%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO653-1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n010.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 36.01s 11.54s
% Output : Refutation 37.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 90
% Syntax : Number of formulae : 274 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 4143 ( 72 equ; 0 cnn)
% Maximal formula atoms : 28 ( 15 avg)
% Number of connectives : 25672 (3506 ~;3801 |; 0 &;18365 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 21 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 : 735 ( 0 ^; 735 !; 0 ?; 735 :)
% 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(z_decl,type,
z: $i ).
thf(s_decl,type,
s: $i > $i ).
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/sandbox/benchmark/theBenchmark.p',clause_1719) ).
thf(129,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(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_286) ).
thf(101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(73,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1934) ).
thf(234,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(50,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1983) ).
thf(188,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)],[50]) ).
thf(189,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[188]) ).
thf(30,axiom,
! [A: $i] : ( '0' @ s @ ( A @ f @ 'LE' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2036) ).
thf(149,plain,
! [A: $i] : ( '0' @ s @ ( A @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(422,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[189,149]) ).
thf(423,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[422]) ).
thf(21,axiom,
~ ( '0' @ ( z @ f @ 'LE' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1057) ).
thf(131,plain,
~ ( '0' @ ( z @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(132,plain,
~ ( '0' @ ( z @ f @ 'LE' ) ),
inference(polarity_switch,[status(thm)],[131]) ).
thf(424,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ~ $true
| ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[423,132]) ).
thf(425,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[424]) ).
thf(426,plain,
z @ suc @ f @ ( '0' @ 'E' ),
inference(pattern_uni,[status(thm)],[425:[bind(A,$thf( z ))]]) ).
thf(84,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/sandbox/benchmark/theBenchmark.p',clause_354) ).
thf(256,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)],[84]) ).
thf(257,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)],[256]) ).
thf(1505,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)],[426,257]) ).
thf(1506,plain,
! [A: $i] :
( ( ( z @ suc @ f @ ( '0' @ 'E' ) )
!= ( A @ suc @ f @ ( '0' @ 'E' ) ) )
| ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[1505]) ).
thf(1507,plain,
( ( z @ suc @ ( z @ suc @ iLEQ ) )
| ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ f @ ( '0' @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[1506:[bind(A,$thf( z ))]]) ).
thf(54,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_148) ).
thf(196,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(197,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[196]) ).
thf(287,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[197,149]) ).
thf(288,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[287]) ).
thf(289,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ~ $true
| ( A @ f @ ( '0' @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[288,132]) ).
thf(290,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ( A @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[289]) ).
thf(291,plain,
z @ f @ ( '0' @ 'E' ),
inference(pattern_uni,[status(thm)],[290:[bind(A,$thf( z ))]]) ).
thf(1545,plain,
( ( z @ suc @ ( z @ suc @ iLEQ ) )
| ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[1507,291]) ).
thf(1546,plain,
( ( z @ suc @ ( z @ suc @ iLEQ ) )
| ( z @ suc @ f @ ( z @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[1545]) ).
thf(75,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_38) ).
thf(238,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)],[75]) ).
thf(239,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[238]) ).
thf(709,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[239,149]) ).
thf(710,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[709]) ).
thf(711,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ~ $true
| ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[710,132]) ).
thf(712,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[711]) ).
thf(713,plain,
z @ suc @ suc @ f @ ( '0' @ 'E' ),
inference(pattern_uni,[status(thm)],[712:[bind(A,$thf( z ))]]) ).
thf(56,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1836) ).
thf(200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[200]) ).
thf(275,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( B @ suc @ ( A @ suc @ iLEQ ) )
!= ( D @ suc @ ( C @ suc @ iLEQ ) ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[201]) ).
thf(278,plain,
! [B: $i,A: $i] :
( ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[275:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[278]) ).
thf(284,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ suc @ ( B @ suc @ iLEQ ) )
!= ( B @ suc @ ( A @ suc @ iLEQ ) ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[281]) ).
thf(285,plain,
! [A: $i] :
( ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[284:[bind(A,$thf( B ))]]) ).
thf(286,plain,
! [A: $i] :
( ~ ( 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 @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[285]) ).
thf(921,plain,
! [A: $i] :
( ( ( z @ suc @ suc @ f @ ( '0' @ 'E' ) )
!= ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ $true
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[713,286]) ).
thf(922,plain,
! [A: $i] :
( ( ( z @ suc @ suc @ f @ ( '0' @ 'E' ) )
!= ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[921]) ).
thf(923,plain,
( ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[922:[bind(A,$thf( z ))]]) ).
thf(976,plain,
( ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ $true
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ $true
| ~ ( z @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(rewrite,[status(thm)],[923,291,426]) ).
thf(977,plain,
( ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[976]) ).
thf(59,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/sandbox/benchmark/theBenchmark.p',clause_1528) ).
thf(206,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)],[59]) ).
thf(207,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)],[206]) ).
thf(911,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[207,149]) ).
thf(912,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[911]) ).
thf(913,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ~ $true
| ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[912,132]) ).
thf(914,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[913]) ).
thf(915,plain,
z @ suc @ suc @ suc @ f @ ( '0' @ 'E' ),
inference(pattern_uni,[status(thm)],[914:[bind(A,$thf( z ))]]) ).
thf(1010,plain,
( ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ $true ),
inference(rewrite,[status(thm)],[977,915]) ).
thf(1011,plain,
( ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[1010]) ).
thf(1224,plain,
( ( ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) )
!= ( z @ suc @ suc @ f @ ( '0' @ 'E' ) ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ $true
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) ) ),
inference(paramod_ordered,[status(thm)],[713,1011]) ).
thf(1225,plain,
( ( ( z @ suc @ suc @ f @ ( z @ f @ 'E' ) )
!= ( z @ suc @ suc @ f @ ( '0' @ 'E' ) ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[1224]) ).
thf(1245,plain,
( ( ( z @ suc @ suc @ f )
!= ( z @ suc @ suc @ f ) )
| ( ( z @ f )
!= '0' )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[1225]) ).
thf(1248,plain,
( ( ( z @ f )
!= '0' )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[1245]) ).
thf(1254,plain,
( ( ( z @ suc @ f @ ( z @ f @ 'E' ) )
!= ( z @ suc @ f @ ( '0' @ 'E' ) ) )
| ( ( z @ f )
!= '0' )
| ~ $true
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) ) ),
inference(paramod_ordered,[status(thm)],[426,1248]) ).
thf(1255,plain,
( ( ( z @ suc @ f @ ( z @ f @ 'E' ) )
!= ( z @ suc @ f @ ( '0' @ 'E' ) ) )
| ( ( z @ f )
!= '0' )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[1254]) ).
thf(1260,plain,
( ( ( z @ suc @ f )
!= ( z @ suc @ f ) )
| ( ( z @ f )
!= '0' )
| ( ( z @ f )
!= '0' )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[1255]) ).
thf(1264,plain,
( ( ( z @ f )
!= '0' )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[1260]) ).
thf(1547,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)],[1546,1264]) ).
thf(1548,plain,
( ( ( z @ suc @ ( z @ suc @ iLEQ ) )
!= ( z @ suc @ ( z @ suc @ iLEQ ) ) )
| ( ( z @ f )
!= '0' )
| ( z @ suc @ f @ ( z @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[1547]) ).
thf(1549,plain,
( ( ( z @ f )
!= '0' )
| ( z @ suc @ f @ ( z @ f @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[1548:[]]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_51) ).
thf(170,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2031) ).
thf(115,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(57,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1953) ).
thf(202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_68) ).
thf(174,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(48,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1277) ).
thf(184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(1493,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)],[713,257]) ).
thf(1494,plain,
! [A: $i] :
( ( ( z @ suc @ suc @ f @ ( '0' @ 'E' ) )
!= ( A @ suc @ f @ ( '0' @ 'E' ) ) )
| ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[1493]) ).
thf(1495,plain,
( ( z @ suc @ suc @ ( z @ suc @ suc @ iLEQ ) )
| ( z @ suc @ suc @ f @ ( z @ suc @ f @ 'E' ) )
| ~ ( z @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[1494:[bind(A,$thf( z @ suc ))]]) ).
thf(2216,plain,
( ( z @ suc @ suc @ ( z @ suc @ suc @ iLEQ ) )
| ( z @ suc @ suc @ f @ ( z @ suc @ f @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[1495,426]) ).
thf(2217,plain,
( ( z @ suc @ suc @ ( z @ suc @ suc @ iLEQ ) )
| ( z @ suc @ suc @ f @ ( z @ suc @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[2216]) ).
thf(2245,plain,
( ( ( z @ suc @ suc @ ( z @ suc @ suc @ iLEQ ) )
!= ( z @ suc @ ( z @ suc @ iLEQ ) ) )
| ( ( z @ f )
!= '0' )
| ~ $true
| ( z @ suc @ suc @ f @ ( z @ suc @ f @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[2217,1264]) ).
thf(2246,plain,
( ( ( z @ suc @ suc @ ( z @ suc @ suc @ iLEQ ) )
!= ( z @ suc @ ( z @ suc @ iLEQ ) ) )
| ( ( z @ f )
!= '0' )
| ( z @ suc @ suc @ f @ ( z @ suc @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[2245]) ).
thf(2267,plain,
( ( ( z @ suc @ suc )
!= ( z @ suc ) )
| ( ( z @ suc @ suc )
!= ( z @ suc ) )
| ( ( z @ f )
!= '0' )
| ( z @ suc @ suc @ f @ ( z @ suc @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[2246]) ).
thf(2269,plain,
( ( ( z @ suc @ suc )
!= ( z @ suc ) )
| ( ( z @ f )
!= '0' )
| ( z @ suc @ suc @ f @ ( z @ suc @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[2267]) ).
thf(18,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_316) ).
thf(125,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(2,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_482) ).
thf(93,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(70,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2101) ).
thf(228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(1499,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)],[915,257]) ).
thf(1500,plain,
! [A: $i] :
( ( ( z @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
!= ( A @ suc @ f @ ( '0' @ 'E' ) ) )
| ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[1499]) ).
thf(1501,plain,
( ( z @ suc @ suc @ suc @ ( z @ suc @ suc @ suc @ iLEQ ) )
| ( z @ suc @ suc @ suc @ f @ ( z @ suc @ suc @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[1500:[bind(A,$thf( z @ suc @ suc ))]]) ).
thf(3595,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)],[1501,713]) ).
thf(3596,plain,
( ( z @ suc @ suc @ suc @ ( z @ suc @ suc @ suc @ iLEQ ) )
| ( z @ suc @ suc @ suc @ f @ ( z @ suc @ suc @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[3595]) ).
thf(3615,plain,
( ( ( z @ suc @ suc @ suc @ ( z @ suc @ suc @ suc @ iLEQ ) )
!= ( z @ suc @ ( z @ suc @ iLEQ ) ) )
| ( ( z @ f )
!= '0' )
| ~ $true
| ( z @ suc @ suc @ suc @ f @ ( z @ suc @ suc @ f @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[3596,1264]) ).
thf(3616,plain,
( ( ( z @ suc @ suc @ suc @ ( z @ suc @ suc @ suc @ iLEQ ) )
!= ( z @ suc @ ( z @ suc @ iLEQ ) ) )
| ( ( z @ f )
!= '0' )
| ( z @ suc @ suc @ suc @ f @ ( z @ suc @ suc @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[3615]) ).
thf(3655,plain,
( ( ( z @ suc @ suc @ suc )
!= ( z @ suc ) )
| ( ( z @ suc @ suc @ suc )
!= ( z @ suc ) )
| ( ( z @ f )
!= '0' )
| ( z @ suc @ suc @ suc @ f @ ( z @ suc @ suc @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[3616]) ).
thf(3657,plain,
( ( ( z @ suc @ suc @ suc )
!= ( z @ suc ) )
| ( ( z @ f )
!= '0' )
| ( z @ suc @ suc @ suc @ f @ ( z @ suc @ suc @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[3655]) ).
thf(32,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1143) ).
thf(152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(64,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1791) ).
thf(216,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_268) ).
thf(164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1556) ).
thf(121,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(29,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_872) ).
thf(147,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1596) ).
thf(133,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(80,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( 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/sandbox/benchmark/theBenchmark.p',clause_972) ).
thf(248,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( 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)],[80]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_419) ).
thf(117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(66,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1568) ).
thf(220,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(86,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_877) ).
thf(260,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(36,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_683) ).
thf(160,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1480) ).
thf(192,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_498) ).
thf(137,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2175) ).
thf(91,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(92,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[91]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_20) ).
thf(252,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1508) ).
thf(97,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1384) ).
thf(224,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_961) ).
thf(156,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(1496,plain,
! [A: $i] :
( ( ( z @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
!= ( A @ f @ ( '0' @ 'E' ) ) )
| ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[915,257]) ).
thf(1497,plain,
! [A: $i] :
( ( ( z @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
!= ( A @ f @ ( '0' @ 'E' ) ) )
| ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[1496]) ).
thf(1498,plain,
( ( z @ suc @ suc @ suc @ suc @ ( z @ suc @ suc @ suc @ suc @ iLEQ ) )
| ( z @ suc @ suc @ suc @ suc @ f @ ( z @ suc @ suc @ suc @ f @ 'E' ) )
| ~ ( z @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[1497:[bind(A,$thf( z @ suc @ suc @ suc ))]]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_114) ).
thf(141,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(62,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_433) ).
thf(212,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_50) ).
thf(95,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(96,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[95]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_971) ).
thf(109,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(89,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_380) ).
thf(266,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_102) ).
thf(105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(78,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1597) ).
thf(244,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_541) ).
thf(166,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(88,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_942) ).
thf(264,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(46,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1221) ).
thf(180,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(44,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_765) ).
thf(176,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1615) ).
thf(204,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(74,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_931) ).
thf(236,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(42,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2198) ).
thf(172,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1048) ).
thf(113,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(270,plain,
! [A: $i] :
( ( ( '0' @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[149,132]) ).
thf(271,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[270]) ).
thf(272,plain,
! [A: $i] :
( ( ( '0' @ s )
!= '0' )
| ( ( A @ f )
!= ( z @ f ) ) ),
inference(simp,[status(thm)],[271]) ).
thf(273,plain,
! [A: $i] :
( ( ( '0' @ s )
!= '0' )
| ( A != z ) ),
inference(simp,[status(thm)],[272]) ).
thf(274,plain,
( ( '0' @ s )
!= '0' ),
inference(simp,[status(thm)],[273]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1148) ).
thf(230,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(98,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[97]) ).
thf(60,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_295) ).
thf(208,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2102) ).
thf(103,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(76,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1337) ).
thf(240,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(55,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_142) ).
thf(198,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_383) ).
thf(135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(69,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2160) ).
thf(226,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_227) ).
thf(162,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(2271,plain,
( ( ( z @ suc )
!= z )
| ( ( z @ f )
!= '0' )
| ( z @ suc @ suc @ f @ ( z @ suc @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[2269]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_54) ).
thf(123,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2157) ).
thf(194,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(28,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_306) ).
thf(145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(31,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1387) ).
thf(150,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(3659,plain,
( ( ( z @ suc @ suc )
!= z )
| ( ( z @ f )
!= '0' )
| ( z @ suc @ suc @ suc @ f @ ( z @ suc @ suc @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[3657]) ).
thf(47,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1893) ).
thf(182,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2134) ).
thf(127,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(33,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_912) ).
thf(154,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(27,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_244) ).
thf(143,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(81,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_878) ).
thf(250,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1036) ).
thf(99,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(65,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_94) ).
thf(218,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(85,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_246) ).
thf(258,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(35,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_903) ).
thf(158,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(49,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1976) ).
thf(186,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(25,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1550) ).
thf(139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_554) ).
thf(119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(79,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1404) ).
thf(246,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(63,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_107) ).
thf(214,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(4629,plain,
( ( ( z @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
!= ( z @ f @ ( '0' @ 'E' ) ) )
| ( 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(paramod_ordered,[status(thm)],[291,1498]) ).
thf(4630,plain,
( ( ( z @ suc @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
!= ( z @ f @ ( '0' @ 'E' ) ) )
| ( 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)],[4629]) ).
thf(4655,plain,
( ( ( z @ suc @ suc @ suc @ suc @ f )
!= ( z @ f ) )
| ( '0' != '0' )
| ( 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)],[4630]) ).
thf(4670,plain,
( ( ( z @ suc @ suc @ suc @ suc @ f )
!= ( z @ f ) )
| ( 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)],[4655]) ).
thf(51,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_714) ).
thf(190,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(40,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1773) ).
thf(168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1801) ).
thf(262,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(61,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_263) ).
thf(210,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_704) ).
thf(107,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(77,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_391) ).
thf(242,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(90,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1161) ).
thf(268,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(94,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[93]) ).
thf(45,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1091) ).
thf(178,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1371) ).
thf(111,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(83,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1039) ).
thf(254,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(67,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1883) ).
thf(222,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(72,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1315) ).
thf(232,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[99]) ).
thf(6292,plain,
$false,
inference(e,[status(thm)],[129,101,234,1549,170,115,202,174,288,257,184,2269,125,196,1264,2217,93,228,3657,152,216,164,238,121,147,132,133,206,248,117,201,220,260,160,192,137,92,252,97,710,224,156,1498,188,141,3596,212,96,109,256,266,105,244,166,264,180,149,176,423,286,291,281,204,713,236,172,113,274,1011,230,98,208,103,91,240,915,198,912,135,226,426,162,2271,123,194,145,150,95,3659,182,127,154,143,250,99,218,258,158,186,139,119,246,214,4670,1546,190,168,262,210,107,242,268,94,131,200,178,111,254,222,232,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO653-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.17/0.42 % Computer : n010.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 19:43:30 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.88/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.98/1.38 % [INFO] Parsing done (387ms).
% 1.98/1.39 % [INFO] Running in sequential loop mode.
% 2.98/1.77 % [INFO] eprover registered as external prover.
% 2.98/1.77 % [INFO] Scanning for conjecture ...
% 3.50/1.91 % [INFO] 90 axioms and no conjecture found.
% 4.93/2.30 % [INFO] Problem is propositional (TPTP CNF).
% 4.93/2.32 % [INFO] Type checking passed.
% 4.93/2.32 % [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 ...
% 36.01/11.53 % External prover 'e' found a proof!
% 36.01/11.53 % [INFO] Killing All external provers ...
% 36.01/11.54 % Time passed: 10976ms (effective reasoning time: 10141ms)
% 36.01/11.54 % Axioms used in derivation (90): clause_2157, clause_102, clause_54, clause_872, clause_94, clause_2102, clause_1568, clause_114, clause_1953, clause_1048, clause_316, clause_38, clause_912, clause_877, clause_1934, clause_380, clause_1091, clause_554, clause_878, clause_1801, clause_1596, clause_391, clause_1615, clause_1161, clause_942, clause_498, clause_142, clause_931, clause_1315, clause_1143, clause_1148, clause_20, clause_1371, clause_1773, clause_383, clause_419, clause_1387, clause_704, clause_1404, clause_1508, clause_148, clause_1597, clause_971, clause_286, clause_765, clause_683, clause_961, clause_1036, clause_714, clause_1337, clause_244, clause_1550, clause_1893, clause_1277, clause_107, clause_246, clause_2134, clause_433, clause_1057, clause_50, clause_903, clause_2031, clause_354, clause_268, clause_263, clause_1791, clause_1039, clause_972, clause_2160, clause_541, clause_482, clause_306, clause_2036, clause_1480, clause_2198, clause_1528, clause_295, clause_2101, clause_51, clause_1883, clause_1983, clause_1221, clause_68, clause_1976, clause_1556, clause_227, clause_2175, clause_1719, clause_1384, clause_1836
% 36.01/11.54 % No. of inferences in proof: 274
% 36.01/11.54 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 10976 ms resp. 10141 ms w/o parsing
% 37.34/11.88 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 37.34/11.88 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------