TSTP Solution File: SYO673-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SYO673-1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:36:57 EDT 2023
% Result : Unsatisfiable 6.46s 2.49s
% Output : Refutation 7.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 73
% Syntax : Number of formulae : 139 ( 5 unt; 8 typ; 0 def)
% Number of atoms : 1745 ( 0 equ; 0 cnn)
% Maximal formula atoms : 19 ( 13 avg)
% Number of connectives : 11330 (1496 ~;1614 |; 0 &;8220 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 20 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 416 ( 0 ^; 416 !; 0 ?; 416 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'E\'_type',type,
'\'E\'': $i > $i > $o ).
thf(s_type,type,
s: $i > $i ).
thf('\'0\'_type',type,
'\'0\'': $i ).
thf(f_type,type,
f: $i > $i ).
thf(suc_type,type,
suc: $i > $i ).
thf(iLEQ_type,type,
iLEQ: $i > $i > $o ).
thf('\'LE\'_type',type,
'\'LE\'': $i > $i > $o ).
thf(z_type,type,
z: $i ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1130) ).
thf(101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(26,axiom,
~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_709) ).
thf(115,plain,
~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(45,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_354) ).
thf(153,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(61,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1270) ).
thf(185,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_715) ).
thf(97,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(21,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_1472) ).
thf(105,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)],[21]) ).
thf(64,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_1261) ).
thf(191,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)],[64]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_367) ).
thf(95,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(28,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_874) ).
thf(119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(31,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_120) ).
thf(125,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)],[31]) ).
thf(47,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_596) ).
thf(157,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(63,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1302) ).
thf(189,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_721) ).
thf(93,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_530) ).
thf(179,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(29,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1183) ).
thf(121,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(42,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_987) ).
thf(147,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_104) ).
thf(74,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1397) ).
thf(89,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(35,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_35) ).
thf(133,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(27,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_772) ).
thf(117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1074) ).
thf(85,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_981) ).
thf(70,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(37,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_332) ).
thf(137,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)],[37]) ).
thf(51,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1365) ).
thf(165,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_69) ).
thf(169,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1017) ).
thf(141,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_855) ).
thf(109,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(7,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_345) ).
thf(77,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(65,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_666) ).
thf(193,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(55,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_752) ).
thf(173,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(33,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_71) ).
thf(129,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(49,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_460) ).
thf(161,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(43,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_1256) ).
thf(149,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)],[43]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_129) ).
thf(181,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(48,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1143) ).
thf(159,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(62,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_509) ).
thf(187,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(25,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_165) ).
thf(113,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_625) ).
thf(81,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [A: $i] : ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1497) ).
thf(76,plain,
! [A: $i] : ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_692) ).
thf(103,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(14,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_418) ).
thf(91,plain,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_618) ).
thf(66,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(46,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_601) ).
thf(155,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(36,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1322) ).
thf(135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1106) ).
thf(167,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_382) ).
thf(123,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_44) ).
thf(145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(57,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1445) ).
thf(177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(32,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_243) ).
thf(127,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)],[32]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1288) ).
thf(72,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(56,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_292) ).
thf(175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(40,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1374) ).
thf(143,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(18,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_1415) ).
thf(99,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)],[18]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_594) ).
thf(87,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1142) ).
thf(171,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(38,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_1439) ).
thf(139,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)],[38]) ).
thf(44,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_712) ).
thf(151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(60,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1132) ).
thf(183,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(22,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_225) ).
thf(107,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)],[22]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1452) ).
thf(79,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(34,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_1246) ).
thf(131,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)],[34]) ).
thf(50,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_1442) ).
thf(163,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)],[50]) ).
thf(2,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1370) ).
thf(68,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_639) ).
thf(111,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1113) ).
thf(83,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ D ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ D ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ C ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(195,plain,
$false,
inference(e,[status(thm)],[101,115,153,185,97,105,191,95,119,125,157,189,93,179,121,147,74,89,133,117,85,70,137,165,169,141,109,77,193,173,129,161,149,181,159,187,113,81,76,103,91,66,155,135,167,123,145,177,127,72,175,143,99,87,171,139,151,183,107,79,131,163,68,111,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO673-1 : TPTP v8.1.2. Released v7.3.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n024.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 18:34:53 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.86/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.54/1.04 % [INFO] Parsing done (199ms).
% 1.54/1.05 % [INFO] Running in sequential loop mode.
% 2.21/1.24 % [INFO] eprover registered as external prover.
% 2.21/1.24 % [INFO] cvc4 registered as external prover.
% 2.21/1.25 % [INFO] Scanning for conjecture ...
% 2.45/1.34 % [INFO] 65 axioms and no conjecture found.
% 2.90/1.52 % [INFO] Problem is propositional (TPTP CNF).
% 2.90/1.53 % [INFO] Type checking passed.
% 2.90/1.53 % [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 ...
% 6.46/2.49 % External prover 'e' found a proof!
% 6.46/2.49 % [INFO] Killing All external provers ...
% 6.46/2.49 % Time passed: 1969ms (effective reasoning time: 1436ms)
% 6.46/2.49 % Axioms used in derivation (65): clause_1132, clause_1106, clause_509, clause_460, clause_69, clause_1261, clause_618, clause_1472, clause_1370, clause_1397, clause_367, clause_666, clause_1302, clause_715, clause_639, clause_855, clause_1183, clause_1270, clause_1322, clause_981, clause_1445, clause_1374, clause_1246, clause_71, clause_120, clause_1130, clause_1143, clause_243, clause_772, clause_530, clause_874, clause_418, clause_712, clause_1256, clause_225, clause_1415, clause_345, clause_1442, clause_1288, clause_987, clause_354, clause_382, clause_1142, clause_44, clause_1113, clause_129, clause_752, clause_292, clause_594, clause_1365, clause_596, clause_1452, clause_709, clause_1497, clause_1017, clause_625, clause_601, clause_332, clause_35, clause_1439, clause_1074, clause_692, clause_721, clause_165, clause_104
% 6.46/2.49 % No. of inferences in proof: 131
% 6.46/2.49 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1969 ms resp. 1436 ms w/o parsing
% 7.81/2.70 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.81/2.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------