TSTP Solution File: SYO688-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SYO688-1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:37:00 EDT 2023
% Result : Unsatisfiable 24.86s 8.66s
% Output : Refutation 26.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 1175
% Syntax : Number of formulae : 2343 ( 5 unt; 8 typ; 0 def)
% Number of atoms : 24945 ( 0 equ; 0 cnn)
% Maximal formula atoms : 14 ( 10 avg)
% Number of connectives : 185920 (20016 ~;22610 |; 0 &;143294 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 18 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 6320 ( 0 ^;6320 !; 0 ?;6320 :)
% Comments :
%------------------------------------------------------------------------------
thf(iLEQ_type,type,
iLEQ: $i > $i > $o ).
thf(suc_type,type,
suc: $i > $i ).
thf('\'E\'_type',type,
'\'E\'': $i > $i > $o ).
thf(f_type,type,
f: $i > $i ).
thf(s_type,type,
s: $i > $i ).
thf('\'0\'_type',type,
'\'0\'': $i ).
thf('\'LE\'_type',type,
'\'LE\'': $i > $i > $o ).
thf(z_type,type,
z: $i ).
thf(499,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1109) ).
thf(2163,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(168,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_771) ).
thf(1501,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(357,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_325) ).
thf(1879,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(123,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_547) ).
thf(1411,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_877) ).
thf(1469,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(234,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_636) ).
thf(1633,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(301,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_889) ).
thf(1767,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(197,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_638) ).
thf(1559,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(282,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_255) ).
thf(1729,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(1001,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_513) ).
thf(3167,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).
thf(631,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_991) ).
thf(2427,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(583,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_681) ).
thf(2331,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(192,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_150) ).
thf(1549,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(517,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_392) ).
thf(2199,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(928,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_197) ).
thf(3021,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_230) ).
thf(1322,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(250,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1068) ).
thf(1665,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_277) ).
thf(1369,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(862,axiom,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1155) ).
thf(2889,plain,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).
thf(329,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_825) ).
thf(1823,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_556) ).
thf(1190,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_311) ).
thf(1168,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(565,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_921) ).
thf(2295,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(944,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_671) ).
thf(3053,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).
thf(1090,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_157) ).
thf(3345,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).
thf(588,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_293) ).
thf(2341,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(472,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_94) ).
thf(2109,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(483,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_174) ).
thf(2131,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(433,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_404) ).
thf(2031,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(1117,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_302) ).
thf(3399,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).
thf(415,axiom,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_134) ).
thf(1995,plain,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(549,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_125) ).
thf(2263,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(878,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_373) ).
thf(2921,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).
thf(1156,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_796) ).
thf(3477,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).
thf(649,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_562) ).
thf(2463,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(1116,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1037) ).
thf(3397,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).
thf(367,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_711) ).
thf(1899,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(811,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1078) ).
thf(2787,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(715,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_432) ).
thf(2595,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(667,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_273) ).
thf(2499,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(697,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_136) ).
thf(2559,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(1142,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
thf(3449,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).
thf(1010,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_239) ).
thf(3185,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).
thf(572,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_654) ).
thf(2309,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(476,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_397) ).
thf(2117,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(1076,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1005) ).
thf(3317,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_433) ).
thf(1290,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(533,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_768) ).
thf(2231,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(615,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_301) ).
thf(2395,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(1060,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_424) ).
thf(3285,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).
thf(753,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_49) ).
thf(2671,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(836,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_319) ).
thf(2837,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).
thf(136,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_179) ).
thf(1437,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(599,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_446) ).
thf(2363,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(345,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_536) ).
thf(1855,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_815) ).
thf(1200,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(456,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_845) ).
thf(2077,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(665,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_213) ).
thf(2495,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(608,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_347) ).
thf(2381,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(139,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1123) ).
thf(1443,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(747,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1082) ).
thf(2659,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(1126,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1045) ).
thf(3417,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).
thf(1106,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1025) ).
thf(3377,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).
thf(681,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_602) ).
thf(2527,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(994,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_60) ).
thf(3153,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).
thf(894,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_298) ).
thf(2953,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_949) ).
thf(1401,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(891,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_926) ).
thf(2947,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).
thf(202,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1063) ).
thf(1569,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(387,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_867) ).
thf(1939,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(467,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_402) ).
thf(2099,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(213,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1074) ).
thf(1591,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(403,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_979) ).
thf(1971,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(314,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_732) ).
thf(1793,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(184,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_19) ).
thf(1533,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(1026,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_745) ).
thf(3217,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).
thf(253,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_642) ).
thf(1671,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(1137,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_582) ).
thf(3439,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).
thf(245,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_450) ).
thf(1655,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(1132,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_772) ).
thf(3429,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).
thf(942,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_605) ).
thf(3049,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).
thf(721,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_559) ).
thf(2607,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(72,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_697) ).
thf(1310,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(985,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_707) ).
thf(3135,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).
thf(1100,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_512) ).
thf(3365,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).
thf(285,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_598) ).
thf(1735,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(417,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_525) ).
thf(1999,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(884,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_555) ).
thf(2933,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).
thf(488,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_521) ).
thf(2141,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(705,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_31) ).
thf(2575,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(166,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1135) ).
thf(1497,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(926,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_735) ).
thf(3017,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).
thf(515,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_346) ).
thf(2195,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(270,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1048) ).
thf(1705,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(435,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_576) ).
thf(2035,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(1101,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_360) ).
thf(3367,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).
thf(351,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_409) ).
thf(1867,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(1005,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_93) ).
thf(3175,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).
thf(731,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_76) ).
thf(2627,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_669) ).
thf(1260,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(377,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_737) ).
thf(1919,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(1044,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_666) ).
thf(3253,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).
thf(647,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1064) ).
thf(2459,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(298,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_682) ).
thf(1761,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_253) ).
thf(1342,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(978,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_184) ).
thf(3121,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).
thf(1158,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_808) ).
thf(3481,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).
thf(868,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_733) ).
thf(2901,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).
thf(1074,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_649) ).
thf(3313,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).
thf(171,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_643) ).
thf(1507,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_763) ).
thf(1222,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(969,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1115) ).
thf(3103,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).
thf(335,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_699) ).
thf(1835,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(779,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1020) ).
thf(2723,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(224,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_274) ).
thf(1613,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(385,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_476) ).
thf(1935,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(97,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_892) ).
thf(1359,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(155,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1069) ).
thf(1475,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(504,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
thf(2173,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(269,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1162) ).
thf(1703,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(852,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1089) ).
thf(2869,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).
thf(361,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_90) ).
thf(1887,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(896,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_429) ).
thf(2957,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).
thf(1085,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_698) ).
thf(3335,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_879) ).
thf(1196,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(663,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_139) ).
thf(2491,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(799,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_394) ).
thf(2763,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(910,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1024) ).
thf(2985,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).
thf(531,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_578) ).
thf(2227,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(113,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_425) ).
thf(1391,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(1042,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_472) ).
thf(3249,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).
thf(138,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_406) ).
thf(1441,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(240,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_770) ).
thf(1645,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(378,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1124) ).
thf(1921,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(218,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_542) ).
thf(1601,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(1058,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_704) ).
thf(3281,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).
thf(182,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_941) ).
thf(1529,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(401,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_601) ).
thf(1967,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(451,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_103) ).
thf(2067,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(830,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_641) ).
thf(2825,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).
thf(827,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_304) ).
thf(2819,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).
thf(319,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_204) ).
thf(1803,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(683,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_829) ).
thf(2531,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(620,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_33) ).
thf(2405,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_493) ).
thf(1228,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(229,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_964) ).
thf(1623,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_52) ).
thf(1254,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_235) ).
thf(1409,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(272,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_466) ).
thf(1709,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(719,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_639) ).
thf(2603,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(1130,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_938) ).
thf(3425,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).
thf(751,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_976) ).
thf(2667,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(587,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_778) ).
thf(2339,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(552,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_908) ).
thf(2269,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(353,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_585) ).
thf(1871,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(948,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_133) ).
thf(3061,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).
thf(980,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_674) ).
thf(3125,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).
thf(962,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_291) ).
thf(3089,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).
thf(866,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_78) ).
thf(2897,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).
thf(1094,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_725) ).
thf(3353,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).
thf(939,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_490) ).
thf(3043,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).
thf(769,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_38) ).
thf(2703,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(1049,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_856) ).
thf(3263,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).
thf(1028,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_881) ).
thf(3221,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).
thf(1015,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_276) ).
thf(3195,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).
thf(932,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1016) ).
thf(3029,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).
thf(785,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_382) ).
thf(2735,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(410,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_191) ).
thf(1985,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(437,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_88) ).
thf(2039,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(1055,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_475) ).
thf(3275,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).
thf(983,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_451) ).
thf(3131,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).
thf(66,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_330) ).
thf(1298,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(795,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_776) ).
thf(2755,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(1165,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_219) ).
thf(3495,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).
thf(371,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1093) ).
thf(1907,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(668,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1141) ).
thf(2501,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(82,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1130) ).
thf(1330,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_645) ).
thf(1264,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(526,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_648) ).
thf(2217,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(173,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1102) ).
thf(1511,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(1160,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_249) ).
thf(3485,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).
thf(510,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_981) ).
thf(2185,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(206,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_58) ).
thf(1577,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(145,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_904) ).
thf(1455,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(790,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_200) ).
thf(2745,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(703,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1051) ).
thf(2571,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(190,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1023) ).
thf(1545,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(763,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_866) ).
thf(2691,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(967,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_581) ).
thf(3099,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).
thf(774,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_469) ).
thf(2713,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(846,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_400) ).
thf(2857,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).
thf(442,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_928) ).
thf(2049,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(801,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_66) ).
thf(2767,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(604,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_36) ).
thf(2373,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(288,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_837) ).
thf(1741,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(383,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_984) ).
thf(1931,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(238,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_316) ).
thf(1641,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(304,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_751) ).
thf(1773,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(355,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_790) ).
thf(1875,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(1033,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_833) ).
thf(3231,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).
thf(684,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_383) ).
thf(2533,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1059) ).
thf(1232,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(341,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_349) ).
thf(1847,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(832,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_606) ).
thf(2829,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(1110,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_428) ).
thf(3385,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).
thf(1149,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_147) ).
thf(3463,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).
thf(107,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_730) ).
thf(1379,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(502,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1143) ).
thf(2169,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(619,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_0) ).
thf(2403,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(157,axiom,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_583) ).
thf(1479,plain,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(222,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_240) ).
thf(1609,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(735,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_955) ).
thf(2635,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(882,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1166) ).
thf(2929,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).
thf(568,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_408) ).
thf(2301,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(325,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_203) ).
thf(1815,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(912,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1165) ).
thf(2989,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).
thf(399,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_221) ).
thf(1963,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(421,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1050) ).
thf(2007,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(150,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1053) ).
thf(1465,plain,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(1133,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
thf(3431,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_448) ).
thf(1302,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(431,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_352) ).
thf(2027,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(1017,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_126) ).
thf(3199,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).
thf(1114,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_26) ).
thf(3393,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_720) ).
thf(1373,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(547,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_83) ).
thf(2259,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(999,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_339) ).
thf(3163,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).
thf(880,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_477) ).
thf(2925,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).
thf(256,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1096) ).
thf(1677,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(806,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_959) ).
thf(2777,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(454,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1142) ).
thf(2073,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(426,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_610) ).
thf(2017,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_412) ).
thf(1489,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(536,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1031) ).
thf(2237,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_743) ).
thf(1415,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(470,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_473) ).
thf(2105,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(955,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_726) ).
thf(3075,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).
thf(323,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_764) ).
thf(1811,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(373,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_996) ).
thf(1911,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(1065,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_32) ).
thf(3295,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).
thf(864,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_573) ).
thf(2893,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).
thf(652,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_113) ).
thf(2469,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(1144,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_971) ).
thf(3453,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).
thf(643,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_377) ).
thf(2451,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_541) ).
thf(1334,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(1154,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_623) ).
thf(3473,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).
thf(563,axiom,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_170) ).
thf(2291,plain,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(109,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_218) ).
thf(1383,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(1096,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_262) ).
thf(3357,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).
thf(695,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_597) ).
thf(2555,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(964,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_186) ).
thf(3093,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).
thf(208,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_114) ).
thf(1581,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(585,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_705) ).
thf(2335,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(1112,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_141) ).
thf(3389,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).
thf(339,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_508) ).
thf(1843,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_875) ).
thf(1377,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(848,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_50) ).
thf(2861,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).
thf(1128,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1077) ).
thf(3421,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).
thf(679,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_809) ).
thf(2523,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(996,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_951) ).
thf(3157,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).
thf(486,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_419) ).
thf(2137,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(93,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10) ).
thf(1351,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(389,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_897) ).
thf(1943,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(900,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_357) ).
thf(2965,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).
thf(520,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_225) ).
thf(2205,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(405,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
thf(1975,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(601,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_127) ).
thf(2367,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(636,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_332) ).
thf(2437,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(834,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_967) ).
thf(2833,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(1012,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_746) ).
thf(3189,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).
thf(558,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1058) ).
thf(2281,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(141,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_27) ).
thf(1447,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(659,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_317) ).
thf(2483,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(603,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_95) ).
thf(2371,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(907,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_491) ).
thf(2979,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).
thf(1098,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1100) ).
thf(3361,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).
thf(1039,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_146) ).
thf(3243,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).
thf(822,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_947) ).
thf(2809,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(817,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_224) ).
thf(2799,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).
thf(737,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_122) ).
thf(2639,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(1081,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_248) ).
thf(3327,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_685) ).
thf(1433,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(469,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_603) ).
thf(2103,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(120,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_427) ).
thf(1405,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(266,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_194) ).
thf(1697,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(38,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_523) ).
thf(1242,plain,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(1023,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_906) ).
thf(3211,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).
thf(178,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_727) ).
thf(1521,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(243,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_363) ).
thf(1651,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(1032,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_637) ).
thf(3229,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).
thf(1147,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_388) ).
thf(3459,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).
thf(654,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_48) ).
thf(2473,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(263,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_939) ).
thf(1691,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(70,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_510) ).
thf(1306,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(86,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_421) ).
thf(1338,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(441,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_557) ).
thf(2047,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(571,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_911) ).
thf(2307,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(738,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_251) ).
thf(2641,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(870,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1049) ).
thf(2905,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).
thf(936,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_568) ).
thf(3037,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).
thf(349,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_647) ).
thf(1863,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(1135,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_822) ).
thf(3435,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).
thf(993,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_679) ).
thf(3151,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).
thf(423,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_693) ).
thf(2011,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(966,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1011) ).
thf(3097,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).
thf(923,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_305) ).
thf(3011,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_97) ).
thf(1206,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1068,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_154) ).
thf(3301,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).
thf(1069,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_675) ).
thf(3303,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).
thf(1002,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1028) ).
thf(3169,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).
thf(1050,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_999) ).
thf(3265,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).
thf(375,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_927) ).
thf(1915,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(464,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1113) ).
thf(2093,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(309,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_257) ).
thf(1783,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(786,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_261) ).
thf(2737,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(459,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_323) ).
thf(2083,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(728,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_854) ).
thf(2621,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(448,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_781) ).
thf(2061,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(804,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_953) ).
thf(2773,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(712,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_567) ).
thf(2589,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(1048,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_201) ).
thf(3261,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).
thf(718,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1002) ).
thf(2601,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(542,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_516) ).
thf(2249,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(688,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_997) ).
thf(2541,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(177,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1056) ).
thf(1519,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(491,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_843) ).
thf(2147,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(293,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_831) ).
thf(1751,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(161,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1117) ).
thf(1487,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(902,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_842) ).
thf(2969,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).
thf(227,axiom,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_599) ).
thf(1619,plain,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(1021,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_17) ).
thf(3207,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_577) ).
thf(1274,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(638,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1006) ).
thf(2441,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(754,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_544) ).
thf(2673,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(770,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_104) ).
thf(2705,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(622,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_415) ).
thf(2409,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_719) ).
thf(1387,plain,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(279,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_237) ).
thf(1723,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(784,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_53) ).
thf(2733,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(820,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_835) ).
thf(2805,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(95,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_862) ).
thf(1355,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(556,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_435) ).
thf(2277,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_233) ).
thf(1174,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(484,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_622) ).
thf(2133,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(1037,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_172) ).
thf(3239,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).
thf(952,axiom,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_372) ).
thf(3069,plain,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).
thf(1034,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_462) ).
thf(3233,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).
thf(1103,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1087) ).
thf(3371,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).
thf(886,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_617) ).
thf(2937,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).
thf(1087,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_530) ).
thf(3339,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1095) ).
thf(1238,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(425,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_350) ).
thf(2015,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(1153,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_420) ).
thf(3471,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).
thf(359,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_974) ).
thf(1883,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_795) ).
thf(1365,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1120) ).
thf(1178,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(393,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_538) ).
thf(1951,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_744) ).
thf(1296,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(327,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_558) ).
thf(1819,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(722,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_965) ).
thf(2609,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(507,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_969) ).
thf(2179,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_314) ).
thf(1210,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(590,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_207) ).
thf(2345,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(788,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_378) ).
thf(2741,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(934,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1035) ).
thf(3033,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).
thf(204,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1046) ).
thf(1573,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(744,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_673) ).
thf(2653,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(129,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_64) ).
thf(1423,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(1071,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_722) ).
thf(3307,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).
thf(1053,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_970) ).
thf(3271,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).
thf(640,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_539) ).
thf(2445,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(1013,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_211) ).
thf(3191,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).
thf(854,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_328) ).
thf(2873,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).
thf(336,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1152) ).
thf(1837,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(1052,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_374) ).
thf(3269,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).
thf(634,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_624) ).
thf(2433,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(656,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_234) ).
thf(2477,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(1119,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_750) ).
thf(3403,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).
thf(700,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_914) ).
thf(2565,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(749,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_937) ).
thf(2663,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(195,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_110) ).
thf(1555,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(1066,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_92) ).
thf(3297,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).
thf(986,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_12) ).
thf(3137,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).
thf(1167,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_543) ).
thf(3499,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).
thf(950,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_131) ).
thf(3065,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).
thf(1092,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_282) ).
thf(3349,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).
thf(261,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_441) ).
thf(1687,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(146,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_403) ).
thf(1457,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(311,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_504) ).
thf(1787,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(508,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_283) ).
thf(2181,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(581,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_106) ).
thf(2327,plain,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(524,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_966) ).
thf(2213,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(523,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_803) ).
thf(2211,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_849) ).
thf(1407,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(691,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_871) ).
thf(2547,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(574,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_702) ).
thf(2313,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(802,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_850) ).
thf(2769,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(1140,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_828) ).
thf(3445,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).
thf(409,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_700) ).
thf(1983,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(865,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_899) ).
thf(2895,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).
thf(772,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_723) ).
thf(2709,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(211,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1145) ).
thf(1587,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_551) ).
thf(1425,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(672,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_560) ).
thf(2509,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(733,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_142) ).
thf(2631,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(977,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_956) ).
thf(3119,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).
thf(1020,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1116) ).
thf(3205,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).
thf(918,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_245) ).
thf(3001,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).
thf(540,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_124) ).
thf(2245,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(92,axiom,
! [A: $i] : ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_299) ).
thf(1350,plain,
! [A: $i] : ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(970,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_890) ).
thf(3105,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).
thf(1151,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_297) ).
thf(3467,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_869) ).
thf(1234,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(188,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_579) ).
thf(1541,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(496,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_331) ).
thf(2157,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(475,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_690) ).
thf(2115,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(675,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_137) ).
thf(2515,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(1124,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_62) ).
thf(3413,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).
thf(52,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_657) ).
thf(1270,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(343,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_456) ).
thf(1851,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(606,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_22) ).
thf(2377,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(818,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_488) ).
thf(2801,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(394,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_123) ).
thf(1953,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(760,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_279) ).
thf(2685,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(838,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_913) ).
thf(2841,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_811) ).
thf(1328,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(904,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_14) ).
thf(2973,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).
thf(597,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_502) ).
thf(2359,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(105,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_633) ).
thf(1375,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(706,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_891) ).
thf(2577,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(1108,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_461) ).
thf(3381,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).
thf(277,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_595) ).
thf(1719,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(686,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_135) ).
thf(2537,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(1036,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_193) ).
thf(3237,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).
thf(295,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1001) ).
thf(1755,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(961,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_145) ).
thf(3087,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).
thf(116,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_268) ).
thf(1397,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(201,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_531) ).
thf(1567,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(429,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1086) ).
thf(2023,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(989,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_934) ).
thf(3143,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_684) ).
thf(1361,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(247,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_492) ).
thf(1659,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_736) ).
thf(1292,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_668) ).
thf(1182,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(627,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_81) ).
thf(2419,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(444,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_832) ).
thf(2053,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(313,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_755) ).
thf(1791,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(362,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_318) ).
thf(1889,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(742,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_630) ).
thf(2649,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(576,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_672) ).
thf(2317,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(164,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_680) ).
thf(1493,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(259,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1061) ).
thf(1683,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(988,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_228) ).
thf(3141,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).
thf(1073,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_656) ).
thf(3311,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).
thf(856,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_180) ).
thf(2877,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).
thf(579,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_935) ).
thf(2323,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(1007,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1159) ).
thf(3179,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).
thf(1121,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_785) ).
thf(3407,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).
thf(698,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_501) ).
thf(2561,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(287,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1148) ).
thf(1739,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(148,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_171) ).
thf(1461,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(1138,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_596) ).
thf(3441,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).
thf(645,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_410) ).
thf(2455,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(724,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_847) ).
thf(2613,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(386,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_759) ).
thf(1937,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_686) ).
thf(1214,plain,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(592,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_767) ).
thf(2349,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(693,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1107) ).
thf(2551,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(460,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
thf(2085,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(808,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_74) ).
thf(2781,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_468) ).
thf(1419,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(480,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_280) ).
thf(2125,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(677,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_470) ).
thf(2519,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(758,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_777) ).
thf(2681,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(143,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_522) ).
thf(1451,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(187,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1122) ).
thf(1539,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(670,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_68) ).
thf(2505,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(666,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_216) ).
thf(2497,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(317,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_724) ).
thf(1799,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(391,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_846) ).
thf(1947,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(824,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_896) ).
thf(2813,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(975,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_169) ).
thf(3115,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).
thf(330,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_524) ).
thf(1825,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_271) ).
thf(1324,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(560,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_220) ).
thf(2285,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(661,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_517) ).
thf(2487,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(840,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_992) ).
thf(2845,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(947,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_25) ).
thf(3059,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1129) ).
thf(1266,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(494,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_358) ).
thf(2153,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(611,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_762) ).
thf(2387,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(333,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_353) ).
thf(1831,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(843,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_288) ).
thf(2851,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(539,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1097) ).
thf(2243,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(595,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_290) ).
thf(2355,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_289) ).
thf(1192,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(708,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_709) ).
thf(2581,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(650,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_858) ).
thf(2465,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_437) ).
thf(1429,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(1041,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_281) ).
thf(3247,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).
thf(1122,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1012) ).
thf(3409,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).
thf(217,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_902) ).
thf(1599,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(766,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_486) ).
thf(2697,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_79) ).
thf(1246,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(275,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1161) ).
thf(1715,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(1084,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_586) ).
thf(3333,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).
thf(972,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_526) ).
thf(3109,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).
thf(407,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_535) ).
thf(1979,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(920,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_532) ).
thf(3005,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).
thf(959,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_851) ).
thf(3083,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).
thf(1018,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_449) ).
thf(3201,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).
thf(297,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_554) ).
thf(1759,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(114,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_102) ).
thf(1393,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(231,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_852) ).
thf(1627,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(1025,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_100) ).
thf(3215,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).
thf(180,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_259) ).
thf(1525,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(991,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1032) ).
thf(3147,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).
thf(1030,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_303) ).
thf(3225,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).
thf(798,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_379) ).
thf(2761,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(307,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_497) ).
thf(1779,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(265,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_138) ).
thf(1695,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(199,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_994) ).
thf(1563,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(446,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_954) ).
thf(2057,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_61) ).
thf(1170,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(875,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_292) ).
thf(2915,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).
thf(365,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1010) ).
thf(1895,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(726,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_423) ).
thf(2617,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(872,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_208) ).
thf(2909,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).
thf(792,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_588) ).
thf(2749,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(346,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_932) ).
thf(1857,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(413,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1136) ).
thf(1991,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1147) ).
thf(1318,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_677) ).
thf(1202,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(519,axiom,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_368) ).
thf(2203,plain,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(439,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_728) ).
thf(2043,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(1057,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_185) ).
thf(3279,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).
thf(1009,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_805) ).
thf(3183,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).
thf(859,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_821) ).
thf(2883,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).
thf(1004,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_295) ).
thf(3173,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).
thf(899,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_651) ).
thf(2963,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).
thf(60,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_695) ).
thf(1286,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(1078,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_689) ).
thf(3321,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).
thf(814,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_278) ).
thf(2793,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(249,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1084) ).
thf(1663,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(462,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_545) ).
thf(2089,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(175,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1038) ).
thf(1515,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(528,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_222) ).
thf(2221,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(740,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_537) ).
thf(2645,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(512,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1153) ).
thf(2189,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(915,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_43) ).
thf(2995,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).
thf(629,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_753) ).
thf(2423,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(682,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
thf(2529,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(56,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_344) ).
thf(1278,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(782,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_163) ).
thf(2729,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(418,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_848) ).
thf(2001,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(281,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_390) ).
thf(1727,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(624,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_758) ).
thf(2413,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(756,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_694) ).
thf(2677,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(613,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_418) ).
thf(2391,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(397,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_42) ).
thf(1959,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(710,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_111) ).
thf(2585,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(381,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_986) ).
thf(1927,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(1062,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_459) ).
thf(3289,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).
thf(973,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_706) ).
thf(3111,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).
thf(233,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1044) ).
thf(1631,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(1089,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1027) ).
thf(3343,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).
thf(478,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_616) ).
thf(2121,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(535,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_160) ).
thf(2235,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(544,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_143) ).
thf(2253,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(555,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_337) ).
thf(2275,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(434,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_769) ).
thf(2033,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(492,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_844) ).
thf(2149,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(1046,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_933) ).
thf(3257,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).
thf(776,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_590) ).
thf(2717,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(1163,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_244) ).
thf(3491,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_51) ).
thf(1483,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(957,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1036) ).
thf(3079,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).
thf(291,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1160) ).
thf(1747,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(888,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_960) ).
thf(2941,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).
thf(1105,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_250) ).
thf(3375,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).
thf(215,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_788) ).
thf(1595,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(334,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_30) ).
thf(1833,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(781,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1067) ).
thf(2727,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(1077,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_613) ).
thf(3319,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).
thf(847,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_265) ).
thf(2859,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).
thf(530,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1118) ).
thf(2225,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(813,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_880) ).
thf(2791,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(812,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_741) ).
thf(2789,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(908,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_156) ).
thf(2981,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).
thf(662,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_552) ).
thf(2489,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(614,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_55) ).
thf(2393,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(1059,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_310) ).
thf(3283,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).
thf(119,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_67) ).
thf(1403,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(400,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_241) ).
thf(1965,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(826,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_618) ).
thf(2817,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).
thf(831,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_243) ).
thf(2827,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(1111,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_440) ).
thf(3387,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).
thf(1011,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_667) ).
thf(3187,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_940) ).
thf(1615,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(112,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_987) ).
thf(1389,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(1045,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_296) ).
thf(3255,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).
thf(680,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1156) ).
thf(2525,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(746,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_734) ).
thf(2657,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(842,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_246) ).
thf(2849,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).
thf(958,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_119) ).
thf(3081,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).
thf(382,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1075) ).
thf(1929,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(185,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1029) ).
thf(1535,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(913,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_748) ).
thf(2991,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).
thf(315,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1108) ).
thf(1795,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(268,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_653) ).
thf(1701,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(30,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_391) ).
thf(1226,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(765,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_313) ).
thf(2695,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1088) ).
thf(1256,plain,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(897,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_814) ).
thf(2959,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).
thf(1024,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_807) ).
thf(3213,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).
thf(169,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_269) ).
thf(1503,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(432,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_688) ).
thf(2029,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(73,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_153) ).
thf(1312,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(350,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_857) ).
thf(1865,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(416,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1033) ).
thf(1997,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(300,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_454) ).
thf(1765,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(630,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1072) ).
thf(2425,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_710) ).
thf(1258,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(963,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_35) ).
thf(3091,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).
thf(255,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1004) ).
thf(1675,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(1029,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_870) ).
thf(3223,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).
thf(498,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_270) ).
thf(2161,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(514,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_864) ).
thf(2193,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(929,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1127) ).
thf(3023,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).
thf(252,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_455) ).
thf(1669,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(271,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_376) ).
thf(1707,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(564,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_285) ).
thf(2293,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(943,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_794) ).
thf(3051,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).
thf(863,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_782) ).
thf(2891,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_494) ).
thf(1371,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(956,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_865) ).
thf(3077,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).
thf(235,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_665) ).
thf(1635,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(885,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1137) ).
thf(2935,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).
thf(284,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_566) ).
thf(1733,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(83,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_801) ).
thf(1332,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(979,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_878) ).
thf(3123,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).
thf(797,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_178) ).
thf(2759,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(794,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_701) ).
thf(2753,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(1161,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_924) ).
thf(3487,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).
thf(445,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1106) ).
thf(2055,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(646,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_188) ).
thf(2457,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(366,axiom,
~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_546) ).
thf(1897,plain,
~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(696,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_708) ).
thf(2557,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(1095,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_520) ).
thf(3355,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1000) ).
thf(1224,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(704,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_359) ).
thf(2573,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(577,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_611) ).
thf(2319,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_99) ).
thf(1194,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(757,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_824) ).
thf(2679,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(344,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_215) ).
thf(1853,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(609,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_608) ).
thf(2383,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(736,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_621) ).
thf(2637,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(1061,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_661) ).
thf(3287,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).
thf(1127,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1146) ).
thf(3419,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).
thf(466,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_797) ).
thf(2097,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(752,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_841) ).
thf(2669,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(837,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_187) ).
thf(2839,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(450,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_592) ).
thf(2065,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(457,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1139) ).
thf(2079,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(598,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_21) ).
thf(2361,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(573,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_247) ).
thf(2311,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(968,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_655) ).
thf(3101,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).
thf(678,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_915) ).
thf(2521,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(778,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_670) ).
thf(2721,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(477,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_471) ).
thf(2119,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_286) ).
thf(1282,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(1043,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_227) ).
thf(3251,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).
thf(493,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_175) ).
thf(2151,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(995,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_355) ).
thf(3155,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).
thf(532,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1057) ).
thf(2229,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(625,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_65) ).
thf(2415,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(664,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_922) ).
thf(2493,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(911,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_804) ).
thf(2987,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).
thf(384,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_813) ).
thf(1933,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(546,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1099) ).
thf(2257,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1014) ).
thf(1589,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(895,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_625) ).
thf(2955,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).
thf(219,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_354) ).
thf(1603,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(567,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_918) ).
thf(2299,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(303,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_155) ).
thf(1771,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(889,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_87) ).
thf(2943,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).
thf(890,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_264) ).
thf(2945,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).
thf(1016,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_474) ).
thf(3197,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).
thf(318,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_972) ).
thf(1801,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(203,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_612) ).
thf(1571,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(853,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_254) ).
thf(2871,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).
thf(137,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_236) ).
thf(1439,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(516,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1144) ).
thf(2197,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(402,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_436) ).
thf(1969,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(251,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_963) ).
thf(1667,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(1027,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_308) ).
thf(3219,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).
thf(430,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1022) ).
thf(2025,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(414,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_28) ).
thf(1993,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(551,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_327) ).
thf(2267,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(372,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_978) ).
thf(1909,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(796,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_619) ).
thf(2757,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(1000,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_515) ).
thf(3165,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).
thf(879,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_380) ).
thf(2923,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).
thf(694,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_333) ).
thf(2553,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(108,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_457) ).
thf(1381,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(648,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_439) ).
thf(2461,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(582,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_995) ).
thf(2329,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(873,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_195) ).
thf(2911,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).
thf(356,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_886) ).
thf(1877,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(153,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1158) ).
thf(1471,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(720,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_256) ).
thf(2605,plain,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(931,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_16) ).
thf(3027,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).
thf(984,axiom,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_443) ).
thf(3133,plain,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).
thf(945,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_326) ).
thf(3055,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).
thf(196,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_983) ).
thf(1557,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(482,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1041) ).
thf(2129,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(589,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_121) ).
thf(2343,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(730,axiom,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_334) ).
thf(2625,plain,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(473,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_528) ).
thf(2111,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(954,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_907) ).
thf(3073,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).
thf(548,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_634) ).
thf(2261,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(328,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_209) ).
thf(1821,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(283,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_627) ).
thf(1731,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(810,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1079) ).
thf(2785,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(714,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1083) ).
thf(2593,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(1143,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_223) ).
thf(3451,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).
thf(1159,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_786) ).
thf(3483,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_919) ).
thf(1344,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(562,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_307) ).
thf(2289,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(741,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_242) ).
thf(2647,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(455,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_511) ).
thf(2075,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(600,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_635) ).
thf(2365,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(503,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_70) ).
thf(2171,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(835,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1163) ).
thf(2835,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(140,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_389) ).
thf(1445,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(239,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_453) ).
thf(1643,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(487,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_780) ).
thf(2139,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_944) ).
thf(1176,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(883,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_151) ).
thf(2931,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).
thf(569,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_460) ).
thf(2303,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(917,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_839) ).
thf(2999,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).
thf(521,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_266) ).
thf(2207,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(764,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1034) ).
thf(2693,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_46) ).
thf(1198,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(338,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_658) ).
thf(1841,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(637,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_739) ).
thf(2439,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(780,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_108) ).
thf(2725,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(618,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1133) ).
thf(2401,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(267,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_977) ).
thf(1699,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(443,axiom,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_80) ).
thf(2051,plain,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(800,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_426) ).
thf(2765,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(1129,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_678) ).
thf(3423,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).
thf(658,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_721) ).
thf(2481,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(997,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_712) ).
thf(3159,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).
thf(602,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_140) ).
thf(2369,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(1038,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1128) ).
thf(3241,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).
thf(816,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1110) ).
thf(2797,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(305,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_129) ).
thf(1775,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(135,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_773) ).
thf(1435,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(734,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_565) ).
thf(2633,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(1099,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_948) ).
thf(3363,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).
thf(156,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_620) ).
thf(1477,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(1080,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_190) ).
thf(3325,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).
thf(685,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_351) ).
thf(2535,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(468,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_760) ).
thf(2101,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(901,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_45) ).
thf(2967,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_322) ).
thf(1250,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(404,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_484) ).
thf(1973,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(320,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_660) ).
thf(1805,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(452,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1085) ).
thf(2069,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(851,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_482) ).
thf(2867,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).
thf(922,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_789) ).
thf(3009,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).
thf(537,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_885) ).
thf(2239,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(322,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_792) ).
thf(1809,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(471,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_912) ).
thf(2107,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_214) ).
thf(1208,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(750,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_836) ).
thf(2665,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(151,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_757) ).
thf(1467,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(436,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_411) ).
thf(2037,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(669,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1157) ).
thf(2503,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(87,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_774) ).
thf(1340,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(1145,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_714) ).
thf(3455,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).
thf(584,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
thf(2333,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(716,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_775) ).
thf(2597,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(867,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_336) ).
thf(2899,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).
thf(193,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_742) ).
thf(1551,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(420,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1071) ).
thf(2005,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1134) ).
thf(1413,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(933,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_202) ).
thf(3031,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).
thf(209,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_232) ).
thf(1583,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(69,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_287) ).
thf(1304,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(354,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_740) ).
thf(1873,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(1014,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_159) ).
thf(3193,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).
thf(1131,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1013) ).
thf(3427,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).
thf(1115,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_731) ).
thf(3395,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).
thf(553,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_715) ).
thf(2271,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(1064,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_765) ).
thf(3293,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).
thf(653,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
thf(2471,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(998,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_909) ).
thf(3161,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).
thf(370,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_34) ).
thf(1905,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(642,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1149) ).
thf(2449,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(172,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_752) ).
thf(1509,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(881,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_198) ).
thf(2927,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).
thf(732,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_267) ).
thf(2629,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(191,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_888) ).
thf(1547,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(1113,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_584) ).
thf(3391,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).
thf(775,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_799) ).
thf(2715,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(398,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1008) ).
thf(1961,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(616,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_192) ).
thf(2397,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(748,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_505) ).
thf(2661,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(289,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_161) ).
thf(1743,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(489,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_916) ).
thf(2143,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(220,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_324) ).
thf(1605,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(241,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_217) ).
thf(1647,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(982,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_115) ).
thf(3129,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).
thf(505,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_369) ).
thf(2175,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(183,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_640) ).
thf(1531,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_574) ).
thf(1230,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(340,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_165) ).
thf(1845,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(674,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_957) ).
thf(2513,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(701,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_626) ).
thf(2567,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(849,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1060) ).
thf(2863,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).
thf(1075,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_713) ).
thf(3315,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).
thf(906,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1065) ).
thf(2977,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_393) ).
thf(1611,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(605,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_884) ).
thf(2375,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(388,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_275) ).
thf(1941,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_942) ).
thf(1252,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(828,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1092) ).
thf(2821,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(1022,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_263) ).
thf(3209,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).
thf(294,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1103) ).
thf(1753,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(621,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_819) ).
thf(2407,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(833,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_23) ).
thf(2831,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(762,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_309) ).
thf(2689,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(702,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_361) ).
thf(2569,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(411,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_990) ).
thf(1987,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(949,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_118) ).
thf(3063,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).
thf(352,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_82) ).
thf(1869,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(310,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_371) ).
thf(1785,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(48,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_158) ).
thf(1262,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(586,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_168) ).
thf(2337,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(527,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_591) ).
thf(2219,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(368,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_59) ).
thf(1901,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(257,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_329) ).
thf(1679,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_802) ).
thf(1579,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(85,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_628) ).
thf(1336,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_950) ).
thf(1220,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(273,axiom,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_593) ).
thf(1711,plain,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(927,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_810) ).
thf(3019,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).
thf(791,axiom,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_876) ).
thf(2747,plain,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(167,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_164) ).
thf(1499,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(1070,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_166) ).
thf(3305,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).
thf(500,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_210) ).
thf(2165,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(324,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_152) ).
thf(1813,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1125) ).
thf(1300,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(236,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1132) ).
thf(1637,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(1054,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_13) ).
thf(3273,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_101) ).
thf(1188,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_365) ).
thf(1186,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1155,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_883) ).
thf(3475,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).
thf(632,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_861) ).
thf(2429,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(299,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_116) ).
thf(1763,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(981,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1105) ).
thf(3127,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).
thf(768,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_894) ).
thf(2701,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(869,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_998) ).
thf(2903,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).
thf(690,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_96) ).
thf(2545,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(717,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_575) ).
thf(2599,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(1097,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_387) ).
thf(3359,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).
thf(1082,axiom,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_464) ).
thf(3329,plain,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_398) ).
thf(1218,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(938,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_56) ).
thf(3041,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).
thf(965,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_716) ).
thf(3095,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).
thf(623,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_717) ).
thf(2411,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(342,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_729) ).
thf(1849,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(408,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_238) ).
thf(1981,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(1164,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_882) ).
thf(3493,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).
thf(607,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_128) ).
thf(2379,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(689,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_644) ).
thf(2543,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(707,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_362) ).
thf(2579,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(316,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_367) ).
thf(1797,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(276,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_917) ).
thf(1717,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(887,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_563) ).
thf(2939,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).
thf(953,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_676) ).
thf(3071,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).
thf(921,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_816) ).
thf(3007,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).
thf(755,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1017) ).
thf(2675,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(541,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_63) ).
thf(2247,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(189,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1131) ).
thf(1543,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(971,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_925) ).
thf(3107,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).
thf(474,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_69) ).
thf(2113,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(1125,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_321) ).
thf(3415,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).
thf(59,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_431) ).
thf(1284,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(905,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_887) ).
thf(2975,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_144) ).
thf(1353,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(557,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_830) ).
thf(2279,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(596,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_485) ).
thf(2357,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(395,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_506) ).
thf(1955,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(839,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_929) ).
thf(2843,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(490,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1062) ).
thf(2145,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(160,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_72) ).
thf(1485,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(773,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_900) ).
thf(2711,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(292,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_130) ).
thf(1749,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(131,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1080) ).
thf(1427,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(210,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_519) ).
thf(1585,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(673,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1030) ).
thf(2511,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(976,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_483) ).
thf(3117,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).
thf(892,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1140) ).
thf(2949,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).
thf(358,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_855) ).
thf(1881,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(821,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1026) ).
thf(2807,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(53,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_300) ).
thf(1272,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(37,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_91) ).
thf(1240,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(226,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_199) ).
thf(1617,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(635,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_413) ).
thf(2435,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(1134,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_452) ).
thf(3433,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).
thf(657,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_39) ).
thf(2479,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(1118,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_395) ).
thf(3401,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).
thf(194,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_366) ).
thf(1553,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(392,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_962) ).
thf(1949,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(374,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_853) ).
thf(1913,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(1141,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_564) ).
thf(3447,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).
thf(591,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_89) ).
thf(2347,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(937,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_823) ).
thf(3039,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).
thf(850,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_943) ).
thf(2865,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).
thf(855,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_132) ).
thf(2875,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).
thf(128,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_756) ).
thf(1421,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(424,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_112) ).
thf(2013,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(337,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_463) ).
thf(1839,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(987,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_594) ).
thf(3139,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).
thf(1146,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1070) ).
thf(3457,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1098) ).
thf(1316,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(242,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_499) ).
thf(1649,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(147,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_572) ).
thf(1459,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(440,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_399) ).
thf(2045,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(951,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_181) ).
thf(3067,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_550) ).
thf(1180,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(260,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_370) ).
thf(1685,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(860,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_587) ).
thf(2885,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).
thf(326,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_229) ).
thf(1817,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(1003,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_859) ).
thf(3171,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).
thf(525,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_553) ).
thf(2215,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(176,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1090) ).
thf(1517,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(723,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_84) ).
thf(2611,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(580,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_231) ).
thf(2325,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(308,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_910) ).
thf(1781,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(25,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_703) ).
thf(1216,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(522,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_183) ).
thf(2209,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(789,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_148) ).
thf(2743,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(916,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_258) ).
thf(2997,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).
thf(511,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_615) ).
thf(2187,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(570,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_430) ).
thf(2305,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(877,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_422) ).
thf(2919,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).
thf(205,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_903) ).
thf(1575,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1007) ).
thf(1453,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(739,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_549) ).
thf(2643,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(453,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_827) ).
thf(2071,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(805,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_54) ).
thf(2775,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(321,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1055) ).
thf(1807,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(871,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_345) ).
thf(2907,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).
thf(639,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_467) ).
thf(2443,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_401) ).
thf(1326,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(771,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_341) ).
thf(2707,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(290,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_212) ).
thf(1745,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(903,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_447) ).
thf(2971,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).
thf(179,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1154) ).
thf(1523,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(1083,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_905) ).
thf(3331,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).
thf(960,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1009) ).
thf(3085,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).
thf(1150,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_936) ).
thf(3465,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_315) ).
thf(1276,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(713,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_480) ).
thf(2591,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(110,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_664) ).
thf(1385,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(278,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_481) ).
thf(1721,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(501,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_312) ).
thf(2167,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(554,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_478) ).
thf(2273,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(559,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_226) ).
thf(2283,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(612,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_500) ).
thf(2389,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(845,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1018) ).
thf(2855,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).
thf(237,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_982) ).
thf(1639,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(844,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_646) ).
thf(2853,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).
thf(543,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_691) ).
thf(2251,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(369,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1047) ).
thf(1903,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(485,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_496) ).
thf(2135,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(158,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_652) ).
thf(1481,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(1109,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_872) ).
thf(3383,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).
thf(1102,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_335) ).
thf(3369,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).
thf(829,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1052) ).
thf(2823,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).
thf(823,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1094) ).
thf(2811,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(232,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_662) ).
thf(1629,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(1035,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1150) ).
thf(3235,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).
thf(633,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1003) ).
thf(2431,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(919,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1114) ).
thf(3003,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_985) ).
thf(1244,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(641,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_787) ).
thf(2447,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_961) ).
thf(1491,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(1166,axiom,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_818) ).
thf(3497,plain,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).
thf(306,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_396) ).
thf(1777,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(992,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_162) ).
thf(3149,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).
thf(71,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_993) ).
thf(1308,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(221,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_381) ).
thf(1607,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(248,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_826) ).
thf(1661,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(465,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1121) ).
thf(2095,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(364,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_272) ).
thf(1893,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(575,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_77) ).
thf(2315,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(787,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_968) ).
thf(2739,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(628,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1104) ).
thf(2421,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(422,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_205) ).
thf(2009,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(348,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_683) ).
thf(1861,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(262,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_806) ).
thf(1689,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(458,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_798) ).
thf(2081,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(1008,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_920) ).
thf(3181,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).
thf(655,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_507) ).
thf(2475,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(617,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_609) ).
thf(2399,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(438,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_294) ).
thf(2041,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(1051,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_989) ).
thf(3267,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).
thf(64,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1138) ).
thf(1294,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(509,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_509) ).
thf(2183,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_206) ).
thf(1212,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1093,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1066) ).
thf(3351,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).
thf(174,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_120) ).
thf(1513,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(876,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1126) ).
thf(2917,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).
thf(729,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_444) ).
thf(2623,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(807,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_973) ).
thf(2779,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(427,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_182) ).
thf(2019,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(479,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_527) ).
thf(2123,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(91,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_348) ).
thf(1348,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(561,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1164) ).
thf(2287,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(396,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_407) ).
thf(1957,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(610,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_86) ).
thf(2385,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(1063,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_754) ).
thf(3291,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).
thf(711,axiom,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_868) ).
thf(2587,plain,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(534,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_600) ).
thf(2233,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(893,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_791) ).
thf(2951,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).
thf(825,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_945) ).
thf(2815,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1081) ).
thf(1248,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(296,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_614) ).
thf(1757,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(1019,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_343) ).
thf(3203,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).
thf(1152,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_632) ).
thf(3469,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).
thf(419,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_37) ).
thf(2003,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(1107,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_659) ).
thf(3379,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).
thf(676,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1091) ).
thf(2517,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(759,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_384) ).
thf(2683,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(280,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_487) ).
thf(1725,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(57,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_834) ).
thf(1280,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(495,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_85) ).
thf(2155,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(545,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_812) ).
thf(2255,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(909,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_540) ).
thf(2983,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).
thf(777,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_580) ).
thf(2719,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(115,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_458) ).
thf(1395,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(230,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11) ).
thf(1625,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(1104,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1019) ).
thf(3373,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).
thf(214,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_252) ).
thf(1593,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_445) ).
thf(1527,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(1086,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_980) ).
thf(3337,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).
thf(254,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_838) ).
thf(1673,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(925,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_548) ).
thf(3015,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).
thf(347,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1151) ).
thf(1859,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(793,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_465) ).
thf(2751,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(165,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_503) ).
thf(1495,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(246,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_176) ).
thf(1657,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(1006,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_604) ).
thf(3177,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).
thf(264,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_196) ).
thf(1693,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(198,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_47) ).
thf(1561,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(312,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_784) ).
thf(1789,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(363,axiom,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_434) ).
thf(1891,plain,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(727,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1111) ).
thf(2619,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(940,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_779) ).
thf(3045,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).
thf(743,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_405) ).
thf(2651,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(809,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_105) ).
thf(2783,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(692,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_149) ).
thf(2549,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(1072,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_718) ).
thf(3309,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).
thf(990,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_766) ).
thf(3145,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).
thf(518,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_342) ).
thf(2201,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(412,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_793) ).
thf(1989,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_498) ).
thf(1363,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1112) ).
thf(1314,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(1091,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_533) ).
thf(3347,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).
thf(1056,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1021) ).
thf(3277,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_975) ).
thf(1172,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1157,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_20) ).
thf(3479,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).
thf(626,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_518) ).
thf(2417,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(898,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_570) ).
thf(2961,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_863) ).
thf(1288,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(874,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1040) ).
thf(2913,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).
thf(463,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_817) ).
thf(2091,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(1079,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1119) ).
thf(3323,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).
thf(529,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_338) ).
thf(2223,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(815,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_631) ).
thf(2795,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_529) ).
thf(1473,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(428,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_356) ).
thf(2021,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(90,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_107) ).
thf(1346,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(449,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_946) ).
thf(2063,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(594,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_663) ).
thf(2353,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_416) ).
thf(1268,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(550,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_874) ).
thf(2265,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(651,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_495) ).
thf(2467,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(1162,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1039) ).
thf(3489,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).
thf(671,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_873) ).
thf(2507,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(380,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_893) ).
thf(1925,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(974,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_747) ).
thf(3113,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).
thf(1088,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_534) ).
thf(3341,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_73) ).
thf(1236,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(538,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_385) ).
thf(2241,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(481,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_692) ).
thf(2127,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(497,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_306) ).
thf(2159,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(783,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_18) ).
thf(2731,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(332,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1101) ).
thf(1829,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(406,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
thf(1977,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(930,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1076) ).
thf(3025,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).
thf(331,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1042) ).
thf(1827,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(946,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_167) ).
thf(3057,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).
thf(819,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_901) ).
thf(2803,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(841,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1015) ).
thf(2847,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(1123,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_41) ).
thf(3411,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).
thf(660,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_840) ).
thf(2485,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(186,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_479) ).
thf(1537,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(96,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_761) ).
thf(1357,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(709,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1043) ).
thf(2583,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(1047,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_442) ).
thf(3259,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).
thf(379,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_749) ).
thf(1923,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(1040,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1073) ).
thf(3245,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).
thf(687,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_561) ).
thf(2539,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(274,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_417) ).
thf(1713,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(216,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_117) ).
thf(1597,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(761,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_931) ).
thf(2687,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(133,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_783) ).
thf(1431,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(360,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_340) ).
thf(1885,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(767,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_364) ).
thf(2699,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(170,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_438) ).
thf(1505,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(117,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_320) ).
thf(1399,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(228,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_173) ).
thf(1621,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(924,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1054) ).
thf(3013,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).
thf(857,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_629) ).
thf(2879,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).
thf(1136,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_650) ).
thf(3437,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).
thf(286,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_98) ).
thf(1737,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(447,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_375) ).
thf(2059,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(644,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_15) ).
thf(2453,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(593,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_177) ).
thf(2351,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(461,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_29) ).
thf(2087,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(941,axiom,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_687) ).
thf(3047,plain,
! [B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).
thf(935,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_514) ).
thf(3035,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).
thf(1148,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_75) ).
thf(3461,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_489) ).
thf(1320,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(578,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_958) ).
thf(2321,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(244,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_923) ).
thf(1653,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(1031,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_24) ).
thf(3227,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_589) ).
thf(1367,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(699,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_895) ).
thf(2563,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(858,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_109) ).
thf(2881,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).
thf(390,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_284) ).
thf(1945,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(1067,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_57) ).
thf(3299,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).
thf(258,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_952) ).
thf(1681,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ B ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(861,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_571) ).
thf(2887,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_260) ).
thf(1184,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1120,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_820) ).
thf(3405,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).
thf(149,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_800) ).
thf(1463,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ '\'0\'' ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(200,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_738) ).
thf(1565,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ C ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'LE\'' @ ( f @ C ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(566,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_607) ).
thf(2297,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(1139,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_71) ).
thf(3443,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).
thf(725,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_930) ).
thf(2615,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(302,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_386) ).
thf(1769,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(376,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_44) ).
thf(1917,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(914,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_569) ).
thf(2993,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).
thf(513,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_696) ).
thf(2191,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_40) ).
thf(1204,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ B ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'LE\'' @ ( f @ B ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(142,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_189) ).
thf(1449,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(506,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_988) ).
thf(2177,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(745,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_414) ).
thf(2655,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(126,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_898) ).
thf(1417,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(803,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_860) ).
thf(2771,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'LE\'' @ ( f @ ( suc @ C ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ( '\'LE\'' @ ( f @ C ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(3501,plain,
$false,
inference(e,[status(thm)],[2163,1501,1879,1411,1469,1633,1767,1559,1729,3167,2427,2331,1549,2199,3021,1322,1665,1369,2889,1823,1190,1168,2295,3053,3345,2341,2109,2131,2031,3399,1995,2263,2921,3477,2463,3397,1899,2787,2595,2499,2559,3449,3185,2309,2117,3317,1290,2231,2395,3285,2671,2837,1437,2363,1855,1200,2077,2495,2381,1443,2659,3417,3377,2527,3153,2953,1401,2947,1569,1939,2099,1591,1971,1793,1533,3217,1671,3439,1655,3429,3049,2607,1310,3135,3365,1735,1999,2933,2141,2575,1497,3017,2195,1705,2035,3367,1867,3175,2627,1260,1919,3253,2459,1761,1342,3121,3481,2901,3313,1507,1222,3103,1835,2723,1613,1935,1359,1475,2173,1703,2869,1887,2957,3335,1196,2491,2763,2985,2227,1391,3249,1441,1645,1921,1601,3281,1529,1967,2067,2825,2819,1803,2531,2405,1228,1623,1254,1409,1709,2603,3425,2667,2339,2269,1871,3061,3125,3089,2897,3353,3043,2703,3263,3221,3195,3029,2735,1985,2039,3275,3131,1298,2755,3495,1907,2501,1330,1264,2217,1511,3485,2185,1577,1455,2745,2571,1545,2691,3099,2713,2857,2049,2767,2373,1741,1931,1641,1773,1875,3231,2533,1232,1847,2829,3385,3463,1379,2169,2403,1479,1609,2635,2929,2301,1815,2989,1963,2007,1465,3431,1302,2027,3199,3393,1373,2259,3163,2925,1677,2777,2073,2017,1489,2237,1415,2105,3075,1811,1911,3295,2893,2469,3453,2451,1334,3473,2291,1383,3357,2555,3093,1581,2335,3389,1843,1377,2861,3421,2523,3157,2137,1351,1943,2965,2205,1975,2367,2437,2833,3189,2281,1447,2483,2371,2979,3361,3243,2809,2799,2639,3327,1433,2103,1405,1697,1242,3211,1521,1651,3229,3459,2473,1691,1306,1338,2047,2307,2641,2905,3037,1863,3435,3151,2011,3097,3011,1206,3301,3303,3169,3265,1915,2093,1783,2737,2083,2621,2061,2773,2589,3261,2601,2249,2541,1519,2147,1751,1487,2969,1619,3207,1274,2441,2673,2705,2409,1387,1723,2733,2805,1355,2277,1174,2133,3239,3069,3233,3371,2937,3339,1238,2015,3471,1883,1365,1178,1951,1296,1819,2609,2179,1210,2345,2741,3033,1573,2653,1423,3307,3271,2445,3191,2873,1837,3269,2433,2477,3403,2565,2663,1555,3297,3137,3499,3065,3349,1687,1457,1787,2181,2327,2213,2211,1407,2547,2313,2769,3445,1983,2895,2709,1587,1425,2509,2631,3119,3205,3001,2245,1350,3105,3467,1234,1541,2157,2115,2515,3413,1270,1851,2377,2801,1953,2685,2841,1328,2973,2359,1375,2577,3381,1719,2537,3237,1755,3087,1397,1567,2023,3143,1361,1659,1292,1182,2419,2053,1791,1889,2649,2317,1493,1683,3141,3311,2877,2323,3179,3407,2561,1739,1461,3441,2455,2613,1937,1214,2349,2551,2085,2781,1419,2125,2519,2681,1451,1539,2505,2497,1799,1947,2813,3115,1825,1324,2285,2487,2845,3059,1266,2153,2387,1831,2851,2243,2355,1192,2581,2465,1429,3247,3409,1599,2697,1246,1715,3333,3109,1979,3005,3083,3201,1759,1393,1627,3215,1525,3147,3225,2761,1779,1695,1563,2057,1170,2915,1895,2617,2909,2749,1857,1991,1318,1202,2203,2043,3279,3183,2883,3173,2963,1286,3321,2793,1663,2089,1515,2221,2645,2189,2995,2423,2529,1278,2729,2001,1727,2413,2677,2391,1959,2585,1927,3289,3111,1631,3343,2121,2235,2253,2275,2033,2149,3257,2717,3491,1483,3079,1747,2941,3375,1595,1833,2727,3319,2859,2225,2791,2789,2981,2489,2393,3283,1403,1965,2817,2827,3387,3187,1615,1389,3255,2525,2657,2849,3081,1929,1535,2991,1795,1701,1226,2695,1256,2959,3213,1503,2029,1312,1865,1997,1765,2425,1258,3091,1675,3223,2161,2193,3023,1669,1707,2293,3051,2891,1371,3077,1635,2935,1733,1332,3123,2759,2753,3487,2055,2457,1897,2557,3355,1224,2573,2319,1194,2679,1853,2383,2637,3287,3419,2097,2669,2839,2065,2079,2361,2311,3101,2521,2721,2119,1282,3251,2151,3155,2229,2415,2493,2987,1933,2257,1589,2955,1603,2299,1771,2943,2945,3197,1801,1571,2871,1439,2197,1969,1667,3219,2025,1993,2267,1909,2757,3165,2923,2553,1381,2461,2329,2911,1877,1471,2605,3027,3133,3055,1557,2129,2343,2625,2111,3073,2261,1821,1731,2785,2593,3451,3483,1344,2289,2647,2075,2365,2171,2835,1445,1643,2139,1176,2931,2303,2999,2207,2693,1198,1841,2439,2725,2401,1699,2051,2765,3423,2481,3159,2369,3241,2797,1775,1435,2633,3363,1477,3325,2535,2101,2967,1250,1973,1805,2069,2867,3009,2239,1809,2107,1208,2665,1467,2037,2503,1340,3455,2333,2597,2899,1551,2005,1413,3031,1583,1304,1873,3193,3427,3395,2271,3293,2471,3161,1905,2449,1509,2927,2629,1547,3391,2715,1961,2397,2661,1743,2143,1605,1647,3129,2175,1531,1230,1845,2513,2567,2863,3315,2977,1611,2375,1941,1252,2821,3209,1753,2407,2831,2689,2569,1987,3063,1869,1785,1262,2337,2219,1901,1679,1579,1336,1220,1711,3019,2747,1499,3305,2165,1813,1300,1637,3273,1188,1186,3475,2429,1763,3127,2701,2903,2545,2599,3359,3329,1218,3041,3095,2411,1849,1981,3493,2379,2543,2579,1797,1717,2939,3071,3007,2675,2247,1543,3107,2113,3415,1284,2975,1353,2279,2357,1955,2843,2145,1485,2711,1749,1427,1585,2511,3117,2949,1881,2807,1272,1240,1617,2435,3433,2479,3401,1553,1949,1913,3447,2347,3039,2865,2875,1421,2013,1839,3139,3457,1316,1649,1459,2045,3067,1180,1685,2885,1817,3171,2215,1517,2611,2325,1781,1216,2209,2743,2997,2187,2305,2919,1575,1453,2643,2071,2775,1807,2907,2443,1326,2707,1745,2971,1523,3331,3085,3465,1276,2591,1385,1721,2167,2273,2283,2389,2855,1639,2853,2251,1903,2135,1481,3383,3369,2823,2811,1629,3235,2431,3003,1244,2447,1491,3497,1777,3149,1308,1607,1661,2095,1893,2315,2739,2421,2009,1861,1689,2081,3181,2475,2399,2041,3267,1294,2183,1212,3351,1513,2917,2623,2779,2019,2123,1348,2287,1957,2385,3291,2587,2233,2951,2815,1248,1757,3203,3469,2003,3379,2517,2683,1725,1280,2155,2255,2983,2719,1395,1625,3373,1593,1527,3337,1673,3015,1859,2751,1495,1657,3177,1693,1561,1789,1891,2619,3045,2651,2783,2549,3309,3145,2201,1989,1363,1314,3347,3277,1172,3479,2417,2961,1288,2913,2091,3323,2223,2795,1473,2021,1346,2063,2353,1268,2265,2467,3489,2507,1925,3113,3341,1236,2241,2127,2159,2731,1829,1977,3025,1827,3057,2803,2847,3411,2485,1537,1357,2583,3259,1923,3245,2539,1713,1597,2687,1431,1885,2699,1505,1399,1621,3013,2879,3437,1737,2059,2453,2351,2087,3047,3035,3461,1320,2321,1653,3227,1367,2563,2881,1945,3299,1681,2887,1184,3405,1463,1565,2297,3443,2615,1769,1917,2993,2191,1204,1449,2177,2655,1417,2771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO688-1 : TPTP v8.1.2. Released v7.3.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n023.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 18:55:30 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.95/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.16/1.21 % [INFO] Parsing done (363ms).
% 2.16/1.22 % [INFO] Running in sequential loop mode.
% 2.70/1.41 % [INFO] eprover registered as external prover.
% 2.70/1.42 % [INFO] cvc4 registered as external prover.
% 2.85/1.42 % [INFO] Scanning for conjecture ...
% 3.45/1.62 % [INFO] 1167 axioms and no conjecture found.
% 5.52/2.43 % [INFO] Problem is propositional (TPTP CNF).
% 5.52/2.46 % [INFO] Type checking passed.
% 5.52/2.46 % [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 ...
% 24.86/8.65 % External prover 'e' found a proof!
% 24.86/8.65 % [INFO] Killing All external provers ...
% 24.86/8.66 % Time passed: 8127ms (effective reasoning time: 7430ms)
% 24.86/8.66 % Axioms used in derivation (1167): clause_127, clause_108, clause_551, clause_212, clause_410, clause_261, clause_331, clause_119, clause_747, clause_835, clause_708, clause_1004, clause_1119, clause_815, clause_979, clause_822, clause_685, clause_438, clause_1145, clause_895, clause_758, clause_239, clause_1150, clause_449, clause_849, clause_379, clause_435, clause_480, clause_469, clause_1099, clause_927, clause_215, clause_427, clause_901, clause_114, clause_1077, clause_350, clause_277, clause_169, clause_677, clause_884, clause_288, clause_934, clause_824, clause_272, clause_389, clause_1026, clause_789, clause_833, clause_969, clause_473, clause_1034, clause_827, clause_357, clause_487, clause_921, clause_462, clause_804, clause_346, clause_569, clause_375, clause_602, clause_819, clause_90, clause_484, clause_372, clause_688, clause_846, clause_1048, clause_1134, clause_719, clause_316, clause_191, clause_584, clause_266, clause_1085, clause_103, clause_171, clause_793, clause_899, clause_1075, clause_368, clause_491, clause_384, clause_414, clause_562, clause_49, clause_38, clause_851, clause_595, clause_1080, clause_932, clause_231, clause_209, clause_5, clause_465, clause_716, clause_558, clause_912, clause_923, clause_367, clause_476, clause_137, clause_577, clause_395, clause_769, clause_305, clause_607, clause_361, clause_105, clause_888, clause_1001, clause_958, clause_992, clause_125, clause_905, clause_1050, clause_910, clause_856, clause_996, clause_877, clause_233, clause_838, clause_1015, clause_180, clause_705, clause_64, clause_83, clause_666, clause_158, clause_1123, clause_617, clause_866, clause_808, clause_1096, clause_204, clause_604, clause_985, clause_23, clause_338, clause_663, clause_446, clause_1110, clause_700, clause_420, clause_45, clause_380, clause_111, clause_1140, clause_52, clause_750, clause_1067, clause_195, clause_160, clause_283, clause_862, clause_919, clause_1105, clause_495, clause_206, clause_1071, clause_1098, clause_715, clause_116, clause_841, clause_1012, clause_527, clause_245, clause_790, clause_639, clause_1091, clause_34, clause_634, clause_855, clause_547, clause_554, clause_364, clause_190, clause_878, clause_93, clause_294, clause_592, clause_684, clause_1059, clause_588, clause_916, clause_628, clause_1138, clause_581, clause_100, clause_323, clause_889, clause_908, clause_786, clause_599, clause_669, clause_237, clause_867, clause_146, clause_67, clause_87, clause_181, clause_873, clause_27, clause_248, clause_953, clause_1087, clause_797, clause_391, clause_349, clause_1156, clause_722, clause_533, clause_184, clause_573, clause_30, clause_133, clause_603, clause_974, clause_301, clause_1037, clause_454, clause_946, clause_796, clause_1045, clause_442, clause_711, clause_609, clause_1008, clause_189, clause_1115, clause_41, clause_431, clause_424, clause_859, clause_1060, clause_178, clause_200, clause_327, clause_1023, clause_981, clause_1127, clause_153, clause_2, clause_290, clause_76, clause_98, clause_226, clause_1056, clause_964, clause_543, clause_696, clause_1149, clause_256, clause_335, clause_538, clause_164, clause_830, clause_56, clause_761, clause_122, clause_500, clause_726, clause_458, clause_823, clause_234, clause_1161, clause_228, clause_970, clause_71, clause_942, clause_516, clause_82, clause_16, clause_938, clause_656, clause_498, clause_142, clause_960, clause_353, clause_673, clause_736, clause_175, clause_1078, clause_505, clause_312, clause_403, clause_223, clause_138, clause_217, clause_342, clause_565, clause_968, clause_440, clause_621, clause_920, clause_779, clause_801, clause_707, clause_1047, clause_298, clause_1, clause_1084, clause_1051, clause_120, clause_631, clause_993, clause_739, clause_1031, clause_931, clause_812, clause_400, clause_340, clause_475, clause_986, clause_409, clause_355, clause_428, clause_1130, clause_198, clause_307, clause_1143, clause_65, clause_1148, clause_187, clause_1019, clause_660, clause_526, clause_260, clause_534, clause_415, clause_620, clause_80, clause_362, clause_373, clause_464, clause_768, clause_407, clause_453, clause_334, clause_166, clause_8, clause_214, clause_671, clause_676, clause_890, clause_913, clause_949, clause_351, clause_504, clause_834, clause_15, clause_243, clause_627, clause_20, clause_318, clause_662, clause_60, clause_179, clause_906, clause_451, clause_613, clause_718, clause_267, clause_113, clause_570, clause_653, clause_732, clause_1126, clause_772, clause_892, clause_1014, clause_1116, clause_149, clause_170, clause_1151, clause_383, clause_278, clause_479, clause_419, clause_870, clause_799, clause_1109, clause_1095, clause_486, clause_232, clause_978, clause_1025, clause_183, clause_289, clause_250, clause_1154, clause_124, clause_770, clause_935, clause_26, clause_845, clause_135, clause_404, clause_445, clause_924, clause_515, clause_1020, clause_699, clause_78, clause_194, clause_638, clause_781, clause_1003, clause_530, clause_874, clause_144, clause_649, clause_439, clause_704, clause_293, clause_155, clause_304, clause_89, clause_693, clause_211, clause_259, clause_665, clause_337, clause_1121, clause_1069, clause_682, clause_1062, clause_1141, clause_642, clause_282, clause_902, clause_1112, clause_1137, clause_102, clause_1132, clause_91, clause_657, clause_788, clause_329, clause_957, clause_508, clause_557, clause_74, clause_43, clause_468, clause_598, clause_687, clause_785, clause_366, clause_537, clause_863, clause_729, clause_881, clause_795, clause_587, clause_418, clause_470, clause_222, clause_441, clause_53, clause_1072, clause_576, clause_147, clause_928, clause_546, clause_481, clause_430, clause_1081, clause_990, clause_712, clause_322, clause_152, clause_148, clause_1007, clause_1064, clause_519, clause_275, clause_695, clause_9, clause_939, clause_236, clause_315, clause_701, clause_348, clause_842, clause_606, clause_723, clause_141, clause_560, clause_297, clause_936, clause_220, clause_967, clause_159, clause_255, clause_762, clause_136, clause_300, clause_852, clause_733, clause_512, clause_553, clause_646, clause_390, clause_982, clause_163, clause_954, clause_286, clause_109, clause_386, clause_1106, clause_725, clause_600, clause_773, clause_765, clause_683, clause_564, clause_971, clause_0, clause_1165, clause_203, clause_501, clause_75, clause_989, clause_130, clause_492, clause_48, clause_1092, clause_784, clause_397, clause_1159, clause_635, clause_1101, clause_37, clause_811, clause_326, clause_751, clause_831, clause_271, clause_816, clause_359, clause_225, clause_253, clause_86, clause_754, clause_356, clause_885, clause_826, clause_961, clause_311, clause_703, clause_943, clause_593, clause_434, clause_523, clause_805, clause_264, clause_743, clause_950, clause_542, clause_97, clause_411, clause_624, clause_975, clause_1036, clause_896, clause_672, clause_945, clause_1029, clause_423, clause_1162, clause_174, clause_42, clause_917, clause_1058, clause_457, clause_714, clause_394, clause_19, clause_378, clause_616, clause_820, clause_690, clause_345, clause_997, clause_568, clause_582, clause_1042, clause_247, clause_740, clause_776, clause_242, clause_800, clause_1061, clause_59, clause_965, clause_14, clause_1053, clause_791, clause_244, clause_837, clause_31, clause_497, clause_848, clause_387, clause_1079, clause_352, clause_1024, clause_186, clause_452, clause_787, clause_336, clause_363, clause_948, clause_107, clause_956, clause_341, clause_591, clause_959, clause_429, clause_308, clause_893, clause_610, clause_907, clause_531, clause_1013, clause_650, clause_858, clause_489, clause_229, clause_1120, clause_1052, clause_121, clause_156, clause_140, clause_999, clause_798, clause_590, clause_1032, clause_994, clause_246, clause_132, clause_1163, clause_802, clause_25, clause_1125, clause_661, clause_987, clause_197, clause_1136, clause_717, clause_398, clause_224, clause_101, clause_509, clause_914, clause_10, clause_365, clause_134, clause_1046, clause_1131, clause_1147, clause_529, clause_412, clause_637, clause_333, clause_55, clause_422, clause_374, clause_7, clause_296, clause_749, clause_813, clause_467, clause_433, clause_706, clause_622, clause_1057, clause_474, clause_235, clause_50, clause_112, clause_485, clause_274, clause_1133, clause_66, clause_648, clause_459, clause_240, clause_1068, clause_1063, clause_123, clause_659, clause_518, clause_571, clause_393, clause_735, clause_343, clause_728, clause_575, clause_535, clause_182, clause_903, clause_173, clause_730, clause_619, clause_499, clause_444, clause_1094, clause_21, clause_864, clause_319, clause_61, clause_1103, clause_406, clause_210, clause_258, clause_382, clause_478, clause_1122, clause_1018, clause_251, clause_1142, clause_44, clause_626, clause_520, clause_698, clause_1021, clause_79, clause_354, clause_202, clause_548, clause_780, clause_193, clause_1117, clause_1083, clause_268, clause_4, clause_263, clause_882, clause_871, clause_207, clause_1070, clause_930, clause_1155, clause_162, clause_257, clause_597, clause_1002, clause_745, clause_925, clause_951, clause_270, clause_1158, clause_62, clause_746, clause_32, clause_668, clause_755, clause_13, clause_940, clause_448, clause_579, clause_339, clause_408, clause_875, clause_605, clause_809, clause_1039, clause_85, clause_724, clause_763, clause_347, clause_869, clause_572, clause_734, clause_894, clause_774, clause_559, clause_507, clause_73, clause_310, clause_972, clause_615, clause_829, clause_679, clause_221, clause_567, clause_401, clause_460, clause_1065, clause_966, clause_991, clause_1054, clause_47, clause_521, clause_853, clause_929, clause_757, clause_317, clause_586, clause_490, clause_524, clause_643, clause_686, clause_1166, clause_325, clause_281, clause_694, clause_847, clause_1006, clause_1107, clause_1113, clause_129, clause_358, clause_792, clause_561, clause_541, clause_744, clause_493, clause_254, clause_213, clause_513, clause_552, clause_482, clause_983, clause_583, clause_306, clause_741, clause_680, clause_456, clause_510, clause_18, clause_496, clause_303, clause_944, clause_675, clause_471, clause_563, clause_1043, clause_806, clause_836, clause_654, clause_955, clause_299, clause_1144, clause_58, clause_1035, clause_502, clause_1164, clause_640, clause_131, clause_783, clause_720, clause_328, clause_664, clause_611, clause_794, clause_1028, clause_69, clause_651, clause_886, clause_1040, clause_825, clause_691, clause_738, clause_151, clause_29, clause_344, clause_766, clause_713, clause_977, clause_1073, clause_218, clause_962, clause_897, clause_988, clause_1010, clause_976, clause_1030, clause_545, clause_370, clause_437, clause_369, clause_285, clause_752, clause_1129, clause_777, clause_314, clause_817, clause_96, clause_292, clause_118, clause_580, clause_1152, clause_377, clause_426, clause_632, clause_918, clause_36, clause_463, clause_594, clause_702, clause_556, clause_417, clause_810, clause_1102, clause_998, clause_54, clause_860, clause_321, clause_911, clause_230, clause_177, clause_596, clause_1089, clause_1118, clause_1090, clause_883, clause_199, clause_168, clause_832, clause_1100, clause_371, clause_6, clause_205, clause_566, clause_900, clause_324, clause_388, clause_511, clause_973, clause_821, clause_645, clause_276, clause_455, clause_807, clause_709, clause_550, clause_447, clause_984, clause_273, clause_814, clause_1146, clause_241, clause_667, clause_926, clause_106, clause_208, clause_872, clause_589, clause_150, clause_95, clause_933, clause_309, clause_1005, clause_549, clause_532, clause_40, clause_544, clause_1027, clause_262, clause_574, clause_608, clause_636, clause_413, clause_425, clause_295, clause_555, clause_625, clause_601, clause_1124, clause_742, clause_759, clause_1076, clause_265, clause_405, clause_332, clause_775, clause_1000, clause_1017, clause_915, clause_678, clause_689, clause_216, clause_1135, clause_904, clause_839, clause_396, clause_1104, clause_1016, clause_522, clause_385, clause_399, clause_39, clause_1033, clause_287, clause_11, clause_828, clause_22, clause_818, clause_313, clause_63, clause_764, clause_84, clause_252, clause_436, clause_843, clause_748, clause_922, clause_24, clause_623, clause_1093, clause_51, clause_330, clause_1049, clause_517, clause_753, clause_192, clause_3, clause_857, clause_1082, clause_647, clause_840, clause_536, clause_157, clause_302, clause_697, clause_1038, clause_947, clause_392, clause_980, clause_92, clause_461, clause_1128, clause_1108, clause_1157, clause_381, clause_376, clause_868, clause_33, clause_731, clause_674, clause_450, clause_618, clause_514, clause_1160, clause_629, clause_506, clause_279, clause_644, clause_139, clause_72, clause_1044, clause_658, clause_284, clause_539, clause_161, clause_1139, clause_269, clause_167, clause_128, clause_172, clause_1011, clause_655, clause_421, clause_1097, clause_612, clause_432, clause_126, clause_771, clause_941, clause_1066, clause_710, clause_782, clause_238, clause_1086, clause_844, clause_35, clause_756, clause_70, clause_88, clause_68, clause_850, clause_652, clause_12, clause_110, clause_472, clause_28, clause_320, clause_402, clause_909, clause_196, clause_1111, clause_227, clause_670, clause_1074, clause_887, clause_143, clause_854, clause_760, clause_876, clause_249, clause_952, clause_57, clause_81, clause_219, clause_46, clause_360, clause_681, clause_692, clause_466, clause_614, clause_721, clause_176, clause_879, clause_77, clause_767, clause_865, clause_201, clause_165, clause_280, clause_630, clause_115, clause_1088, clause_1114, clause_17, clause_1055, clause_963, clause_778, clause_503, clause_727, clause_494, clause_104, clause_641, clause_1153, clause_737, clause_1041, clause_154, clause_861, clause_1022, clause_1009, clause_488, clause_937, clause_188, clause_995, clause_898, clause_145, clause_483, clause_633, clause_585, clause_525, clause_416, clause_443, clause_477, clause_803, clause_891, clause_578, clause_880, clause_540, clause_185, clause_291, clause_528, clause_99, clause_117, clause_94
% 24.86/8.66 % No. of inferences in proof: 2335
% 24.86/8.66 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8127 ms resp. 7430 ms w/o parsing
% 26.78/9.66 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 26.78/9.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------