf(2899,plain,
( ( ( sk3 @ ( n0 @ leq ) )
!= ( pv12 @ ( n0 @ leq ) ) )
| ( sk1 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,1647]) ).
thf(2900,plain,
( ( ( sk3 @ ( n0 @ leq ) )
!= ( pv12 @ ( n0 @ leq ) ) )
| ( sk1 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[2899]) ).
thf(2946,plain,
( ( sk3 != pv12 )
| ( n0 != n0 )
| ( sk1 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[2900]) ).
thf(2979,plain,
( ( sk3 != pv12 )
| ( sk1 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[2946]) ).
thf(977,plain,
! [A: $i] :
( ( ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
!= ( n1 @ ( pv10 @ minus ) @ ( pv10 @ leq ) ) )
| ~ $true
| ( ( A @ ( pv10 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[104,953]) ).
thf(978,plain,
! [A: $i] :
( ( ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
!= ( n1 @ ( pv10 @ minus ) @ ( pv10 @ leq ) ) )
| ( ( A @ ( pv10 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[977]) ).
thf(998,plain,
! [A: $i] :
( ( ( n1 @ ( n5 @ minus ) )
!= ( n1 @ ( pv10 @ minus ) ) )
| ( pv12 != pv10 )
| ( ( A @ ( pv10 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[978]) ).
thf(5037,plain,
! [A: $i] :
( ( n1 != n1 )
| ( n5 != pv10 )
| ( pv12 != pv10 )
| ( ( A @ ( pv10 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[998]) ).
thf(5343,plain,
! [A: $i] :
( ( n5 != pv10 )
| ( pv12 != pv10 )
| ( ( A @ ( pv10 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[5037]) ).
thf(7,axiom,
! [A: $i] :
( ( n2 @ ( A @ plus ) )
= ( A @ succ @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_2_r) ).
thf(131,plain,
! [A: $i] :
( ( n2 @ ( A @ plus ) )
= ( A @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(132,plain,
! [A: $i] :
( ( n2 @ ( A @ plus ) )
= ( A @ succ @ succ ) ),
inference(cnf,[status(esa)],[131]) ).
thf(133,plain,
! [A: $i] :
( ( n2 @ ( A @ plus ) )
= ( A @ succ @ succ ) ),
inference(lifteq,[status(thm)],[132]) ).
thf(40,axiom,
! [A: $i] :
( ( ( n0 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( A = n0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_0) ).
thf(248,plain,
! [A: $i] :
( ( ( n0 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( A = n0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(18893,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv12 )
| ( sk3 != pv10 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[556,7567]) ).
thf(18894,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv12 )
| ( sk3 != pv10 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) ) ),
inference(simp,[status(thm)],[18893]) ).
thf(18921,plain,
! [A: $i] :
( ( A
!= ( n1 @ ( pv10 @ minus ) ) )
| ( A != sk3 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv12 )
| ( sk3 != pv10 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) ) ),
inference(simp,[status(thm)],[18894]) ).
thf(18941,plain,
( ( ( n1 @ ( pv10 @ minus ) )
!= sk3 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv12 )
| ( sk3 != pv10 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) ) ),
inference(simp,[status(thm)],[18921]) ).
thf(1308,plain,
! [A: $i] :
( ( ( n1 @ ( pv10 @ minus ) @ ( pv12 @ leq ) )
!= ( pv12 @ ( n0 @ leq ) ) )
| ~ $true
| ( ( A @ ( pv12 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[101,969]) ).
thf(1309,plain,
! [A: $i] :
( ( ( n1 @ ( pv10 @ minus ) @ ( pv12 @ leq ) )
!= ( pv12 @ ( n0 @ leq ) ) )
| ( ( A @ ( pv12 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[1308]) ).
thf(1338,plain,
! [A: $i] :
( ( ( n1 @ ( pv10 @ minus ) )
!= pv12 )
| ( pv12 != n0 )
| ( ( A @ ( pv12 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[1309]) ).
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_msub ) @ a_select3 ) ) )
= ( D @ ( E @ ( B @ ( A @ tptp_msub ) @ a_select3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',matrix_symm_sub) ).
thf(366,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( B @ a_select3 ) ) )
= ( D @ ( E @ ( B @ a_select3 ) ) ) ) )
& ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( A @ a_select3 ) ) )
= ( D @ ( E @ ( A @ a_select3 ) ) ) ) ) )
=> ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( B @ ( A @ tptp_msub ) @ a_select3 ) ) )
= ( D @ ( E @ ( B @ ( A @ tptp_msub ) @ a_select3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(2053,plain,
( ( ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
!= ( pv10 @ ( n0 @ leq ) ) )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[100,1728]) ).
thf(2054,plain,
( ( ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
!= ( pv10 @ ( n0 @ leq ) ) )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) ) ),
inference(simp,[status(thm)],[2053]) ).
thf(2083,plain,
( ( ( n1 @ ( pv10 @ minus ) )
!= pv10 )
| ( sk3 != n0 )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) ) ),
inference(simp,[status(thm)],[2054]) ).
thf(2033,plain,
( ( ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
!= ( pv12 @ ( n0 @ leq ) ) )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ $true
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[101,1728]) ).
thf(2034,plain,
( ( ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
!= ( pv12 @ ( n0 @ leq ) ) )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[2033]) ).
thf(2061,plain,
( ( ( n1 @ ( pv12 @ minus ) )
!= pv12 )
| ( sk1 != n0 )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[2034]) ).
thf(23,axiom,
n2 @ ( n135300 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135300_2) ).
thf(169,plain,
n2 @ ( n135300 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(15484,plain,
! [B: $i,A: $i] :
( ( ( n2 @ ( n135300 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[169,161]) ).
thf(15485,plain,
! [B: $i,A: $i] :
( ( ( n2 @ ( n135300 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15484]) ).
thf(15486,plain,
n135300 @ ( n2 @ lt ),
inference(pattern_uni,[status(thm)],[15485:[bind(A,$thf( n2 )),bind(B,$thf( n135300 ))]]) ).
thf(45,axiom,
tptp_minus_1 @ ( n135300 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135300_tptp_minus_1) ).
thf(349,plain,
tptp_minus_1 @ ( n135300 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(79,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(561,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)],[79]) ).
thf(89,axiom,
n1 @ ( n5 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_1) ).
thf(580,plain,
n1 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(15529,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[580,161]) ).
thf(15530,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15529]) ).
thf(15531,plain,
n5 @ ( n1 @ lt ),
inference(pattern_uni,[status(thm)],[15530:[bind(A,$thf( n1 )),bind(B,$thf( n5 ))]]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ ( n4 @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_4_l) ).
thf(165,plain,
! [A: $i] :
( ( A @ ( n4 @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(14771,plain,
! [A: $i] :
( ( ( n2 @ succ )
!= ( A @ succ ) )
| ( ( n3 @ pred )
= A ) ),
inference(paramod_ordered,[status(thm)],[5592,146]) ).
thf(14772,plain,
( ( n3 @ pred )
= n2 ),
inference(pattern_uni,[status(thm)],[14771:[bind(A,$thf( n2 ))]]) ).
thf(58,axiom,
! [A: $i] :
( ( n5 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_5_r) ).
thf(429,plain,
! [A: $i] :
( ( n5 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(81,axiom,
n4 @ ( n5 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_4) ).
thf(566,plain,
n4 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(88,axiom,
n5 @ ( n135300 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135300_5) ).
thf(579,plain,
n5 @ ( n135300 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(4722,plain,
! [A: $i] :
( ( ( n5 @ ( n135300 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[579,152]) ).
thf(4723,plain,
! [A: $i] :
( ( n5 @ ( n135300 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[4722]) ).
thf(4724,plain,
! [A: $i] :
( ( n5 != A )
| ( n135300 != A ) ),
inference(simp,[status(thm)],[4723]) ).
thf(4725,plain,
n5 != n135300,
inference(simp,[status(thm)],[4724]) ).
thf(7624,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( n135300 != pv12 )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[556,7501]) ).
thf(7625,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( n135300 != pv12 )
| ( sk1 != pv10 )
| ( sk3 != pv10 ) ),
inference(simp,[status(thm)],[7624]) ).
thf(7720,plain,
! [A: $i] :
( ( A
!= ( n1 @ ( pv10 @ minus ) ) )
| ( A != sk3 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( n135300 != pv12 )
| ( sk1 != pv10 )
| ( sk3 != pv10 ) ),
inference(simp,[status(thm)],[7625]) ).
thf(7762,plain,
( ( ( n1 @ ( pv10 @ minus ) )
!= sk3 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( n135300 != pv12 )
| ( sk1 != pv10 )
| ( sk3 != pv10 ) ),
inference(simp,[status(thm)],[7720]) ).
thf(936,plain,
! [B: $i,A: $i] :
( ( ( pv10 @ ( n0 @ leq ) )
!= ( n1 @ ( pv10 @ minus ) @ ( A @ leq ) ) )
| ~ $true
| ~ ( A @ ( n0 @ leq ) )
| ( ( B @ ( A @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[100,118]) ).
thf(937,plain,
! [B: $i,A: $i] :
( ( ( pv10 @ ( n0 @ leq ) )
!= ( n1 @ ( pv10 @ minus ) @ ( A @ leq ) ) )
| ~ ( A @ ( n0 @ leq ) )
| ( ( B @ ( A @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[936]) ).
thf(949,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( pv10 @ minus ) )
!= pv10 )
| ( n0 != A )
| ~ ( A @ ( n0 @ leq ) )
| ( ( B @ ( A @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[937]) ).
thf(965,plain,
! [A: $i] :
( ( ( n1 @ ( pv10 @ minus ) )
!= pv10 )
| ~ ( n0 @ ( n0 @ leq ) )
| ( ( A @ ( n0 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[949]) ).
thf(3315,plain,
! [A: $i] :
( ( ( pv10 @ ( n0 @ leq ) )
!= ( n0 @ ( n0 @ leq ) ) )
| ( ( n1 @ ( pv10 @ minus ) )
!= pv10 )
| ~ $true
| ( ( A @ ( n0 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[100,965]) ).
thf(3316,plain,
! [A: $i] :
( ( ( pv10 @ ( n0 @ leq ) )
!= ( n0 @ ( n0 @ leq ) ) )
| ( ( n1 @ ( pv10 @ minus ) )
!= pv10 )
| ( ( A @ ( n0 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[3315]) ).
thf(3330,plain,
! [A: $i] :
( ( pv10 != n0 )
| ( n0 != n0 )
| ( ( n1 @ ( pv10 @ minus ) )
!= pv10 )
| ( ( A @ ( n0 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[3316]) ).
thf(3349,plain,
! [A: $i] :
( ( pv10 != n0 )
| ( ( n1 @ ( pv10 @ minus ) )
!= pv10 )
| ( ( A @ ( n0 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[3330]) ).
thf(90,axiom,
n4 @ ( n135300 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135300_4) ).
thf(581,plain,
n4 @ ( n135300 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(15544,plain,
! [B: $i,A: $i] :
( ( ( n4 @ ( n135300 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[581,161]) ).
thf(15545,plain,
! [B: $i,A: $i] :
( ( ( n4 @ ( n135300 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15544]) ).
thf(15546,plain,
n135300 @ ( n4 @ lt ),
inference(pattern_uni,[status(thm)],[15545:[bind(A,$thf( n4 )),bind(B,$thf( n135300 ))]]) ).
thf(15469,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n135300 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[349,161]) ).
thf(15470,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n135300 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15469]) ).
thf(15471,plain,
n135300 @ ( tptp_minus_1 @ lt ),
inference(pattern_uni,[status(thm)],[15470:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n135300 ))]]) ).
thf(62,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(493,plain,
! [A: $i,B: $i] :
( ( A @ ( n0 @ leq ) )
=> ( A @ ( A @ ( B @ uniform_int_rnd ) @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(1577,plain,
( ( ( sk1 @ ( n0 @ leq ) )
!= ( pv12 @ ( n0 @ leq ) ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ $true
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ~ ( sk3 @ ( n0 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[101,1204]) ).
thf(1578,plain,
( ( ( sk1 @ ( n0 @ leq ) )
!= ( pv12 @ ( n0 @ leq ) ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ~ ( sk3 @ ( n0 @ leq ) ) ),
inference(simp,[status(thm)],[1577]) ).
thf(1634,plain,
( ( sk1 != pv12 )
| ( n0 != n0 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ~ ( sk3 @ ( n0 @ leq ) ) ),
inference(simp,[status(thm)],[1578]) ).
thf(1656,plain,
( ( sk1 != pv12 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ~ ( sk3 @ ( n0 @ leq ) ) ),
inference(simp,[status(thm)],[1634]) ).
thf(1288,plain,
! [A: $i] :
( ( ( n2 @ ( n135300 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[169,152]) ).
thf(1289,plain,
! [A: $i] :
( ( n2 @ ( n135300 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[1288]) ).
thf(1290,plain,
! [A: $i] :
( ( n2 != A )
| ( n135300 != A ) ),
inference(simp,[status(thm)],[1289]) ).
thf(1291,plain,
n2 != n135300,
inference(simp,[status(thm)],[1290]) ).
thf(15496,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n135300 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[339,161]) ).
thf(15497,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n135300 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15496]) ).
thf(15498,plain,
n135300 @ ( n0 @ lt ),
inference(pattern_uni,[status(thm)],[15497:[bind(A,$thf( n0 )),bind(B,$thf( n135300 ))]]) ).
thf(46,axiom,
n0 @ ( n5 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_0) ).
thf(350,plain,
n0 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(15511,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[350,161]) ).
thf(15512,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15511]) ).
thf(15513,plain,
n5 @ ( n0 @ lt ),
inference(pattern_uni,[status(thm)],[15512:[bind(A,$thf( n0 )),bind(B,$thf( n5 ))]]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( B @ pred @ ( A @ leq ) )
<=> ( A @ ( B @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt_pred) ).
thf(356,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ gt ) )
=> ( B @ pred @ ( A @ leq ) ) )
& ( ( B @ pred @ ( A @ leq ) )
=> ( A @ ( B @ gt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(15457,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n2 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[138,161]) ).
thf(15458,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n2 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15457]) ).
thf(15459,plain,
n2 @ ( tptp_minus_1 @ lt ),
inference(pattern_uni,[status(thm)],[15458:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n2 ))]]) ).
thf(108,plain,
( ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ( ( sk1 @ ( pv10 @ ( q @ a_select3 ) ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) )
| ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( n0
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(120,plain,
( ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( ( sk1 @ ( pv10 @ ( q @ a_select3 ) ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(lifteq,[status(thm)],[108]) ).
thf(3940,plain,
( ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ( ( sk1 @ ( pv10 @ ( q @ a_select3 ) ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(rewrite,[status(thm)],[120,100,101,104,106]) ).
thf(3941,plain,
( ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ( ( sk1 @ ( pv10 @ ( q @ a_select3 ) ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk2 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( sk1 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ divide ) ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(simp,[status(thm)],[3940]) ).
thf(18037,plain,
! [B: $i,A: $i] :
( ( ( pv10 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true
| ( ( n1 @ ( n5 @ minus ) )
!= tptp_minus_1 )
| ( n5 @ ( pv10 @ gt ) ) ),
inference(paramod_ordered,[status(thm)],[14396,161]) ).
thf(18038,plain,
! [B: $i,A: $i] :
( ( ( pv10 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ( ( n1 @ ( n5 @ minus ) )
!= tptp_minus_1 )
| ( n5 @ ( pv10 @ gt ) ) ),
inference(simp,[status(thm)],[18037]) ).
thf(18039,plain,
( ( n5 @ ( pv10 @ lt ) )
| ( ( n1 @ ( n5 @ minus ) )
!= tptp_minus_1 )
| ( n5 @ ( pv10 @ gt ) ) ),
inference(pattern_uni,[status(thm)],[18038:[bind(A,$thf( pv10 )),bind(B,$thf( n5 ))]]) ).
thf(7350,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
!= ( B @ ( pv10 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( pv10 @ leq ) )
| ( n1 = n0 ) ),
inference(paramod_ordered,[status(thm)],[194,953]) ).
thf(7450,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ ( pv10 @ ( q @ a_select3 ) ) ) )
| ( ( n1 @ ( n5 @ minus ) )
!= tptp_minus_1 )
| ( n0 != n0 )
| ~ ( n1 @ ( pv10 @ minus ) @ ( pv10 @ leq ) )
| ( n1 = n0 ) ),
inference(simp,[status(thm)],[7350]) ).
thf(7520,plain,
( ( ( n1 @ ( n5 @ minus ) )
!= tptp_minus_1 )
| ~ ( n1 @ ( pv10 @ minus ) @ ( pv10 @ leq ) )
| ( n1 = n0 ) ),
inference(simp,[status(thm)],[7450]) ).
thf(19783,plain,
( ( ( n1 @ ( n5 @ minus ) )
!= tptp_minus_1 )
| ~ ( n1 @ ( pv10 @ minus ) @ ( pv10 @ leq ) ) ),
inference(simplifyReflect,[status(thm)],[7520,4285]) ).
thf(154,plain,
! [A: $i] :
( ( n4 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
inference(cnf,[status(esa)],[153]) ).
thf(155,plain,
! [A: $i] :
( ( n4 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
inference(lifteq,[status(thm)],[154]) ).
thf(148,plain,
! [A: $i] :
( ( A @ ( n2 @ plus ) )
= ( A @ succ @ succ ) ),
inference(cnf,[status(esa)],[147]) ).
thf(149,plain,
! [A: $i] :
( ( A @ ( n2 @ plus ) )
= ( A @ succ @ succ ) ),
inference(lifteq,[status(thm)],[148]) ).
thf(15206,plain,
! [B: $i,A: $i] :
( ( ( n4 @ ( A @ plus ) )
!= ( B @ ( n2 @ plus ) ) )
| ( ( A @ succ @ succ @ succ @ succ )
= ( B @ succ @ succ ) ) ),
inference(paramod_ordered,[status(thm)],[155,149]) ).
thf(15207,plain,
( ( n2 @ succ @ succ @ succ @ succ )
= ( n4 @ succ @ succ ) ),
inference(pattern_uni,[status(thm)],[15206:[bind(A,$thf( n2 )),bind(B,$thf( n4 ))]]) ).
thf(15228,plain,
( ( n3 @ succ @ succ @ succ )
= ( n5 @ succ ) ),
inference(rewrite,[status(thm)],[15207,6531,5592]) ).
thf(15267,plain,
! [A: $i] :
( ( ( n3 @ succ @ succ @ succ )
!= ( A @ succ ) )
| ( A @ ( n5 @ succ @ gt ) ) ),
inference(paramod_ordered,[status(thm)],[15228,129]) ).
thf(15268,plain,
n3 @ succ @ succ @ ( n5 @ succ @ gt ),
inference(pattern_uni,[status(thm)],[15267:[bind(A,$thf( n3 @ succ @ succ ))]]) ).
thf(15410,plain,
n5 @ ( n5 @ succ @ gt ),
inference(rewrite,[status(thm)],[15268,6895]) ).
thf(75,axiom,
n0 @ ( n2 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_2_0) ).
thf(554,plain,
n0 @ ( n2 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(14751,plain,
! [A: $i] :
( ( ( n1 @ succ )
!= ( A @ succ ) )
| ( ( n2 @ pred )
= A ) ),
inference(paramod_ordered,[status(thm)],[5348,146]) ).
thf(14752,plain,
( ( n2 @ pred )
= n1 ),
inference(pattern_uni,[status(thm)],[14751:[bind(A,$thf( n1 ))]]) ).
thf(2416,plain,
! [A: $i] :
( ( ( n0 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[350,152]) ).
thf(2417,plain,
! [A: $i] :
( ( n0 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[2416]) ).
thf(2418,plain,
! [A: $i] :
( ( n0 != A )
| ( n5 != A ) ),
inference(simp,[status(thm)],[2417]) ).
thf(2419,plain,
n5 != n0,
inference(simp,[status(thm)],[2418]) ).
thf(34,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(212,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)],[34]) ).
thf(15508,plain,
! [B: $i,A: $i] :
( ( ( n5 @ ( n135300 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[579,161]) ).
thf(15509,plain,
! [B: $i,A: $i] :
( ( ( n5 @ ( n135300 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15508]) ).
thf(15510,plain,
n135300 @ ( n5 @ lt ),
inference(pattern_uni,[status(thm)],[15509:[bind(A,$thf( n5 )),bind(B,$thf( n135300 ))]]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( B @ succ @ ( A @ succ @ leq ) )
<=> ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_succ) ).
thf(225,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)],[35]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( n3 @ plus ) )
= ( A @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_3_l) ).
thf(122,plain,
! [A: $i] :
( ( A @ ( n3 @ plus ) )
= ( A @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(123,plain,
! [A: $i] :
( ( A @ ( n3 @ plus ) )
= ( A @ succ @ succ @ succ ) ),
inference(cnf,[status(esa)],[122]) ).
thf(124,plain,
! [A: $i] :
( ( A @ ( n3 @ plus ) )
= ( A @ succ @ succ @ succ ) ),
inference(lifteq,[status(thm)],[123]) ).
thf(95,plain,
( ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( n0
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(114,plain,
( ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(lifteq,[status(thm)],[95]) ).
thf(1963,plain,
( ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(rewrite,[status(thm)],[114,100,101,104,106]) ).
thf(1964,plain,
( ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(simp,[status(thm)],[1963]) ).
thf(4718,plain,
! [A: $i] :
( ( ( n1 @ ( n2 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[576,152]) ).
thf(4719,plain,
! [A: $i] :
( ( n1 @ ( n2 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[4718]) ).
thf(4720,plain,
! [A: $i] :
( ( n1 != A )
| ( n2 != A ) ),
inference(simp,[status(thm)],[4719]) ).
thf(4721,plain,
n2 != n1,
inference(simp,[status(thm)],[4720]) ).
thf(78,axiom,
n0 @ ( n4 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_0) ).
thf(560,plain,
n0 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(4164,plain,
! [A: $i] :
( ( ( n0 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[560,152]) ).
thf(4165,plain,
! [A: $i] :
( ( n0 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[4164]) ).
thf(4166,plain,
! [A: $i] :
( ( n0 != A )
| ( n4 != A ) ),
inference(simp,[status(thm)],[4165]) ).
thf(4167,plain,
n4 != n0,
inference(simp,[status(thm)],[4166]) ).
thf(584,plain,
! [A: $i] :
( ( ( n2 @ ( n3 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[137,152]) ).
thf(585,plain,
! [A: $i] :
( ( n2 @ ( n3 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[584]) ).
thf(588,plain,
! [A: $i] :
( ( n2 != A )
| ( n3 != A ) ),
inference(simp,[status(thm)],[585]) ).
thf(590,plain,
n2 != n3,
inference(simp,[status(thm)],[588]) ).
thf(2055,plain,
( ( ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
!= ( pv10 @ ( n0 @ leq ) ) )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ $true
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[100,1728]) ).
thf(2056,plain,
( ( ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
!= ( pv10 @ ( n0 @ leq ) ) )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[2055]) ).
thf(2085,plain,
( ( ( n1 @ ( pv12 @ minus ) )
!= pv10 )
| ( sk1 != n0 )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[2056]) ).
thf(15553,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n4 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[560,161]) ).
thf(15554,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n4 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15553]) ).
thf(15555,plain,
n4 @ ( n0 @ lt ),
inference(pattern_uni,[status(thm)],[15554:[bind(A,$thf( n0 )),bind(B,$thf( n4 ))]]) ).
thf(14783,plain,
! [A: $i] :
( ( ( n0 @ succ )
!= ( A @ succ ) )
| ( ( n1 @ pred )
= A ) ),
inference(paramod_ordered,[status(thm)],[171,146]) ).
thf(14784,plain,
( ( n1 @ pred )
= n0 ),
inference(pattern_uni,[status(thm)],[14783:[bind(A,$thf( n0 ))]]) ).
thf(13,axiom,
n3 @ ( n4 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_3) ).
thf(143,plain,
n3 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(908,plain,
! [A: $i] :
( ( ( n3 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[143,152]) ).
thf(909,plain,
! [A: $i] :
( ( n3 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[908]) ).
thf(910,plain,
! [A: $i] :
( ( n3 != A )
| ( n4 != A ) ),
inference(simp,[status(thm)],[909]) ).
thf(911,plain,
n4 != n3,
inference(simp,[status(thm)],[910]) ).
thf(8,axiom,
! [A: $i] :
( ( n3 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_3_r) ).
thf(134,plain,
! [A: $i] :
( ( n3 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(38,axiom,
tptp_minus_1 @ ( n0 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_0_tptp_minus_1) ).
thf(244,plain,
tptp_minus_1 @ ( n0 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( A @ ( B @ succ @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_gt_equiv) ).
thf(508,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)],[64]) ).
thf(22,axiom,
n1 @ ( n3 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_1) ).
thf(168,plain,
n1 @ ( n3 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(15550,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( n3 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[168,161]) ).
thf(15551,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( n3 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15550]) ).
thf(15552,plain,
n3 @ ( n1 @ lt ),
inference(pattern_uni,[status(thm)],[15551:[bind(A,$thf( n1 )),bind(B,$thf( n3 ))]]) ).
thf(56,axiom,
! [A: $i] :
( ( ( n1 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n1 )
| ( A = n0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_1) ).
thf(425,plain,
! [A: $i] :
( ( ( n1 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n1 )
| ( A = n0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(85,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(573,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)],[85]) ).
thf(598,plain,
! [A: $i] :
( ( ( n2 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[142,152]) ).
thf(599,plain,
! [A: $i] :
( ( n2 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[598]) ).
thf(600,plain,
! [A: $i] :
( ( n2 != A )
| ( n4 != A ) ),
inference(simp,[status(thm)],[599]) ).
thf(601,plain,
n4 != n2,
inference(simp,[status(thm)],[600]) ).
thf(2025,plain,
! [A: $i] :
( ( ( tptp_minus_1 @ ( n0 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[244,152]) ).
thf(2026,plain,
! [A: $i] :
( ( tptp_minus_1 @ ( n0 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[2025]) ).
thf(2027,plain,
! [A: $i] :
( ( tptp_minus_1 != A )
| ( n0 != A ) ),
inference(simp,[status(thm)],[2026]) ).
thf(2028,plain,
tptp_minus_1 != n0,
inference(simp,[status(thm)],[2027]) ).
thf(15472,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n3 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[424,161]) ).
thf(15473,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n3 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15472]) ).
thf(15474,plain,
n3 @ ( n0 @ lt ),
inference(pattern_uni,[status(thm)],[15473:[bind(A,$thf( n0 )),bind(B,$thf( n3 ))]]) ).
thf(175,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ tptp_update2 ) ) @ a_select2 ) )
= C ),
inference(cnf,[status(esa)],[174]) ).
thf(176,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ tptp_update2 ) ) @ a_select2 ) )
= C ),
inference(lifteq,[status(thm)],[175]) ).
thf(30,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(187,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)],[30]) ).
thf(188,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)],[187]) ).
thf(189,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)],[188]) ).
thf(190,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)],[189]) ).
thf(191,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)],[190]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ gt ) )
=> ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt1) ).
thf(577,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ gt ) )
=> ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(109,plain,
( ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ( sk1 @ ( n0 @ leq ) )
| ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( n0
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(116,plain,
( ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ( sk1 @ ( n0 @ leq ) )
| ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(lifteq,[status(thm)],[109]) ).
thf(2816,plain,
( ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ( sk1 @ ( n0 @ leq ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(rewrite,[status(thm)],[116,100,101,104,106]) ).
thf(2817,plain,
( ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
| ( sk1 @ ( n0 @ leq ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(simp,[status(thm)],[2816]) ).
thf(4168,plain,
! [A: $i] :
( ( ( n4 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[566,152]) ).
thf(4169,plain,
! [A: $i] :
( ( n4 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[4168]) ).
thf(4170,plain,
! [A: $i] :
( ( n4 != A )
| ( n5 != A ) ),
inference(simp,[status(thm)],[4169]) ).
thf(4171,plain,
n4 != n5,
inference(simp,[status(thm)],[4170]) ).
thf(159,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ lt ) ) ),
inference(cnfConj,[status(thm)],[158]) ).
thf(7313,plain,
! [A: $i] :
( ( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) )
| ( sk3 @ ( n0 @ leq ) )
| ( sk1 @ ( n0 @ leq ) )
| ( n0 != n0 ) ),
inference(paramod_ordered,[status(thm)],[194,597]) ).
thf(7314,plain,
! [A: $i] :
( ( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) )
| ( sk3 @ ( n0 @ leq ) )
| ( sk1 @ ( n0 @ leq ) ) ),
inference(simp,[status(thm)],[7313]) ).
thf(7444,plain,
! [A: $i] :
( ( A
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt ) )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( n0 != n0 )
| ( sk3 @ ( n0 @ leq ) )
| ( sk1 @ ( n0 @ leq ) ) ),
inference(simp,[status(thm)],[7314]) ).
thf(7514,plain,
( ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk3 @ ( n0 @ leq ) )
| ( sk1 @ ( n0 @ leq ) ) ),
inference(simp,[status(thm)],[7444]) ).
thf(2412,plain,
! [A: $i] :
( ( ( tptp_minus_1 @ ( n135300 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[349,152]) ).
thf(2413,plain,
! [A: $i] :
( ( tptp_minus_1 @ ( n135300 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[2412]) ).
thf(2414,plain,
! [A: $i] :
( ( tptp_minus_1 != A )
| ( n135300 != A ) ),
inference(simp,[status(thm)],[2413]) ).
thf(2415,plain,
tptp_minus_1 != n135300,
inference(simp,[status(thm)],[2414]) ).
thf(15505,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n0 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[244,161]) ).
thf(15506,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n0 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15505]) ).
thf(15507,plain,
n0 @ ( tptp_minus_1 @ lt ),
inference(pattern_uni,[status(thm)],[15506:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n0 ))]]) ).
thf(983,plain,
! [A: $i] :
( ( ( n1 @ ( pv10 @ minus ) @ ( pv10 @ leq ) )
!= ( pv12 @ ( n0 @ leq ) ) )
| ~ $true
| ( ( A @ ( pv10 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[101,953]) ).
thf(984,plain,
! [A: $i] :
( ( ( n1 @ ( pv10 @ minus ) @ ( pv10 @ leq ) )
!= ( pv12 @ ( n0 @ leq ) ) )
| ( ( A @ ( pv10 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[983]) ).
thf(996,plain,
! [A: $i] :
( ( ( n1 @ ( pv10 @ minus ) )
!= pv12 )
| ( pv10 != n0 )
| ( ( A @ ( pv10 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[984]) ).
thf(39,axiom,
! [A: $i] :
( ( n1 @ ( A @ minus ) )
= ( A @ pred ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pred_minus_1) ).
thf(245,plain,
! [A: $i] :
( ( n1 @ ( A @ minus ) )
= ( A @ pred ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(82,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(567,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)],[82]) ).
thf(925,plain,
! [B: $i,A: $i] :
( ( ( pv12 @ ( n0 @ leq ) )
!= ( n1 @ ( pv10 @ minus ) @ ( A @ leq ) ) )
| ~ $true
| ~ ( A @ ( n0 @ leq ) )
| ( ( B @ ( A @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[101,118]) ).
thf(926,plain,
! [B: $i,A: $i] :
( ( ( pv12 @ ( n0 @ leq ) )
!= ( n1 @ ( pv10 @ minus ) @ ( A @ leq ) ) )
| ~ ( A @ ( n0 @ leq ) )
| ( ( B @ ( A @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[925]) ).
thf(950,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( pv10 @ minus ) )
!= pv12 )
| ( n0 != A )
| ~ ( A @ ( n0 @ leq ) )
| ( ( B @ ( A @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[926]) ).
thf(966,plain,
! [A: $i] :
( ( ( n1 @ ( pv10 @ minus ) )
!= pv12 )
| ~ ( n0 @ ( n0 @ leq ) )
| ( ( A @ ( n0 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[950]) ).
thf(4292,plain,
! [A: $i] :
( ( ( pv12 @ ( n0 @ leq ) )
!= ( n0 @ ( n0 @ leq ) ) )
| ( ( n1 @ ( pv10 @ minus ) )
!= pv12 )
| ~ $true
| ( ( A @ ( n0 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[101,966]) ).
thf(4293,plain,
! [A: $i] :
( ( ( pv12 @ ( n0 @ leq ) )
!= ( n0 @ ( n0 @ leq ) ) )
| ( ( n1 @ ( pv10 @ minus ) )
!= pv12 )
| ( ( A @ ( n0 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[4292]) ).
thf(4420,plain,
! [A: $i] :
( ( pv12 != n0 )
| ( n0 != n0 )
| ( ( n1 @ ( pv10 @ minus ) )
!= pv12 )
| ( ( A @ ( n0 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[4293]) ).
thf(4430,plain,
! [A: $i] :
( ( pv12 != n0 )
| ( ( n1 @ ( pv10 @ minus ) )
!= pv12 )
| ( ( A @ ( n0 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[4420]) ).
thf(15463,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n1 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[570,161]) ).
thf(15464,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n1 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15463]) ).
thf(15465,plain,
n1 @ ( n0 @ lt ),
inference(pattern_uni,[status(thm)],[15464:[bind(A,$thf( n0 )),bind(B,$thf( n1 ))]]) ).
thf(4385,plain,
! [A: $i] :
( ( ( pv10 @ ( n0 @ leq ) )
!= ( n0 @ ( n0 @ leq ) ) )
| ( ( n1 @ ( pv10 @ minus ) )
!= pv12 )
| ~ $true
| ( ( A @ ( n0 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[100,966]) ).
thf(4386,plain,
! [A: $i] :
( ( ( pv10 @ ( n0 @ leq ) )
!= ( n0 @ ( n0 @ leq ) ) )
| ( ( n1 @ ( pv10 @ minus ) )
!= pv12 )
| ( ( A @ ( n0 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[4385]) ).
thf(4400,plain,
! [A: $i] :
( ( pv10 != n0 )
| ( n0 != n0 )
| ( ( n1 @ ( pv10 @ minus ) )
!= pv12 )
| ( ( A @ ( n0 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[4386]) ).
thf(4445,plain,
! [A: $i] :
( ( pv10 != n0 )
| ( ( n1 @ ( pv10 @ minus ) )
!= pv12 )
| ( ( A @ ( n0 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[4400]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ succ @ leq ) )
=> ( A @ ( B @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_gt) ).
thf(552,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ succ @ leq ) )
=> ( A @ ( B @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(15541,plain,
! [B: $i,A: $i] :
( ( ( n3 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[231,161]) ).
thf(15542,plain,
! [B: $i,A: $i] :
( ( ( n3 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15541]) ).
thf(15543,plain,
n5 @ ( n3 @ lt ),
inference(pattern_uni,[status(thm)],[15542:[bind(A,$thf( n3 )),bind(B,$thf( n5 ))]]) ).
thf(41,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(251,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)],[41]) ).
thf(32,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(195,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)],[32]) ).
thf(196,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)],[195]) ).
thf(197,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)],[196]) ).
thf(198,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)],[197]) ).
thf(19,axiom,
tptp_minus_1 @ ( n4 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_tptp_minus_1) ).
thf(162,plain,
tptp_minus_1 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(15526,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n4 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[162,161]) ).
thf(15527,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n4 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15526]) ).
thf(15528,plain,
n4 @ ( tptp_minus_1 @ lt ),
inference(pattern_uni,[status(thm)],[15527:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n4 ))]]) ).
thf(7311,plain,
! [A: $i] :
( ( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ( n0 != n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[194,1728]) ).
thf(7312,plain,
! [A: $i] :
( ( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[7311]) ).
thf(7483,plain,
! [A: $i] :
( ( A
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt ) )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( n0 != n0 )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[7312]) ).
thf(7553,plain,
( ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[7483]) ).
thf(16379,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[556,7553]) ).
thf(16380,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) ) ),
inference(simp,[status(thm)],[16379]) ).
thf(16397,plain,
! [A: $i] :
( ( A
!= ( n1 @ ( pv10 @ minus ) ) )
| ( A != sk3 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) ) ),
inference(simp,[status(thm)],[16380]) ).
thf(16408,plain,
( ( ( n1 @ ( pv10 @ minus ) )
!= sk3 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) ) ),
inference(simp,[status(thm)],[16397]) ).
thf(16476,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) ) )
| ( ( n1 @ ( pv10 @ minus ) )
!= sk3 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[556,16408]) ).
thf(16477,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) ) )
| ( ( n1 @ ( pv10 @ minus ) )
!= sk3 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv10 )
| ( sk3 != pv10 ) ),
inference(simp,[status(thm)],[16476]) ).
thf(16483,plain,
! [A: $i] :
( ( A
!= ( n1 @ ( pv12 @ minus ) ) )
| ( A != sk1 )
| ( ( n1 @ ( pv10 @ minus ) )
!= sk3 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv10 )
| ( sk3 != pv10 ) ),
inference(simp,[status(thm)],[16477]) ).
thf(16493,plain,
( ( ( n1 @ ( pv12 @ minus ) )
!= sk1 )
| ( ( n1 @ ( pv10 @ minus ) )
!= sk3 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv10 )
| ( sk3 != pv10 ) ),
inference(simp,[status(thm)],[16483]) ).
thf(3107,plain,
! [A: $i] :
( ( ( n2 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[428,152]) ).
thf(3108,plain,
! [A: $i] :
( ( n2 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[3107]) ).
thf(3109,plain,
! [A: $i] :
( ( n2 != A )
| ( n5 != A ) ),
inference(simp,[status(thm)],[3108]) ).
thf(3110,plain,
n2 != n5,
inference(simp,[status(thm)],[3109]) ).
thf(989,plain,
! [A: $i] :
( ( ( n1 @ ( pv10 @ minus ) @ ( pv10 @ leq ) )
!= ( pv10 @ ( n0 @ leq ) ) )
| ~ $true
| ( ( A @ ( pv10 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[100,953]) ).
thf(990,plain,
! [A: $i] :
( ( ( n1 @ ( pv10 @ minus ) @ ( pv10 @ leq ) )
!= ( pv10 @ ( n0 @ leq ) ) )
| ( ( A @ ( pv10 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[989]) ).
thf(1000,plain,
! [A: $i] :
( ( ( n1 @ ( pv10 @ minus ) )
!= pv10 )
| ( pv10 != n0 )
| ( ( A @ ( pv10 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[990]) ).
thf(166,plain,
! [A: $i] :
( ( A @ ( n4 @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
inference(cnf,[status(esa)],[165]) ).
thf(167,plain,
! [A: $i] :
( ( A @ ( n4 @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
inference(lifteq,[status(thm)],[166]) ).
thf(27,axiom,
n3 @ ( n135300 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135300_3) ).
thf(177,plain,
n3 @ ( n135300 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(15532,plain,
! [B: $i,A: $i] :
( ( ( n3 @ ( n135300 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[177,161]) ).
thf(15533,plain,
! [B: $i,A: $i] :
( ( ( n3 @ ( n135300 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15532]) ).
thf(15534,plain,
n135300 @ ( n3 @ lt ),
inference(pattern_uni,[status(thm)],[15533:[bind(A,$thf( n3 )),bind(B,$thf( n135300 ))]]) ).
thf(7593,plain,
( ( ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
!= ( pv10 @ ( n0 @ leq ) ) )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( n135300 != pv12 )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[100,7501]) ).
thf(7594,plain,
( ( ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
!= ( pv10 @ ( n0 @ leq ) ) )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( n135300 != pv12 )
| ( sk1 != pv10 )
| ( sk3 != pv10 ) ),
inference(simp,[status(thm)],[7593]) ).
thf(7598,plain,
( ( ( n1 @ ( pv10 @ minus ) )
!= pv10 )
| ( sk3 != n0 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( n135300 != pv12 )
| ( sk1 != pv10 )
| ( sk3 != pv10 ) ),
inference(simp,[status(thm)],[7594]) ).
thf(3244,plain,
! [A: $i] :
( ( ( pv12 @ ( n0 @ leq ) )
!= ( n0 @ ( n0 @ leq ) ) )
| ( ( n1 @ ( pv10 @ minus ) )
!= pv10 )
| ~ $true
| ( ( A @ ( n0 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(paramod_ordered,[status(thm)],[101,965]) ).
thf(3245,plain,
! [A: $i] :
( ( ( pv12 @ ( n0 @ leq ) )
!= ( n0 @ ( n0 @ leq ) ) )
| ( ( n1 @ ( pv10 @ minus ) )
!= pv10 )
| ( ( A @ ( n0 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[3244]) ).
thf(3329,plain,
! [A: $i] :
( ( pv12 != n0 )
| ( n0 != n0 )
| ( ( n1 @ ( pv10 @ minus ) )
!= pv10 )
| ( ( A @ ( n0 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[3245]) ).
thf(3348,plain,
! [A: $i] :
( ( pv12 != n0 )
| ( ( n1 @ ( pv10 @ minus ) )
!= pv10 )
| ( ( A @ ( n0 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
= n1 ) ),
inference(simp,[status(thm)],[3329]) ).
thf(19002,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) )
| ( ( n1 @ ( pv12 @ minus ) )
!= sk1 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv12 )
| ( sk3 != pv10 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[556,18933]) ).
thf(19003,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) )
| ( ( n1 @ ( pv12 @ minus ) )
!= sk1 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv12 )
| ( sk3 != pv10 ) ),
inference(simp,[status(thm)],[19002]) ).
thf(19013,plain,
! [A: $i] :
( ( A
!= ( n1 @ ( pv10 @ minus ) ) )
| ( A != sk3 )
| ( ( n1 @ ( pv12 @ minus ) )
!= sk1 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv12 )
| ( sk3 != pv10 ) ),
inference(simp,[status(thm)],[19003]) ).
thf(19018,plain,
( ( ( n1 @ ( pv10 @ minus ) )
!= sk3 )
| ( ( n1 @ ( pv12 @ minus ) )
!= sk1 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv12 )
| ( sk3 != pv10 ) ),
inference(simp,[status(thm)],[19013]) ).
thf(48,axiom,
( ( tptp_minus_1 @ succ )
= n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_tptp_minus_1) ).
thf(354,plain,
( ( tptp_minus_1 @ succ )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(355,plain,
( ( tptp_minus_1 @ succ )
= n0 ),
inference(lifteq,[status(thm)],[354]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( B @ succ @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ) ).
thf(531,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( B @ succ @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(66,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(516,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)],[66]) ).
thf(29,axiom,
n1 @ ( n4 @ gt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_1) ).
thf(186,plain,
n1 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(1745,plain,
! [A: $i] :
( ( ( n1 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[186,152]) ).
thf(1746,plain,
! [A: $i] :
( ( n1 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[1745]) ).
thf(1747,plain,
! [A: $i] :
( ( n1 != A )
| ( n4 != A ) ),
inference(simp,[status(thm)],[1746]) ).
thf(1748,plain,
n4 != n1,
inference(simp,[status(thm)],[1747]) ).
thf(15547,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( n4 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[186,161]) ).
thf(15548,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( n4 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15547]) ).
thf(15549,plain,
n4 @ ( n1 @ lt ),
inference(pattern_uni,[status(thm)],[15548:[bind(A,$thf( n1 )),bind(B,$thf( n4 ))]]) ).
thf(422,plain,
! [A: $i] :
( tptp_float_0_0
= ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) ) ),
inference(cnf,[status(esa)],[421]) ).
thf(423,plain,
! [A: $i] :
( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
= tptp_float_0_0 ),
inference(lifteq,[status(thm)],[422]) ).
thf(7586,plain,
tptp_float_0_0 = n0,
inference(rewrite,[status(thm)],[423,194]) ).
thf(77,axiom,
! [A: $i] :
( ( A @ ( n1 @ plus ) )
= ( A @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_1_l) ).
thf(557,plain,
! [A: $i] :
( ( A @ ( n1 @ plus ) )
= ( A @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(103,plain,
( ( ( sk4 @ ( sk3 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
!= n1 )
| ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( n0
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(119,plain,
( ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( ( sk4 @ ( sk3 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
!= n1 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(lifteq,[status(thm)],[103]) ).
thf(3375,plain,
( ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ( ( sk4 @ ( sk3 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
!= n1 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(rewrite,[status(thm)],[119,100,101,104,106]) ).
thf(3376,plain,
( ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ( ( sk4 @ ( sk3 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
!= n1 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(simp,[status(thm)],[3375]) ).
thf(33,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(199,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)],[33]) ).
thf(61,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(441,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)],[61]) ).
thf(15517,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( n135300 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[362,161]) ).
thf(15518,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( n135300 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15517]) ).
thf(15519,plain,
n135300 @ ( n1 @ lt ),
inference(pattern_uni,[status(thm)],[15518:[bind(A,$thf( n1 )),bind(B,$thf( n135300 ))]]) ).
thf(15502,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ succ @ gt ) )
!= ( B @ ( C @ gt ) ) )
| ( C @ ( B @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[129,161]) ).
thf(15503,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ succ @ gt ) )
!= ( B @ ( C @ gt ) ) )
| ( C @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[15502]) ).
thf(15504,plain,
! [A: $i] : ( A @ succ @ ( A @ lt ) ),
inference(pattern_uni,[status(thm)],[15503:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ succ ))]]) ).
thf(15556,plain,
! [A: $i] : ( A @ succ @ ( A @ lt ) ),
inference(simp,[status(thm)],[15504]) ).
thf(3652,plain,
! [A: $i] :
( ( ( n0 @ ( n2 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[554,152]) ).
thf(3653,plain,
! [A: $i] :
( ( n0 @ ( n2 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[3652]) ).
thf(3654,plain,
! [A: $i] :
( ( n0 != A )
| ( n2 != A ) ),
inference(simp,[status(thm)],[3653]) ).
thf(3655,plain,
n2 != n0,
inference(simp,[status(thm)],[3654]) ).
thf(6822,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ succ @ gt ) )
!= ( B @ ( B @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[129,152]) ).
thf(6823,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ succ @ gt ) )
!= ( B @ ( B @ gt ) ) ),
inference(simp,[status(thm)],[6822]) ).
thf(6840,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( A @ succ )
!= B ) ),
inference(simp,[status(thm)],[6823]) ).
thf(6842,plain,
! [A: $i] :
( ( A @ succ )
!= A ),
inference(simp,[status(thm)],[6840]) ).
thf(6986,plain,
! [B: $i,A: $i] :
( ( ( A @ pred @ succ )
!= ( B @ succ ) )
| ( A != B ) ),
inference(paramod_ordered,[status(thm)],[127,6842]) ).
thf(6987,plain,
! [A: $i] :
( ( A @ pred )
!= A ),
inference(pattern_uni,[status(thm)],[6986:[bind(A,$thf( C )),bind(B,$thf( C @ pred ))]]) ).
thf(6994,plain,
! [A: $i] :
( ( A @ pred )
!= A ),
inference(simp,[status(thm)],[6987]) ).
thf(18776,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ pred @ ( A @ gt ) )
!= ( B @ ( C @ gt ) ) )
| ( C @ ( B @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6841,161]) ).
thf(18777,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ pred @ ( A @ gt ) )
!= ( B @ ( C @ gt ) ) )
| ( C @ ( B @ lt ) ) ),
inference(simp,[status(thm)],[18776]) ).
thf(18778,plain,
! [A: $i] : ( A @ ( A @ pred @ lt ) ),
inference(pattern_uni,[status(thm)],[18777:[bind(A,$thf( D )),bind(B,$thf( D @ pred )),bind(C,$thf( D ))]]) ).
thf(18788,plain,
! [A: $i] : ( A @ ( A @ pred @ lt ) ),
inference(simp,[status(thm)],[18778]) ).
thf(5344,plain,
! [A: $i] :
( ( ( n4 @ ( n135300 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[581,152]) ).
thf(5345,plain,
! [A: $i] :
( ( n4 @ ( n135300 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[5344]) ).
thf(5346,plain,
! [A: $i] :
( ( n4 != A )
| ( n135300 != A ) ),
inference(simp,[status(thm)],[5345]) ).
thf(5347,plain,
n4 != n135300,
inference(simp,[status(thm)],[5346]) ).
thf(15481,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[551,161]) ).
thf(15482,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15481]) ).
thf(15483,plain,
n5 @ ( tptp_minus_1 @ lt ),
inference(pattern_uni,[status(thm)],[15482:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n5 ))]]) ).
thf(592,plain,
! [A: $i] :
( ( ( tptp_minus_1 @ ( n2 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[138,152]) ).
thf(593,plain,
! [A: $i] :
( ( tptp_minus_1 @ ( n2 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[592]) ).
thf(594,plain,
! [A: $i] :
( ( tptp_minus_1 != A )
| ( n2 != A ) ),
inference(simp,[status(thm)],[593]) ).
thf(595,plain,
n2 != tptp_minus_1,
inference(simp,[status(thm)],[594]) ).
thf(7587,plain,
( ( ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
!= ( pv12 @ ( n0 @ leq ) ) )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( n135300 != pv12 )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,7501]) ).
thf(7588,plain,
( ( ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
!= ( pv12 @ ( n0 @ leq ) ) )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( n135300 != pv12 )
| ( sk1 != pv10 )
| ( sk3 != pv10 ) ),
inference(simp,[status(thm)],[7587]) ).
thf(7595,plain,
( ( ( n1 @ ( pv10 @ minus ) )
!= pv12 )
| ( sk3 != n0 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( n135300 != pv12 )
| ( sk1 != pv10 )
| ( sk3 != pv10 ) ),
inference(simp,[status(thm)],[7588]) ).
thf(15499,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n2 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[554,161]) ).
thf(15500,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n2 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15499]) ).
thf(15501,plain,
n2 @ ( n0 @ lt ),
inference(pattern_uni,[status(thm)],[15500:[bind(A,$thf( n0 )),bind(B,$thf( n2 ))]]) ).
thf(72,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(539,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)],[72]) ).
thf(15523,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n3 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[130,161]) ).
thf(15524,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n3 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15523]) ).
thf(15525,plain,
n3 @ ( tptp_minus_1 @ lt ),
inference(pattern_uni,[status(thm)],[15524:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n3 ))]]) ).
thf(51,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(363,plain,
! [A: $i,B: $i] :
( ( A @ ( n0 @ leq ) )
=> ( A @ ( B @ uniform_int_rnd ) @ ( n0 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ ( n5 @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_5_l) ).
thf(351,plain,
! [A: $i] :
( ( A @ ( n5 @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(53,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(418,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( D @ ( C @ ( B @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(14769,plain,
! [A: $i] :
( ( ( tptp_minus_1 @ succ )
!= ( A @ succ ) )
| ( ( n0 @ pred )
= A ) ),
inference(paramod_ordered,[status(thm)],[355,146]) ).
thf(14770,plain,
( ( n0 @ pred )
= tptp_minus_1 ),
inference(pattern_uni,[status(thm)],[14769:[bind(A,$thf( tptp_minus_1 ))]]) ).
thf(1190,plain,
! [A: $i] :
( ( ( tptp_minus_1 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[162,152]) ).
thf(1191,plain,
! [A: $i] :
( ( tptp_minus_1 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[1190]) ).
thf(1192,plain,
! [A: $i] :
( ( tptp_minus_1 != A )
| ( n4 != A ) ),
inference(simp,[status(thm)],[1191]) ).
thf(1193,plain,
n4 != tptp_minus_1,
inference(simp,[status(thm)],[1192]) ).
thf(15307,plain,
! [A: $i] :
( ( ( n3 @ succ @ succ @ succ )
!= ( A @ succ ) )
| ( ( n5 @ succ )
!= A ) ),
inference(paramod_ordered,[status(thm)],[15228,6842]) ).
thf(15308,plain,
( ( n3 @ succ @ succ )
!= ( n5 @ succ ) ),
inference(pattern_uni,[status(thm)],[15307:[bind(A,$thf( n3 @ succ @ succ ))]]) ).
thf(15362,plain,
( ( n5 @ succ )
!= n5 ),
inference(rewrite,[status(thm)],[15308,6895]) ).
thf(18819,plain,
! [A: $i] :
( ( ( n3 @ succ @ succ @ succ )
!= ( A @ succ ) )
| ( n5 @ succ @ ( A @ lt ) ) ),
inference(paramod_ordered,[status(thm)],[15228,15556]) ).
thf(18820,plain,
n5 @ succ @ ( n3 @ succ @ succ @ lt ),
inference(pattern_uni,[status(thm)],[18819:[bind(A,$thf( n3 @ succ @ succ ))]]) ).
thf(19537,plain,
n5 @ succ @ ( n5 @ lt ),
inference(rewrite,[status(thm)],[18820,6895]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( ( A != B )
& ( B @ ( A @ leq ) ) )
=> ( A @ ( B @ gt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt2) ).
thf(346,plain,
! [A: $i,B: $i] :
( ( ( A != B )
& ( B @ ( A @ leq ) ) )
=> ( A @ ( B @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(71,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(536,plain,
! [A: $i] :
( ( ( n2 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n2 )
| ( A = n1 )
| ( A = n0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(59,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(432,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)],[59]) ).
thf(15478,plain,
! [B: $i,A: $i] :
( ( ( n4 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[566,161]) ).
thf(15479,plain,
! [B: $i,A: $i] :
( ( ( n4 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15478]) ).
thf(15480,plain,
n5 @ ( n4 @ lt ),
inference(pattern_uni,[status(thm)],[15479:[bind(A,$thf( n4 )),bind(B,$thf( n5 ))]]) ).
thf(180,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( B @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D )
| ~ ( B @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( A @ ( B @ ( C @ ( D @ sk5 ) ) ) @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[179]) ).
thf(183,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( A @ ( B @ ( C @ ( D @ sk5 ) ) ) @ ( n0 @ leq ) )
| ( ( A @ ( D @ ( B @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D ) ),
inference(lifteq,[status(thm)],[180]) ).
thf(17974,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) ) )
| ( ( n1 @ ( pv10 @ minus ) )
!= sk3 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv12 )
| ( sk3 != pv12 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[556,17907]) ).
thf(17975,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) ) )
| ( ( n1 @ ( pv10 @ minus ) )
!= sk3 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv12 )
| ( sk3 != pv12 ) ),
inference(simp,[status(thm)],[17974]) ).
thf(17984,plain,
! [A: $i] :
( ( A
!= ( n1 @ ( pv12 @ minus ) ) )
| ( A != sk1 )
| ( ( n1 @ ( pv10 @ minus ) )
!= sk3 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv12 )
| ( sk3 != pv12 ) ),
inference(simp,[status(thm)],[17975]) ).
thf(17989,plain,
( ( ( n1 @ ( pv12 @ minus ) )
!= sk1 )
| ( ( n1 @ ( pv10 @ minus ) )
!= sk3 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv12 )
| ( sk3 != pv12 ) ),
inference(simp,[status(thm)],[17984]) ).
thf(80,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(564,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(135,plain,
! [A: $i] :
( ( n3 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ ) ),
inference(cnf,[status(esa)],[134]) ).
thf(136,plain,
! [A: $i] :
( ( n3 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ ) ),
inference(lifteq,[status(thm)],[135]) ).
thf(15538,plain,
! [B: $i,A: $i] :
( ( ( n3 @ ( n4 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[143,161]) ).
thf(15539,plain,
! [B: $i,A: $i] :
( ( ( n3 @ ( n4 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[15538]) ).
thf(15540,plain,
n4 @ ( n3 @ lt ),
inference(pattern_uni,[status(thm)],[15539:[bind(A,$thf( n3 )),bind(B,$thf( n4 ))]]) ).
thf(60,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(437,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)],[60]) ).
thf(1558,plain,
! [A: $i] :
( ( ( n3 @ ( n135300 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[177,152]) ).
thf(1559,plain,
! [A: $i] :
( ( n3 @ ( n135300 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[1558]) ).
thf(1560,plain,
! [A: $i] :
( ( n3 != A )
| ( n135300 != A ) ),
inference(simp,[status(thm)],[1559]) ).
thf(1561,plain,
n3 != n135300,
inference(simp,[status(thm)],[1560]) ).
thf(1194,plain,
! [A: $i] :
( ( ( n1 @ ( n3 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[168,152]) ).
thf(1195,plain,
! [A: $i] :
( ( n1 @ ( n3 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[1194]) ).
thf(1196,plain,
! [A: $i] :
( ( n1 != A )
| ( n3 != A ) ),
inference(simp,[status(thm)],[1195]) ).
thf(1197,plain,
n3 != n1,
inference(simp,[status(thm)],[1196]) ).
thf(2031,plain,
( ( ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
!= ( pv12 @ ( n0 @ leq ) ) )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[101,1728]) ).
thf(2032,plain,
( ( ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) )
!= ( pv12 @ ( n0 @ leq ) ) )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) ) ),
inference(simp,[status(thm)],[2031]) ).
thf(2063,plain,
( ( ( n1 @ ( pv10 @ minus ) )
!= pv12 )
| ( sk3 != n0 )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 )
| ~ ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) ) ),
inference(simp,[status(thm)],[2032]) ).
thf(67,axiom,
! [A: $i] :
( ( n1 @ ( A @ plus ) )
= ( A @ succ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_1_r) ).
thf(528,plain,
! [A: $i] :
( ( n1 @ ( A @ plus ) )
= ( A @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(16381,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) ) )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ~ $true
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[556,7553]) ).
thf(16382,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) ) )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[16381]) ).
thf(16402,plain,
! [A: $i] :
( ( A
!= ( n1 @ ( pv12 @ minus ) ) )
| ( A != sk1 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[16382]) ).
thf(16412,plain,
( ( ( n1 @ ( pv12 @ minus ) )
!= sk1 )
| ( ( n1 @ ( n0 @ minus ) )
!= tptp_minus_1 )
| ( sk1 != pv10 )
| ( sk3 != pv10 )
| ~ ( n1 @ ( pv10 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[16402]) ).
thf(99,plain,
( ( sk3 @ ( n0 @ leq ) )
| ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( n0
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(121,plain,
( ( sk3 @ ( n0 @ leq ) )
| ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(lifteq,[status(thm)],[99]) ).
thf(4626,plain,
( ( sk3 @ ( n0 @ leq ) )
| ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(rewrite,[status(thm)],[121,100,101,104,106]) ).
thf(4627,plain,
( ( sk3 @ ( n0 @ leq ) )
| ( n1 @ ( pv12 @ minus ) @ ( sk1 @ leq ) )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(simp,[status(thm)],[4626]) ).
thf(16547,plain,
! [B: $i,A: $i] :
( ( ( pv10 @ ( n135300 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true
| ( ( n1 @ ( n5 @ minus ) )
!= tptp_minus_1 )
| ( n135300 @ ( pv10 @ gt ) ) ),
inference(paramod_ordered,[status(thm)],[13970,161]) ).
thf(16548,plain,
! [B: $i,A: $i] :
( ( ( pv10 @ ( n135300 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ( ( n1 @ ( n5 @ minus ) )
!= tptp_minus_1 )
| ( n135300 @ ( pv10 @ gt ) ) ),
inference(simp,[status(thm)],[16547]) ).
thf(16549,plain,
( ( n135300 @ ( pv10 @ lt ) )
| ( ( n1 @ ( n5 @ minus ) )
!= tptp_minus_1 )
| ( n135300 @ ( pv10 @ gt ) ) ),
inference(pattern_uni,[status(thm)],[16548:[bind(A,$thf( pv10 )),bind(B,$thf( n135300 ))]]) ).
thf(4855,plain,
! [A: $i] :
( ( ( n1 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[580,152]) ).
thf(4856,plain,
! [A: $i] :
( ( n1 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[4855]) ).
thf(4857,plain,
! [A: $i] :
( ( n1 != A )
| ( n5 != A ) ),
inference(simp,[status(thm)],[4856]) ).
thf(4858,plain,
n5 != n1,
inference(simp,[status(thm)],[4857]) ).
thf(63,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(496,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)],[63]) ).
thf(37,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(232,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)],[37]) ).
thf(107,plain,
( ( ( sk4 @ ( sk3 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
!= n1 )
| ( sk1 @ ( n0 @ leq ) )
| ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( n0
!= ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) ) ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(115,plain,
( ( sk1 @ ( n0 @ leq ) )
| ~ ( n1 @ ( n5 @ minus ) @ ( pv12 @ leq ) )
| ~ ( n1 @ ( n135300 @ minus ) @ ( pv10 @ leq ) )
| ~ ( pv12 @ ( n0 @ leq ) )
| ~ ( pv10 @ ( n0 @ leq ) )
| ( ( sk4 @ ( sk3 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
!= n1 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(lifteq,[status(thm)],[107]) ).
thf(2296,plain,
( ( sk1 @ ( n0 @ leq ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ( ( sk4 @ ( sk3 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
!= n1 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(rewrite,[status(thm)],[115,100,101,104,106]) ).
thf(2297,plain,
( ( sk1 @ ( n0 @ leq ) )
| ( ( sk4 @ ( sk3 @ ( q @ a_select3 ) ) @ ( n1 @ ( n5 @ minus ) @ ( n0 @ sum ) ) )
!= n1 )
| ( ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ ( pv10 @ ( x @ a_select2 ) @ ( n0 @ ( pv71 @ ( center @ a_select3 ) ) @ minus ) @ times ) @ sqrt @ ( n1 @ ( n0 @ minus ) @ ( n0 @ sum ) ) )
!= n0 ) ),
inference(simp,[status(thm)],[2296]) ).
thf(213,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)],[212]) ).
thf(214,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 @ sk9 ) @ ( A @ ( B @ sk8 ) @ ( A @ a_select3 ) ) )
!= ( A @ ( B @ sk8 ) @ ( A @ ( B @ sk9 ) @ ( 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 @ sk9 ) @ 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 @ sk9 ) @ ( 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 @ sk8 ) @ 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 @ sk8 ) @ ( n0 @ leq ) ) ) ),
inference(cnf,[status(esa)],[213]) ).
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 @ sk9 ) @ ( A @ ( B @ sk8 ) @ ( A @ a_select3 ) ) )
!= ( A @ ( B @ sk8 ) @ ( A @ ( B @ sk9 ) @ ( A @ a_select3 ) ) ) ) ),
inference(cnfConj,[status(thm)],[214]) ).
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 ) )
| ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) )
| ( ( A @ ( B @ sk8 ) @ ( A @ ( B @ sk9 ) @ ( A @ a_select3 ) ) )
!= ( A @ ( B @ sk9 ) @ ( A @ ( B @ sk8 ) @ ( A @ a_select3 ) ) ) ) ),
inference(lifteq,[status(thm)],[219]) ).
thf(23735,plain,
$false,
inference(e,[status(thm)],[1337,138,101,15537,555,1411,14782,3534,170,582,2808,15143,1728,2114,5348,597,533,142,340,153,17907,3530,174,185,13970,14396,570,18933,184,125,2897,15477,421,969,152,2024,15462,164,14780,591,6176,514,6895,2893,6135,15468,17916,106,15522,6841,147,2979,5343,133,998,428,4285,1651,248,18941,1338,1915,366,2083,2061,15486,349,561,15531,424,192,137,165,14772,429,566,4725,7762,3349,7501,15546,551,92,15471,493,1656,1291,15498,1328,15513,356,169,15459,141,3941,18039,19783,156,15410,339,554,14752,2419,5588,212,15510,225,124,1964,4721,4167,590,2085,15555,14784,911,129,134,128,244,508,15552,953,1732,425,573,7785,601,161,7599,2028,15474,7567,149,176,191,577,579,118,2817,144,4171,350,159,187,172,7514,2415,15507,996,245,362,567,4430,15465,4445,552,535,15543,251,155,198,7561,15528,3627,16493,3110,1000,167,15534,7598,130,16408,3348,19018,112,355,194,162,531,516,6517,1748,580,15549,150,1647,5592,7586,557,3376,199,177,441,15519,15556,3655,127,576,6994,18788,6188,5347,15483,595,7784,7595,571,143,6531,231,15501,539,15525,581,104,363,556,1646,351,186,15228,171,139,418,14770,1193,15362,19537,346,536,432,168,146,15480,183,17989,603,564,136,15540,195,437,1561,1197,2063,1352,1129,528,131,163,16412,178,7553,122,4627,354,16549,1204,4858,496,232,100,1009,6842,2297,560,222,2087]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV053+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
% 0.14/0.40 % Computer : n011.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 13:08:44 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.28/1.18 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.38/1.61 % [INFO] Parsing done (427ms).
% 2.38/1.63 % [INFO] Running in sequential loop mode.
% 3.41/2.23 % [INFO] eprover registered as external prover.
% 3.41/2.24 % [INFO] Scanning for conjecture ...
% 3.98/2.50 % [INFO] Found a conjecture (or negated_conjecture) and 91 axioms. Running axiom selection ...
% 4.16/2.69 % [INFO] Axiom selection finished. Selected 89 axioms (removed 2 axioms).
% 4.58/2.84 % [INFO] Problem is first-order (TPTP FOF).
% 4.58/2.86 % [INFO] Type checking passed.
% 4.58/2.86 % [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 ...
% 90.05/22.02 % External prover 'e' found a proof!
% 90.05/22.02 % [INFO] Killing All external provers ...
% 90.05/22.03 % Time passed: 21433ms (effective reasoning time: 20385ms)
% 90.05/22.03 % 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)>
% 90.05/22.03 % Axioms used in derivation (89): sel3_update_2, gt_135300_0, gt_0_tptp_minus_1, gt_3_1, leq_minus, sel2_update_2, succ_plus_5_l, lt_gt, gt_5_tptp_minus_1, succ_plus_3_r, gt_4_3, transitivity_gt, matrix_symm_inv, matrix_symm_trans, finite_domain_1, gt_5_0, const_array2_select, gt_2_tptp_minus_1, gt_135300_1, sel3_update_3, leq_geq, gt_1_0, leq_gt2, gt_5_4, gt_135300_5, succ_plus_1_l, gt_3_2, matrix_symm_add, leq_succ_gt, finite_domain_5, pred_minus_1, successor_3, gt_3_tptp_minus_1, matrix_symm_update_diagonal, sel2_update_1, gt_4_2, matrix_symm_sub, gt_135300_4, 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_135300_3, leq_succ_succ, sum_plus_base_float, succ_plus_2_l, gt_4_1, gt_2_0, gt_5_2, const_array1_select, leq_gt_pred, matrix_symm_joseph_update, succ_pred, totality, transitivity_leq, finite_domain_3, uniform_int_rand_ranges_lo, sel3_update_1, successor_1, gt_135300_tptp_minus_1, sum_plus_base, irreflexivity_gt, successor_5, gt_3_0, sel2_update_3, pred_succ, gt_135300_2, succ_plus_1_r, succ_plus_3_l, gt_4_tptp_minus_1, succ_plus_4_r, gt_4_0, succ_plus_2_r, leq_succ_gt_equiv, gt_5_1, uniform_int_rand_ranges_hi, gt_2_1, finite_domain_0, leq_succ
% 90.05/22.03 % No. of inferences in proof: 755
% 90.05/22.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 21433 ms resp. 20385 ms w/o parsing
% 92.95/22.50 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 92.95/22.51 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------