%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO681-1 : 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 : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:45:10 AM UTC 2026
% Result : Unsatisfiable 24.54s 10.16s
% Output : Refutation 25.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 54
% Syntax : Number of formulae : 171 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 1316 ( 39 equ; 0 cnn)
% Maximal formula atoms : 15 ( 7 avg)
% Number of connectives : 8637 (1041 ~;1121 |; 0 &;6475 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 328 ( 0 ^; 328 !; 0 ?; 328 :)
% Comments :
%------------------------------------------------------------------------------
thf('LE_decl',type,
'LE': $i > $i > $o ).
thf(f_decl,type,
f: $i > $i ).
thf(s_decl,type,
s: $i > $i ).
thf('0_decl',type,
'0': $i ).
thf('E_decl',type,
'E': $i > $i > $o ).
thf(iLEQ_decl,type,
iLEQ: $i > $i > $o ).
thf(suc_decl,type,
suc: $i > $i ).
thf(z_decl,type,
z: $i ).
thf(34,axiom,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_457) ).
thf(120,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_291) ).
thf(142,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_131) ).
thf(128,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(129,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(cnf,[status(esa)],[128]) ).
thf(30,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_450) ).
thf(112,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(43,axiom,
! [A: $i] :
( ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_550) ).
thf(138,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(18,axiom,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_497) ).
thf(88,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(28,axiom,
! [A: $i] :
( ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_103) ).
thf(108,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(109,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[108]) ).
thf(3,axiom,
! [A: $i] : ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_556) ).
thf(59,plain,
! [A: $i] : ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2338,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[109,59]) ).
thf(2339,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[2338]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_563) ).
thf(110,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(139,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ suc @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[138]) ).
thf(2216,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[139,59]) ).
thf(2217,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[2216]) ).
thf(1,axiom,
! [A: $i] :
( ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_658) ).
thf(55,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(56,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[55]) ).
thf(343,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[56,59]) ).
thf(344,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[343]) ).
thf(52,axiom,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_508) ).
thf(156,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(157,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[156]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_145) ).
thf(152,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_592) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_209) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(27,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_560) ).
thf(106,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)],[27]) ).
thf(121,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ suc @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[120]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_528) ).
thf(84,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(89,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[88]) ).
thf(181,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ 'E' ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,89]) ).
thf(182,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[181]) ).
thf(219,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s )
!= ( '0' @ s ) )
| ( ( A @ f )
!= ( B @ f ) )
| ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[182]) ).
thf(1123,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s )
!= ( '0' @ s ) )
| ( A != B )
| ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[219]) ).
thf(1377,plain,
! [A: $i] :
( ( ( '0' @ s @ s @ s @ s )
!= ( '0' @ s ) )
| ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[1123]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_227) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(cnf,[status(esa)],[60]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_41) ).
thf(132,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_283) ).
thf(116,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_479) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(133,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(cnf,[status(esa)],[132]) ).
thf(85,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(cnf,[status(esa)],[84]) ).
thf(25,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_61) ).
thf(102,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)],[25]) ).
thf(42,axiom,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_44) ).
thf(136,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(137,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[136]) ).
thf(300,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,137]) ).
thf(301,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ s @ ( B @ f @ 'LE' ) ) )
| ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[300]) ).
thf(326,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s )
!= ( '0' @ s @ s ) )
| ( ( A @ f )
!= ( B @ f ) )
| ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[301]) ).
thf(4844,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s )
!= ( '0' @ s ) )
| ( A != B )
| ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[326]) ).
thf(5420,plain,
! [A: $i] :
( ( ( '0' @ s @ s @ s )
!= ( '0' @ s ) )
| ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[4844]) ).
thf(5512,plain,
! [A: $i] :
( ( ( '0' @ s @ s )
!= '0' )
| ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[5420]) ).
thf(54,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_35) ).
thf(160,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_614) ).
thf(70,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_534) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(22,axiom,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_95) ).
thf(96,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(97,plain,
! [A: $i] :
( ( '0' @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ ( A @ suc @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[96]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_363) ).
thf(150,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(151,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[150]) ).
thf(167,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( A @ suc @ ( C @ suc @ iLEQ ) )
!= ( B @ suc @ ( A @ suc @ iLEQ ) ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[151]) ).
thf(168,plain,
! [A: $i] :
( ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[167:[bind(A,$thf( C )),bind(B,$thf( C ))]]) ).
thf(169,plain,
! [A: $i] :
( ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[168]) ).
thf(2823,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( A @ suc @ ( C @ suc @ iLEQ ) )
!= ( B @ suc @ ( A @ suc @ iLEQ ) ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[85]) ).
thf(2961,plain,
! [A: $i] :
( ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[2823:[bind(A,$thf( C )),bind(B,$thf( C ))]]) ).
thf(3001,plain,
! [A: $i] :
( ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(simp,[status(thm)],[2961]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_663) ).
thf(124,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(6277,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( A @ suc @ ( C @ suc @ iLEQ ) )
!= ( B @ suc @ ( A @ suc @ iLEQ ) ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(eqfactor_ordered,[status(thm)],[129]) ).
thf(6564,plain,
! [A: $i] :
( ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(pattern_uni,[status(thm)],[6277:[bind(A,$thf( C )),bind(B,$thf( C ))]]) ).
thf(6720,plain,
! [A: $i] :
( ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[6564]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_223) ).
thf(134,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(10,axiom,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_607) ).
thf(72,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(73,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[72]) ).
thf(51,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_595) ).
thf(154,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)],[51]) ).
thf(155,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[154]) ).
thf(242,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ ( B @ suc @ f @ 'LE' ) ) )
| ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,155]) ).
thf(243,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ s @ ( B @ suc @ f @ 'LE' ) ) )
| ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[242]) ).
thf(278,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s )
!= ( '0' @ s ) )
| ( ( A @ f )
!= ( B @ suc @ f ) )
| ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[243]) ).
thf(3199,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s )
!= '0' )
| ( A
!= ( B @ suc ) )
| ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[278]) ).
thf(3660,plain,
! [A: $i] :
( ( ( '0' @ s @ s @ s )
!= '0' )
| ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[3199]) ).
thf(17,axiom,
~ ( '0' @ ( z @ f @ 'LE' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_359) ).
thf(86,plain,
~ ( '0' @ ( z @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(87,plain,
~ ( '0' @ ( z @ f @ 'LE' ) ),
inference(polarity_switch,[status(thm)],[86]) ).
thf(162,plain,
! [A: $i] :
( ( ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59,87]) ).
thf(163,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
!= ( '0' @ ( z @ f @ 'LE' ) ) ),
inference(simp,[status(thm)],[162]) ).
thf(164,plain,
! [A: $i] :
( ( ( '0' @ s @ s @ s @ s )
!= '0' )
| ( ( A @ f )
!= ( z @ f ) ) ),
inference(simp,[status(thm)],[163]) ).
thf(165,plain,
! [A: $i] :
( ( ( '0' @ s @ s @ s @ s )
!= '0' )
| ( A != z ) ),
inference(simp,[status(thm)],[164]) ).
thf(166,plain,
( ( '0' @ s @ s @ s @ s )
!= '0' ),
inference(simp,[status(thm)],[165]) ).
thf(48,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_594) ).
thf(148,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_330) ).
thf(64,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_137) ).
thf(118,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_383) ).
thf(144,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_723) ).
thf(76,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_352) ).
thf(98,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(103,plain,
! [A: $i] :
( ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( '0' @ s @ ( A @ suc @ suc @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[102]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_325) ).
thf(140,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(7,axiom,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_300) ).
thf(66,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_458) ).
thf(130,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_486) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3197,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s @ s )
!= ( '0' @ s ) )
| ( A
!= ( B @ suc ) )
| ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[278]) ).
thf(3659,plain,
! [A: $i] :
( ( ( '0' @ s @ s @ s @ s )
!= ( '0' @ s ) )
| ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[3197]) ).
thf(67,plain,
! [A: $i] :
( ( '0' @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(cnf,[status(esa)],[66]) ).
thf(26,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_713) ).
thf(104,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)],[26]) ).
thf(53,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_671) ).
thf(158,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_501) ).
thf(114,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(cnf,[status(esa)],[57]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_687) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_473) ).
thf(146,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(826,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( A @ suc @ ( C @ suc @ iLEQ ) )
!= ( B @ suc @ ( A @ suc @ iLEQ ) ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(eqfactor_ordered,[status(thm)],[133]) ).
thf(863,plain,
! [A: $i] :
( ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(pattern_uni,[status(thm)],[826:[bind(A,$thf( C )),bind(B,$thf( C ))]]) ).
thf(897,plain,
! [A: $i] :
( ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[863]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_228) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(37,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_572) ).
thf(126,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1125,plain,
! [B: $i,A: $i] :
( ( ( '0' @ s @ s @ s )
!= '0' )
| ( A != B )
| ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[219]) ).
thf(1378,plain,
! [A: $i] :
( ( ( '0' @ s @ s @ s )
!= '0' )
| ( '0' @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ 'E' ) ) ),
inference(simp,[status(thm)],[1125]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_415) ).
thf(68,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_80) ).
thf(62,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_463) ).
thf(90,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_515) ).
thf(122,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_125) ).
thf(100,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(8229,plain,
$false,
inference(e,[status(thm)],[120,142,129,112,138,88,2339,110,2217,344,157,152,57,78,106,121,84,1377,61,132,116,74,89,133,60,85,102,5512,160,70,137,92,97,156,169,3001,124,6720,96,134,73,128,3660,166,148,64,59,118,144,86,76,98,103,140,66,155,108,130,80,150,3659,67,5420,154,72,87,104,158,55,114,58,82,151,146,326,897,94,126,136,1378,68,62,90,122,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO681-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.07 % 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
% 0.13/0.39 % Computer : n020.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 19:46:19 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 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
% 0.85/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.83/1.31 % [INFO] Parsing done (327ms).
% 1.83/1.32 % [INFO] Running in sequential loop mode.
% 2.65/1.72 % [INFO] eprover registered as external prover.
% 2.65/1.73 % [INFO] Scanning for conjecture ...
% 2.84/1.83 % [INFO] 54 axioms and no conjecture found.
% 3.42/2.03 % [INFO] Problem is propositional (TPTP CNF).
% 3.42/2.04 % [INFO] Type checking passed.
% 3.42/2.04 % [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 ...
% 24.54/10.15 % External prover 'e' found a proof!
% 24.54/10.15 % [INFO] Killing All external provers ...
% 24.54/10.15 % Time passed: 9613ms (effective reasoning time: 8826ms)
% 24.54/10.16 % Axioms used in derivation (54): clause_473, clause_41, clause_501, clause_359, clause_61, clause_44, clause_572, clause_325, clause_330, clause_614, clause_103, clause_595, clause_209, clause_137, clause_607, clause_125, clause_663, clause_283, clause_592, clause_458, clause_228, clause_223, clause_534, clause_415, clause_80, clause_671, clause_383, clause_479, clause_515, clause_486, clause_508, clause_687, clause_723, clause_560, clause_300, clause_457, clause_497, clause_352, clause_363, clause_131, clause_563, clause_713, clause_463, clause_594, clause_556, clause_95, clause_550, clause_450, clause_658, clause_35, clause_227, clause_145, clause_291, clause_528
% 24.54/10.16 % No. of inferences in proof: 171
% 24.54/10.16 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 9613 ms resp. 8826 ms w/o parsing
% 25.18/10.34 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 25.18/10.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------