%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO649-1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:45:06 AM UTC 2026
% Result : Unsatisfiable 20.86s 6.36s
% Output : Refutation 21.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 38
% Syntax : Number of formulae : 184 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 1479 ( 67 equ; 0 cnn)
% Maximal formula atoms : 22 ( 8 avg)
% Number of connectives : 9740 (1162 ~;1219 |; 0 &;7359 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 188 ( 0 ^; 188 !; 0 ?; 188 :)
% Comments :
%------------------------------------------------------------------------------
thf('E_decl',type,
'E': $i > $i > $o ).
thf('0_decl',type,
'0': $i ).
thf(f_decl,type,
f: $i > $i ).
thf(suc_decl,type,
suc: $i > $i ).
thf(iLEQ_decl,type,
iLEQ: $i > $i > $o ).
thf('LE_decl',type,
'LE': $i > $i > $o ).
thf(s_decl,type,
s: $i > $i ).
thf(z_decl,type,
z: $i ).
thf(33,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_314) ).
thf(103,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(104,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[103]) ).
thf(37,axiom,
! [A: $i] : ( '0' @ s @ ( A @ f @ 'LE' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1382) ).
thf(111,plain,
! [A: $i] : ( '0' @ s @ ( A @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(119,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[104,111]) ).
thf(120,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[119]) ).
thf(26,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_519) ).
thf(89,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(90,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[89]) ).
thf(454,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[90,111]) ).
thf(455,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[454]) ).
thf(7,axiom,
~ ( '0' @ ( z @ f @ 'LE' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_716) ).
thf(51,plain,
~ ( '0' @ ( z @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(52,plain,
~ ( '0' @ ( z @ f @ 'LE' ) ),
inference(polarity_switch,[status(thm)],[51]) ).
thf(456,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ~ $true
| ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[455,52]) ).
thf(457,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[456]) ).
thf(458,plain,
z @ suc @ suc @ f @ ( '0' @ 'E' ),
inference(pattern_uni,[status(thm)],[457:[bind(A,$thf( z ))]]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ~ ( B @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1046) ).
thf(79,plain,
! [B: $i,A: $i] :
( ~ ( B @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ~ ( B @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[79]) ).
thf(562,plain,
! [B: $i,A: $i] :
( ( ( z @ suc @ suc @ f @ ( '0' @ 'E' ) )
!= ( B @ suc @ suc @ f @ ( '0' @ 'E' ) ) )
| ~ ( B @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ $true
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[458,80]) ).
thf(563,plain,
! [B: $i,A: $i] :
( ( ( z @ suc @ suc @ f @ ( '0' @ 'E' ) )
!= ( B @ suc @ suc @ f @ ( '0' @ 'E' ) ) )
| ~ ( B @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[562]) ).
thf(564,plain,
! [A: $i] :
( ~ ( z @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( z @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[563:[bind(A,$thf( A )),bind(B,$thf( z ))]]) ).
thf(38,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1518) ).
thf(112,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(113,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[112]) ).
thf(259,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[113,111]) ).
thf(260,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[259]) ).
thf(261,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ~ $true
| ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[260,52]) ).
thf(262,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[261]) ).
thf(263,plain,
z @ suc @ f @ ( '0' @ 'E' ),
inference(pattern_uni,[status(thm)],[262:[bind(A,$thf( z ))]]) ).
thf(121,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ~ $true
| ( A @ f @ ( '0' @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[120,52]) ).
thf(122,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ( A @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[121]) ).
thf(123,plain,
z @ f @ ( '0' @ 'E' ),
inference(pattern_uni,[status(thm)],[122:[bind(A,$thf( z ))]]) ).
thf(622,plain,
! [A: $i] :
( ~ ( z @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ $true
| ~ ( z @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ $true
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(rewrite,[status(thm)],[564,263,123]) ).
thf(623,plain,
! [A: $i] :
( ~ ( z @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( z @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[622]) ).
thf(706,plain,
! [A: $i] :
( ( ( z @ suc @ suc @ f @ ( '0' @ 'E' ) )
!= ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) )
| ~ ( z @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( z @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ $true
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[458,623]) ).
thf(707,plain,
! [A: $i] :
( ( ( z @ suc @ suc @ f @ ( '0' @ 'E' ) )
!= ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) )
| ~ ( z @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( z @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[706]) ).
thf(708,plain,
( ~ ( z @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[707:[bind(A,$thf( z ))]]) ).
thf(785,plain,
( ~ ( z @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[708]) ).
thf(806,plain,
( ~ ( z @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ $true
| ~ ( z @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ $true
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(rewrite,[status(thm)],[785,263,123]) ).
thf(807,plain,
( ~ ( z @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[806]) ).
thf(16,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1214) ).
thf(69,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(70,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ suc @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[69]) ).
thf(617,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[70,111]) ).
thf(618,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[617]) ).
thf(619,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ~ $true
| ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[618,52]) ).
thf(620,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[619]) ).
thf(621,plain,
z @ suc @ suc @ suc @ f @ ( '0' @ 'E' ),
inference(pattern_uni,[status(thm)],[620:[bind(A,$thf( z ))]]) ).
thf(884,plain,
( ~ ( z @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[807,621]) ).
thf(885,plain,
( ~ ( z @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[884]) ).
thf(6,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ suc @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_62) ).
thf(49,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ suc @ suc @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(50,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ suc @ suc @ suc @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[49]) ).
thf(1409,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[50,111]) ).
thf(1410,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[1409]) ).
thf(1411,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ~ $true
| ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[1410,52]) ).
thf(1412,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[1411]) ).
thf(1413,plain,
z @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ),
inference(pattern_uni,[status(thm)],[1412:[bind(A,$thf( z ))]]) ).
thf(18,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1033) ).
thf(73,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ suc @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(74,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ suc @ suc @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[73]) ).
thf(1042,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[74,111]) ).
thf(1043,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[1042]) ).
thf(1044,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ~ $true
| ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[1043,52]) ).
thf(1045,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[1044]) ).
thf(1046,plain,
z @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ),
inference(pattern_uni,[status(thm)],[1045:[bind(A,$thf( z ))]]) ).
thf(1670,plain,
( ~ $true
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ $true
| ~ ( z @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) ) ),
inference(rewrite,[status(thm)],[885,1413,1046]) ).
thf(1671,plain,
( ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[1670]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_909) ).
thf(85,plain,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_999) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_375) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1480) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_649) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_258) ).
thf(81,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(82,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[81]) ).
thf(1651,plain,
! [A: $i] :
( ( ( z @ suc @ suc @ f @ ( '0' @ 'E' ) )
!= ( A @ suc @ f @ ( '0' @ 'E' ) ) )
| ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ $true
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[458,82]) ).
thf(1652,plain,
! [A: $i] :
( ( ( z @ suc @ suc @ f @ ( '0' @ 'E' ) )
!= ( A @ suc @ f @ ( '0' @ 'E' ) ) )
| ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[1651]) ).
thf(1653,plain,
( ( z @ suc @ suc @ ( z @ suc @ suc @ iLEQ ) )
| ( z @ suc @ suc @ f @ ( z @ suc @ f @ 'E' ) )
| ~ ( z @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[1652:[bind(A,$thf( z @ suc ))]]) ).
thf(1834,plain,
( ( z @ suc @ suc @ ( z @ suc @ suc @ iLEQ ) )
| ( z @ suc @ suc @ f @ ( z @ suc @ f @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[1653,263]) ).
thf(1835,plain,
( ( z @ suc @ suc @ ( z @ suc @ suc @ iLEQ ) )
| ( z @ suc @ suc @ f @ ( z @ suc @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[1834]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[41]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_703) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[45]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1522) ).
thf(93,plain,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_774) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_962) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1501) ).
thf(65,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_369) ).
thf(97,plain,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1370) ).
thf(109,plain,
! [B: $i,A: $i] :
( ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1172) ).
thf(77,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_102) ).
thf(105,plain,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[43]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_771) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(114,plain,
! [A: $i] :
( ( ( '0' @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[111,52]) ).
thf(115,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(116,plain,
! [A: $i] :
( ( ( '0' @ s )
!= '0' )
| ( ( A @ f )
!= ( z @ f ) ) ),
inference(simp,[status(thm)],[115]) ).
thf(117,plain,
! [A: $i] :
( ( ( '0' @ s )
!= '0' )
| ( A != z ) ),
inference(simp,[status(thm)],[116]) ).
thf(118,plain,
( ( '0' @ s )
!= '0' ),
inference(simp,[status(thm)],[117]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_365) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1610,plain,
! [A: $i] :
( ( ( z @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
!= ( A @ suc @ f @ ( '0' @ 'E' ) ) )
| ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ $true
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[621,82]) ).
thf(1611,plain,
! [A: $i] :
( ( ( z @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
!= ( A @ suc @ f @ ( '0' @ 'E' ) ) )
| ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[1610]) ).
thf(1612,plain,
( ( z @ suc @ suc @ suc @ ( z @ suc @ suc @ suc @ iLEQ ) )
| ( z @ suc @ suc @ suc @ f @ ( z @ suc @ suc @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[1611:[bind(A,$thf( z @ suc @ suc ))]]) ).
thf(2078,plain,
( ( z @ suc @ suc @ suc @ ( z @ suc @ suc @ suc @ iLEQ ) )
| ( z @ suc @ suc @ suc @ f @ ( z @ suc @ suc @ f @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[1612,458]) ).
thf(2079,plain,
( ( z @ suc @ suc @ suc @ ( z @ suc @ suc @ suc @ iLEQ ) )
| ( z @ suc @ suc @ suc @ f @ ( z @ suc @ suc @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[2078]) ).
thf(1,axiom,
! [B: $i,A: $i] :
( ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_252) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1121) ).
thf(91,plain,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(1695,plain,
( ( ( z @ suc @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
!= ( z @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ $true
| ~ ( z @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[1046,1671]) ).
thf(1696,plain,
( ( ( z @ suc @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
!= ( z @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[1695]) ).
thf(1729,plain,
( ( ( z @ suc @ suc @ suc @ suc @ f )
!= ( z @ suc @ suc @ suc @ suc @ f ) )
| ( ( z @ f )
!= '0' )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[1696]) ).
thf(1750,plain,
( ( ( z @ f )
!= '0' )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[1729]) ).
thf(1756,plain,
( ( ( z @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
!= ( z @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) )
| ( ( z @ f )
!= '0' )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ $true
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[621,1750]) ).
thf(1757,plain,
( ( ( z @ suc @ suc @ suc @ f @ ( z @ f @ 'E' ) )
!= ( z @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) )
| ( ( z @ f )
!= '0' )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[1756]) ).
thf(1813,plain,
( ( ( z @ suc @ suc @ suc @ f )
!= ( z @ suc @ suc @ suc @ f ) )
| ( ( z @ f )
!= '0' )
| ( ( z @ f )
!= '0' )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[1757]) ).
thf(1831,plain,
( ( ( z @ f )
!= '0' )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[1813]) ).
thf(2159,plain,
( ( ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) )
!= ( z @ suc @ suc @ f @ ( '0' @ 'E' ) ) )
| ( ( z @ f )
!= '0' )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[458,1831]) ).
thf(2160,plain,
( ( ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) )
!= ( z @ suc @ suc @ f @ ( '0' @ 'E' ) ) )
| ( ( z @ f )
!= '0' )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[2159]) ).
thf(2172,plain,
( ( ( z @ suc @ suc @ f )
!= ( z @ suc @ suc @ f ) )
| ( ( z @ f )
!= '0' )
| ( ( z @ f )
!= '0' )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[2160]) ).
thf(2194,plain,
( ( ( z @ f )
!= '0' )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[2172]) ).
thf(2200,plain,
( ( ( z @ suc @ f @ ( z @ f @ 'E' ) )
!= ( z @ suc @ f @ ( '0' @ 'E' ) ) )
| ( ( z @ f )
!= '0' )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[263,2194]) ).
thf(2201,plain,
( ( ( z @ suc @ f @ ( z @ f @ 'E' ) )
!= ( z @ suc @ f @ ( '0' @ 'E' ) ) )
| ( ( z @ f )
!= '0' )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[2200]) ).
thf(2227,plain,
( ( ( z @ suc @ f )
!= ( z @ suc @ f ) )
| ( ( z @ f )
!= '0' )
| ( ( z @ f )
!= '0' )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[2201]) ).
thf(2234,plain,
( ( ( z @ f )
!= '0' )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[2227]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1282) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_349) ).
thf(95,plain,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1012) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1616,plain,
! [A: $i] :
( ( ( z @ suc @ f @ ( '0' @ 'E' ) )
!= ( A @ suc @ f @ ( '0' @ 'E' ) ) )
| ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ $true
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[263,82]) ).
thf(1617,plain,
! [A: $i] :
( ( ( z @ suc @ f @ ( '0' @ 'E' ) )
!= ( A @ suc @ f @ ( '0' @ 'E' ) ) )
| ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[1616]) ).
thf(1618,plain,
( ( z @ suc @ ( z @ suc @ iLEQ ) )
| ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ f @ ( '0' @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[1617:[bind(A,$thf( z ))]]) ).
thf(1656,plain,
( ( z @ suc @ ( z @ suc @ iLEQ ) )
| ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[1618,123]) ).
thf(1657,plain,
( ( z @ suc @ ( z @ suc @ iLEQ ) )
| ( z @ suc @ f @ ( z @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[1656]) ).
thf(2274,plain,
( ( ( z @ suc @ ( z @ suc @ iLEQ ) )
!= ( z @ suc @ ( z @ suc @ iLEQ ) ) )
| ( ( z @ f )
!= '0' )
| ~ $true
| ( z @ suc @ f @ ( z @ f @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[1657,2234]) ).
thf(2275,plain,
( ( ( z @ suc @ ( z @ suc @ iLEQ ) )
!= ( z @ suc @ ( z @ suc @ iLEQ ) ) )
| ( ( z @ f )
!= '0' )
| ( z @ suc @ f @ ( z @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[2274]) ).
thf(2276,plain,
( ( ( z @ f )
!= '0' )
| ( z @ suc @ f @ ( z @ f @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[2275:[]]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_412) ).
thf(99,plain,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_985) ).
thf(87,plain,
! [B: $i,A: $i] :
( ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[39]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_512) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1136) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1514) ).
thf(107,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(1640,plain,
! [A: $i] :
( ( ( z @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
!= ( A @ suc @ f @ ( '0' @ 'E' ) ) )
| ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ $true
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[1413,82]) ).
thf(1641,plain,
! [A: $i] :
( ( ( z @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
!= ( A @ suc @ f @ ( '0' @ 'E' ) ) )
| ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[1640]) ).
thf(1642,plain,
( ( z @ suc @ suc @ suc @ suc @ suc @ ( z @ suc @ suc @ suc @ suc @ suc @ iLEQ ) )
| ( z @ suc @ suc @ suc @ suc @ suc @ f @ ( z @ suc @ suc @ suc @ suc @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[1641:[bind(A,$thf( z @ suc @ suc @ suc @ suc ))]]) ).
thf(2240,plain,
( ( z @ suc @ suc @ suc @ suc @ suc @ ( z @ suc @ suc @ suc @ suc @ suc @ iLEQ ) )
| ( z @ suc @ suc @ suc @ suc @ suc @ f @ ( z @ suc @ suc @ suc @ suc @ f @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[1642,1046]) ).
thf(2241,plain,
( ( z @ suc @ suc @ suc @ suc @ suc @ ( z @ suc @ suc @ suc @ suc @ suc @ iLEQ ) )
| ( z @ suc @ suc @ suc @ suc @ suc @ f @ ( z @ suc @ suc @ suc @ suc @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[2240]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1507) ).
thf(47,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_162) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1628,plain,
! [A: $i] :
( ( ( z @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
!= ( A @ suc @ f @ ( '0' @ 'E' ) ) )
| ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ $true
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[1046,82]) ).
thf(1629,plain,
! [A: $i] :
( ( ( z @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
!= ( A @ suc @ f @ ( '0' @ 'E' ) ) )
| ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[1628]) ).
thf(1630,plain,
( ( z @ suc @ suc @ suc @ suc @ ( z @ suc @ suc @ suc @ suc @ iLEQ ) )
| ( z @ suc @ suc @ suc @ suc @ f @ ( z @ suc @ suc @ suc @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[1629:[bind(A,$thf( z @ suc @ suc @ suc ))]]) ).
thf(2105,plain,
( ( z @ suc @ suc @ suc @ suc @ ( z @ suc @ suc @ suc @ suc @ iLEQ ) )
| ( z @ suc @ suc @ suc @ suc @ f @ ( z @ suc @ suc @ suc @ f @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[1630,621]) ).
thf(2106,plain,
( ( z @ suc @ suc @ suc @ suc @ ( z @ suc @ suc @ suc @ suc @ iLEQ ) )
| ( z @ suc @ suc @ suc @ suc @ f @ ( z @ suc @ suc @ suc @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[2105]) ).
thf(2817,plain,
$false,
inference(e,[status(thm)],[120,1671,52,85,260,53,41,43,51,69,101,1835,42,1046,46,93,57,61,89,65,97,109,77,73,105,618,45,44,59,118,71,49,2079,81,39,1043,103,621,91,455,80,1413,2234,112,123,458,63,95,263,67,2276,99,87,40,55,75,82,107,1657,79,1410,2241,47,111,83,2106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO649-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.16/0.41 % Computer : n020.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 19:43:50 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.87/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.92/1.30 % [INFO] Parsing done (310ms).
% 1.92/1.32 % [INFO] Running in sequential loop mode.
% 2.93/1.71 % [INFO] eprover registered as external prover.
% 2.93/1.72 % [INFO] Scanning for conjecture ...
% 3.15/1.81 % [INFO] 38 axioms and no conjecture found.
% 3.47/2.01 % [INFO] Problem is propositional (TPTP CNF).
% 3.47/2.02 % [INFO] Type checking passed.
% 3.47/2.02 % [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 ...
% 20.86/6.36 % External prover 'e' found a proof!
% 20.86/6.36 % [INFO] Killing All external provers ...
% 20.86/6.36 % Time passed: 5801ms (effective reasoning time: 5036ms)
% 20.86/6.36 % 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
% 20.86/6.36 % No. of inferences in proof: 184
% 20.86/6.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5801 ms resp. 5036 ms w/o parsing
% 21.63/6.57 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 21.63/6.57 % [INFO] Killing All external provers ...
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