%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO673-1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n011.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 09:45:09 AM UTC 2026
% Result : Unsatisfiable 103.34s 36.69s
% Output : Refutation 105.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 65
% Syntax : Number of formulae : 329 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 2888 ( 286 equ; 0 cnn)
% Maximal formula atoms : 20 ( 8 avg)
% Number of connectives : 16838 (2148 ~;2403 |; 0 &;12287 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 13 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 : 632 ( 0 ^; 632 !; 0 ?; 632 :)
% Comments :
%------------------------------------------------------------------------------
thf('E_decl',type,
'E': $i > $i > $o ).
thf(s_decl,type,
s: $i > $i ).
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(45,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_354) ).
thf(153,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(2,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1370) ).
thf(68,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(69,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[68]) ).
thf(50,axiom,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1442) ).
thf(163,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(164,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[163]) ).
thf(6,axiom,
! [A: $i] : ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1497) ).
thf(76,plain,
! [A: $i] : ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(236,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[164,76]) ).
thf(237,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[236]) ).
thf(34,axiom,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1246) ).
thf(131,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(132,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ suc @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[131]) ).
thf(244,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( B @ suc @ f @ 'LE' ) ) )
| ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ $true
| ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[237,132]) ).
thf(245,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( B @ suc @ f @ 'LE' ) ) )
| ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[244]) ).
thf(246,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[245:[bind(A,$thf( C @ suc )),bind(B,$thf( C ))]]) ).
thf(256,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[246]) ).
thf(26,axiom,
~ ( '0' @ ( z @ f @ 'LE' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_709) ).
thf(115,plain,
~ ( '0' @ ( z @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(116,plain,
~ ( '0' @ ( z @ f @ 'LE' ) ),
inference(polarity_switch,[status(thm)],[115]) ).
thf(743,plain,
! [A: $i] :
( ( ( '0' @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ~ $true
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[256,116]) ).
thf(744,plain,
! [A: $i] :
( ( ( '0' @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[743]) ).
thf(752,plain,
! [A: $i] :
( ( ( '0' @ s )
!= '0' )
| ( ( A @ f )
!= ( z @ f ) )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[744]) ).
thf(6500,plain,
! [A: $i] :
( ~ $true
| ( ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
!= ( A @ suc @ f @ ( '0' @ s @ 'E' ) ) )
| ( ( '0' @ s )
!= '0' )
| ( ( A @ f )
!= ( z @ f ) )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[752]) ).
thf(6631,plain,
! [A: $i] :
( ( ( A @ suc @ f )
!= ( A @ suc @ f ) )
| ( ( '0' @ s @ s )
!= ( '0' @ s ) )
| ( ( '0' @ s )
!= '0' )
| ( A != z )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[6500]) ).
thf(6881,plain,
( ( ( '0' @ s @ s )
!= ( '0' @ s ) )
| ( ( '0' @ s )
!= '0' )
| ( z @ suc @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[6631]) ).
thf(6918,plain,
( ( ( '0' @ s )
!= '0' )
| ( ( '0' @ s )
!= '0' )
| ( z @ suc @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[6881]) ).
thf(7487,plain,
( ( ( '0' @ s )
!= '0' )
| ( z @ suc @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[6918]) ).
thf(64,axiom,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1261) ).
thf(191,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(192,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[191]) ).
thf(4898,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[192,76]) ).
thf(4899,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[4898]) ).
thf(4908,plain,
! [A: $i] :
( ( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ~ $true
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[4899,116]) ).
thf(4909,plain,
! [A: $i] :
( ( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[4908]) ).
thf(4919,plain,
! [A: $i] :
( ( ( '0' @ s @ s )
!= '0' )
| ( ( A @ f )
!= ( z @ f ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[4909]) ).
thf(4923,plain,
! [A: $i] :
( ( ( '0' @ s @ s )
!= '0' )
| ( A != z )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[4919]) ).
thf(5416,plain,
( ( ( '0' @ s @ s )
!= '0' )
| ( z @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[4923]) ).
thf(18,axiom,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1415) ).
thf(99,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(100,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[99]) ).
thf(249,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ $true
| ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[237,100]) ).
thf(250,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[249]) ).
thf(251,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[250:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(62,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_509) ).
thf(187,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(188,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[187]) ).
thf(590,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ 'E' ) )
| ~ $true
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[251,188]) ).
thf(591,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ 'E' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[590]) ).
thf(592,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[591:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(6903,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ~ $true
| ( A @ f @ ( '0' @ 'E' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[592,116]) ).
thf(6904,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[6903]) ).
thf(6905,plain,
( ( z @ f @ ( '0' @ 'E' ) )
| ( z @ f @ ( '0' @ s @ 'E' ) )
| ( z @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[6904:[bind(A,$thf( z ))]]) ).
thf(8315,plain,
( ~ $true
| ( ( z @ f @ ( '0' @ s @ s @ 'E' ) )
!= ( z @ f @ ( '0' @ 'E' ) ) )
| ( z @ f @ ( '0' @ 'E' ) )
| ( z @ f @ ( '0' @ s @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[6905]) ).
thf(8321,plain,
( ( ( z @ f )
!= ( z @ f ) )
| ( ( '0' @ s @ s )
!= '0' )
| ( z @ f @ ( '0' @ 'E' ) )
| ( z @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[8315]) ).
thf(8417,plain,
( ( ( '0' @ s @ s )
!= '0' )
| ( z @ f @ ( '0' @ 'E' ) )
| ( z @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[8321]) ).
thf(8635,plain,
( ~ $true
| ( ( z @ f @ ( '0' @ s @ 'E' ) )
!= ( z @ f @ ( '0' @ 'E' ) ) )
| ( ( '0' @ s @ s )
!= '0' )
| ( z @ f @ ( '0' @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[8417]) ).
thf(8642,plain,
( ( ( z @ f )
!= ( z @ f ) )
| ( ( '0' @ s )
!= '0' )
| ( ( '0' @ s @ s )
!= '0' )
| ( z @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[8635]) ).
thf(8741,plain,
( ( ( '0' @ s )
!= '0' )
| ( ( '0' @ s @ s )
!= '0' )
| ( z @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[8642]) ).
thf(8942,plain,
( ( '0' != '0' )
| ( ( '0' @ s @ s )
!= ( '0' @ s ) )
| ( ( '0' @ s )
!= '0' )
| ( z @ f @ ( '0' @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[8741]) ).
thf(8971,plain,
( ( ( '0' @ s )
!= '0' )
| ( ( '0' @ s )
!= '0' )
| ( z @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[8942]) ).
thf(9036,plain,
( ( ( '0' @ s )
!= '0' )
| ( z @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[8971]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1397) ).
thf(89,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(90,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[89]) ).
thf(200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( B @ suc @ ( D @ suc @ iLEQ ) )
!= ( C @ suc @ ( B @ suc @ iLEQ ) ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[90]) ).
thf(203,plain,
! [B: $i,A: $i] :
( ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[200:[bind(A,$thf( A )),bind(B,$thf( D )),bind(C,$thf( D ))]]) ).
thf(206,plain,
! [B: $i,A: $i] :
( ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[203]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ suc @ ( B @ suc @ iLEQ ) )
!= ( B @ suc @ ( B @ suc @ iLEQ ) ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[206]) ).
thf(210,plain,
! [A: $i] :
( ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[209:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(211,plain,
! [A: $i] :
( ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[210]) ).
thf(9128,plain,
! [A: $i] :
( ( ( z @ f @ ( '0' @ 'E' ) )
!= ( A @ f @ ( '0' @ 'E' ) ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ $true
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ( ( '0' @ s )
!= '0' ) ),
inference(paramod_ordered,[status(thm)],[9036,211]) ).
thf(9129,plain,
! [A: $i] :
( ( ( z @ f @ ( '0' @ 'E' ) )
!= ( A @ f @ ( '0' @ 'E' ) ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ( ( '0' @ s )
!= '0' ) ),
inference(simp,[status(thm)],[9128]) ).
thf(9130,plain,
( ~ ( z @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ ( z @ suc @ f @ ( '0' @ 'E' ) )
| ( ( '0' @ s )
!= '0' ) ),
inference(pattern_uni,[status(thm)],[9129:[bind(A,$thf( z ))]]) ).
thf(11094,plain,
( ( ( z @ suc @ f @ ( '0' @ s @ 'E' ) )
!= ( z @ suc @ f @ ( '0' @ 'E' ) ) )
| ~ ( z @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ~ $true
| ( ( '0' @ s )
!= '0' )
| ( ( '0' @ s )
!= '0' ) ),
inference(paramod_ordered,[status(thm)],[7487,9130]) ).
thf(11095,plain,
( ( ( z @ suc @ f @ ( '0' @ s @ 'E' ) )
!= ( z @ suc @ f @ ( '0' @ 'E' ) ) )
| ~ ( z @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ( ( '0' @ s )
!= '0' ) ),
inference(simp,[status(thm)],[11094]) ).
thf(11245,plain,
( ( ( z @ suc @ f )
!= ( z @ suc @ f ) )
| ( ( '0' @ s )
!= '0' )
| ~ ( z @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ( ( '0' @ s )
!= '0' ) ),
inference(simp,[status(thm)],[11095]) ).
thf(11314,plain,
( ~ ( z @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ( ( '0' @ s )
!= '0' ) ),
inference(simp,[status(thm)],[11245]) ).
thf(11364,plain,
( ( ( z @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
!= ( z @ suc @ suc @ f @ ( '0' @ 'E' ) ) )
| ~ $true
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ( ( '0' @ s )
!= '0' )
| ( ( '0' @ s @ s )
!= '0' ) ),
inference(paramod_ordered,[status(thm)],[5416,11314]) ).
thf(11365,plain,
( ( ( z @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
!= ( z @ suc @ suc @ f @ ( '0' @ 'E' ) ) )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ( ( '0' @ s )
!= '0' )
| ( ( '0' @ s @ s )
!= '0' ) ),
inference(simp,[status(thm)],[11364]) ).
thf(11429,plain,
( ( ( z @ suc @ suc @ f )
!= ( z @ suc @ suc @ f ) )
| ( ( '0' @ s @ s )
!= '0' )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ( ( '0' @ s )
!= '0' )
| ( ( '0' @ s @ s )
!= '0' ) ),
inference(simp,[status(thm)],[11365]) ).
thf(11470,plain,
( ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ( ( '0' @ s )
!= '0' )
| ( ( '0' @ s @ s )
!= '0' ) ),
inference(simp,[status(thm)],[11429]) ).
thf(14708,plain,
( ( '0' != '0' )
| ( ( '0' @ s @ s )
!= ( '0' @ s ) )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ( ( '0' @ s )
!= '0' ) ),
inference(eqfactor_ordered,[status(thm)],[11470]) ).
thf(14720,plain,
( ( ( '0' @ s )
!= '0' )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ( ( '0' @ s )
!= '0' ) ),
inference(simp,[status(thm)],[14708]) ).
thf(14743,plain,
( ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ ( z @ suc @ f @ ( z @ f @ 'E' ) )
| ( ( '0' @ s )
!= '0' ) ),
inference(simp,[status(thm)],[14720]) ).
thf(14791,plain,
( ( ( z @ suc @ f @ ( z @ f @ 'E' ) )
!= ( z @ suc @ f @ ( '0' @ s @ 'E' ) ) )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ~ $true
| ( ( '0' @ s )
!= '0' )
| ( ( '0' @ s )
!= '0' ) ),
inference(paramod_ordered,[status(thm)],[7487,14743]) ).
thf(14792,plain,
( ( ( z @ suc @ f @ ( z @ f @ 'E' ) )
!= ( z @ suc @ f @ ( '0' @ s @ 'E' ) ) )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ( ( '0' @ s )
!= '0' ) ),
inference(simp,[status(thm)],[14791]) ).
thf(14832,plain,
( ( ( z @ suc @ f )
!= ( z @ suc @ f ) )
| ( ( z @ f )
!= ( '0' @ s ) )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ( ( '0' @ s )
!= '0' ) ),
inference(simp,[status(thm)],[14792]) ).
thf(14852,plain,
( ( ( z @ f )
!= ( '0' @ s ) )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ( ( '0' @ s )
!= '0' ) ),
inference(simp,[status(thm)],[14832]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1130) ).
thf(101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(38,axiom,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1439) ).
thf(139,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(140,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ suc @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[139]) ).
thf(896,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[140,76]) ).
thf(897,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[896]) ).
thf(906,plain,
! [A: $i] :
( ( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ~ $true
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[897,116]) ).
thf(907,plain,
! [A: $i] :
( ( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[906]) ).
thf(917,plain,
! [A: $i] :
( ( ( '0' @ s @ s )
!= '0' )
| ( ( A @ f )
!= ( z @ f ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[907]) ).
thf(921,plain,
! [A: $i] :
( ( ( '0' @ s @ s )
!= '0' )
| ( A != z )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[917]) ).
thf(1237,plain,
( ( ( '0' @ s @ s )
!= '0' )
| ( z @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[921]) ).
thf(4914,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ $true
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[4899,100]) ).
thf(4915,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[4914]) ).
thf(4916,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[4915:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(5474,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ 'E' ) )
| ~ $true
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[4916,188]) ).
thf(5475,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ 'E' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[5474]) ).
thf(5476,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[5475:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(13473,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ~ $true
| ( A @ f @ ( '0' @ 'E' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[5476,116]) ).
thf(13474,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[13473]) ).
thf(13475,plain,
( ( z @ f @ ( '0' @ 'E' ) )
| ( z @ f @ ( '0' @ s @ 'E' ) )
| ( z @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[13474:[bind(A,$thf( z ))]]) ).
thf(598,plain,
! [A: $i] :
( ( ( '0' @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ~ $true
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[251,116]) ).
thf(599,plain,
! [A: $i] :
( ( ( '0' @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[598]) ).
thf(607,plain,
! [A: $i] :
( ( ( '0' @ s )
!= '0' )
| ( ( A @ f )
!= ( z @ f ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[599]) ).
thf(1662,plain,
! [A: $i] :
( ~ $true
| ( ( A @ f @ ( '0' @ s @ s @ 'E' ) )
!= ( A @ f @ ( '0' @ s @ 'E' ) ) )
| ( ( '0' @ s )
!= '0' )
| ( ( A @ f )
!= ( z @ f ) )
| ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[607]) ).
thf(1761,plain,
! [A: $i] :
( ( ( A @ f )
!= ( A @ f ) )
| ( ( '0' @ s @ s )
!= ( '0' @ s ) )
| ( ( '0' @ s )
!= '0' )
| ( ( A @ f )
!= ( z @ f ) )
| ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[1662]) ).
thf(1913,plain,
! [A: $i] :
( ( ( '0' @ s @ s )
!= ( '0' @ s ) )
| ( ( '0' @ s )
!= '0' )
| ( ( A @ f )
!= ( z @ f ) )
| ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[1761]) ).
thf(3081,plain,
! [A: $i] :
( ( ( '0' @ s )
!= '0' )
| ( ( '0' @ s )
!= '0' )
| ( ( A @ f )
!= ( z @ f ) )
| ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[1913]) ).
thf(3549,plain,
! [A: $i] :
( ( ( '0' @ s )
!= '0' )
| ( ( A @ f )
!= ( z @ f ) )
| ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[3081]) ).
thf(61,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1270) ).
thf(185,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_120) ).
thf(125,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(47,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_596) ).
thf(157,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(63,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1302) ).
thf(189,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_721) ).
thf(93,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_345) ).
thf(77,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(78,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(cnf,[status(esa)],[77]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_530) ).
thf(179,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(21,axiom,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1472) ).
thf(105,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(106,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[105]) ).
thf(29,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1183) ).
thf(121,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1113) ).
thf(83,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(84,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(cnf,[status(esa)],[83]) ).
thf(247,plain,
! [A: $i] :
( ( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ~ $true
| ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[237,116]) ).
thf(248,plain,
! [A: $i] :
( ( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[247]) ).
thf(253,plain,
! [A: $i] :
( ( ( '0' @ s @ s )
!= '0' )
| ( ( A @ f )
!= ( z @ f ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[248]) ).
thf(42,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_987) ).
thf(147,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(257,plain,
! [A: $i] :
( ( ( '0' @ s @ s )
!= '0' )
| ( A != z )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[253]) ).
thf(428,plain,
( ( ( '0' @ s @ s )
!= '0' )
| ( z @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[257]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_104) ).
thf(74,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(35,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_35) ).
thf(133,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(903,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( B @ suc @ f @ 'LE' ) ) )
| ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ $true
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[897,132]) ).
thf(904,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( B @ suc @ f @ 'LE' ) ) )
| ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[903]) ).
thf(905,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[904:[bind(A,$thf( C @ suc )),bind(B,$thf( C ))]]) ).
thf(920,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[905]) ).
thf(27,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_772) ).
thf(117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1074) ).
thf(85,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(515,plain,
! [B: $i,A: $i] :
( ( ( A @ f @ ( '0' @ s @ s @ 'E' ) )
!= ( B @ suc @ f @ ( '0' @ 'E' ) ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ $true
| ( ( '0' @ s @ s )
!= '0' )
| ( ( A @ f )
!= ( z @ f ) ) ),
inference(paramod_ordered,[status(thm)],[253,211]) ).
thf(516,plain,
! [B: $i,A: $i] :
( ( ( A @ f @ ( '0' @ s @ s @ 'E' ) )
!= ( B @ suc @ f @ ( '0' @ 'E' ) ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( ( '0' @ s @ s )
!= '0' )
| ( ( A @ f )
!= ( z @ f ) ) ),
inference(simp,[status(thm)],[515]) ).
thf(525,plain,
! [B: $i,A: $i] :
( ( ( A @ f )
!= ( B @ suc @ f ) )
| ( ( '0' @ s @ s )
!= '0' )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( ( '0' @ s @ s )
!= '0' )
| ( A != z ) ),
inference(simp,[status(thm)],[516]) ).
thf(537,plain,
! [A: $i] :
( ( ( A @ suc @ f )
!= ( z @ f ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( ( '0' @ s @ s )
!= '0' ) ),
inference(simp,[status(thm)],[525]) ).
thf(547,plain,
! [B: $i,A: $i] :
( ( ( A @ f @ ( '0' @ s @ s @ 'E' ) )
!= ( B @ suc @ f @ ( B @ f @ 'E' ) ) )
| ( ( B @ suc @ f )
!= ( z @ f ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ $true
| ( ( '0' @ s @ s )
!= '0' )
| ( ( '0' @ s @ s )
!= '0' )
| ( ( A @ f )
!= ( z @ f ) ) ),
inference(paramod_ordered,[status(thm)],[253,537]) ).
thf(548,plain,
! [B: $i,A: $i] :
( ( ( A @ f @ ( '0' @ s @ s @ 'E' ) )
!= ( B @ suc @ f @ ( B @ f @ 'E' ) ) )
| ( ( B @ suc @ f )
!= ( z @ f ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ( ( '0' @ s @ s )
!= '0' )
| ( ( A @ f )
!= ( z @ f ) ) ),
inference(simp,[status(thm)],[547]) ).
thf(557,plain,
! [B: $i,A: $i] :
( ( ( A @ f )
!= ( B @ suc @ f ) )
| ( ( B @ f )
!= ( '0' @ s @ s ) )
| ( ( B @ suc @ f )
!= ( z @ f ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ( ( '0' @ s @ s )
!= '0' )
| ( A != z ) ),
inference(simp,[status(thm)],[548]) ).
thf(576,plain,
! [A: $i] :
( ( ( A @ f )
!= ( '0' @ s @ s ) )
| ( ( A @ suc @ f )
!= ( z @ f ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ( ( '0' @ s @ s )
!= '0' ) ),
inference(simp,[status(thm)],[557]) ).
thf(1262,plain,
! [B: $i,A: $i] :
( ( ( A @ f @ ( '0' @ s @ s @ 'E' ) )
!= ( B @ suc @ suc @ f @ ( '0' @ 'E' ) ) )
| ( ( B @ f )
!= ( '0' @ s @ s ) )
| ( ( B @ suc @ f )
!= ( z @ f ) )
| ~ $true
| ~ ( B @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ( ( '0' @ s @ s )
!= '0' )
| ( ( '0' @ s @ s )
!= '0' )
| ( ( A @ f )
!= ( z @ f ) ) ),
inference(paramod_ordered,[status(thm)],[253,576]) ).
thf(1263,plain,
! [B: $i,A: $i] :
( ( ( A @ f @ ( '0' @ s @ s @ 'E' ) )
!= ( B @ suc @ suc @ f @ ( '0' @ 'E' ) ) )
| ( ( B @ f )
!= ( '0' @ s @ s ) )
| ( ( B @ suc @ f )
!= ( z @ f ) )
| ~ ( B @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ( ( '0' @ s @ s )
!= '0' )
| ( ( A @ f )
!= ( z @ f ) ) ),
inference(simp,[status(thm)],[1262]) ).
thf(1284,plain,
! [B: $i,A: $i] :
( ( ( A @ f )
!= ( B @ suc @ suc @ f ) )
| ( ( '0' @ s @ s )
!= '0' )
| ( ( B @ f )
!= ( '0' @ s @ s ) )
| ( ( B @ suc )
!= z )
| ~ ( B @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ( ( '0' @ s @ s )
!= '0' )
| ( A != z ) ),
inference(simp,[status(thm)],[1263]) ).
thf(1306,plain,
! [A: $i] :
( ( ( A @ suc @ suc @ f )
!= ( z @ f ) )
| ( ( A @ f )
!= ( '0' @ s @ s ) )
| ( ( A @ suc )
!= z )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ( ( '0' @ s @ s )
!= '0' ) ),
inference(simp,[status(thm)],[1284]) ).
thf(1255,plain,
! [A: $i] :
( ( ( A @ f )
!= ( '0' @ s @ s ) )
| ( ( A @ suc )
!= z )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ( ( '0' @ s @ s )
!= '0' ) ),
inference(simp,[status(thm)],[576]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_981) ).
thf(70,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_332) ).
thf(137,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)],[37]) ).
thf(51,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1365) ).
thf(165,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_715) ).
thf(97,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(735,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ 'E' ) )
| ~ $true
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[256,188]) ).
thf(736,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[735]) ).
thf(737,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[736:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(11490,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ~ $true
| ( A @ f @ ( '0' @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[737,116]) ).
thf(11491,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[11490]) ).
thf(11492,plain,
( ( z @ f @ ( '0' @ 'E' ) )
| ( z @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( z @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[11491:[bind(A,$thf( z ))]]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_69) ).
thf(169,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1017) ).
thf(141,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(8314,plain,
( ~ $true
| ( ( z @ f @ ( '0' @ s @ s @ 'E' ) )
!= ( z @ f @ ( '0' @ s @ 'E' ) ) )
| ( z @ f @ ( '0' @ 'E' ) )
| ( z @ f @ ( '0' @ s @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[6905]) ).
thf(8352,plain,
( ( ( z @ f )
!= ( z @ f ) )
| ( ( '0' @ s @ s )
!= ( '0' @ s ) )
| ( z @ f @ ( '0' @ 'E' ) )
| ( z @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[8314]) ).
thf(8428,plain,
( ( ( '0' @ s @ s )
!= ( '0' @ s ) )
| ( z @ f @ ( '0' @ 'E' ) )
| ( z @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[8352]) ).
thf(9622,plain,
( ~ $true
| ( ( z @ f @ ( '0' @ s @ 'E' ) )
!= ( z @ f @ ( '0' @ 'E' ) ) )
| ( ( '0' @ s @ s )
!= ( '0' @ s ) )
| ( z @ f @ ( '0' @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[8428]) ).
thf(9825,plain,
( ( ( z @ f @ ( '0' @ s @ 'E' ) )
!= ( z @ f @ ( '0' @ 'E' ) ) )
| ( ( '0' @ s @ s )
!= ( '0' @ s ) )
| ( z @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[9622]) ).
thf(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_855) ).
thf(109,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(65,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_666) ).
thf(193,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(55,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_752) ).
thf(173,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(33,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_71) ).
thf(129,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1288) ).
thf(72,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(73,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(cnf,[status(esa)],[72]) ).
thf(4902,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( B @ suc @ suc @ f @ 'LE' ) ) )
| ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ $true
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[4899,106]) ).
thf(4903,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( B @ suc @ suc @ f @ 'LE' ) ) )
| ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[4902]) ).
thf(4904,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[4903:[bind(A,$thf( D @ suc @ suc )),bind(B,$thf( D ))]]) ).
thf(4921,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ suc @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[4904]) ).
thf(8641,plain,
( ( ( z @ f @ ( '0' @ s @ 'E' ) )
!= ( z @ f @ ( '0' @ 'E' ) ) )
| ( ( '0' @ s @ s )
!= '0' )
| ( z @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[8635]) ).
thf(49,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_460) ).
thf(161,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(43,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1256) ).
thf(149,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)],[43]) ).
thf(71,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(900,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( B @ suc @ suc @ f @ 'LE' ) ) )
| ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ $true
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[897,106]) ).
thf(901,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( B @ suc @ suc @ f @ 'LE' ) ) )
| ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[900]) ).
thf(902,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[901:[bind(A,$thf( D @ suc @ suc )),bind(B,$thf( D ))]]) ).
thf(919,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[902]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_129) ).
thf(181,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(86,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[85]) ).
thf(48,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1143) ).
thf(159,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(912,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ $true
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[897,100]) ).
thf(913,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[912]) ).
thf(914,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[913:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(1370,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ 'E' ) )
| ~ $true
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[914,188]) ).
thf(1371,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ 'E' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[1370]) ).
thf(1372,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[1371:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(9420,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ~ $true
| ( A @ f @ ( '0' @ 'E' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[1372,116]) ).
thf(9421,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[9420]) ).
thf(9422,plain,
( ( z @ f @ ( '0' @ 'E' ) )
| ( z @ f @ ( '0' @ s @ 'E' ) )
| ( z @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[9421:[bind(A,$thf( z ))]]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_165) ).
thf(113,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(9,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' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_625) ).
thf(81,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' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_692) ).
thf(103,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(150,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[149]) ).
thf(593,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ ( B @ suc @ f @ 'LE' ) ) )
| ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ $true
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[251,150]) ).
thf(594,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ ( B @ suc @ f @ 'LE' ) ) )
| ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ suc @ f @ ( '0' @ 'E' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[593]) ).
thf(595,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[594:[bind(A,$thf( C @ suc )),bind(B,$thf( C ))]]) ).
thf(608,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[595]) ).
thf(14861,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ~ $true
| ( A @ suc @ f @ ( '0' @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[608,116]) ).
thf(14862,plain,
! [A: $i] :
( ( ( '0' @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ( A @ suc @ f @ ( '0' @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[14861]) ).
thf(14863,plain,
( ( z @ suc @ f @ ( '0' @ 'E' ) )
| ( z @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( z @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[14862:[bind(A,$thf( z ))]]) ).
thf(16418,plain,
( ~ $true
| ( ( z @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
!= ( z @ suc @ f @ ( '0' @ 'E' ) ) )
| ( z @ suc @ f @ ( '0' @ 'E' ) )
| ( z @ suc @ f @ ( '0' @ s @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[14863]) ).
thf(16509,plain,
( ( ( z @ suc @ f )
!= ( z @ suc @ f ) )
| ( ( '0' @ s @ s )
!= '0' )
| ( z @ suc @ f @ ( '0' @ 'E' ) )
| ( z @ suc @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[16418]) ).
thf(16570,plain,
( ( ( '0' @ s @ s )
!= '0' )
| ( z @ suc @ f @ ( '0' @ 'E' ) )
| ( z @ suc @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[16509]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_418) ).
thf(91,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( 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)],[14]) ).
thf(1,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_618) ).
thf(66,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(22,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_225) ).
thf(107,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)],[22]) ).
thf(108,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[107]) ).
thf(12567,plain,
( ~ $true
| ( ( z @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
!= ( z @ suc @ f @ ( '0' @ s @ 'E' ) ) )
| ( z @ f @ ( '0' @ 'E' ) )
| ( z @ suc @ f @ ( '0' @ s @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[11492]) ).
thf(12659,plain,
( ( ( z @ suc @ f )
!= ( z @ suc @ f ) )
| ( ( '0' @ s @ s )
!= ( '0' @ s ) )
| ( z @ f @ ( '0' @ 'E' ) )
| ( z @ suc @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[12567]) ).
thf(12697,plain,
( ( ( '0' @ s @ s )
!= ( '0' @ s ) )
| ( z @ f @ ( '0' @ 'E' ) )
| ( z @ suc @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[12659]) ).
thf(46,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_601) ).
thf(155,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(36,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1322) ).
thf(135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1452) ).
thf(79,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(80,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[79]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1106) ).
thf(167,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_382) ).
thf(123,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_44) ).
thf(145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(860,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( B @ suc @ suc @ f @ 'LE' ) ) )
| ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ $true
| ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[237,106]) ).
thf(861,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( B @ suc @ suc @ f @ 'LE' ) ) )
| ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[860]) ).
thf(862,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[861:[bind(A,$thf( D @ suc @ suc )),bind(B,$thf( D ))]]) ).
thf(872,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[862]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_367) ).
thf(95,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(4905,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( B @ suc @ f @ 'LE' ) ) )
| ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ $true
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[4899,132]) ).
thf(4906,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( B @ suc @ f @ 'LE' ) ) )
| ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[4905]) ).
thf(4907,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[4906:[bind(A,$thf( C @ suc )),bind(B,$thf( C ))]]) ).
thf(4922,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ( A @ suc @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[4907]) ).
thf(67,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(cnf,[status(esa)],[66]) ).
thf(195,plain,
! [A: $i] :
( ( ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,116]) ).
thf(196,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[195]) ).
thf(197,plain,
! [A: $i] :
( ( ( '0' @ s @ s @ s )
!= '0' )
| ( ( A @ f )
!= ( z @ f ) ) ),
inference(simp,[status(thm)],[196]) ).
thf(198,plain,
! [A: $i] :
( ( ( '0' @ s @ s @ s )
!= '0' )
| ( A != z ) ),
inference(simp,[status(thm)],[197]) ).
thf(199,plain,
( ( '0' @ s @ s @ s )
!= '0' ),
inference(simp,[status(thm)],[198]) ).
thf(57,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1445) ).
thf(177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_243) ).
thf(127,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(56,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_292) ).
thf(175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(40,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1374) ).
thf(143,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(2962,plain,
! [A: $i] :
( ( ( z @ f @ ( '0' @ s @ s @ 'E' ) )
!= ( A @ f @ ( '0' @ 'E' ) ) )
| ( ( A @ suc @ suc @ f )
!= ( z @ f ) )
| ( ( A @ f )
!= ( '0' @ s @ s ) )
| ( ( A @ suc )
!= z )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ $true
| ( ( '0' @ s @ s )
!= '0' )
| ( ( '0' @ s @ s )
!= '0' ) ),
inference(paramod_ordered,[status(thm)],[428,1306]) ).
thf(2963,plain,
! [A: $i] :
( ( ( z @ f @ ( '0' @ s @ s @ 'E' ) )
!= ( A @ f @ ( '0' @ 'E' ) ) )
| ( ( A @ suc @ suc @ f )
!= ( z @ f ) )
| ( ( A @ f )
!= ( '0' @ s @ s ) )
| ( ( A @ suc )
!= z )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( ( '0' @ s @ s )
!= '0' ) ),
inference(simp,[status(thm)],[2962]) ).
thf(2980,plain,
! [A: $i] :
( ( ( z @ f )
!= ( A @ f ) )
| ( ( '0' @ s @ s )
!= '0' )
| ( ( A @ suc @ suc )
!= z )
| ( ( A @ f )
!= ( '0' @ s @ s ) )
| ( ( A @ suc )
!= z )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( ( '0' @ s @ s )
!= '0' ) ),
inference(simp,[status(thm)],[2963]) ).
thf(3007,plain,
! [A: $i] :
( ( ( z @ f )
!= ( A @ f ) )
| ( ( A @ suc @ suc )
!= z )
| ( ( A @ f )
!= ( '0' @ s @ s ) )
| ( ( A @ suc )
!= z )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( ( '0' @ s @ s )
!= '0' ) ),
inference(simp,[status(thm)],[2980]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_594) ).
thf(87,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1142) ).
thf(171,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(75,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(cnf,[status(esa)],[74]) ).
thf(82,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' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[81]) ).
thf(28,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_874) ).
thf(119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(44,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_712) ).
thf(151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(1762,plain,
! [A: $i] :
( ( ( A @ f )
!= ( A @ f ) )
| ( ( '0' @ s @ s )
!= ( '0' @ s ) )
| ( ( '0' @ s )
!= '0' )
| ( A != z )
| ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[1662]) ).
thf(1914,plain,
( ( ( '0' @ s @ s )
!= ( '0' @ s ) )
| ( ( '0' @ s )
!= '0' )
| ( z @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[1762]) ).
thf(2269,plain,
( ( ( '0' @ s )
!= '0' )
| ( ( '0' @ s )
!= '0' )
| ( z @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[1914]) ).
thf(2683,plain,
( ( ( '0' @ s )
!= '0' )
| ( z @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[2269]) ).
thf(2951,plain,
! [A: $i] :
( ( ( A @ suc @ suc )
!= z )
| ( ( A @ f )
!= ( '0' @ s @ s ) )
| ( ( A @ suc )
!= z )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ( ( '0' @ s @ s )
!= '0' ) ),
inference(simp,[status(thm)],[1306]) ).
thf(60,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1132) ).
thf(183,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(5465,plain,
! [A: $i] :
( ( z != z )
| ( ( A @ suc @ suc )
!= ( A @ suc ) )
| ( ( z @ f )
!= ( A @ f ) )
| ( ( A @ f )
!= ( '0' @ s @ s ) )
| ( ( A @ suc )
!= z )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( ( '0' @ s @ s )
!= '0' ) ),
inference(eqfactor_ordered,[status(thm)],[3007]) ).
thf(5469,plain,
! [A: $i] :
( ( ( A @ suc )
!= A )
| ( z != A )
| ( ( A @ f )
!= ( '0' @ s @ s ) )
| ( ( A @ suc )
!= z )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( ( '0' @ s @ s )
!= '0' ) ),
inference(simp,[status(thm)],[5465]) ).
thf(5472,plain,
( ( ( z @ suc )
!= z )
| ( ( z @ f )
!= ( '0' @ s @ s ) )
| ( ( z @ suc )
!= z )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ( ( '0' @ s @ s )
!= '0' ) ),
inference(simp,[status(thm)],[5469]) ).
thf(5473,plain,
( ( ( z @ f )
!= ( '0' @ s @ s ) )
| ( ( z @ suc )
!= z )
| ~ ( z @ suc @ ( z @ suc @ iLEQ ) )
| ( ( '0' @ s @ s )
!= '0' ) ),
inference(simp,[status(thm)],[5472]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_639) ).
thf(111,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( D @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(27675,plain,
$false,
inference(e,[status(thm)],[153,69,14852,101,4899,1237,8417,115,13475,3549,185,5476,4916,917,125,157,189,6905,93,78,179,106,121,84,211,253,147,132,116,428,74,89,133,920,117,5416,85,1306,9036,1255,70,137,165,97,11492,188,169,141,77,9825,109,256,193,537,173,129,73,237,105,4921,4919,8641,161,149,191,7487,71,14743,919,181,86,159,187,9422,113,81,76,737,103,16570,91,66,251,108,12697,155,608,135,80,167,123,145,872,150,95,4922,67,199,177,8428,127,576,72,175,1372,143,3007,99,87,171,139,75,82,119,914,151,752,2683,2951,183,107,79,897,131,163,68,5473,83,14863,592,100,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO673-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.38 % Computer : n011.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 19:44:59 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.12/1.13 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.70/1.64 % [INFO] Parsing done (505ms).
% 2.70/1.66 % [INFO] Running in sequential loop mode.
% 4.04/2.24 % [INFO] eprover registered as external prover.
% 4.04/2.25 % [INFO] Scanning for conjecture ...
% 4.49/2.40 % [INFO] 65 axioms and no conjecture found.
% 5.21/2.77 % [INFO] Problem is propositional (TPTP CNF).
% 5.21/2.78 % [INFO] Type checking passed.
% 5.21/2.79 % [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 ...
% 103.34/36.68 % External prover 'e' found a proof!
% 103.34/36.68 % [INFO] Killing All external provers ...
% 103.34/36.69 % Time passed: 36116ms (effective reasoning time: 35020ms)
% 103.34/36.69 % Axioms used in derivation (65): clause_1132, clause_1106, clause_509, clause_460, clause_69, clause_1261, clause_618, clause_1472, clause_1370, clause_1397, clause_367, clause_666, clause_1302, clause_715, clause_639, clause_855, clause_1183, clause_1270, clause_1322, clause_981, clause_1445, clause_1374, clause_1246, clause_71, clause_120, clause_1130, clause_1143, clause_243, clause_772, clause_530, clause_874, clause_418, clause_712, clause_1256, clause_225, clause_1415, clause_345, clause_1442, clause_1288, clause_987, clause_354, clause_382, clause_1142, clause_44, clause_1113, clause_129, clause_752, clause_292, clause_594, clause_1365, clause_596, clause_1452, clause_709, clause_1497, clause_1017, clause_625, clause_601, clause_332, clause_35, clause_1439, clause_1074, clause_692, clause_721, clause_165, clause_104
% 103.34/36.69 % No. of inferences in proof: 329
% 103.34/36.69 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 36116 ms resp. 35020 ms w/o parsing
% 105.26/37.09 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 105.26/37.10 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------