%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO634-1 : TPTP v9.3.1. Released v7.1.0.
% 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 : n002.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 09:45:04 AM UTC 2026
% Result : Unsatisfiable 7.05s 13.25s
% Output : Refutation 7.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 23
% Syntax : Number of formulae : 47 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 283 ( 0 equ; 0 cnn)
% Maximal formula atoms : 11 ( 6 avg)
% Number of connectives : 3432 ( 238 ~; 236 |; 0 &;2958 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 24 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 278 ( 0 ^; 278 !; 0 ?; 278 :)
% Comments :
%------------------------------------------------------------------------------
thf('E_decl',type,
'E': $i > $i > $o ).
thf(f_decl,type,
f: $i > $i ).
thf(s_decl,type,
s: $i > $i ).
thf('0_decl',type,
'0': $i ).
thf('LEQ_decl',type,
'LEQ': $i > $i > $o ).
thf('AP_decl',type,
'AP': $i > $i > $i ).
thf(21,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( F @ ( '0' @ s @ s @ s @ s @ s @ 'AP' ) @ 'LEQ' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_22_21) ).
thf(61,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( F @ ( '0' @ s @ s @ s @ s @ s @ 'AP' ) @ 'LEQ' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(23,axiom,
! [B: $i,A: $i] : ( B @ ( A @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ 'LEQ' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_19_23) ).
thf(65,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ 'LEQ' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(17,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '0' @ ( K @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( J @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( I @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( H @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( G @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ ( F @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3_17) ).
thf(53,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( '0' @ ( K @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( J @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( I @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( H @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( G @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ ( F @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( '0' @ s @ s @ s @ ( H @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( G @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( F @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_18_15) ).
thf(49,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( '0' @ s @ s @ s @ ( H @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( G @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( F @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(9,axiom,
! [A: $i] : ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_17_09) ).
thf(39,plain,
! [A: $i] : ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ ( H @ ( '0' @ s @ s @ s @ 'AP' ) @ 'LEQ' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( G @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( F @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5_07) ).
thf(35,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ ( H @ ( '0' @ s @ s @ s @ 'AP' ) @ 'LEQ' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( G @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( F @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(22,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( '0' @ ( K @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( J @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( I @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( H @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( G @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ ( F @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10_22) ).
thf(63,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( '0' @ ( K @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( J @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( I @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( H @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( G @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ ( F @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ 'LEQ' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7_05) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ 'LEQ' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( '0' @ s @ s @ s @ s @ s @ s @ 'AP' ) @ 'LEQ' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2_16) ).
thf(51,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( '0' @ s @ s @ s @ s @ s @ s @ 'AP' ) @ 'LEQ' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_12_14) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(11,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( '0' @ s @ ( J @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( I @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( H @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( G @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( F @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8_11) ).
thf(42,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( '0' @ s @ ( J @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( I @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( H @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( G @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( F @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1,axiom,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_21_01) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ ( G @ ( '0' @ s @ s @ s @ s @ 'AP' ) @ 'LEQ' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( F @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_20_08) ).
thf(37,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ ( G @ ( '0' @ s @ s @ s @ s @ 'AP' ) @ 'LEQ' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( F @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [B: $i,A: $i] : ( B @ ( A @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ 'LEQ' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6_13) ).
thf(46,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ 'LEQ' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(19,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( '0' @ s @ s @ ( I @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( H @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( G @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( F @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_0_19) ).
thf(57,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( '0' @ s @ s @ ( I @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( H @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( G @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( F @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(4,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ ( I @ ( '0' @ s @ s @ 'AP' ) @ 'LEQ' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( H @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( G @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( F @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4_04) ).
thf(29,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ ( I @ ( '0' @ s @ s @ 'AP' ) @ 'LEQ' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( H @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( G @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( F @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $i] : ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11_03) ).
thf(28,plain,
! [A: $i] : ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1_06) ).
thf(33,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ ( G @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( F @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9_12) ).
thf(44,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ ( G @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( F @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(20,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_15_20) ).
thf(59,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(10,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( J @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ ( J @ ( '0' @ s @ 'AP' ) @ 'LEQ' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( I @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( H @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( G @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( F @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_16_10) ).
thf(40,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( J @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ ( J @ ( '0' @ s @ 'AP' ) @ 'LEQ' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( I @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( H @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( G @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( F @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(2,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ ( K @ ( '0' @ 'AP' ) @ 'LEQ' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( J @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( I @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( H @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( G @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ ( F @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_14_02) ).
thf(26,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ ( K @ ( '0' @ 'AP' ) @ 'LEQ' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ ( J @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( I @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ ( H @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ ( G @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ ( F @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ ( E @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( D @ f @ 'E' ) )
| ~ ( '0' @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ 'LEQ' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_13_18) ).
thf(55,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( '0' @ s @ s @ s @ s @ s @ s @ s @ 'AP' ) @ 'LEQ' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ ( C @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( B @ f @ 'E' ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ s @ s @ s @ s @ ( A @ f @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(66,plain,
$false,
inference(e,[status(thm)],[61,65,53,49,39,35,63,31,51,47,42,24,37,46,57,29,28,33,44,59,40,26,55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYO634-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.12 % 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
% 0.24/11.05 % Computer : n002.cluster.edu
% 0.24/11.05 % Model : x86_64 x86_64
% 0.24/11.05 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/11.05 % Memory : 8046.5625MB
% 0.24/11.05 % OS : Linux 6.8.0-71-generic
% 0.24/11.05 % CPULimit : 300
% 0.24/11.05 % WCLimit : 300
% 0.24/11.05 % DateTime : Sat Sep 26 19:43:46 UTC 2026
% 0.24/11.05 % CPUTime :
% 0.24/11.05 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
% 0.28/11.51 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.28/11.76 % [INFO] Parsing done (240ms).
% 0.28/11.77 % [INFO] Running in sequential loop mode.
% 2.62/12.10 % [INFO] eprover registered as external prover.
% 2.62/12.10 % [INFO] Scanning for conjecture ...
% 2.92/12.18 % [INFO] 23 axioms and no conjecture found.
% 3.43/12.32 % [INFO] Problem is propositional (TPTP CNF).
% 3.43/12.33 % [INFO] Type checking passed.
% 3.43/12.33 % [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 ...
% 7.05/13.25 % External prover 'e' found a proof!
% 7.05/13.25 % [INFO] Killing All external provers ...
% 7.05/13.25 % Time passed: 2074ms (effective reasoning time: 1475ms)
% 7.05/13.25 % Axioms used in derivation (23): clause_2_16, clause_7_05, clause_1_06, clause_3_17, clause_15_20, clause_6_13, clause_9_12, clause_22_21, clause_17_09, clause_18_15, clause_16_10, clause_20_08, clause_5_07, clause_0_19, clause_10_22, clause_4_04, clause_21_01, clause_14_02, clause_19_23, clause_13_18, clause_8_11, clause_11_03, clause_12_14
% 7.05/13.25 % No. of inferences in proof: 47
% 7.05/13.25 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2074 ms resp. 1475 ms w/o parsing
% 7.66/13.36 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.66/13.36 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------