TSTP Solution File: NUM756^4 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM756^4 : TPTP v8.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n029.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 21 01:17:06 EDT 2024
% Result : Theorem 103.07s 13.52s
% Output : CNFRefutation 103.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 45
% Syntax : Number of formulae : 96 ( 42 unt; 26 typ; 0 def)
% Number of atoms : 325 ( 59 equ; 0 cnn)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 1284 ( 69 ~; 61 |; 8 &;1102 @)
% ( 0 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 53 ( 53 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 7 con; 0-3 aty)
% Number of variables : 133 ( 94 ^ 39 !; 0 ?; 133 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
is_of: $i > ( $i > $o ) > $o ).
thf(decl_23,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_25,type,
in: $i > $i > $o ).
thf(decl_61,type,
imp: $o > $o > $o ).
thf(decl_62,type,
d_not: $o > $o ).
thf(decl_67,type,
l_or: $o > $o > $o ).
thf(decl_72,type,
l_some: $i > ( $i > $o ) > $o ).
thf(decl_77,type,
e_is: $i > $i > $i > $o ).
thf(decl_123,type,
nat: $i ).
thf(decl_124,type,
n_is: $i > $i > $o ).
thf(decl_127,type,
n_some: ( $i > $o ) > $o ).
thf(decl_147,type,
diffprop: $i > $i > $i > $o ).
thf(decl_148,type,
d_29_ii: $i > $i > $o ).
thf(decl_149,type,
iii: $i > $i > $o ).
thf(decl_162,type,
n_ts: $i > $i > $i ).
thf(decl_189,type,
frac: $i ).
thf(decl_191,type,
num: $i > $i ).
thf(decl_192,type,
den: $i > $i ).
thf(decl_193,type,
n_eq: $i > $i > $o ).
thf(decl_194,type,
moref: $i > $i > $o ).
thf(decl_195,type,
lessf: $i > $i > $o ).
thf(decl_197,type,
lesseq: $i > $i > $o ).
thf(decl_198,type,
n_pf: $i > $i > $i ).
thf(decl_201,type,
esk1_0: $i ).
thf(decl_202,type,
esk2_0: $i ).
thf(decl_203,type,
esk3_0: $i ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_e_is) ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_imp) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_iii) ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_d_29_ii) ).
thf(def_n_eq,axiom,
( n_eq
= ( ^ [X1: $i,X436: $i] : ( n_is @ ( n_ts @ ( num @ X1 ) @ ( den @ X436 ) ) @ ( n_ts @ ( num @ X436 ) @ ( den @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_n_eq) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_n_is) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X83: $o] : ( imp @ ( d_not @ X83 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_l_or) ).
thf(def_lessf,axiom,
( lessf
= ( ^ [X1: $i,X450: $i] : ( iii @ ( n_ts @ ( num @ X1 ) @ ( den @ X450 ) ) @ ( n_ts @ ( num @ X450 ) @ ( den @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_lessf) ).
thf(def_n_some,axiom,
( n_some
= ( l_some @ nat ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_n_some) ).
thf(def_all_of,axiom,
( all_of
= ( ^ [X3: $i > $o,X2: $i > $o] :
! [X4: $i] :
( ( is_of @ X4 @ X3 )
=> ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM007^0.ax',def_is_of) ).
thf(def_moref,axiom,
( moref
= ( ^ [X1: $i,X449: $i] : ( d_29_ii @ ( n_ts @ ( num @ X1 ) @ ( den @ X449 ) ) @ ( n_ts @ ( num @ X449 ) @ ( den @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_moref) ).
thf(def_lesseq,axiom,
( lesseq
= ( ^ [X1: $i,X466: $i] : ( l_or @ ( lessf @ X1 @ X466 ) @ ( n_eq @ X1 @ X466 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_lesseq) ).
thf(satz63a,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X542: $i] : ( in @ X542 @ frac )
@ ^ [X543: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( ( moref @ ( n_pf @ X1 @ X4 ) @ ( n_pf @ X543 @ X4 ) )
=> ( moref @ X1 @ X543 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz63a) ).
thf(satz63b,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X544: $i] : ( in @ X544 @ frac )
@ ^ [X545: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( ( n_eq @ ( n_pf @ X1 @ X4 ) @ ( n_pf @ X545 @ X4 ) )
=> ( n_eq @ X1 @ X545 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz63b) ).
thf(satz62c,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X526: $i] : ( in @ X526 @ frac )
@ ^ [X527: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ frac )
@ ^ [X4: $i] :
( ( lessf @ X1 @ X527 )
=> ( lessf @ ( n_pf @ X1 @ X4 ) @ ( n_pf @ X527 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62c) ).
thf(satz41d,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X469: $i] : ( in @ X469 @ frac )
@ ^ [X470: $i] :
( ( lesseq @ X1 @ X470 )
=> ( d_not @ ( moref @ X1 @ X470 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz41d) ).
thf(satz41e,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ frac )
@ ^ [X1: $i] :
( all_of
@ ^ [X471: $i] : ( in @ X471 @ frac )
@ ^ [X472: $i] :
( ( d_not @ ( moref @ X1 @ X472 ) )
=> ( lesseq @ X1 @ X472 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz41e) ).
thf(c_0_19,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_20,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_21,plain,
( imp
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_imp]) ).
thf(c_0_22,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_23,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_d_29_ii]) ).
thf(c_0_24,plain,
( n_eq
= ( ^ [Z0: $i,Z1: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_n_eq]) ).
thf(c_0_25,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_19]) ).
thf(c_0_26,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_l_or]) ).
thf(c_0_27,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_28,plain,
( lessf
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_lessf]) ).
thf(c_0_29,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_22,def_n_some]) ).
thf(c_0_30,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_all_of]) ).
thf(c_0_31,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_32,plain,
( moref
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_moref]) ).
thf(c_0_33,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_23,def_n_some]) ).
thf(c_0_34,plain,
( lesseq
= ( ^ [Z0: $i,Z1: $i] :
( ( ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) ) )
=> ~ $true )
=> ( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[def_lesseq]) ).
thf(c_0_35,plain,
( n_eq
= ( ^ [Z0: $i,Z1: $i] :
( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_36,plain,
( l_or
= ( ^ [Z0: $o,Z1: $o] :
( ( Z0
=> ~ $true )
=> Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_26,c_0_21]),c_0_27]) ).
thf(c_0_37,plain,
( lessf
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_38,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_39,plain,
( moref
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_32,c_0_33]) ).
thf(c_0_40,plain,
( lesseq
= ( ^ [Z0: $i,Z1: $i] :
( ( ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) @ ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) ) ) )
=> ~ $true )
=> ( ( n_ts @ ( num @ Z0 ) @ ( den @ Z1 ) )
= ( n_ts @ ( num @ Z1 ) @ ( den @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_37]) ).
thf(c_0_41,plain,
! [X689: $i] :
( ( in @ X689 @ frac )
=> ! [X688: $i] :
( ( in @ X688 @ frac )
=> ! [X687: $i] :
( ( in @ X687 @ frac )
=> ( ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ ( n_pf @ X689 @ X687 ) ) @ ( den @ ( n_pf @ X688 @ X687 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ X688 @ X687 ) ) @ ( den @ ( n_pf @ X689 @ X687 ) ) ) ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ X689 ) @ ( den @ X688 ) ) @ ( n_ts @ ( num @ X688 ) @ ( den @ X689 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz63a]),c_0_38]),c_0_39]) ).
thf(c_0_42,negated_conjecture,
~ ! [X601: $i] :
( ( in @ X601 @ frac )
=> ! [X600: $i] :
( ( in @ X600 @ frac )
=> ! [X599: $i] :
( ( in @ X599 @ frac )
=> ( ( ( n_ts @ ( num @ ( n_pf @ X601 @ X599 ) ) @ ( den @ ( n_pf @ X600 @ X599 ) ) )
= ( n_ts @ ( num @ ( n_pf @ X600 @ X599 ) ) @ ( den @ ( n_pf @ X601 @ X599 ) ) ) )
=> ( ( n_ts @ ( num @ X601 ) @ ( den @ X600 ) )
= ( n_ts @ ( num @ X600 ) @ ( den @ X601 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[satz63b])]),c_0_35]),c_0_38]) ).
thf(c_0_43,plain,
! [X680: $i] :
( ( in @ X680 @ frac )
=> ! [X679: $i] :
( ( in @ X679 @ frac )
=> ! [X678: $i] :
( ( in @ X678 @ frac )
=> ( ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ X679 ) @ ( den @ X680 ) ) @ ( n_ts @ ( num @ X680 ) @ ( den @ X679 ) ) ) )
=> ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ ( n_pf @ X679 @ X678 ) ) @ ( den @ ( n_pf @ X680 @ X678 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ X680 @ X678 ) ) @ ( den @ ( n_pf @ X679 @ X678 ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz62c]),c_0_38]),c_0_37]) ).
thf(c_0_44,plain,
! [X852: $i] :
( ( in @ X852 @ frac )
=> ! [X851: $i] :
( ( in @ X851 @ frac )
=> ( ( ( ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ X851 ) @ ( den @ X852 ) ) @ ( n_ts @ ( num @ X852 ) @ ( den @ X851 ) ) ) )
=> ~ $true )
=> ( ( n_ts @ ( num @ X852 ) @ ( den @ X851 ) )
= ( n_ts @ ( num @ X851 ) @ ( den @ X852 ) ) ) )
=> ( ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ X852 ) @ ( den @ X851 ) ) @ ( n_ts @ ( num @ X851 ) @ ( den @ X852 ) ) ) )
=> ~ $true ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz41d]),c_0_38]),c_0_27]),c_0_40]),c_0_39]) ).
thf(c_0_45,plain,
! [X1162: $i,X1163: $i,X1164: $i] :
( ~ ( in @ X1162 @ frac )
| ~ ( in @ X1163 @ frac )
| ~ ( in @ X1164 @ frac )
| ~ ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ ( n_pf @ X1162 @ X1164 ) ) @ ( den @ ( n_pf @ X1163 @ X1164 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ X1163 @ X1164 ) ) @ ( den @ ( n_pf @ X1162 @ X1164 ) ) ) ) )
| ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ X1162 ) @ ( den @ X1163 ) ) @ ( n_ts @ ( num @ X1163 ) @ ( den @ X1162 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])])]) ).
thf(c_0_46,negated_conjecture,
( ( in @ esk1_0 @ frac )
& ( in @ esk2_0 @ frac )
& ( in @ esk3_0 @ frac )
& ( ( n_ts @ ( num @ ( n_pf @ esk1_0 @ esk3_0 ) ) @ ( den @ ( n_pf @ esk2_0 @ esk3_0 ) ) )
= ( n_ts @ ( num @ ( n_pf @ esk2_0 @ esk3_0 ) ) @ ( den @ ( n_pf @ esk1_0 @ esk3_0 ) ) ) )
& ( ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) )
!= ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])]) ).
thf(c_0_47,plain,
! [X1153: $i,X1154: $i,X1155: $i] :
( ~ ( in @ X1153 @ frac )
| ~ ( in @ X1154 @ frac )
| ~ ( in @ X1155 @ frac )
| ~ ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ X1154 ) @ ( den @ X1153 ) ) @ ( n_ts @ ( num @ X1153 ) @ ( den @ X1154 ) ) ) )
| ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ ( n_pf @ X1154 @ X1155 ) ) @ ( den @ ( n_pf @ X1153 @ X1155 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ X1153 @ X1155 ) ) @ ( den @ ( n_pf @ X1154 @ X1155 ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])])])]) ).
thf(c_0_48,plain,
! [X1326: $i,X1327: $i] :
( ( ~ ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ X1327 ) @ ( den @ X1326 ) ) @ ( n_ts @ ( num @ X1326 ) @ ( den @ X1327 ) ) ) )
| ~ $true
| ~ ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ X1326 ) @ ( den @ X1327 ) ) @ ( n_ts @ ( num @ X1327 ) @ ( den @ X1326 ) ) ) )
| ~ $true
| ~ ( in @ X1327 @ frac )
| ~ ( in @ X1326 @ frac ) )
& ( ( ( n_ts @ ( num @ X1326 ) @ ( den @ X1327 ) )
!= ( n_ts @ ( num @ X1327 ) @ ( den @ X1326 ) ) )
| ~ ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ X1326 ) @ ( den @ X1327 ) ) @ ( n_ts @ ( num @ X1327 ) @ ( den @ X1326 ) ) ) )
| ~ $true
| ~ ( in @ X1327 @ frac )
| ~ ( in @ X1326 @ frac ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])])]) ).
thf(c_0_49,plain,
! [X1: $i,X4: $i,X5: $i] :
( ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) ) )
| ~ ( in @ X1 @ frac )
| ~ ( in @ X4 @ frac )
| ~ ( in @ X5 @ frac )
| ~ ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ ( n_pf @ X1 @ X5 ) ) @ ( den @ ( n_pf @ X4 @ X5 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ X4 @ X5 ) ) @ ( den @ ( n_pf @ X1 @ X5 ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
thf(c_0_50,negated_conjecture,
( ( n_ts @ ( num @ ( n_pf @ esk1_0 @ esk3_0 ) ) @ ( den @ ( n_pf @ esk2_0 @ esk3_0 ) ) )
= ( n_ts @ ( num @ ( n_pf @ esk2_0 @ esk3_0 ) ) @ ( den @ ( n_pf @ esk1_0 @ esk3_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_51,negated_conjecture,
in @ esk3_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_52,negated_conjecture,
in @ esk1_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_53,negated_conjecture,
in @ esk2_0 @ frac,
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_54,plain,
! [X1: $i,X5: $i,X4: $i] :
( ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ ( n_pf @ X4 @ X5 ) ) @ ( den @ ( n_pf @ X1 @ X5 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ X1 @ X5 ) ) @ ( den @ ( n_pf @ X4 @ X5 ) ) ) ) )
| ~ ( in @ X1 @ frac )
| ~ ( in @ X4 @ frac )
| ~ ( in @ X5 @ frac )
| ~ ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) @ ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
thf(c_0_55,plain,
! [X854: $i] :
( ( in @ X854 @ frac )
=> ! [X853: $i] :
( ( in @ X853 @ frac )
=> ( ( ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ X854 ) @ ( den @ X853 ) ) @ ( n_ts @ ( num @ X853 ) @ ( den @ X854 ) ) ) )
=> ~ $true )
=> ( ( ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ X853 ) @ ( den @ X854 ) ) @ ( n_ts @ ( num @ X854 ) @ ( den @ X853 ) ) ) )
=> ~ $true )
=> ( ( n_ts @ ( num @ X854 ) @ ( den @ X853 ) )
= ( n_ts @ ( num @ X853 ) @ ( den @ X854 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz41e]),c_0_38]),c_0_27]),c_0_40]),c_0_39]) ).
thf(c_0_56,plain,
! [X1: $i,X4: $i] :
( ~ ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) ) )
| ~ $true
| ~ ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) @ ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) ) )
| ~ $true
| ~ ( in @ X1 @ frac )
| ~ ( in @ X4 @ frac ) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
thf(c_0_57,negated_conjecture,
( ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) ) )
| ~ ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ ( n_pf @ esk1_0 @ esk3_0 ) ) @ ( den @ ( n_pf @ esk2_0 @ esk3_0 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ esk1_0 @ esk3_0 ) ) @ ( den @ ( n_pf @ esk2_0 @ esk3_0 ) ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_52]),c_0_53])]) ).
thf(c_0_58,negated_conjecture,
( ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ ( n_pf @ esk1_0 @ esk3_0 ) ) @ ( den @ ( n_pf @ esk2_0 @ esk3_0 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ esk1_0 @ esk3_0 ) ) @ ( den @ ( n_pf @ esk2_0 @ esk3_0 ) ) ) ) )
| ~ ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_50]),c_0_51]),c_0_52]),c_0_53])]) ).
thf(c_0_59,plain,
! [X1328: $i,X1329: $i] :
( ( ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ X1329 ) @ ( den @ X1328 ) ) @ ( n_ts @ ( num @ X1328 ) @ ( den @ X1329 ) ) ) )
| ( ( n_ts @ ( num @ X1328 ) @ ( den @ X1329 ) )
= ( n_ts @ ( num @ X1329 ) @ ( den @ X1328 ) ) )
| ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ X1328 ) @ ( den @ X1329 ) ) @ ( n_ts @ ( num @ X1329 ) @ ( den @ X1328 ) ) ) )
| ~ ( in @ X1329 @ frac )
| ~ ( in @ X1328 @ frac ) )
& ( $true
| ( ( n_ts @ ( num @ X1328 ) @ ( den @ X1329 ) )
= ( n_ts @ ( num @ X1329 ) @ ( den @ X1328 ) ) )
| ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ X1328 ) @ ( den @ X1329 ) ) @ ( n_ts @ ( num @ X1329 ) @ ( den @ X1328 ) ) ) )
| ~ ( in @ X1329 @ frac )
| ~ ( in @ X1328 @ frac ) )
& ( ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ X1329 ) @ ( den @ X1328 ) ) @ ( n_ts @ ( num @ X1328 ) @ ( den @ X1329 ) ) ) )
| ( ( n_ts @ ( num @ X1328 ) @ ( den @ X1329 ) )
= ( n_ts @ ( num @ X1329 ) @ ( den @ X1328 ) ) )
| $true
| ~ ( in @ X1329 @ frac )
| ~ ( in @ X1328 @ frac ) )
& ( $true
| ( ( n_ts @ ( num @ X1328 ) @ ( den @ X1329 ) )
= ( n_ts @ ( num @ X1329 ) @ ( den @ X1328 ) ) )
| $true
| ~ ( in @ X1329 @ frac )
| ~ ( in @ X1328 @ frac ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])])])]) ).
thf(c_0_60,plain,
! [X4: $i,X1: $i] :
( ~ ( in @ X4 @ frac )
| ~ ( in @ X1 @ frac )
| ~ ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) @ ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) ) )
| ~ ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) ) ) ),
inference(cn,[status(thm)],[c_0_56]) ).
thf(c_0_61,negated_conjecture,
( ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) ) )
| ~ ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
thf(c_0_62,plain,
! [X1: $i,X4: $i] :
( ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) ) )
| ( ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) )
= ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) )
| ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ X4 ) @ ( den @ X1 ) ) @ ( n_ts @ ( num @ X1 ) @ ( den @ X4 ) ) ) )
| ~ ( in @ X1 @ frac )
| ~ ( in @ X4 @ frac ) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
thf(c_0_63,negated_conjecture,
( ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) ) )
| ~ ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ ( n_pf @ esk1_0 @ esk3_0 ) ) @ ( den @ ( n_pf @ esk2_0 @ esk3_0 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ esk1_0 @ esk3_0 ) ) @ ( den @ ( n_pf @ esk2_0 @ esk3_0 ) ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_53]),c_0_52])]) ).
thf(c_0_64,negated_conjecture,
( ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ ( n_pf @ esk1_0 @ esk3_0 ) ) @ ( den @ ( n_pf @ esk2_0 @ esk3_0 ) ) ) @ ( n_ts @ ( num @ ( n_pf @ esk1_0 @ esk3_0 ) ) @ ( den @ ( n_pf @ esk2_0 @ esk3_0 ) ) ) ) )
| ~ ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_50]),c_0_51]),c_0_53]),c_0_52])]) ).
thf(c_0_65,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_53]),c_0_52])]) ).
thf(c_0_66,negated_conjecture,
! [X1: $i] :
( ( ( n_ts @ ( num @ X1 ) @ ( den @ esk2_0 ) )
= ( n_ts @ ( num @ esk2_0 ) @ ( den @ X1 ) ) )
| ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ X1 ) @ ( den @ esk2_0 ) ) @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ X1 ) ) ) )
| ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ X1 ) ) @ ( n_ts @ ( num @ X1 ) @ ( den @ esk2_0 ) ) ) )
| ~ ( in @ X1 @ frac ) ),
inference(spm,[status(thm)],[c_0_62,c_0_53]) ).
thf(c_0_67,negated_conjecture,
( ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) )
!= ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_68,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ ( n_ts @ ( num @ esk2_0 ) @ ( den @ esk1_0 ) ) @ ( n_ts @ ( num @ esk1_0 ) @ ( den @ esk2_0 ) ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]) ).
thf(c_0_69,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_52]),c_0_67]),c_0_65]),c_0_68]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM756^4 : TPTP v8.2.0. Released v7.1.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 04:55:53 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.20/0.46 Running higher-order theorem proving
% 0.20/0.46 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 103.07/13.52 # Version: 3.1.0-ho
% 103.07/13.52 # Preprocessing class: HSLMSMSMLLLCHSA.
% 103.07/13.52 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 103.07/13.52 # Starting pre_casc_4 with 1200s (4) cores
% 103.07/13.52 # Starting full_lambda_6 with 300s (1) cores
% 103.07/13.52 # Starting sh10 with 300s (1) cores
% 103.07/13.52 # Starting post_as_ho9 with 300s (1) cores
% 103.07/13.52 # Starting post_as_ho8 with 300s (1) cores
% 103.07/13.52 # full_lambda_6 with pid 23858 completed with status 0
% 103.07/13.52 # Result found by full_lambda_6
% 103.07/13.52 # Preprocessing class: HSLMSMSMLLLCHSA.
% 103.07/13.52 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 103.07/13.52 # Starting pre_casc_4 with 1200s (4) cores
% 103.07/13.52 # Starting full_lambda_6 with 300s (1) cores
% 103.07/13.52 # SinE strategy is GSinE(CountTerms,hypos,4,,4,20000,1.0,true)
% 103.07/13.52 # Search class: HGHSS-FSLM32-DHSMMFBN
% 103.07/13.52 # partial match(3): HGHSM-FSLM32-MHSMMSBN
% 103.07/13.52 # Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 103.07/13.52 # Starting full_lambda_5 with 25s (1) cores
% 103.07/13.52 # full_lambda_5 with pid 23868 completed with status 0
% 103.07/13.52 # Result found by full_lambda_5
% 103.07/13.52 # Preprocessing class: HSLMSMSMLLLCHSA.
% 103.07/13.52 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 103.07/13.52 # Starting pre_casc_4 with 1200s (4) cores
% 103.07/13.52 # Starting full_lambda_6 with 300s (1) cores
% 103.07/13.52 # SinE strategy is GSinE(CountTerms,hypos,4,,4,20000,1.0,true)
% 103.07/13.52 # Search class: HGHSS-FSLM32-DHSMMFBN
% 103.07/13.52 # partial match(3): HGHSM-FSLM32-MHSMMSBN
% 103.07/13.52 # Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 103.07/13.52 # Starting full_lambda_5 with 25s (1) cores
% 103.07/13.52 # Preprocessing time : 0.009 s
% 103.07/13.52 # Presaturation interreduction done
% 103.07/13.52
% 103.07/13.52 # Proof found!
% 103.07/13.52 # SZS status Theorem
% 103.07/13.52 # SZS output start CNFRefutation
% See solution above
% 103.07/13.52 # Parsed axioms : 593
% 103.07/13.52 # Removed by relevancy pruning/SinE : 348
% 103.07/13.52 # Initial clauses : 530
% 103.07/13.52 # Removed in clause preprocessing : 249
% 103.07/13.52 # Initial clauses in saturation : 281
% 103.07/13.52 # Processed clauses : 16451
% 103.07/13.52 # ...of these trivial : 147
% 103.07/13.52 # ...subsumed : 12617
% 103.07/13.52 # ...remaining for further processing : 3687
% 103.07/13.52 # Other redundant clauses eliminated : 153
% 103.07/13.52 # Clauses deleted for lack of memory : 0
% 103.07/13.52 # Backward-subsumed : 50
% 103.07/13.52 # Backward-rewritten : 63
% 103.07/13.52 # Generated clauses : 220474
% 103.07/13.52 # ...of the previous two non-redundant : 218711
% 103.07/13.52 # ...aggressively subsumed : 0
% 103.07/13.52 # Contextual simplify-reflections : 100
% 103.07/13.52 # Paramodulations : 219357
% 103.07/13.52 # Factorizations : 0
% 103.07/13.52 # NegExts : 292
% 103.07/13.52 # Equation resolutions : 196
% 103.07/13.52 # Disequality decompositions : 0
% 103.07/13.52 # Total rewrite steps : 55372
% 103.07/13.52 # ...of those cached : 55279
% 103.07/13.52 # Propositional unsat checks : 0
% 103.07/13.52 # Propositional check models : 0
% 103.07/13.52 # Propositional check unsatisfiable : 0
% 103.07/13.52 # Propositional clauses : 0
% 103.07/13.52 # Propositional clauses after purity: 0
% 103.07/13.52 # Propositional unsat core size : 0
% 103.07/13.52 # Propositional preprocessing time : 0.000
% 103.07/13.52 # Propositional encoding time : 0.000
% 103.07/13.52 # Propositional solver time : 0.000
% 103.07/13.52 # Success case prop preproc time : 0.000
% 103.07/13.52 # Success case prop encoding time : 0.000
% 103.07/13.52 # Success case prop solver time : 0.000
% 103.07/13.52 # Current number of processed clauses : 3386
% 103.07/13.52 # Positive orientable unit clauses : 69
% 103.07/13.52 # Positive unorientable unit clauses: 10
% 103.07/13.52 # Negative unit clauses : 392
% 103.07/13.52 # Non-unit-clauses : 2915
% 103.07/13.52 # Current number of unprocessed clauses: 202590
% 103.07/13.52 # ...number of literals in the above : 1389731
% 103.07/13.52 # Current number of archived formulas : 0
% 103.07/13.52 # Current number of archived clauses : 271
% 103.07/13.52 # Clause-clause subsumption calls (NU) : 8069205
% 103.07/13.52 # Rec. Clause-clause subsumption calls : 552889
% 103.07/13.52 # Non-unit clause-clause subsumptions : 8372
% 103.07/13.52 # Unit Clause-clause subsumption calls : 301218
% 103.07/13.52 # Rewrite failures with RHS unbound : 192
% 103.07/13.52 # BW rewrite match attempts : 129
% 103.07/13.52 # BW rewrite match successes : 39
% 103.07/13.52 # Condensation attempts : 0
% 103.07/13.52 # Condensation successes : 0
% 103.07/13.52 # Termbank termtop insertions : 10403042
% 103.07/13.52 # Search garbage collected termcells : 37220
% 103.07/13.52
% 103.07/13.52 # -------------------------------------------------
% 103.07/13.52 # User time : 12.634 s
% 103.07/13.52 # System time : 0.226 s
% 103.07/13.52 # Total time : 12.861 s
% 103.07/13.52 # Maximum resident set size: 8068 pages
% 103.07/13.52
% 103.07/13.52 # -------------------------------------------------
% 103.07/13.52 # User time : 12.659 s
% 103.07/13.52 # System time : 0.229 s
% 103.07/13.52 # Total time : 12.888 s
% 103.07/13.52 # Maximum resident set size: 2856 pages
% 103.07/13.52 % E---3.1 exiting
% 103.07/13.52 % E exiting
%------------------------------------------------------------------------------