TSTP Solution File: SYO649-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SYO649-1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.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 12:36:50 EDT 2023
% Result : Unsatisfiable 5.36s 2.16s
% Output : Refutation 6.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 46
% Syntax : Number of formulae : 85 ( 5 unt; 8 typ; 0 def)
% Number of atoms : 849 ( 0 equ; 0 cnn)
% Maximal formula atoms : 21 ( 11 avg)
% Number of connectives : 5912 ( 724 ~; 772 |; 0 &;4416 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 18 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 : 124 ( 0 ^; 124 !; 0 ?; 124 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'E\'_type',type,
'\'E\'': $i > $i > $o ).
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(s_type,type,
s: $i > $i ).
thf(z_type,type,
z: $i ).
thf(24,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_909) ).
thf(85,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_999) ).
thf(53,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_375) ).
thf(41,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_703) ).
thf(45,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_771) ).
thf(59,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(38,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_1518) ).
thf(112,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)],[38]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1012) ).
thf(67,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1480) ).
thf(43,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_512) ).
thf(55,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1136) ).
thf(75,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(7,axiom,
~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_716) ).
thf(51,plain,
~ ( '\'LE\'' @ ( f @ z ) @ '\'0\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1507) ).
thf(47,plain,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,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_1214) ).
thf(69,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)],[16]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_649) ).
thf(101,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1522) ).
thf(93,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_774) ).
thf(57,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_962) ).
thf(61,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(26,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_519) ).
thf(89,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)],[26]) ).
thf(14,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1501) ).
thf(65,plain,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_369) ).
thf(97,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1370) ).
thf(109,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(20,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_1172) ).
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)],[20]) ).
thf(18,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1033) ).
thf(73,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_102) ).
thf(105,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_365) ).
thf(71,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_62) ).
thf(49,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(22,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_258) ).
thf(81,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)],[22]) ).
thf(1,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_252) ).
thf(39,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(33,axiom,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_314) ).
thf(103,plain,
! [A: $i] :
( ~ ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) )
| ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'LE\'' @ ( f @ A ) @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1121) ).
thf(91,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1282) ).
thf(63,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_349) ).
thf(95,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_412) ).
thf(99,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_985) ).
thf(87,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(35,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1514) ).
thf(107,plain,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1046) ).
thf(79,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ A ) ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ ( suc @ ( suc @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(37,axiom,
! [A: $i] : ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1382) ).
thf(111,plain,
! [A: $i] : ( '\'LE\'' @ ( f @ A ) @ ( s @ '\'0\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_162) ).
thf(83,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(114,plain,
$false,
inference(e,[status(thm)],[85,53,41,45,59,112,67,43,55,75,51,47,69,101,93,57,61,89,65,97,109,77,73,105,71,49,81,39,103,91,63,95,99,87,107,79,111,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO649-1 : TPTP v8.1.2. Released v7.3.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n020.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 18:10:48 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.89/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/1.02 % [INFO] Parsing done (191ms).
% 1.61/1.03 % [INFO] Running in sequential loop mode.
% 2.12/1.23 % [INFO] eprover registered as external prover.
% 2.12/1.23 % [INFO] cvc4 registered as external prover.
% 2.12/1.24 % [INFO] Scanning for conjecture ...
% 2.12/1.30 % [INFO] 38 axioms and no conjecture found.
% 2.61/1.43 % [INFO] Problem is propositional (TPTP CNF).
% 2.61/1.44 % [INFO] Type checking passed.
% 2.61/1.44 % [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 ...
% 5.36/2.16 % External prover 'e' found a proof!
% 5.36/2.16 % [INFO] Killing All external provers ...
% 5.36/2.16 % Time passed: 1650ms (effective reasoning time: 1126ms)
% 5.36/2.16 % Axioms used in derivation (38): clause_1370, clause_985, clause_1012, clause_1172, clause_649, clause_512, clause_999, clause_1480, clause_716, clause_1514, clause_375, clause_349, clause_1507, clause_1282, clause_1214, clause_1121, clause_102, clause_1382, clause_1518, clause_519, clause_703, clause_1501, clause_1046, clause_1136, clause_412, clause_365, clause_258, clause_162, clause_62, clause_774, clause_314, clause_962, clause_1522, clause_369, clause_1033, clause_252, clause_771, clause_909
% 5.36/2.16 % No. of inferences in proof: 77
% 5.36/2.16 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1650 ms resp. 1126 ms w/o parsing
% 6.34/2.37 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.34/2.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------