%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO656-1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n018.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 09:45:07 AM UTC 2026
% Result : Unsatisfiable 12.88s 4.14s
% Output : Refutation 13.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 71
% Syntax : Number of formulae : 143 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 3369 ( 0 equ; 0 cnn)
% Maximal formula atoms : 29 ( 23 avg)
% Number of connectives : 20046 (2964 ~;3226 |; 0 &;13856 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 32 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 780 ( 0 ^; 780 !; 0 ?; 780 :)
% Comments :
%------------------------------------------------------------------------------
thf('E_decl',type,
'E': $i > $i > $o ).
thf('0_decl',type,
'0': $i ).
thf(f_decl,type,
f: $i > $i ).
thf(suc_decl,type,
suc: $i > $i ).
thf(iLEQ_decl,type,
iLEQ: $i > $i > $o ).
thf('LE_decl',type,
'LE': $i > $i > $o ).
thf(z_decl,type,
z: $i ).
thf(s_decl,type,
s: $i > $i ).
thf(36,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1201) ).
thf(142,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(52,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_193) ).
thf(174,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(11,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_741) ).
thf(92,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(40,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_528) ).
thf(150,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(56,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_146) ).
thf(182,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(34,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1024) ).
thf(138,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(9,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_612) ).
thf(88,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(50,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1081) ).
thf(170,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(25,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1014) ).
thf(120,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(57,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_35) ).
thf(184,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(20,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_958) ).
thf(110,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(63,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1005) ).
thf(196,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(41,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_97) ).
thf(152,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(4,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_164) ).
thf(78,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(47,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1169) ).
thf(164,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(71,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_388) ).
thf(211,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(18,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_79) ).
thf(106,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(7,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1019) ).
thf(84,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(31,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_52) ).
thf(132,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(23,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_769) ).
thf(116,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(2,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_431) ).
thf(74,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(66,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_522) ).
thf(201,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(16,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1154) ).
thf(102,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(45,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1078) ).
thf(160,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(61,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_702) ).
thf(192,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(43,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_646) ).
thf(156,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(59,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_454) ).
thf(188,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(27,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_861) ).
thf(124,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(13,axiom,
~ ( '0' @ ( z @ f @ 'LE' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_613) ).
thf(96,plain,
~ ( '0' @ ( z @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(32,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_606) ).
thf(134,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(29,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1058) ).
thf(128,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(68,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_200) ).
thf(205,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(48,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_230) ).
thf(166,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(39,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_463) ).
thf(148,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(55,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_841) ).
thf(180,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(53,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1008) ).
thf(176,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(24,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_150) ).
thf(118,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(37,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1177) ).
thf(144,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(8,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1156) ).
thf(86,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(51,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_391) ).
thf(172,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(3,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_258) ).
thf(76,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_888) ).
thf(98,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(35,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_931) ).
thf(140,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(64,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_180) ).
thf(198,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(19,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_227) ).
thf(108,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(30,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_478) ).
thf(130,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(5,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_435) ).
thf(80,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(46,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_968) ).
thf(162,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)],[46]) ).
thf(70,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/sandbox/benchmark/theBenchmark.p',clause_854) ).
thf(209,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)],[70]) ).
thf(21,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_467) ).
thf(112,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(62,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_56) ).
thf(194,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(42,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1266) ).
thf(154,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(1,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_797) ).
thf(72,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(67,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_415) ).
thf(203,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(17,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_844) ).
thf(104,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(44,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_806) ).
thf(158,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(58,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_498) ).
thf(186,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(22,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1004) ).
thf(114,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(69,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_890) ).
thf(207,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(6,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1185) ).
thf(82,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(49,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_374) ).
thf(168,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(38,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_433) ).
thf(146,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(60,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1066) ).
thf(190,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(12,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1180) ).
thf(94,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(28,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_675) ).
thf(126,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(33,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_10) ).
thf(136,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(65,axiom,
! [A: $i] : ( '0' @ s @ ( A @ f @ 'LE' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1153) ).
thf(200,plain,
! [A: $i] : ( '0' @ s @ ( A @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(54,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_444) ).
thf(178,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_181) ).
thf(90,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)],[10]) ).
thf(26,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_158) ).
thf(122,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(15,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_73) ).
thf(100,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)],[15]) ).
thf(248,plain,
$false,
inference(e,[status(thm)],[142,174,92,150,182,138,88,170,120,184,110,196,152,78,164,211,106,84,132,116,74,201,102,160,192,156,188,124,96,134,128,205,166,148,180,176,118,144,86,172,76,98,140,198,108,130,80,162,209,112,194,154,72,203,104,158,186,114,207,82,168,146,190,94,126,136,200,178,90,122,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO656-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.39 % Computer : n018.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sat Sep 26 19:45:22 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.84/0.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.84/1.36 % [INFO] Parsing done (384ms).
% 1.84/1.37 % [INFO] Running in sequential loop mode.
% 2.67/1.76 % [INFO] eprover registered as external prover.
% 2.67/1.77 % [INFO] Scanning for conjecture ...
% 2.86/1.90 % [INFO] 71 axioms and no conjecture found.
% 3.97/2.28 % [INFO] Problem is propositional (TPTP CNF).
% 3.97/2.30 % [INFO] Type checking passed.
% 4.37/2.30 % [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 ...
% 12.88/4.14 % External prover 'e' found a proof!
% 12.88/4.14 % [INFO] Killing All external provers ...
% 12.88/4.14 % Time passed: 3596ms (effective reasoning time: 2757ms)
% 12.88/4.14 % Axioms used in derivation (71): clause_1154, clause_97, clause_1058, clause_1024, clause_444, clause_1004, clause_1180, clause_435, clause_180, clause_769, clause_158, clause_888, clause_958, clause_841, clause_52, clause_1156, clause_454, clause_146, clause_181, clause_797, clause_391, clause_1008, clause_431, clause_164, clause_200, clause_56, clause_498, clause_1078, clause_968, clause_931, clause_1019, clause_415, clause_890, clause_613, clause_1014, clause_1081, clause_606, clause_646, clause_1185, clause_374, clause_10, clause_467, clause_433, clause_1169, clause_79, clause_193, clause_258, clause_478, clause_1177, clause_73, clause_1266, clause_741, clause_675, clause_806, clause_463, clause_702, clause_230, clause_388, clause_150, clause_1005, clause_1201, clause_522, clause_35, clause_612, clause_1066, clause_227, clause_844, clause_854, clause_1153, clause_861, clause_528
% 12.88/4.14 % No. of inferences in proof: 143
% 12.88/4.14 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3596 ms resp. 2757 ms w/o parsing
% 13.19/4.29 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.19/4.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------