TSTP Solution File: SYO682-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SYO682-1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 12:36:59 EDT 2023
% Result : Unsatisfiable 8.15s 2.91s
% Output : Refutation 9.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 94
% Syntax : Number of formulae : 181 ( 5 unt; 8 typ; 0 def)
% Number of atoms : 2325 ( 0 equ; 0 cnn)
% Maximal formula atoms : 19 ( 13 avg)
% Number of connectives : 15798 (1994 ~;2152 |; 0 &;11652 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 21 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 : 554 ( 0 ^; 554 !; 0 ?; 554 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'E\'_type',type,
'\'E\'': $i > $i > $o ).
thf(s_type,type,
s: $i > $i ).
thf('\'0\'_type',type,
'\'0\'': $i ).
thf(f_type,type,
f: $i > $i ).
thf(suc_type,type,
suc: $i > $i ).
thf(iLEQ_type,type,
iLEQ: $i > $i > $o ).
thf('\'LE\'_type',type,
'\'LE\'': $i > $i > $o ).
thf(z_type,type,
z: $i ).
thf(29,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2033) ).
thf(142,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(45,axiom,
! [D: $i,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 @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2237) ).
thf(174,plain,
! [D: $i,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 @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(22,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_1914) ).
thf(129,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)],[22]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2044) ).
thf(226,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(35,axiom,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ( '\'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_596) ).
thf(154,plain,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ( '\'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)],[35]) ).
thf(27,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_1537) ).
thf(138,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)],[27]) ).
thf(8,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_2710) ).
thf(101,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)],[8]) ).
thf(75,axiom,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'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_2899) ).
thf(234,plain,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'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)],[75]) ).
thf(43,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_165) ).
thf(170,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1807) ).
thf(115,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2433) ).
thf(202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(50,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2717) ).
thf(184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1045) ).
thf(125,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(56,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_258) ).
thf(196,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(4,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_2548) ).
thf(93,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)],[4]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2895) ).
thf(152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(72,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'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_2923) ).
thf(228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'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)],[72]) ).
thf(66,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'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_2752) ).
thf(216,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'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)],[66]) ).
thf(40,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_491) ).
thf(164,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)],[40]) ).
thf(77,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_134) ).
thf(238,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(18,axiom,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_826) ).
thf(121,plain,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_147) ).
thf(132,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(2,axiom,
! [D: $i,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 @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1739) ).
thf(89,plain,
! [D: $i,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 @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(61,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_625) ).
thf(206,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1409) ).
thf(248,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_550) ).
thf(117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(68,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_679) ).
thf(220,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)],[68]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1178) ).
thf(160,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(54,axiom,
! [D: $i,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 @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1577) ).
thf(192,plain,
! [D: $i,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 @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(84,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1709) ).
thf(252,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(6,axiom,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_911) ).
thf(97,plain,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(70,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_1426) ).
thf(224,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)],[70]) ).
thf(36,axiom,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2388) ).
thf(156,plain,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(52,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_2240) ).
thf(188,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)],[52]) ).
thf(64,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2497) ).
thf(212,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(12,axiom,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2645) ).
thf(109,plain,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(86,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_1131) ).
thf(256,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)],[86]) ).
thf(25,axiom,
! [D: $i,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 @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1622) ).
thf(134,plain,
! [D: $i,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 @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(10,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_2217) ).
thf(105,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)],[10]) ).
thf(80,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'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_2160) ).
thf(244,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'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)],[80]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1684) ).
thf(166,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(32,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1226) ).
thf(148,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(48,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_777) ).
thf(180,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)],[48]) ).
thf(46,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_2902) ).
thf(176,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)],[46]) ).
thf(60,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_2414) ).
thf(204,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)],[60]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2038) ).
thf(144,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(76,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_2704) ).
thf(236,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)],[76]) ).
thf(44,axiom,
! [D: $i,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 @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_190) ).
thf(172,plain,
! [D: $i,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 @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(14,axiom,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2971) ).
thf(113,plain,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(73,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2095) ).
thf(230,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(62,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2576) ).
thf(208,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1331) ).
thf(103,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(28,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_1799) ).
thf(140,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)],[28]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1492) ).
thf(91,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(78,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1230) ).
thf(240,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(57,axiom,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1145) ).
thf(198,plain,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(39,axiom,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1497) ).
thf(162,plain,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1838) ).
thf(123,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(55,axiom,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_797) ).
thf(194,plain,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(33,axiom,
! [D: $i,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 @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1197) ).
thf(150,plain,
! [D: $i,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 @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1268) ).
thf(95,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(49,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2749) ).
thf(182,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(21,axiom,
! [D: $i,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 @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2487) ).
thf(127,plain,
! [D: $i,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 @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(83,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_988) ).
thf(250,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)],[83]) ).
thf(7,axiom,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1275) ).
thf(99,plain,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,axiom,
! [D: $i,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 @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2815) ).
thf(87,plain,
! [D: $i,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 @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(67,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'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_2897) ).
thf(218,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'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)],[67]) ).
thf(37,axiom,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2537) ).
thf(158,plain,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(51,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2619) ).
thf(186,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(17,axiom,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2031) ).
thf(119,plain,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(81,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_591) ).
thf(246,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(65,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_885) ).
thf(214,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(42,axiom,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1006) ).
thf(168,plain,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(31,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1815) ).
thf(146,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(53,axiom,
~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1450) ).
thf(190,plain,
~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(63,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_409) ).
thf(210,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(11,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_1737) ).
thf(107,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)],[11]) ).
thf(79,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_1659) ).
thf(242,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)],[79]) ).
thf(26,axiom,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1979) ).
thf(136,plain,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(23,axiom,
! [A: $i] : ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2205) ).
thf(131,plain,
! [A: $i] : ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2543) ).
thf(200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(47,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_17) ).
thf(178,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(13,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_2463) ).
thf(111,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)],[13]) ).
thf(85,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2861) ).
thf(254,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(69,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_705) ).
thf(222,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(74,axiom,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2084) ).
thf(232,plain,
! [D: $i,C: $i,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 ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(258,plain,
$false,
inference(e,[status(thm)],[142,174,129,226,154,138,101,234,170,115,202,184,125,196,93,152,228,216,164,238,121,132,89,206,248,117,220,160,192,252,97,224,156,188,212,109,256,134,105,244,166,148,180,176,204,144,236,172,113,230,208,103,140,91,240,198,162,123,194,150,95,182,127,250,99,87,218,158,186,119,246,214,168,146,190,210,107,242,136,131,200,178,111,254,222,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : SYO682-1 : TPTP v8.1.2. Released v7.3.0.
% 0.09/0.17 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n015.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Thu May 18 18:34:23 EDT 2023
% 0.17/0.38 % CPUTime :
% 1.04/0.94 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.45/1.18 % [INFO] Parsing done (238ms).
% 1.88/1.19 % [INFO] Running in sequential loop mode.
% 2.35/1.40 % [INFO] eprover registered as external prover.
% 2.35/1.41 % [INFO] cvc4 registered as external prover.
% 2.35/1.41 % [INFO] Scanning for conjecture ...
% 2.66/1.49 % [INFO] 86 axioms and no conjecture found.
% 3.07/1.69 % [INFO] Problem is propositional (TPTP CNF).
% 3.35/1.70 % [INFO] Type checking passed.
% 3.35/1.70 % [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 ...
% 8.15/2.91 % External prover 'e' found a proof!
% 8.15/2.91 % [INFO] Killing All external provers ...
% 8.15/2.91 % Time passed: 2358ms (effective reasoning time: 1716ms)
% 8.15/2.91 % Axioms used in derivation (86): clause_491, clause_1268, clause_1450, clause_1799, clause_591, clause_2217, clause_2645, clause_1145, clause_2897, clause_2497, clause_2388, clause_2902, clause_1178, clause_2971, clause_2084, clause_2095, clause_1815, clause_705, clause_2752, clause_2717, clause_2237, clause_1409, clause_2710, clause_190, clause_2044, clause_2433, clause_797, clause_1045, clause_2033, clause_2038, clause_2240, clause_1537, clause_2923, clause_1275, clause_1979, clause_409, clause_1331, clause_2815, clause_147, clause_1739, clause_1807, clause_1426, clause_2543, clause_1230, clause_885, clause_826, clause_1131, clause_2861, clause_134, clause_2463, clause_2031, clause_2576, clause_2537, clause_258, clause_2704, clause_2548, clause_679, clause_2160, clause_1006, clause_1226, clause_1659, clause_2899, clause_1684, clause_2487, clause_777, clause_1577, clause_2895, clause_988, clause_1492, clause_911, clause_596, clause_2749, clause_1197, clause_2205, clause_2619, clause_550, clause_1497, clause_1709, clause_625, clause_1838, clause_2414, clause_17, clause_1914, clause_165, clause_1622, clause_1737
% 8.15/2.91 % No. of inferences in proof: 173
% 8.15/2.91 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2358 ms resp. 1716 ms w/o parsing
% 9.15/3.14 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.15/3.14 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------