TSTP Solution File: SYO678-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SYO678-1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.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 12:36:58 EDT 2023
% Result : Unsatisfiable 6.83s 2.58s
% Output : Refutation 7.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 74
% Syntax : Number of formulae : 141 ( 5 unt; 8 typ; 0 def)
% Number of atoms : 981 ( 0 equ; 0 cnn)
% Maximal formula atoms : 13 ( 7 avg)
% Number of connectives : 6930 ( 778 ~; 848 |; 0 &;5304 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 13 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 : 202 ( 0 ^; 202 !; 0 ?; 202 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'E\'_type',type,
'\'E\'': $i > $i > $o ).
thf(f_type,type,
f: $i > $i ).
thf(suc_type,type,
suc: $i > $i ).
thf('\'0\'_type',type,
'\'0\'': $i ).
thf(iLEQ_type,type,
iLEQ: $i > $i > $o ).
thf(s_type,type,
s: $i > $i ).
thf('\'LE\'_type',type,
'\'LE\'': $i > $i > $o ).
thf(z_type,type,
z: $i ).
thf(44,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_447) ).
thf(153,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(55,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_66) ).
thf(174,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)],[55]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_396) ).
thf(93,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_38) ).
thf(97,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(32,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_133) ).
thf(129,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(56,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_42) ).
thf(176,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)],[56]) ).
thf(3,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_105) ).
thf(71,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)],[3]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_419) ).
thf(135,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_280) ).
thf(95,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(39,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_322) ).
thf(143,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_317) ).
thf(69,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,axiom,
~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_237) ).
thf(101,plain,
~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(53,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_160) ).
thf(170,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(25,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_410) ).
thf(115,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_143) ).
thf(184,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(30,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_338) ).
thf(125,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_311) ).
thf(196,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(46,axiom,
! [A: $i] : ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_330) ).
thf(157,plain,
! [A: $i] : ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_197) ).
thf(164,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
thf(121,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_244) ).
thf(147,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_71) ).
thf(89,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(34,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_146) ).
thf(133,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(26,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_281) ).
thf(117,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_226) ).
thf(85,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(48,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_147) ).
thf(160,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(64,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_425) ).
thf(192,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_18) ).
thf(137,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(62,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ '\'0\'' ) ) )
| ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_137) ).
thf(188,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)],[62]) ).
thf(38,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_233) ).
thf(141,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_253) ).
thf(109,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_345) ).
thf(77,plain,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_350) ).
thf(73,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(20,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_414) ).
thf(105,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(51,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11) ).
thf(166,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)],[51]) ).
thf(58,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_455) ).
thf(180,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_351) ).
thf(149,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_415) ).
thf(172,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_328) ).
thf(113,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_441) ).
thf(81,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(19,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_388) ).
thf(103,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_402) ).
thf(91,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_424) ).
thf(155,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(49,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_442) ).
thf(162,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)],[49]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_369) ).
thf(123,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(65,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_202) ).
thf(194,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_292) ).
thf(145,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_113) ).
thf(67,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(59,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_139) ).
thf(182,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(31,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_37) ).
thf(127,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_45) ).
thf(99,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(11,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_14) ).
thf(87,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(47,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_246) ).
thf(158,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)],[47]) ).
thf(61,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_173) ).
thf(186,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(37,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ A ) ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_46) ).
thf(139,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)],[37]) ).
thf(5,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_219) ).
thf(75,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)],[5]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_103) ).
thf(119,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(43,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_334) ).
thf(151,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)],[43]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_326) ).
thf(168,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(63,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_423) ).
thf(190,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_263) ).
thf(107,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_273) ).
thf(79,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(33,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_161) ).
thf(131,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ '\'0\'' ) @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(57,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_91) ).
thf(178,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ B ) )
| ~ ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(23,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ A ) ) @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) )
| ( '\'E\'' @ ( s @ ( s @ '\'0\'' ) ) @ ( f @ ( suc @ A ) ) )
| ( '\'LE\'' @ ( f @ A ) @ ( s @ ( s @ '\'0\'' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_252) ).
thf(111,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)],[23]) ).
thf(9,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_154) ).
thf(83,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ A ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( s @ ( s @ ( s @ '\'0\'' ) ) ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(198,plain,
$false,
inference(e,[status(thm)],[153,174,93,97,129,176,71,135,95,143,69,101,170,115,184,125,196,157,164,121,147,89,133,117,85,160,192,137,188,141,109,77,73,105,166,180,149,172,113,81,103,91,155,162,123,194,145,67,182,127,99,87,158,186,139,75,119,151,168,190,107,79,131,178,111,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO678-1 : TPTP v8.1.2. Released v7.3.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n022.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 18:31:03 EDT 2023
% 0.14/0.36 % CPUTime :
% 1.08/0.94 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.79/1.17 % [INFO] Parsing done (228ms).
% 1.79/1.18 % [INFO] Running in sequential loop mode.
% 2.29/1.40 % [INFO] eprover registered as external prover.
% 2.29/1.40 % [INFO] cvc4 registered as external prover.
% 2.29/1.41 % [INFO] Scanning for conjecture ...
% 2.54/1.47 % [INFO] 66 axioms and no conjecture found.
% 2.87/1.61 % [INFO] Problem is propositional (TPTP CNF).
% 2.87/1.62 % [INFO] Type checking passed.
% 2.87/1.62 % [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 ...
% 6.83/2.57 % External prover 'e' found a proof!
% 6.83/2.57 % [INFO] Killing All external provers ...
% 6.83/2.57 % Time passed: 2044ms (effective reasoning time: 1391ms)
% 6.83/2.57 % Axioms used in derivation (66): clause_410, clause_350, clause_71, clause_415, clause_419, clause_91, clause_246, clause_197, clause_154, clause_103, clause_414, clause_38, clause_137, clause_233, clause_105, clause_338, clause_160, clause_45, clause_237, clause_133, clause_146, clause_442, clause_226, clause_424, clause_351, clause_113, clause_334, clause_147, clause_441, clause_322, clause_37, clause_311, clause_326, clause_253, clause_423, clause_42, clause_345, clause_14, clause_244, clause_66, clause_173, clause_202, clause_263, clause_281, clause_317, clause_18, clause_328, clause_292, clause_369, clause_388, clause_455, clause_447, clause_273, clause_425, clause_396, clause_252, clause_11, clause_330, clause_3, clause_139, clause_161, clause_402, clause_143, clause_280, clause_219, clause_46
% 6.83/2.57 % No. of inferences in proof: 133
% 6.83/2.58 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2044 ms resp. 1391 ms w/o parsing
% 7.97/2.82 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.97/2.83 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------