%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HWV015-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 : Fri Sep 25 01:37:53 PM UTC 2026
% Result : Unsatisfiable 9.62s 1.74s
% Output : Proof 9.62s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t114,axiom,
sF0 = p_Rd(x_139),
introduced(definition) ).
cnf(f91,negated_conjecture,
p_Rd(x_139),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_2) ).
fof(f91_nnf,plain,
p_Rd(x_139),
inference(nnf_transformation,[status(thm)],[f91]) ).
cnf(c91,plain,
p_Rd(x_139),
inference(cnf_transformation,[status(esa)],[f91_nnf]) ).
cnf(t2,plain,
p_Rd(x_139) = true,
inference(equality_encoding,[status(esa)],[c91]) ).
cnf(t126,plain,
p_Rd(x_139) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t2116,plain,
sF0 = true,
inference(step,[status(thm)],[t114,t126]) ).
cnf(t129,plain,
true = sF0,
inference(orient,[status(thm)],[t2116]) ).
cnf(t115,axiom,
sF1 = p_Reset(x_139),
introduced(definition) ).
cnf(f93,negated_conjecture,
~ p_Reset(x_139),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_4) ).
fof(f93_nnf,plain,
~ p_Reset(x_139),
inference(nnf_transformation,[status(thm)],[f93]) ).
fof(f93_sk,plain,
~ p_Reset(x_139),
inference(skolemisation,[status(esa)],[f93_nnf]) ).
cnf(c93,plain,
~ p_Reset(x_139),
inference(cnf_transformation,[status(esa)],[f93_sk]) ).
cnf(t3,plain,
p_Reset(x_139) = false,
inference(equality_encoding,[status(esa)],[c93]) ).
cnf(t127,plain,
p_Reset(x_139) = false,
inference(orient,[status(thm)],[t3]) ).
cnf(t2124,plain,
sF1 = false,
inference(step,[status(thm)],[t115,t127]) ).
cnf(t137,plain,
false = sF1,
inference(orient,[status(thm)],[t2124]) ).
cnf(f52,axiom,
( int_level(plus(X_t_42,n1)) = int_level(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ~ p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| p_Reset(X_t_42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_53) ).
fof(f52_nnf,plain,
! [X_t_42] :
( int_level(plus(X_t_42,n1)) = int_level(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ~ p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| p_Reset(X_t_42) ),
inference(nnf_transformation,[status(thm)],[f52]) ).
fof(f52_sk,plain,
! [X_t_42] :
( int_level(plus(X_t_42,n1)) = int_level(X_t_42)
| ~ gt(int_level(X_t_42),n0)
| ~ p_Rd(X_t_42)
| ~ p_Wr(X_t_42)
| p_Reset(X_t_42) ),
inference(skolemisation,[status(esa)],[f52_nnf]) ).
cnf(c52,plain,
( int_level(plus(X0,n1)) = int_level(X0)
| ~ gt(int_level(X0),n0)
| ~ p_Rd(X0)
| ~ p_Wr(X0)
| p_Reset(X0) ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(t91,plain,
ifeq(p_Wr(X1),true,ifeq(p_Rd(X1),true,ifeq(gt(int_level(X1),n0),true,or(p_Reset(X1),eq(int_level(plus(X1,n1)),int_level(X1))),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c52]) ).
cnf(t2764,plain,
ifeq(p_Wr(X1),sF0,ifeq(p_Rd(X1),true,ifeq(gt(int_level(X1),n0),true,or(p_Reset(X1),eq(int_level(plus(X1,n1)),int_level(X1))),true),true),true) = true,
inference(step,[status(thm)],[t91,t129]) ).
cnf(t2765,plain,
ifeq(p_Wr(X1),sF0,ifeq(p_Rd(X1),sF0,ifeq(gt(int_level(X1),n0),true,or(p_Reset(X1),eq(int_level(plus(X1,n1)),int_level(X1))),true),true),true) = true,
inference(step,[status(thm)],[t2764,t129]) ).
cnf(t2766,plain,
ifeq(p_Wr(X1),sF0,ifeq(p_Rd(X1),sF0,ifeq(gt(int_level(X1),n0),sF0,or(p_Reset(X1),eq(int_level(plus(X1,n1)),int_level(X1))),true),true),true) = true,
inference(step,[status(thm)],[t2765,t129]) ).
cnf(t2767,plain,
ifeq(p_Wr(X1),sF0,ifeq(p_Rd(X1),sF0,ifeq(gt(int_level(X1),n0),sF0,or(p_Reset(X1),eq(int_level(plus(X1,n1)),int_level(X1))),sF0),true),true) = true,
inference(step,[status(thm)],[t2766,t129]) ).
cnf(t2768,plain,
ifeq(p_Wr(X1),sF0,ifeq(p_Rd(X1),sF0,ifeq(gt(int_level(X1),n0),sF0,or(p_Reset(X1),eq(int_level(plus(X1,n1)),int_level(X1))),sF0),sF0),true) = true,
inference(step,[status(thm)],[t2767,t129]) ).
cnf(t2769,plain,
ifeq(p_Wr(X1),sF0,ifeq(p_Rd(X1),sF0,ifeq(gt(int_level(X1),n0),sF0,or(p_Reset(X1),eq(int_level(plus(X1,n1)),int_level(X1))),sF0),sF0),sF0) = true,
inference(step,[status(thm)],[t2768,t129]) ).
cnf(t2770,plain,
ifeq(p_Wr(X1),sF0,ifeq(p_Rd(X1),sF0,ifeq(gt(int_level(X1),n0),sF0,or(p_Reset(X1),eq(int_level(plus(X1,n1)),int_level(X1))),sF0),sF0),sF0) = sF0,
inference(step,[status(thm)],[t2769,t129]) ).
cnf(t1962,plain,
ifeq(p_Wr(X1),sF0,ifeq(p_Rd(X1),sF0,ifeq(gt(int_level(X1),n0),sF0,or(p_Reset(X1),eq(int_level(plus(X1,n1)),int_level(X1))),sF0),sF0),sF0) = sF0,
inference(orient,[status(thm)],[t2770]) ).
cnf(t2120,plain,
p_Rd(x_139) = sF0,
inference(step,[status(thm)],[t126,t129]) ).
cnf(t133,plain,
p_Rd(x_139) = sF0,
inference(orient,[status(thm)],[t2120]) ).
cnf(t1963,plain,
sF0 = ifeq(p_Wr(x_139),sF0,ifeq(sF0,sF0,ifeq(gt(int_level(x_139),n0),sF0,or(p_Reset(x_139),eq(int_level(plus(x_139,n1)),int_level(x_139))),sF0),sF0),sF0),
inference(cp,[status(thm)],[t1962,t133]) ).
cnf(f92,negated_conjecture,
p_Wr(x_139),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_3) ).
fof(f92_nnf,plain,
p_Wr(x_139),
inference(nnf_transformation,[status(thm)],[f92]) ).
cnf(c92,plain,
p_Wr(x_139),
inference(cnf_transformation,[status(esa)],[f92_nnf]) ).
cnf(t4,plain,
p_Wr(x_139) = true,
inference(equality_encoding,[status(esa)],[c92]) ).
cnf(t128,plain,
p_Wr(x_139) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t2122,plain,
p_Wr(x_139) = sF0,
inference(step,[status(thm)],[t128,t129]) ).
cnf(t135,plain,
p_Wr(x_139) = sF0,
inference(orient,[status(thm)],[t2122]) ).
cnf(t2771,plain,
sF0 = ifeq(sF0,sF0,ifeq(sF0,sF0,ifeq(gt(int_level(x_139),n0),sF0,or(p_Reset(x_139),eq(int_level(plus(x_139,n1)),int_level(x_139))),sF0),sF0),sF0),
inference(step,[status(thm)],[t1963,t135]) ).
cnf(t16,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t166,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t16]) ).
cnf(t2772,plain,
sF0 = ifeq(sF0,sF0,ifeq(gt(int_level(x_139),n0),sF0,or(p_Reset(x_139),eq(int_level(plus(x_139,n1)),int_level(x_139))),sF0),sF0),
inference(step,[status(thm)],[t2771,t166]) ).
cnf(t2773,plain,
sF0 = ifeq(gt(int_level(x_139),n0),sF0,or(p_Reset(x_139),eq(int_level(plus(x_139,n1)),int_level(x_139))),sF0),
inference(step,[status(thm)],[t2772,t166]) ).
cnf(t117,axiom,
sF3 = int_level(x_139),
introduced(definition) ).
cnf(t142,plain,
int_level(x_139) = sF3,
inference(orient,[status(thm)],[t117]) ).
cnf(t2774,plain,
sF0 = ifeq(gt(sF3,n0),sF0,or(p_Reset(x_139),eq(int_level(plus(x_139,n1)),int_level(x_139))),sF0),
inference(step,[status(thm)],[t2773,t142]) ).
cnf(f90,negated_conjecture,
gt(level(x_139),n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_1) ).
fof(f90_nnf,plain,
gt(level(x_139),n0),
inference(nnf_transformation,[status(thm)],[f90]) ).
cnf(c90,plain,
gt(level(x_139),n0),
inference(cnf_transformation,[status(esa)],[f90_nnf]) ).
cnf(u0,axiom,
gt(level(x_139),n0) = true,
inference(equality_encoding,[status(esa)],[c90]) ).
cnf(f20,axiom,
level(X_t_32) = int_level(X_t_32),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_21) ).
fof(f20_nnf,plain,
! [X_t_32] : level(X_t_32) = int_level(X_t_32),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [X_t_32] : level(X_t_32) = int_level(X_t_32),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
level(X0) = int_level(X0),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(d0,axiom,
level(X0) = int_level(X0),
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t13,plain,
gt(int_level(x_139),n0) = true,
inference(definition_unfolding,[status(thm)],[u0,d0]) ).
cnf(t2138,plain,
gt(sF3,n0) = true,
inference(step,[status(thm)],[t13,t142]) ).
cnf(t2139,plain,
gt(sF3,n0) = sF0,
inference(step,[status(thm)],[t2138,t129]) ).
cnf(t153,plain,
gt(sF3,n0) = sF0,
inference(orient,[status(thm)],[t2139]) ).
cnf(t2775,plain,
sF0 = ifeq(sF0,sF0,or(p_Reset(x_139),eq(int_level(plus(x_139,n1)),int_level(x_139))),sF0),
inference(step,[status(thm)],[t2774,t153]) ).
cnf(t2776,plain,
sF0 = or(p_Reset(x_139),eq(int_level(plus(x_139,n1)),int_level(x_139))),
inference(step,[status(thm)],[t2775,t166]) ).
cnf(t2126,plain,
p_Reset(x_139) = sF1,
inference(step,[status(thm)],[t127,t137]) ).
cnf(t139,plain,
p_Reset(x_139) = sF1,
inference(orient,[status(thm)],[t2126]) ).
cnf(t2777,plain,
sF0 = or(sF1,eq(int_level(plus(x_139,n1)),int_level(x_139))),
inference(step,[status(thm)],[t2776,t139]) ).
cnf(t9,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t2135,plain,
or(sF1,X1) = X1,
inference(step,[status(thm)],[t9,t137]) ).
cnf(t149,plain,
or(sF1,X1) = X1,
inference(orient,[status(thm)],[t2135]) ).
cnf(t2778,plain,
sF0 = eq(int_level(plus(x_139,n1)),int_level(x_139)),
inference(step,[status(thm)],[t2777,t149]) ).
cnf(t120,axiom,
sF6 = plus(x_139,n1),
introduced(definition) ).
cnf(t152,plain,
plus(x_139,n1) = sF6,
inference(orient,[status(thm)],[t120]) ).
cnf(t2779,plain,
sF0 = eq(int_level(sF6),int_level(x_139)),
inference(step,[status(thm)],[t2778,t152]) ).
cnf(t121,axiom,
sF7 = int_level(plus(x_139,n1)),
introduced(definition) ).
cnf(t2143,plain,
sF7 = int_level(sF6),
inference(step,[status(thm)],[t121,t152]) ).
cnf(t160,plain,
int_level(sF6) = sF7,
inference(orient,[status(thm)],[t2143]) ).
cnf(t2780,plain,
sF0 = eq(sF7,int_level(x_139)),
inference(step,[status(thm)],[t2779,t160]) ).
cnf(t2781,plain,
sF0 = eq(sF7,sF3),
inference(step,[status(thm)],[t2780,t142]) ).
cnf(f94,negated_conjecture,
level(plus(x_139,n1)) != level(x_139),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quest_5) ).
fof(f94_nnf,plain,
level(plus(x_139,n1)) != level(x_139),
inference(nnf_transformation,[status(thm)],[f94]) ).
fof(f94_sk,plain,
level(plus(x_139,n1)) != level(x_139),
inference(skolemisation,[status(esa)],[f94_nnf]) ).
cnf(c94,plain,
level(plus(x_139,n1)) != level(x_139),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(u2,axiom,
eq(level(plus(x_139,n1)),level(x_139)) = false,
inference(equality_encoding,[status(esa)],[c94]) ).
cnf(t19,plain,
eq(int_level(plus(x_139,n1)),int_level(x_139)) = false,
inference(definition_unfolding,[status(thm)],[u2,d0]) ).
cnf(t2158,plain,
eq(int_level(sF6),int_level(x_139)) = false,
inference(step,[status(thm)],[t19,t152]) ).
cnf(t2159,plain,
eq(sF7,int_level(x_139)) = false,
inference(step,[status(thm)],[t2158,t160]) ).
cnf(t2160,plain,
eq(sF7,sF3) = false,
inference(step,[status(thm)],[t2159,t142]) ).
cnf(t2161,plain,
eq(sF7,sF3) = sF1,
inference(step,[status(thm)],[t2160,t137]) ).
cnf(t172,plain,
eq(sF7,sF3) = sF1,
inference(orient,[status(thm)],[t2161]) ).
cnf(t2782,plain,
sF0 = sF1,
inference(step,[status(thm)],[t2781,t172]) ).
cnf(t1966,plain,
sF1 = sF0,
inference(orient,[status(thm)],[t2782]) ).
cnf(t2785,plain,
false = sF0,
inference(step,[status(thm)],[t137,t1966]) ).
cnf(t1969,plain,
false = sF0,
inference(orient,[status(thm)],[t2785]) ).
cnf(f0,axiom,
plus(X_0,n1) != n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f0_nnf,plain,
! [X_0] : plus(X_0,n1) != n0,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X_0] : plus(X_0,n1) != n0,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
plus(X0,n1) != n0,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(f5,axiom,
( ~ gt(X_3,Y_4)
| ~ def_10(Y_4,X_3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
fof(f5_nnf,plain,
! [Y_4,X_3] :
( ~ gt(X_3,Y_4)
| ~ def_10(Y_4,X_3) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [Y_4,X_3] :
( ~ gt(X_3,Y_4)
| ~ def_10(Y_4,X_3) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ gt(X1,X0)
| ~ def_10(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(f6,axiom,
( X_3 != Y_4
| ~ def_10(Y_4,X_3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
fof(f6_nnf,plain,
! [Y_4,X_3] :
( X_3 != Y_4
| ~ def_10(Y_4,X_3) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [Y_4,X_3] :
( X_3 != Y_4
| ~ def_10(Y_4,X_3) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( X1 != X0
| ~ def_10(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(f16,axiom,
~ gt(X_28,X_28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_17) ).
fof(f16_nnf,plain,
! [X_28] : ~ gt(X_28,X_28),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X_28] : ~ gt(X_28,X_28),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
~ gt(X0,X0),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(f28,axiom,
( ~ p_Wr_error(plus(X_t_37,n1))
| ~ p_Reset(X_t_37) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_29) ).
fof(f28_nnf,plain,
! [X_t_37] :
( ~ p_Wr_error(plus(X_t_37,n1))
| ~ p_Reset(X_t_37) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [X_t_37] :
( ~ p_Wr_error(plus(X_t_37,n1))
| ~ p_Reset(X_t_37) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
( ~ p_Wr_error(plus(X0,n1))
| ~ p_Reset(X0) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(f29,axiom,
( ~ p_Rd_error(plus(X_t_37,n1))
| ~ p_Reset(X_t_37) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_30) ).
fof(f29_nnf,plain,
! [X_t_37] :
( ~ p_Rd_error(plus(X_t_37,n1))
| ~ p_Reset(X_t_37) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [X_t_37] :
( ~ p_Rd_error(plus(X_t_37,n1))
| ~ p_Reset(X_t_37) ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
( ~ p_Rd_error(plus(X0,n1))
| ~ p_Reset(X0) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(f30,axiom,
( ~ p_Mem(X_k1_38,X_k2_39,plus(X_t_37,n1))
| ~ p_Reset(X_t_37) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_31) ).
fof(f30_nnf,plain,
! [X_t_37,X_k1_38,X_k2_39] :
( ~ p_Mem(X_k1_38,X_k2_39,plus(X_t_37,n1))
| ~ p_Reset(X_t_37) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [X_t_37,X_k1_38,X_k2_39] :
( ~ p_Mem(X_k1_38,X_k2_39,plus(X_t_37,n1))
| ~ p_Reset(X_t_37) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
( ~ p_Mem(X1,X2,plus(X0,n1))
| ~ p_Reset(X0) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(f31,axiom,
( ~ p_Data_out(X_k1_40,plus(X_t_37,n1))
| ~ p_Reset(X_t_37) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_32) ).
fof(f31_nnf,plain,
! [X_t_37,X_k1_40] :
( ~ p_Data_out(X_k1_40,plus(X_t_37,n1))
| ~ p_Reset(X_t_37) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [X_t_37,X_k1_40] :
( ~ p_Data_out(X_k1_40,plus(X_t_37,n1))
| ~ p_Reset(X_t_37) ),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c31,plain,
( ~ p_Data_out(X1,plus(X0,n1))
| ~ p_Reset(X0) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c5,c6,c16,c28,c29,c30,c31,c93,c94]) ).
cnf(g0_0,plain,
sF0 != false,
inference(rw,[status(thm)],[goal_0,t129]) ).
cnf(g0_1,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_0,t1969]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWV015-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 16:24:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 9.62/1.74 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.62/1.74 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------