TSTP Solution File: SYO672-1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SYO672-1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:36:57 EDT 2023
% Result : Unsatisfiable 8.73s 2.89s
% Output : Refutation 9.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 112
% Syntax : Number of formulae : 217 ( 5 unt; 8 typ; 0 def)
% Number of atoms : 2771 ( 0 equ; 0 cnn)
% Maximal formula atoms : 20 ( 13 avg)
% Number of connectives : 18962 (2366 ~;2562 |; 0 &;14034 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 20 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 : 530 ( 0 ^; 530 !; 0 ?; 530 :)
% 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(73,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 ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_593) ).
thf(249,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 ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(25,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2052) ).
thf(153,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1132) ).
thf(115,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(57,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_109) ).
thf(217,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(103,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1753) ).
thf(308,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(72,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2086) ).
thf(247,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(83,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_604) ).
thf(269,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(41,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_1841) ).
thf(185,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)],[41]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_669) ).
thf(288,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1579) ).
thf(257,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_230) ).
thf(125,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_788) ).
thf(157,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_117) ).
thf(189,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_66) ).
thf(261,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1916) ).
thf(179,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(9,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1108) ).
thf(121,plain,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(54,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1140) ).
thf(211,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_85) ).
thf(253,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_125) ).
thf(147,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(59,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_101) ).
thf(221,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)],[59]) ).
thf(15,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2162) ).
thf(133,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_712) ).
thf(243,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1307) ).
thf(265,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(95,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2017) ).
thf(292,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(65,axiom,
~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1160) ).
thf(233,plain,
~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1427) ).
thf(117,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1187) ).
thf(201,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1197) ).
thf(302,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_22) ).
thf(165,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(86,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_56) ).
thf(275,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_441) ).
thf(137,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1223) ).
thf(229,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_299) ).
thf(197,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(91,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_179) ).
thf(285,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)],[91]) ).
thf(33,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ 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_2357) ).
thf(169,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ 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)],[33]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1424) ).
thf(141,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_607) ).
thf(109,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_77) ).
thf(225,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1986) ).
thf(193,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_831) ).
thf(173,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_275) ).
thf(129,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_838) ).
thf(237,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(1,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2291) ).
thf(105,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_959) ).
thf(205,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_778) ).
thf(298,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_939) ).
thf(161,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_976) ).
thf(279,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2215) ).
thf(296,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1546) ).
thf(149,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_94) ).
thf(191,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1338) ).
thf(281,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(78,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1642) ).
thf(259,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_889) ).
thf(181,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2166) ).
thf(159,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_246) ).
thf(187,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1935) ).
thf(113,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1941) ).
thf(219,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(71,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_465) ).
thf(245,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1610) ).
thf(271,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1637) ).
thf(213,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2247) ).
thf(251,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(26,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_1175) ).
thf(155,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)],[26]) ).
thf(60,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_848) ).
thf(223,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2364) ).
thf(306,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_488) ).
thf(135,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(82,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_298) ).
thf(267,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(69,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 ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2026) ).
thf(241,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 ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_333) ).
thf(167,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1173) ).
thf(255,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(53,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_691) ).
thf(209,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_786) ).
thf(123,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_490) ).
thf(145,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1933) ).
thf(263,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(104,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_199) ).
thf(310,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(48,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1301) ).
thf(199,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(37,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_1449) ).
thf(177,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)],[37]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_610) ).
thf(127,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_839) ).
thf(175,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1978) ).
thf(143,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(64,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1277) ).
thf(231,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(50,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_994) ).
thf(203,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(101,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_1030) ).
thf(304,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)],[101]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2191) ).
thf(171,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2324) ).
thf(139,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(66,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_415) ).
thf(235,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)],[66]) ).
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_362) ).
thf(207,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(92,axiom,
! [A: $i] : ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2366) ).
thf(287,plain,
! [A: $i] : ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_50) ).
thf(290,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1512) ).
thf(119,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_802) ).
thf(151,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(99,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( 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_2111) ).
thf(300,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( 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)],[99]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1465) ).
thf(183,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(85,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_783) ).
thf(273,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)],[85]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_112) ).
thf(107,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(68,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_528) ).
thf(239,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)],[68]) ).
thf(96,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_717) ).
thf(294,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(46,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_921) ).
thf(195,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(90,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_2008) ).
thf(283,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)],[90]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_78) ).
thf(131,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(30,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2285) ).
thf(163,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(87,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1857) ).
thf(277,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1628) ).
thf(111,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1761) ).
thf(227,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(56,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1230) ).
thf(215,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(314,plain,
$false,
inference(e,[status(thm)],[249,153,115,217,308,247,269,185,288,257,125,157,189,261,179,121,211,253,147,221,133,243,265,292,233,117,201,302,165,275,137,229,197,285,169,141,109,225,193,173,129,237,105,205,298,161,279,296,149,191,281,259,181,159,187,113,219,245,271,213,251,155,223,306,135,267,241,167,255,209,123,145,263,310,199,177,127,175,143,231,203,304,171,139,235,207,287,290,119,151,300,183,273,107,239,294,195,283,131,163,277,111,227,215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO672-1 : TPTP v8.1.2. Released v7.3.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n023.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 18:35:45 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.91/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.73/1.06 % [INFO] Parsing done (219ms).
% 1.73/1.07 % [INFO] Running in sequential loop mode.
% 2.20/1.26 % [INFO] eprover registered as external prover.
% 2.20/1.26 % [INFO] cvc4 registered as external prover.
% 2.20/1.27 % [INFO] Scanning for conjecture ...
% 2.51/1.34 % [INFO] 104 axioms and no conjecture found.
% 3.27/1.54 % [INFO] Problem is propositional (TPTP CNF).
% 3.27/1.55 % [INFO] Type checking passed.
% 3.27/1.55 % [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 ...
% 8.73/2.88 % External prover 'e' found a proof!
% 8.73/2.88 % [INFO] Killing All external provers ...
% 8.73/2.88 % Time passed: 2366ms (effective reasoning time: 1811ms)
% 8.73/2.89 % Axioms used in derivation (104): clause_921, clause_2026, clause_22, clause_1761, clause_1841, clause_1579, clause_1978, clause_465, clause_2247, clause_838, clause_1610, clause_607, clause_125, clause_604, clause_1753, clause_1140, clause_889, clause_786, clause_669, clause_1546, clause_1986, clause_2366, clause_56, clause_1223, clause_1512, clause_298, clause_2364, clause_415, clause_362, clause_1916, clause_179, clause_2162, clause_78, clause_1941, clause_1935, clause_1637, clause_2017, clause_1132, clause_2215, clause_788, clause_1449, clause_441, clause_712, clause_275, clause_939, clause_2111, clause_1307, clause_109, clause_1230, clause_593, clause_1173, clause_831, clause_1187, clause_2166, clause_2285, clause_848, clause_959, clause_610, clause_1277, clause_994, clause_246, clause_802, clause_2357, clause_717, clause_333, clause_101, clause_2291, clause_50, clause_112, clause_66, clause_1338, clause_85, clause_1933, clause_490, clause_1427, clause_1857, clause_299, clause_783, clause_1465, clause_691, clause_1628, clause_1175, clause_976, clause_1030, clause_2191, clause_199, clause_230, clause_1197, clause_1301, clause_839, clause_2052, clause_1160, clause_1424, clause_1108, clause_2086, clause_1642, clause_2324, clause_2008, clause_77, clause_778, clause_488, clause_528, clause_117, clause_94
% 8.73/2.89 % No. of inferences in proof: 209
% 8.73/2.89 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2366 ms resp. 1811 ms w/o parsing
% 9.46/3.06 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.46/3.07 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------