TSTP Solution File: SYO687-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SYO687-1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:37:00 EDT 2023
% Result : Unsatisfiable 9.22s 3.13s
% Output : Refutation 10.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 135
% Syntax : Number of formulae : 263 ( 5 unt; 8 typ; 0 def)
% Number of atoms : 2425 ( 0 equ; 0 cnn)
% Maximal formula atoms : 17 ( 9 avg)
% Number of connectives : 18784 (2012 ~;2170 |; 0 &;14602 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 16 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 : 412 ( 0 ^; 412 !; 0 ?; 412 :)
% 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(iLEQ_type,type,
iLEQ: $i > $i > $o ).
thf(suc_type,type,
suc: $i > $i ).
thf('\'LE\'_type',type,
'\'LE\'': $i > $i > $o ).
thf(z_type,type,
z: $i ).
thf(8,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1896) ).
thf(142,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)],[8]) ).
thf(116,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2387) ).
thf(357,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(111,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/sandbox/benchmark/theBenchmark.p',clause_1204) ).
thf(347,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)],[111]) ).
thf(120,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1981) ).
thf(365,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2107) ).
thf(138,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)],[6]) ).
thf(104,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_734) ).
thf(333,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2189) ).
thf(249,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_19) ).
thf(217,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(61,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_818) ).
thf(247,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1034) ).
thf(379,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_409) ).
thf(269,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1682) ).
thf(185,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(88,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_415) ).
thf(301,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)],[88]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_368) ).
thf(257,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(32,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_380) ).
thf(189,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(100,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1376) ).
thf(325,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(13,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_161) ).
thf(152,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)],[13]) ).
thf(82,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2293) ).
thf(289,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(68,axiom,
~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1188) ).
thf(261,plain,
~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(27,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/sandbox/benchmark/theBenchmark.p',clause_2348) ).
thf(179,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)],[27]) ).
thf(98,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_971) ).
thf(321,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(114,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1067) ).
thf(353,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(43,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1539) ).
thf(211,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(64,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1900) ).
thf(253,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(48,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2321) ).
thf(221,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(84,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1635) ).
thf(293,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(3,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_682) ).
thf(132,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(59,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1605) ).
thf(243,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(70,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2405) ).
thf(265,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(91,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/sandbox/benchmark/theBenchmark.p',clause_2224) ).
thf(307,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)],[91]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_26) ).
thf(233,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(38,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1556) ).
thf(201,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(112,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1433) ).
thf(349,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_311) ).
thf(160,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(86,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_80) ).
thf(297,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(75,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1081) ).
thf(275,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_374) ).
thf(165,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2226) ).
thf(229,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2443) ).
thf(197,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(118,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2289) ).
thf(361,plain,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(102,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1366) ).
thf(329,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(80,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_222) ).
thf(285,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
thf(317,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(15,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2053) ).
thf(156,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(22,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1522) ).
thf(169,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1172) ).
thf(225,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(107,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1185) ).
thf(339,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(34,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1143) ).
thf(193,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1924) ).
thf(173,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(123,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_522) ).
thf(371,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1174) ).
thf(134,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1796) ).
thf(205,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(93,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2159) ).
thf(311,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(1,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1841) ).
thf(128,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(109,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/sandbox/benchmark/theBenchmark.p',clause_1248) ).
thf(343,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)],[109]) ).
thf(56,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1073) ).
thf(237,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(11,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1659) ).
thf(148,plain,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(77,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/sandbox/benchmark/theBenchmark.p',clause_1403) ).
thf(279,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)],[77]) ).
thf(125,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/sandbox/benchmark/theBenchmark.p',clause_1064) ).
thf(375,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)],[125]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2066) ).
thf(191,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(83,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1953) ).
thf(291,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(78,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2337) ).
thf(281,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(67,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_603) ).
thf(259,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(94,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_232) ).
thf(313,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(9,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/sandbox/benchmark/theBenchmark.p',clause_1473) ).
thf(144,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)],[9]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1524) ).
thf(335,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(28,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/sandbox/benchmark/theBenchmark.p',clause_1701) ).
thf(181,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)],[28]) ).
thf(31,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/sandbox/benchmark/theBenchmark.p',clause_231) ).
thf(187,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)],[31]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_355) ).
thf(219,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(126,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_739) ).
thf(377,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1196) ).
thf(245,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( 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)],[60]) ).
thf(89,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2214) ).
thf(303,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(73,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1232) ).
thf(271,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(99,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1752) ).
thf(323,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2273) ).
thf(140,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_381) ).
thf(213,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1697) ).
thf(251,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(110,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_774) ).
thf(345,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(121,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1589) ).
thf(367,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1240) ).
thf(130,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(49,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2369) ).
thf(223,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(87,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2500) ).
thf(299,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(71,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_881) ).
thf(267,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(58,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/sandbox/benchmark/theBenchmark.p',clause_953) ).
thf(241,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)],[58]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_455) ).
thf(167,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(18,axiom,
! [A: $i] : ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_683) ).
thf(162,plain,
! [A: $i] : ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_478) ).
thf(255,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1598) ).
thf(209,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(115,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1502) ).
thf(355,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(85,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1897) ).
thf(295,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(12,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2054) ).
thf(150,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(101,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_188) ).
thf(327,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2009) ).
thf(263,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(37,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1710) ).
thf(199,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(26,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1424) ).
thf(177,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_216) ).
thf(331,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(117,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/sandbox/benchmark/theBenchmark.p',clause_2489) ).
thf(359,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)],[117]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_887) ).
thf(154,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1503) ).
thf(175,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_475) ).
thf(231,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(119,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_472) ).
thf(363,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(39,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1310) ).
thf(203,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(97,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1778) ).
thf(319,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2472) ).
thf(171,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_213) ).
thf(158,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(113,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_253) ).
thf(351,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(55,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2498) ).
thf(235,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
thf(207,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1670) ).
thf(287,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(95,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/sandbox/benchmark/theBenchmark.p',clause_1408) ).
thf(315,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)],[95]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1019) ).
thf(146,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1405) ).
thf(183,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(74,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_351) ).
thf(273,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(124,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_623) ).
thf(373,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(90,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/sandbox/benchmark/theBenchmark.p',clause_1860) ).
thf(305,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)],[90]) ).
thf(57,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_565) ).
thf(239,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2135) ).
thf(136,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(108,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1301) ).
thf(341,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(35,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1769) ).
thf(195,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(79,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_327) ).
thf(283,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1912) ).
thf(163,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(76,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_920) ).
thf(277,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(122,axiom,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_629) ).
thf(369,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2417) ).
thf(227,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(106,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1340) ).
thf(337,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(92,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1060) ).
thf(309,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_540) ).
thf(215,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(381,plain,
$false,
inference(e,[status(thm)],[142,357,347,365,138,333,249,217,247,379,269,185,301,257,189,325,152,289,261,179,321,353,211,253,221,293,132,243,265,307,233,201,349,160,297,275,165,229,197,361,329,285,317,156,169,225,339,193,173,371,134,205,311,128,343,237,148,279,375,191,291,281,259,313,144,335,181,187,219,377,245,303,271,323,140,213,251,345,367,130,223,299,267,241,167,162,255,209,355,295,150,327,263,199,177,331,359,154,175,231,363,203,319,171,158,351,235,207,287,315,146,183,273,373,305,239,136,341,195,283,163,277,369,227,337,309,215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO687-1 : TPTP v8.1.2. Released v7.3.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n026.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu May 18 18:55:21 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.97/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.56/1.13 % [INFO] Parsing done (250ms).
% 1.56/1.14 % [INFO] Running in sequential loop mode.
% 2.37/1.37 % [INFO] eprover registered as external prover.
% 2.37/1.37 % [INFO] cvc4 registered as external prover.
% 2.37/1.38 % [INFO] Scanning for conjecture ...
% 2.77/1.46 % [INFO] 127 axioms and no conjecture found.
% 3.32/1.68 % [INFO] Problem is propositional (TPTP CNF).
% 3.58/1.69 % [INFO] Type checking passed.
% 3.58/1.69 % [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 ...
% 9.22/3.12 % External prover 'e' found a proof!
% 9.22/3.12 % [INFO] Killing All external provers ...
% 9.22/3.13 % Time passed: 2623ms (effective reasoning time: 1982ms)
% 9.22/3.13 % Axioms used in derivation (127): clause_2135, clause_1248, clause_1682, clause_1900, clause_1841, clause_2405, clause_1034, clause_1953, clause_2066, clause_1408, clause_2214, clause_368, clause_231, clause_2273, clause_1067, clause_2224, clause_2009, clause_380, clause_1240, clause_1635, clause_953, clause_603, clause_2348, clause_1697, clause_1670, clause_327, clause_2500, clause_1524, clause_1060, clause_1981, clause_1403, clause_565, clause_1172, clause_2489, clause_739, clause_2417, clause_920, clause_1, clause_1143, clause_1019, clause_415, clause_475, clause_1778, clause_409, clause_355, clause_80, clause_351, clause_1376, clause_1897, clause_1710, clause_232, clause_1896, clause_26, clause_2337, clause_1503, clause_881, clause_2226, clause_682, clause_1924, clause_1912, clause_1081, clause_222, clause_1064, clause_1605, clause_971, clause_1752, clause_1185, clause_683, clause_1174, clause_2293, clause_253, clause_311, clause_2369, clause_2107, clause_1366, clause_19, clause_2054, clause_1196, clause_2053, clause_2387, clause_374, clause_2289, clause_478, clause_1796, clause_1188, clause_1769, clause_1598, clause_734, clause_774, clause_2159, clause_1659, clause_213, clause_2498, clause_1204, clause_1405, clause_2189, clause_1860, clause_1073, clause_1502, clause_1522, clause_2443, clause_1539, clause_1433, clause_1340, clause_455, clause_1301, clause_216, clause_1310, clause_1589, clause_522, clause_2472, clause_1473, clause_623, clause_818, clause_3, clause_629, clause_1424, clause_161, clause_381, clause_472, clause_1556, clause_887, clause_2321, clause_1701, clause_1232, clause_188, clause_540
% 9.22/3.13 % No. of inferences in proof: 255
% 9.22/3.13 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2623 ms resp. 1982 ms w/o parsing
% 10.60/3.42 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.60/3.42 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------