%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO647-1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:45:06 AM UTC 2026
% Result : Unsatisfiable 74.98s 33.21s
% Output : Refutation 70.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 7
% Syntax : Number of formulae : 83 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 800 ( 21 equ; 0 cnn)
% Maximal formula atoms : 41 ( 9 avg)
% Number of connectives : 4445 ( 625 ~; 675 |; 0 &;3145 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 52 ( 16 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 249 ( 0 ^; 249 !; 0 ?; 249 :)
% Comments :
%------------------------------------------------------------------------------
thf('E_decl',type,
'E': $i > $i > $o ).
thf(f_decl,type,
f: $i > $i ).
thf(suc_decl,type,
suc: $i > $i ).
thf(iLEQ_decl,type,
iLEQ: $i > $i > $o ).
thf('0_decl',type,
'0': $i ).
thf(606,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6260) ).
thf(1943,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(1944,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[1943]) ).
thf(91,axiom,
! [A: $i] : ( A @ f @ ( '0' @ 'E' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6244) ).
thf(914,plain,
! [A: $i] : ( A @ f @ ( '0' @ 'E' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(2201,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ $true
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[1944,914]) ).
thf(2202,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[2201]) ).
thf(126,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6279) ).
thf(983,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)],[126]) ).
thf(984,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[983]) ).
thf(2199,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[984,914]) ).
thf(2200,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[2199]) ).
thf(101,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' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4556) ).
thf(933,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' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(934,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' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(cnf,[status(esa)],[933]) ).
thf(7537,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' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( E @ suc @ iLEQ ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( F @ suc @ ( B @ suc @ iLEQ ) )
| ~ $true
| ~ $true
| ~ ( E @ suc @ ( D @ suc @ iLEQ ) )
| ~ $true
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(rewrite,[status(thm)],[934,914]) ).
thf(7538,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' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[7537]) ).
thf(7577,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( C @ suc @ ( E @ suc @ iLEQ ) )
!= ( E @ suc @ ( D @ suc @ iLEQ ) ) )
| ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( F @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(eqfactor_ordered,[status(thm)],[7538]) ).
thf(7584,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(pattern_uni,[status(thm)],[7577:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C )),bind(E,$thf( C ))]]) ).
thf(7589,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[7584]) ).
thf(7628,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( A @ suc @ ( C @ suc @ iLEQ ) )
!= ( B @ suc @ ( A @ suc @ iLEQ ) ) )
| ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(eqfactor_ordered,[status(thm)],[7589]) ).
thf(7634,plain,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(pattern_uni,[status(thm)],[7628:[bind(A,$thf( C )),bind(B,$thf( C ))]]) ).
thf(7640,plain,
! [B: $i,A: $i] :
( ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[7634]) ).
thf(7653,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ suc @ ( A @ suc @ iLEQ ) )
!= ( C @ suc @ ( B @ suc @ iLEQ ) ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ $true
| ~ ( B @ suc @ ( B @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[2200,7640]) ).
thf(7654,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ suc @ ( A @ suc @ iLEQ ) )
!= ( C @ suc @ ( B @ suc @ iLEQ ) ) )
| ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ ( B @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[7653]) ).
thf(7655,plain,
! [A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[7654:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(7665,plain,
! [A: $i] :
( ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[7655]) ).
thf(7667,plain,
! [B: $i,A: $i] :
( ( ( A @ suc @ ( A @ suc @ iLEQ ) )
!= ( B @ suc @ ( B @ suc @ iLEQ ) ) )
| ~ $true
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[2200,7665]) ).
thf(7668,plain,
! [B: $i,A: $i] :
( ( ( A @ suc @ ( A @ suc @ iLEQ ) )
!= ( B @ suc @ ( B @ suc @ iLEQ ) ) )
| ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[7667]) ).
thf(7669,plain,
! [A: $i] :
( ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[7668:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(7673,plain,
! [A: $i] : ( A @ suc @ f @ ( A @ f @ 'E' ) ),
inference(simp,[status(thm)],[7669]) ).
thf(7688,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[2202,7673]) ).
thf(7689,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[7688]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3293) ).
thf(754,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(755,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[754]) ).
thf(6200,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ $true
| ~ $true
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ $true
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[755,914]) ).
thf(6201,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[6200]) ).
thf(501,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( F @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4547) ).
thf(1733,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( F @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(1734,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( F @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ suc @ f @ ( '0' @ 'E' ) ) ),
inference(cnf,[status(esa)],[1733]) ).
thf(2208,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( F @ suc @ iLEQ ) )
| ~ $true
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( E @ f @ 'E' ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( F @ suc @ suc @ f @ ( F @ f @ 'E' ) )
| ~ $true
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ $true
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ $true
| ~ ( E @ suc @ ( A @ suc @ iLEQ ) )
| ~ $true
| ~ $true
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ $true
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ $true
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[1734,914]) ).
thf(2209,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( E @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[2208]) ).
thf(2279,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( B @ suc @ ( D @ suc @ iLEQ ) )
!= ( A @ suc @ ( B @ suc @ iLEQ ) ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( E @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[2209]) ).
thf(2305,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[2279:[bind(A,$thf( D )),bind(B,$thf( D ))]]) ).
thf(2311,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[2305]) ).
thf(2373,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( D @ suc @ ( A @ suc @ iLEQ ) )
!= ( B @ suc @ ( B @ suc @ iLEQ ) ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( B @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[2311]) ).
thf(2380,plain,
! [B: $i,A: $i] :
( ~ ( B @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[2373:[bind(A,$thf( D )),bind(B,$thf( D ))]]) ).
thf(2393,plain,
! [B: $i,A: $i] :
( ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[2380]) ).
thf(2452,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ suc @ ( B @ suc @ iLEQ ) )
!= ( B @ suc @ ( B @ suc @ iLEQ ) ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( B @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[2393]) ).
thf(2453,plain,
! [A: $i] :
( ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[2452:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(2458,plain,
! [A: $i] :
( ~ ( A @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[2453]) ).
thf(6383,plain,
! [B: $i,A: $i] :
( ( ( A @ suc @ ( A @ suc @ iLEQ ) )
!= ( B @ suc @ ( B @ suc @ iLEQ ) ) )
| ~ $true
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(paramod_ordered,[status(thm)],[6201,2458]) ).
thf(6384,plain,
! [B: $i,A: $i] :
( ( ( A @ suc @ ( A @ suc @ iLEQ ) )
!= ( B @ suc @ ( B @ suc @ iLEQ ) ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[6383]) ).
thf(6385,plain,
! [A: $i] :
( ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(pattern_uni,[status(thm)],[6384:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(6446,plain,
! [A: $i] :
( ~ ( A @ suc @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[6385]) ).
thf(6483,plain,
! [A: $i] :
( ~ $true
| ( ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
!= ( A @ suc @ f @ ( A @ f @ 'E' ) ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(eqfactor_ordered,[status(thm)],[6446]) ).
thf(6491,plain,
! [A: $i] :
( ( ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
!= ( A @ suc @ f @ ( A @ f @ 'E' ) ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(simp,[status(thm)],[6483]) ).
thf(7676,plain,
! [A: $i] :
( ~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ~ $true ),
inference(rewrite,[status(thm)],[6491,7673]) ).
thf(7677,plain,
! [A: $i] :
~ ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) ),
inference(simp,[status(thm)],[7676]) ).
thf(7698,plain,
! [A: $i] :
( ( A @ suc @ ( A @ suc @ iLEQ ) )
| $false ),
inference(rewrite,[status(thm)],[7689,7677]) ).
thf(7699,plain,
! [A: $i] : ( A @ suc @ ( A @ suc @ iLEQ ) ),
inference(simp,[status(thm)],[7698]) ).
thf(113,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( F @ suc @ suc @ f @ ( F @ f @ 'E' ) )
| ( E @ suc @ suc @ f @ ( E @ f @ 'E' ) )
| ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( F @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_433) ).
thf(957,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( F @ suc @ suc @ f @ ( F @ f @ 'E' ) )
| ( E @ suc @ suc @ f @ ( E @ f @ 'E' ) )
| ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( F @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(958,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ suc @ suc @ f @ ( A @ f @ 'E' ) )
| ( D @ suc @ suc @ f @ ( D @ f @ 'E' ) )
| ( F @ suc @ suc @ f @ ( F @ f @ 'E' ) )
| ( E @ suc @ suc @ f @ ( E @ f @ 'E' ) )
| ( C @ suc @ suc @ f @ ( C @ f @ 'E' ) )
| ( B @ suc @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( C @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( F @ suc @ f @ ( F @ f @ 'E' ) )
| ~ ( E @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ f @ ( '0' @ 'E' ) )
| ~ ( D @ f @ ( '0' @ 'E' ) )
| ~ ( C @ suc @ f @ ( C @ f @ 'E' ) )
| ~ ( F @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ f @ ( B @ f @ 'E' ) )
| ~ ( F @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( B @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( D @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( E @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( E @ suc @ f @ ( E @ f @ 'E' ) )
| ~ ( D @ suc @ f @ ( D @ f @ 'E' ) )
| ~ ( D @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ suc @ f @ ( '0' @ 'E' ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( A @ suc @ f @ ( A @ f @ 'E' ) ) ),
inference(cnf,[status(esa)],[957]) ).
thf(7923,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( $false
| $false
| $false
| $false
| $false
| $false
| ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( F @ suc @ ( B @ suc @ iLEQ ) )
| ~ $true
| ~ $true
| ~ ( E @ suc @ ( C @ suc @ iLEQ ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ $true
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) )
| ~ $true ),
inference(rewrite,[status(thm)],[958,914,7673,7677]) ).
thf(7924,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( F @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( A @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[7923]) ).
thf(7934,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ suc @ ( A @ suc @ iLEQ ) )
!= ( G @ suc @ ( C @ suc @ iLEQ ) ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ $true
| ~ ( F @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) ) ),
inference(paramod_ordered,[status(thm)],[7699,7924]) ).
thf(7935,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ suc @ ( A @ suc @ iLEQ ) )
!= ( G @ suc @ ( C @ suc @ iLEQ ) ) )
| ~ ( E @ suc @ ( F @ suc @ iLEQ ) )
| ~ ( F @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( C @ suc @ ( B @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[7934]) ).
thf(7936,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) ) ),
inference(pattern_uni,[status(thm)],[7935:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( A ))]]) ).
thf(7960,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( E @ suc @ ( C @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( A @ suc @ ( B @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[7936]) ).
thf(7984,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ suc @ ( A @ suc @ iLEQ ) )
!= ( E @ suc @ ( F @ suc @ iLEQ ) ) )
| ~ $true
| ~ ( F @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) ) ),
inference(paramod_ordered,[status(thm)],[7699,7960]) ).
thf(7985,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ suc @ ( A @ suc @ iLEQ ) )
!= ( E @ suc @ ( F @ suc @ iLEQ ) ) )
| ~ ( F @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ ( E @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[7984]) ).
thf(7986,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ suc @ ( D @ suc @ iLEQ ) )
| ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) ) ),
inference(pattern_uni,[status(thm)],[7985:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( A ))]]) ).
thf(8014,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ suc @ ( A @ suc @ iLEQ ) )
!= ( B @ suc @ ( E @ suc @ iLEQ ) ) )
| ~ $true
| ~ ( D @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ ( D @ suc @ iLEQ ) ) ),
inference(paramod_ordered,[status(thm)],[7699,7986]) ).
thf(8015,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ suc @ ( A @ suc @ iLEQ ) )
!= ( B @ suc @ ( E @ suc @ iLEQ ) ) )
| ~ ( D @ suc @ ( B @ suc @ iLEQ ) )
| ~ ( C @ suc @ ( D @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[8014]) ).
thf(8016,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) ) ),
inference(pattern_uni,[status(thm)],[8015:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A ))]]) ).
thf(8023,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ suc @ ( A @ suc @ iLEQ ) )
| ~ ( B @ suc @ ( C @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[8016]) ).
thf(8029,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ suc @ ( A @ suc @ iLEQ ) )
!= ( C @ suc @ ( D @ suc @ iLEQ ) ) )
| ~ ( D @ suc @ ( B @ suc @ iLEQ ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7699,8023]) ).
thf(8030,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ suc @ ( A @ suc @ iLEQ ) )
!= ( C @ suc @ ( D @ suc @ iLEQ ) ) )
| ~ ( D @ suc @ ( B @ suc @ iLEQ ) ) ),
inference(simp,[status(thm)],[8029]) ).
thf(8031,plain,
! [B: $i,A: $i] :
~ ( A @ suc @ ( B @ suc @ iLEQ ) ),
inference(pattern_uni,[status(thm)],[8030:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(8038,plain,
$false,
inference(rewrite,[status(thm)],[7699,8031]) ).
thf(8039,plain,
$false,
inference(simp,[status(thm)],[8038]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO647-1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/0.41 % Computer : n004.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 19:42:23 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.84/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.46/1.79 % [INFO] Parsing done (784ms).
% 3.72/1.81 % [INFO] Running in sequential loop mode.
% 4.43/2.21 % [INFO] eprover registered as external prover.
% 4.43/2.21 % [INFO] Scanning for conjecture ...
% 5.49/2.51 % [INFO] 733 axioms and no conjecture found.
% 10.12/5.78 % [INFO] Problem is propositional (TPTP CNF).
% 10.25/5.82 % [INFO] Type checking passed.
% 10.25/5.83 % [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 ...
% 74.87/33.20 % [INFO] Killing All external provers ...
% 74.98/33.20 % Time passed: 32644ms (effective reasoning time: 31387ms)
% 74.98/33.20 % Axioms used in derivation (7): clause_6279, clause_4556, clause_3293, clause_6244, clause_6260, clause_433, clause_4547
% 74.98/33.20 % No. of inferences in proof: 83
% 74.98/33.21 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 32644 ms resp. 31387 ms w/o parsing
% 70.61/33.31 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 70.61/33.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------