TSTP Solution File: SYO647-1 by Leo-III-SAT---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : SYO647-1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 11:05:28 EDT 2024
% Result : Unsatisfiable 101.61s 30.28s
% Output : Refutation 101.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 12
% Syntax : Number of formulae : 79 ( 8 unt; 5 typ; 0 def)
% Number of atoms : 746 ( 13 equ; 0 cnn)
% Maximal formula atoms : 41 ( 10 avg)
% Number of connectives : 4205 ( 595 ~; 646 |; 0 &;2964 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 52 ( 16 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 201 ( 0 ^ 201 !; 0 ?; 201 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'E\'_type',type,
'\'E\'': $i > $i > $o ).
thf(f_type,type,
f: $i > $i ).
thf(suc_type,type,
suc: $i > $i ).
thf(iLEQ_type,type,
iLEQ: $i > $i > $o ).
thf('\'0\'_type',type,
'\'0\'': $i ).
thf(606,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6260) ).
thf(1943,plain,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(1944,plain,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(cnf,[status(esa)],[1943]) ).
thf(91,axiom,
! [A: $i] : ( '\'E\'' @ '\'0\'' @ ( f @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6244) ).
thf(914,plain,
! [A: $i] : ( '\'E\'' @ '\'0\'' @ ( f @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(2201,plain,
! [A: $i] :
( ~ $true
| ~ $true
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ $true
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(rewrite,[status(thm)],[1944,914]) ).
thf(2202,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(simp,[status(thm)],[2201]) ).
thf(126,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6279) ).
thf(983,plain,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(984,plain,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(cnf,[status(esa)],[983]) ).
thf(2199,plain,
! [A: $i] :
( ~ $true
| ~ $true
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(rewrite,[status(thm)],[984,914]) ).
thf(2200,plain,
! [A: $i] :
( ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(simp,[status(thm)],[2199]) ).
thf(101,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ E ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ F ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ E ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ F ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ E ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ F ) ) )
| ~ ( iLEQ @ ( suc @ E ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ E ) @ ( f @ ( suc @ E ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ F ) @ ( f @ ( suc @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4556) ).
thf(933,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ E ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ F ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ E ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ F ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ E ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ F ) ) )
| ~ ( iLEQ @ ( suc @ E ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ E ) @ ( f @ ( suc @ E ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ F ) @ ( f @ ( suc @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(934,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ E ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ F ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ E ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ F ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ E ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ F ) ) )
| ~ ( iLEQ @ ( suc @ E ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ E ) @ ( f @ ( suc @ E ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ F ) @ ( f @ ( suc @ F ) ) ) ),
inference(cnf,[status(esa)],[933]) ).
thf(6313,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ $true
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ E ) )
| ~ $true
| ~ $true
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ F ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( iLEQ @ ( suc @ E ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ E ) @ ( f @ ( suc @ E ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ F ) @ ( f @ ( suc @ F ) ) ) ),
inference(rewrite,[status(thm)],[934,914]) ).
thf(6314,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ E ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ F ) )
| ~ ( iLEQ @ ( suc @ E ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ E ) @ ( f @ ( suc @ E ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ F ) @ ( f @ ( suc @ F ) ) ) ),
inference(simp,[status(thm)],[6313]) ).
thf(6338,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ E ) )
| ~ ( iLEQ @ ( suc @ E ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ E ) @ ( f @ ( suc @ E ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ F ) @ ( f @ ( suc @ F ) ) )
| ( ( iLEQ @ ( suc @ B ) @ ( suc @ F ) )
!= ( iLEQ @ ( suc @ A ) @ ( suc @ B ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[6314]) ).
thf(6345,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ D ) @ ( suc @ D ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) ) ),
inference(pattern_uni,[status(thm)],[6338:[bind(A,$thf( F )),bind(B,$thf( F ))]]) ).
thf(6355,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ D ) @ ( suc @ D ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(simp,[status(thm)],[6345]) ).
thf(6389,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ D ) @ ( suc @ D ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
!= ( iLEQ @ ( suc @ D ) @ ( suc @ D ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[6355]) ).
thf(6395,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[6389:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(6405,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) ) ),
inference(simp,[status(thm)],[6395]) ).
thf(6416,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
!= ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[6405]) ).
thf(6417,plain,
! [A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[6416:[bind(A,$thf( B ))]]) ).
thf(6418,plain,
! [A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ A ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(simp,[status(thm)],[6417]) ).
thf(6421,plain,
! [B: $i,A: $i] :
( ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( ( iLEQ @ ( suc @ A ) @ ( suc @ A ) )
!= ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[2200,6418]) ).
thf(6422,plain,
! [A: $i] :
( ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[6421:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(6425,plain,
! [A: $i] : ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ),
inference(simp,[status(thm)],[6422]) ).
thf(6436,plain,
! [A: $i] :
( ~ $true
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(rewrite,[status(thm)],[2202,6425]) ).
thf(6437,plain,
! [A: $i] :
( ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(simp,[status(thm)],[6436]) ).
thf(11,axiom,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3293) ).
thf(754,plain,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(755,plain,
! [A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(cnf,[status(esa)],[754]) ).
thf(5242,plain,
! [A: $i] :
( ~ $true
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ $true
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ $true
| ~ $true
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(rewrite,[status(thm)],[755,914]) ).
thf(5243,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(simp,[status(thm)],[5242]) ).
thf(501,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ E ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ D ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ F ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( f @ ( suc @ F ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ F ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ E ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ E ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ F ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( f @ ( suc @ E ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ F ) ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( f @ ( suc @ ( suc @ F ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ E ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ F ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( f @ ( suc @ ( suc @ E ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ E ) ) )
| ~ ( iLEQ @ ( suc @ F ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4547) ).
thf(1733,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ E ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ D ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ F ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( f @ ( suc @ F ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ F ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ E ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ E ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ F ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( f @ ( suc @ E ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ F ) ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( f @ ( suc @ ( suc @ F ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ E ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ F ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( f @ ( suc @ ( suc @ E ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ E ) ) )
| ~ ( iLEQ @ ( suc @ F ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(1734,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ A ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ E ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ D ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ F ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( f @ ( suc @ F ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ F ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ E ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ C ) ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ E ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ F ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( f @ ( suc @ E ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ F ) ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( f @ ( suc @ ( suc @ F ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ E ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ ( suc @ B ) ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ F ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( f @ ( suc @ ( suc @ E ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ E ) ) )
| ~ ( iLEQ @ ( suc @ F ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(cnf,[status(esa)],[1733]) ).
thf(2207,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ $true
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ $true
| ~ ( '\'E\'' @ ( f @ F ) @ ( f @ ( suc @ F ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ F ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ $true
| ~ $true
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ E ) )
| ~ $true
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ $true
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( '\'E\'' @ ( f @ E ) @ ( f @ ( suc @ E ) ) )
| ~ $true
| ~ ( '\'E\'' @ ( f @ F ) @ ( f @ ( suc @ ( suc @ F ) ) ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( '\'E\'' @ ( f @ E ) @ ( f @ ( suc @ ( suc @ E ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ $true
| ~ ( iLEQ @ ( suc @ F ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(rewrite,[status(thm)],[1734,914]) ).
thf(2208,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( f @ ( suc @ F ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ F ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ E ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( f @ ( suc @ E ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( f @ ( suc @ ( suc @ F ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( f @ ( suc @ ( suc @ E ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( iLEQ @ ( suc @ F ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(simp,[status(thm)],[2207]) ).
thf(2259,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( f @ ( suc @ F ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ F ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ E ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( f @ ( suc @ E ) ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( f @ ( suc @ ( suc @ F ) ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( f @ ( suc @ ( suc @ E ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( ( iLEQ @ ( suc @ F ) @ ( suc @ D ) )
!= ( iLEQ @ ( suc @ C ) @ ( suc @ F ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2208]) ).
thf(2273,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2259:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( D )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( D ))]]) ).
thf(2283,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(simp,[status(thm)],[2273]) ).
thf(2325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ C ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ D ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( ( iLEQ @ ( suc @ C ) @ ( suc @ B ) )
!= ( iLEQ @ ( suc @ B ) @ ( suc @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2283]) ).
thf(2338,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2325:[bind(A,$thf( C )),bind(B,$thf( C ))]]) ).
thf(2345,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) ) ),
inference(simp,[status(thm)],[2338]) ).
thf(2385,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
!= ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[2345]) ).
thf(2390,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2385:[bind(A,$thf( B ))]]) ).
thf(2391,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(simp,[status(thm)],[2390]) ).
thf(5267,plain,
! [B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ( ( iLEQ @ ( suc @ A ) @ ( suc @ A ) )
!= ( iLEQ @ ( suc @ B ) @ ( suc @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[5243,2391]) ).
thf(5268,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[5267:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(5407,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ),
inference(simp,[status(thm)],[5268]) ).
thf(5437,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
!= ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[5407]) ).
thf(5447,plain,
! [A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ( ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) )
!= ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) ) ) ),
inference(simp,[status(thm)],[5437]) ).
thf(6432,plain,
! [A: $i] :
( ~ $true
| ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(rewrite,[status(thm)],[5447,6425]) ).
thf(6433,plain,
! [A: $i] :
~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ),
inference(simp,[status(thm)],[6432]) ).
thf(6450,plain,
! [A: $i] :
( $false
| ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ) ),
inference(rewrite,[status(thm)],[6437,6433]) ).
thf(6451,plain,
! [A: $i] : ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ),
inference(simp,[status(thm)],[6450]) ).
thf(113,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( f @ ( suc @ E ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ E ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ F ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ F ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ E ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( f @ ( suc @ F ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ E ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ F ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ E ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ F ) ) )
| ~ ( iLEQ @ ( suc @ E ) @ ( suc @ D ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ E ) @ ( f @ ( suc @ ( suc @ E ) ) ) )
| ( '\'E\'' @ ( f @ F ) @ ( f @ ( suc @ ( suc @ F ) ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_433) ).
thf(957,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( f @ ( suc @ E ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ E ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ F ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ F ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ E ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( f @ ( suc @ F ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ E ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ F ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ E ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ F ) ) )
| ~ ( iLEQ @ ( suc @ E ) @ ( suc @ D ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ E ) @ ( f @ ( suc @ ( suc @ E ) ) ) )
| ( '\'E\'' @ ( f @ F ) @ ( f @ ( suc @ ( suc @ F ) ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(958,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ A ) ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ A ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ~ ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ ( f @ E ) @ ( f @ ( suc @ E ) ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ E ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ D ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ B ) ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ F ) )
| ~ ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ B ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ F ) ) ) )
| ~ ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ D ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ B ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ C ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ E ) )
| ~ ( '\'E\'' @ ( f @ F ) @ ( f @ ( suc @ F ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ E ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ F ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ E ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ A ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ ( suc @ A ) ) ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ C ) )
| ~ ( '\'E\'' @ '\'0\'' @ ( f @ ( suc @ F ) ) )
| ~ ( iLEQ @ ( suc @ E ) @ ( suc @ D ) )
| ( '\'E\'' @ ( f @ B ) @ ( f @ ( suc @ ( suc @ B ) ) ) )
| ( '\'E\'' @ ( f @ C ) @ ( f @ ( suc @ ( suc @ C ) ) ) )
| ( '\'E\'' @ ( f @ E ) @ ( f @ ( suc @ ( suc @ E ) ) ) )
| ( '\'E\'' @ ( f @ F ) @ ( f @ ( suc @ ( suc @ F ) ) ) )
| ( '\'E\'' @ ( f @ D ) @ ( f @ ( suc @ ( suc @ D ) ) ) )
| ( '\'E\'' @ ( f @ A ) @ ( f @ ( suc @ ( suc @ A ) ) ) ) ),
inference(cnf,[status(esa)],[957]) ).
thf(6673,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ $true
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ A ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ E ) )
| ~ $true
| ~ $true
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ F ) )
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ ( iLEQ @ ( suc @ E ) @ ( suc @ D ) )
| $false
| $false
| $false
| $false
| $false
| $false ),
inference(rewrite,[status(thm)],[958,6433,914,6425]) ).
thf(6674,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ E ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ F ) )
| ~ ( iLEQ @ ( suc @ E ) @ ( suc @ D ) ) ),
inference(simp,[status(thm)],[6673]) ).
thf(6690,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ E ) )
| ~ ( iLEQ @ ( suc @ E ) @ ( suc @ D ) )
| ( ( iLEQ @ ( suc @ B ) @ ( suc @ F ) )
!= ( iLEQ @ ( suc @ C ) @ ( suc @ E ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[6674]) ).
thf(6695,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ D ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) ) ),
inference(pattern_uni,[status(thm)],[6690:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( D )),bind(E,$thf( F ))]]) ).
thf(6705,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ D ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) ) ),
inference(simp,[status(thm)],[6695]) ).
thf(6730,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ C ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ D ) @ ( suc @ C ) )
| ( ( iLEQ @ ( suc @ B ) @ ( suc @ D ) )
!= ( iLEQ @ ( suc @ C ) @ ( suc @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[6705]) ).
thf(6737,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) )
| ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) ) ),
inference(pattern_uni,[status(thm)],[6730:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(6742,plain,
! [B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ B ) @ ( suc @ A ) )
| ~ ( iLEQ @ ( suc @ A ) @ ( suc @ B ) ) ),
inference(simp,[status(thm)],[6737]) ).
thf(6749,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( iLEQ @ ( suc @ B ) @ ( suc @ C ) )
| ( ( iLEQ @ ( suc @ A ) @ ( suc @ A ) )
!= ( iLEQ @ ( suc @ C ) @ ( suc @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[6451,6742]) ).
thf(6750,plain,
! [A: $i] :
~ ( iLEQ @ ( suc @ A ) @ ( suc @ A ) ),
inference(pattern_uni,[status(thm)],[6749:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(6755,plain,
~ $true,
inference(rewrite,[status(thm)],[6750,6451]) ).
thf(6756,plain,
$false,
inference(simp,[status(thm)],[6755]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO647-1 : TPTP v8.1.2. Released v7.3.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n002.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 20:18:24 EDT 2024
% 0.16/0.38 % CPUTime :
% 0.97/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.57/1.33 % [INFO] Parsing done (467ms).
% 2.57/1.34 % [INFO] Running in sequential loop mode.
% 3.30/1.57 % [INFO] nitpick registered as external prover.
% 3.30/1.58 % [INFO] Scanning for conjecture ...
% 4.28/1.84 % [INFO] 733 axioms and no conjecture found.
% 10.31/6.22 % [INFO] Problem is propositional (TPTP CNF).
% 10.31/6.25 % [INFO] Type checking passed.
% 10.31/6.25 % [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 ...
% 101.61/30.28 % [INFO] Killing All external provers ...
% 101.61/30.28 % Time passed: 29745ms (effective reasoning time: 28933ms)
% 101.61/30.28 % Axioms used in derivation (7): clause_6279, clause_4556, clause_3293, clause_6244, clause_6260, clause_433, clause_4547
% 101.61/30.28 % No. of inferences in proof: 74
% 101.61/30.28 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 29745 ms resp. 28933 ms w/o parsing
% 101.61/30.37 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 101.61/30.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------